Curing, Defects and Mechanical Performance of Fiber-Reinforced ...

UNIVERSIDAD POLITECNICA DE MADRID

ESCUELA TECNICA SUPERIOR DE

INGENIEROS DE CAMINOS, CANALES Y PUERTOS

Curing, Defects and MechanicalPerformance of Fiber-Reinforced Composites

TESIS DOCTORAL

SILVIA HERNANDEZ RUEDA

Ingeniera de Materiales

Licenciada en Fısica

2013

Departamento de Ciencia de Materiales

Escuela Tecnica Superior de Ingenieros deCaminos, Canales y Puertos

Universidad Politecnica de Madrid

Curing, Defects and MechanicalPerformance of Fiber-Reinforced Composites

TESIS DOCTORAL

Silvia Hernandez RuedaIngeniera de Materiales

Licenciada en Fısica

Directores de Tesis

Carlos Daniel Gonzalez MartınezDr. Ingeniero de Caminos, Canales y Puertos

Javier LlorcaDr. Ingeniero de Caminos, Canales y Puertos

2013

A mi familia

Agradecimientos

En primer lugar, deseo expresar mi sincero agradecimiento a mis directores de tesis,

Carlos Gonzalez y Javier Llorca, por su dedicacion y ayuda durante la realizacion de este

trabajo, por compartir su experiencia y por todo el conocimiento transmitido.

Este agradecimiento se hace extensivo a mis companeros del Instituto IMDEA Materi-

ales por su ayuda y animos en numerosas ocasiones y por los buenos momentos compartidos

durante estos anos. En especial, a Vane, Katia y Natha por su apoyo, amistad y sobre

todo por su carino.

Tambien quiero expresar mi agradecimiento a Jon Molina y Federico Sket del Instituto

IMDEA Materiales por su ayuda durante el proyecto DEFCOM (6o Programa Marco) y

su dedicacion, tiempo y ayuda con el tomografo. Agradecimiento que hago extensivo a la

Technical University of Vienna (Austria) y FHOO Forschungs and Entwicklungs (Austria)

por su colaboracion, disposicion y ayuda en el ambito del proyecto DEFCOM. En especial

a Marta Rodriguez Hortala y Dietmar Salaberger por su interes, ayuda y ganas para sacar

adelante el proyecto.

Agradezco al Departamento de Ciencia de Materiales la colaraboracion y facilidades

recibidas durante la realizacion de la tesis.

Me gustarıa agradecer especialmente a mi familia su apoyo, paciencia y compresion

durante esta etapa.

Resumen

Tradicionalmente, la fabricacion de materiales compuestos de altas prestaciones se lleva

a cabo en autoclave mediante la consolidacion de preimpregnados a traves de la aplicacion

simultanea de altas presiones y temperatura. Las elevadas presiones empleadas en au-

toclave reducen la porosidad de los componentes garantizando unas buenas propiedades

mecanicas. Sin embargo, este sistema de fabricacion conlleva tiempos de produccion largos

y grandes inversiones en equipamiento lo que restringe su aplicacion a otros sectores ale-

jados del sector aeronautico. Este hecho ha generado una creciente demanda de sistemas

de fabricacion alternativos al autoclave. Aunque estos sistemas son capaces de reducir los

tiempos de produccion y el gasto energetico, por lo general, dan lugar a materiales con

menores prestaciones mecanicas debido a que se reduce la compactacion del material al

aplicar presiones mas bajas y, por tanto, la fraccion volumetrica de fibras, y disminuye el

control de la porosidad durante el proceso.

Los modelos numericos existentes permiten conocer los fundamentos de los mecanis-

mos de crecimiento de poros durante la fabricacion de materiales compuestos de matriz

polimerica mediante autoclave. Dichos modelos analizan el comportamiento de pequenos

poros esfericos embebidos en una resina viscosa. Su validez no ha sido probada, sin em-

bargo, para la morfolologıa tıpica observada en materiales compuestos fabricados fuera de

autoclave, consistente en poros cilındricos y alargados embebidos en resina y rodeados de

fibras continuas. Por otro lado, aunque existe una clara evidencia experimental del efecto

pernicioso de la porosidad en las prestaciones mecanicas de los materiales compuestos, no

existe informacion detallada sobre la influencia de las condiciones de procesado en la forma,

fraccion volumetrica y distribucion espacial de los poros en los materiales compuestos. Las

tecnicas de analisis convencionales para la caracterizacion microestructural de los mate-

riales compuestos proporcionan informacion en dos dimensiones (2D) (microscopıa optica

y electronica, radiografıa de rayos X, ultrasonidos, emision acustica) y solo algunas son

adecuadas para el analisis de la porosidad.

En esta tesis, se ha analizado el efecto de ciclo de curado en el desarrollo de los poros

durante la consolidacion de preimpregnados Hexply AS4/8552 a bajas presiones mediante

moldeo por compresion, en paneles unidireccionales y multiaxiales utilizando tres ciclos de

curado diferentes. Dichos ciclos fueron cuidadosamente disenados de acuerdo a la carac-

terizacion termica y reologica de los preimpregnados. La fraccion vloumetrica de poros,

su forma y distribucion espacial se analizaron en detalle mediante tomografıa de rayos X.

Esta tecnica no destructiva ha demostrado su capacidad para nalizar la microestructura de

materiales compuestos. Se observo, que la porosidad depende en gran medida de la evolu-

cion de la viscosidad dinamica a lo largo del ciclo y que la mayorıa de la porosidad inicial

procedıa del aire atrapado durante el apilamiento de las laminas de preimpregnado. En

el caso de los laminados multiaxiales, la porosidad tambien se vio afectada por la secuen-

cia de apilamiento. En general, los poros tenıan forma cilındrica y se estaban orientados

en la direccion de las fibras. Ademas, la proyeccion de la poblacion de poros a lo largo

de la direccion de la fibra revelo la existencia de una estructura celular de un diametro

aproximado de 1 mm. Las paredes de las celdas correspondıan con regiones con mayor

densidad de fibra mientras que los poros se concentraban en el interior de las celdas. Esta

distribucion de la porosidad es el resultado de una consolidacion no homogenea. Toda esta

informacion es crıtica a la hora de optimizar las condiciones de procesado y proporcionar

datos de partida para desarrollar herramientas de simulacion de los procesos de fabricacion

de materiales compuestos fuera de autoclave.

Adicionalmente, se determinaron ciertas propiedades mecanicas dependientes de la ma-

triz termoestable con objeto de establecer la relacion entre condiciones de procesado y las

prestaciones mecanicas. En el caso de los laminados unidireccionales, la resistencia inter-

laminar depende de la porosidad para fracciones volumetricas de poros superiores 1%. Las

mismas tendencias se observaron en el caso de GIIc mientras GIc no se vio afectada por la

porosidad. En el caso de los laminados multiaxiales se evaluo la influencia de la porosidad

en la resistencia a compresion, la resistencia a impacto a baja velocidad y la resistencia

a copresion despues de impacto. La resistencia a compresion se redujo con el contenido

en poros, pero este no influyo significativamente en la resistencia a compresion despues de

impacto ya que quedo enmascarada por otros factores como la secuencia de apilamiento o

la magnitud del dano generado tras el impacto.

Finalmente, el efecto de las condiciones de fabricacion en el proceso de compactacion

mediante moldeo por compresion en laminados unidireccionales fue simulado mediante el

metodo de los elementos finitos en una primera aproximacion para simular la fabricacion

de materiales compuestos fuera de autoclave. Los parametros del modelo se obtuvieron

mediante experimentos termicos y reologicos del preimpregnado Hexply AS4/8552. Los

resultados obtenidos en la prediccion de la reduccion de espesor durante el proceso de

consolidacion concordaron razonablemente con los resultados experimentales.

Abstract

Manufacturing of high performance polymer-matrix composites is normally carried out

by means of autoclave using prepreg tapes stacked and consolidated under the simultane-

ous application of pressure and temperature. High autoclave pressures reduce the porosity

in the laminate and ensure excellent mechanical properties. However, this manufactur-

ing route is expensive in terms of capital investment and processing time, hindering its

application in many industrial sectors. This fact has driven the demand of alternative out-

of-autoclave processing routes. These techniques claim to produce composite parts faster

and at lower cost but the mechanical performance is also reduced due to the lower fiber

content and to the higher porosity.

Corrient numerical models are able to simulate the mechanisms of void growth in

polymer-matrix composites processed in autoclave. However these models are restricted to

small spherical voids surrounded by a viscous resin. Their validity is not proved for long

cylindrical voids in a viscous matrix surrounded by aligned fibers, the standard morphology

observed in out-of-autoclave composites. In addition, there is an experimental evidence of

the detrimental effect of voids on the mechanical performance of composites but, there

is detailed information regarding the influence of curing conditions on the actual volume

fraction, shape and spatial distribution of voids within the laminate. The standard tech-

niques of microstructural characterization of composites (optical or electron microscopy,

X-ray radiography, ultrasonics) provide information in two dimensions and are not always

suitable to determine the porosity or void population. Moreover, they can not provide 3D

information.

The effect of curing cycle on the development of voids during consolidation of AS4/8552

prepregs at low pressure by compression molding was studied in unidirectional and multi-

axial panels. They were manufactured using three different curing cycles carefully designed

following the rheological and thermal analysis of the raw prepregs. The void volume frac-

tion, shape and spatial distribution were analyzed in detail by means of X-ray computed

microtomography, which has demonstrated its potential for analyzing the microstructural

features of composites. It was demonstrated that the final void volume fraction depended

on the evolution of the dynamic viscosity throughout the cycle. Most of the initial voids

were the result of air entrapment and wrinkles created during lay-up. Differences in the

final void volume fraction depended on the processing conditions for unidirectional and

multiaxial panels. Voids were rod-like shaped and were oriented parallel to the fibers and

concentrated in channels along the fiber orientation. X-ray computer tomography analy-

sis of voids along the fiber direction showed a cellular structure with an approximate cell

diameter of ≈ 1 mm. The cell walls were fiber-rich regions and porosity was localized at

the center of the cells. This porosity distribution within the laminate was the result of in-

homogeneous consolidation. This information is critical to optimize processing parameters

and to provide inputs for virtual testing and virtual processing tools.

In addition, the matrix-controlled mechanical properties of the panels were measured

in order to establish the relationship between processing conditions and mechanical per-

formance. The interlaminar shear strength (ILSS) and the interlaminar toughness (GIc

and GIIc) were selected to evaluate the effect of porosity on the mechanical performance

of unidirectional panels. The ILSS was strongly affected by the porosity when the void

contents was higher than 1%. The same trends were observed in the case of GIIc while GIc

was insensitive to the void volume fraction. Additionally, the mechanical performance of

multiaxial panels in compression, low velocity impact and compression after impact (CAI)

was measured to address the effect of processing conditions. The compressive strength

decreased with porosity and ply-clustering. However, the porosity did not influence the

impact resistance and the coompression after impact strength because the effect of porosity

was masked by other factors as the damage due to impact or the laminate lay-up.

Finally, the effect of the processing conditions on the compaction behavior of unidi-

rectional AS4/8552 panels manufactured by compression moulding was simulated using

the finite element method, as a first approximation to more complex and accurate models

for out-of autoclave curing and consolidation of composite laminates. The model param-

eters were obtained from rheological and thermo-mechanical experiments carried out in

raw prepreg samples. The predictions of the thickness change during consolidation were in

reasonable agreement with the experimental results.

Contents

List of Figures V

List of Tables XIII

1 Introduction 1

1.1 Fiber-reinforced Polymer Composites . . . . . . . . . . . . . . . . . . . . . 1

1.2 Manufacturing Defects in Composite Laminates . . . . . . . . . . . . . . . 2

1.3 Effect of Defects on Mechanical Performance . . . . . . . . . . . . . . . . . 4

1.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Consolidation and Curing of Thermoset Fiber-Reinforced Composites 11

2.1 Experimental Evidences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Resin Cure Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.2 Resin Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.3 Fiber Bed Permeability and Elasticity . . . . . . . . . . . . . . . . 20

2.3 Flow-compaction modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3 Materials and Cure Cycle Definition 35

3.1 AS4/8552 prepreg system . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2 Cure Cycles Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

I

Contents

3.2.1 Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2.2 Isothermal Viscosity Profiles . . . . . . . . . . . . . . . . . . . . . . 37

3.2.3 Dynamic Viscosity Profiles . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.4 Definition of Cure Cycles . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.5 Thermal Characterization . . . . . . . . . . . . . . . . . . . . . . . 48

3.3 Manufacturing of Composite Laminates . . . . . . . . . . . . . . . . . . . . 53

3.3.1 Thermogravimetric Measurements . . . . . . . . . . . . . . . . . . . 54

4 Simulation of the Compaction Process 57

4.1 Bidimensional Finite Element Model . . . . . . . . . . . . . . . . . . . . . 57

4.1.1 Fiber bed constitutive equation . . . . . . . . . . . . . . . . . . . . 60

4.1.2 Fiber Bed Permeability . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.1.3 Effect of the Temperature Cycle on the Compaction . . . . . . . . . 69

5 X-ray Computed Tomography Characterization of Defects 77

5.1 Non-Destructive Evaluation Techniques . . . . . . . . . . . . . . . . . . . . 77

5.2 X-ray Computed Tomography Fundamentals . . . . . . . . . . . . . . . . . 79

5.3 Characterization of Void Population . . . . . . . . . . . . . . . . . . . . . . 82

5.3.1 Unidirectional Laminates . . . . . . . . . . . . . . . . . . . . . . . . 83

5.3.2 Multiaxial Laminates . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6 Mechanical Behavior 109

6.1 Unidirectional Laminates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.1.1 Interlaminar Shear Strength (ILSS) . . . . . . . . . . . . . . . . . . 110

6.1.2 Mode I and II Interlaminar Toughness . . . . . . . . . . . . . . . . 118

6.2 Multiaxial Laminates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6.2.1 Plain Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

II

Contents

6.2.2 Low Velocity Impact . . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.2.3 Compression After Impact (CAI) . . . . . . . . . . . . . . . . . . . 139

7 Conclusions and Future Work 143

7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Appendices 146

A Mathematica Input for Unidimensional Compaction 149

B Abaqus Input for Unidimensional Compaction 155

Bibliography 161

III

List of Figures

1.1 Interlaminar shear strength as a function of void content for carbon fab-

ric/epoxy laminates Costa et al. (2001). . . . . . . . . . . . . . . . . . . . . 5

1.2 Interlaminar shear strength as a function of void content for carbon fab-

ric/bismaleimide laminates Costa et al. (2001). . . . . . . . . . . . . . . . . 6

1.3 Influence of the void content on the (a) longitudinal and (b) transverse

tensile strength for [0]16 unidirectional carbon/epoxy composites T2H 132

300 EH (A) (Hexcel) and R922 12K (Ciba) (B) Olivier et al. (1995). . . . . 7

1.4 Effect of vacuum pressure on void volume fraction and fatigue life at σmax =

0.8 Chambers et al. (2006). . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1 Possible resin flow patterns, Dusi et al. (1987): a) Normal to the laminate,

b) Parallel to the plies, c) Mixed flow. . . . . . . . . . . . . . . . . . . . . . 12

2.2 Compaction processes. a) resin flow normal to the laminate. b) Resin flow

parallel to the plies. c) Mixed resin flow normal and parallel to the plies. . 13

2.3 Thickness of individual plies of AS4/3501-6 laminates after autoclave curing.

nc stands for the final number of compacted plies Cambell et al. (1985). . . 14

2.4 Representative curing time-temperature-transformation diagram of a ther-

moset polymer, Berglund & J.M. Kenny (1991). . . . . . . . . . . . . . . . 16

2.5 Evolution of viscosity as a function of α and temperature . . . . . . . . . . 19

2.6 Pressure carried by the fibers as a function of the fiber volume fraction,

Gutowski et al. (1986). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

V

LIST OF FIGURES

2.7 Normalized effective stress σ′/[A0/(16π3

β2

E)] (Equation 2.19) vs. fiber volume

fraction for different maximum fiber volume fraction, Va, Gutowski et al.

(1986). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.8 Load-displacement curve for the load-hold test method for AS4/3501-6 com-

posite prepreg, Hubert & Poursartip (2001). . . . . . . . . . . . . . . . . . 26

2.9 Schematic showing the geometry and the deforming coordinate system of a

control volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.10 Boundary conditions and material properties inputs for run R1 . . . . . . . 30

2.11 Simulation results for (a) resin pressure evolution and (b) fiber effective

stress as a function of consolidation time. . . . . . . . . . . . . . . . . . . . 32

2.12 Evolution of compaction displacement as a function of time. . . . . . . . . 33

3.1 Gel point of the AS4/8552 prepreg under isothermal conditions at (a) 110C,

(b) 120C, (c) 140C, (d) 160C, (e) 170C and (f) 180C. . . . . . . . . . 40

3.2 Storage (G′) and loss moduli (G′′) of AS4/8552 prepreg at 120C. . . . . . 41

3.3 Minimum complex viscosity, η∗min, and gel time, tgel, under isothermal con-

ditions for the AS4/8552 prepreg. . . . . . . . . . . . . . . . . . . . . . . . 41

3.4 Isothermal viscosity profiles of AS4/8552 prepreg. . . . . . . . . . . . . . . 42

3.5 Dynamic complex viscosity profiles of the AS4/8552 prepregs at different

heating rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.6 Viscosity measurements of 8552 epoxy resin and of S2/8552 prepregs Boswell

(2000). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.7 Temperature profile of the cure cycles used to process AS4/8552 composite

prepregs and the corresponding evolution of the complex viscosity, η∗, during

the (a) cycle C-1, (b) cycle C-2 and (c) cycle C-3. . . . . . . . . . . . . . . 46

3.8 Gel point of the AS4/8552 prepreg subjected to different cure cycles (a)

cycle C-1, (b) cycle C-2 and (c) cycle C-3. . . . . . . . . . . . . . . . . . . 48

3.9 MDSC Q200 (TA Instruments). . . . . . . . . . . . . . . . . . . . . . . . . 49

VI

LIST OF FIGURES

3.10 Heat flow of the AS4/8552 prepreg as a function of temperature and heating

rate (5, 8 and 10C/min). . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.11 Residual reaction heat of AS4/8552 prepreg after curing cycles C-1, C-2, C-3. 50

3.12 Glass transition temperature of AS4/8552 prepreg after curing cycles C-1,

C-2, C-3 at onset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.13 Evolution of the degree of cure of the AS4/8552 prepreg. Predictions from

Williams and Hubert model for curing cycles C-1, C-2, C-3 and experimental

results of curing cycle C-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.14 Staking and packing process of unidirectional laminates. . . . . . . . . . . 54

3.15 Mass loss of AS4/8552 unidirectional laminates a function of temperature. 55

3.16 Mass loss of AS4/8552 multiaxial clustered laminates as a function of tem-

perature (a) dispersed laminate [45o/0o/-45o/90o]3s and (b) clustered lami-

nate [45o

3/0o

3/-45o

3/90o

3 ]s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.1 Resin bleeding during compression molding of a unidirectional panel. Fibers

run horizontally and resin bleeding only occurred along the borders perpen-

dicular to the fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.2 Sketch and representative section of the panel for the finite element model. 59

4.3 a) Testing rig used for the compaction tests, b) Evolution of the laminate

temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.4 Estimated compaction curve for the AS4/8552 prepreg. . . . . . . . . . . . 63

4.5 Linear fit according to Equation 4.6 of the logarithmic viscosity vs. 1/T at

8C/min and 10C/min. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.6 Non-linear fit according to Equation 2.12 of the viscosity vs. degree of cure

α at 130 and 160C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.7 Evolution of the complex viscosity with cure time: a) 120C, b) 140C, c)

160C and d) 180C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.8 Viscosity profiles for curing cycle (a) C-1, (b) C-2 and (c) C-3. . . . . . . . 71

VII

LIST OF FIGURES

4.9 Numerical simulation of compaction strain as a function of the curing time

for curing cycles C-1, C-2 and C-3 . . . . . . . . . . . . . . . . . . . . . . . 71

4.10 Numerical predictions of the evolution of the hydraulic conductivity as a

function of the curing time for curing cycles (a) C-1, (b) C-2 and (c) C-3,

element 501 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.11 Evolution of the (a) pore pressure (Pr) and (b) effective stress (σ′) along

width of the laminate for curing cycle C-2 . . . . . . . . . . . . . . . . . . 75

5.1 Schematic of a X-ray tomography system. . . . . . . . . . . . . . . . . . . 80

5.2 Principle of tomography and illustration of the Fourier slice theorem. . . . 81

5.3 Nanotom 160NF tomograph. . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.4 X-ray microtomography cross-section of the raw prepreg perpendicular to

the fiber tows. Matrix appears as light gray regions, fibers tows as dark

gray regions and pores are black. . . . . . . . . . . . . . . . . . . . . . . . 83

5.5 (a) OM montage of a cross-section of the composite panel manufactured with

cure cycle C-1. (b) XCT slice of the same cross-section with 4 µm/voxel

resolution. (c) Idem as (b) with 11 µm/voxel resolution. (d) Average of all

the slices along the fiber direction with 4 µm/voxel resolution. (e) Idem as

(d) with 11 µm/voxel resolution. Regions with a large volume fraction of

interply voids are marked with an ellipse. . . . . . . . . . . . . . . . . . . . 84

5.6 (a) X-ray microtomography of void spatial distribution in the uniaxial com-

posite panels manufactured according to the curing cycles C-1, C-2 and C-3.

(b) Typical rod-like void together with its equivalent cylinder. . . . . . . . 86

5.7 Definition of the elongation factor and flatness ratio of individual voids. . . 87

5.8 Elongation factor of individual voids for the different cure cycles. . . . . . . 88

5.9 Dynamic evolution of the complex viscosity, η∗, of unidirectional AS4/8552

composite prepreg at the processing window region. . . . . . . . . . . . . . 89

5.10 Distribution of porosity across the width (Y axis) of the AS4/8552 unidirec-

tional laminates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

VIII

LIST OF FIGURES

5.11 Averaging gray values of X-ray absorption of the composite panel along the

fiber axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.12 Average X-ray absorption of composite panel along the fiber (Z axis). Black

zones stand for low density sections (pores), while white zones represent

high density sections (fibers). Gray zones stand for matrix-rich regions. . . 92

5.13 Void distribution through the thickness of the laminate (X axis). . . . . . . 93

5.14 X-ray microtomography of void spatial distribution in the quasi-isotropic

[453/03/-453/903]s composite panel manufactured following the curing cycle

C-3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.15 Void density (expressed as the number of voids per mm3) as a function

of the orientation of the major axis of the equivalent ellipsoid for the (a)

[45/0/-45/90]3s dispersed quasi-isotropic laminates and (b) [453/03/-453/903]s

clustered quasi-isotropic laminates processed with different cure cycles. . . 96

5.16 Distribution of porosity along the width (Y axis) for AS4/8552 multiaxial

panels (a) dispersed ([45/0/-45/90]3s), (b) clustered ([453/03/-453/903]s). . 97

5.17 (a) Distribution of porosity along the width (Y axis) in a single cluster

of three plies with fibers parallel to Z direction in the [453/03/-453/903]s

laminate manufactured according curing cycle C-3. (b) Average X-ray ab-

sorption of composite panel along the fiber (Z axis) of a single cluster of

plies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.18 Void distribution through the thickness of the multiaxial panels (a) dispersed

([45/0/-45/90]3s), (b) clustered ([453/03/-453/903]s). . . . . . . . . . . . . . 100

5.19 Dimensions of (a) major axis, (b) medium axis and (c) minor axis of indi-

vidual voids for dispersed panels [45/0/-45/90]3s manufactured with curing

cycles C-1, C-2 and C-3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.20 Dimensions of (a) major axis, (b) medium axis and (c) minor axis of individ-

ual voids for clustered panels [453/03/-453/903]s manufactured with curing

cycles C-1, C-2 and C-3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.21 Flatness ratio as a function of the void volume for different laminate ply

clustering stacking sequences cured using cycle C-3. . . . . . . . . . . . . . 105

IX

LIST OF FIGURES

5.22 Elongation factor as a function of the void volume for different laminate ply

clustering stacking sequences cured using cycle C-3. . . . . . . . . . . . . . 105

5.23 (a) Major axis, (b) medium axis and (c) minor axis dimensions of individ-

ual voids for panels manufactured with curing cycle C-3 and different lam-

inate lay-ups: multiaxial dispersed ([45/0/-45/90]3s), multiaxial clustered

([453/03/-453/903]s) and unidirectional ([0]10). . . . . . . . . . . . . . . . . 107

6.1 Three point bending fixture. . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.2 ILSS load-displacement curves. . . . . . . . . . . . . . . . . . . . . . . . . 111

6.3 Interlaminar shear strength of the unidirectional AS4/8552 composite lam-

inates as a function of void content. . . . . . . . . . . . . . . . . . . . . . . 112

6.4 Scanning electron micrograph of the fracture surface of a coupon tested to

measure the ILSS; showing serrated feet for the laimate cured using cycle C-3.113

6.5 Scanning electron micrographs of the fracture surfaces of coupons tested to

measure the ILSS. (a) Cure cycle C-2. (b) Cure cycle C-3. . . . . . . . . . 114

6.6 Cusp formation mechanism Greenhald (2009) . . . . . . . . . . . . . . . . 115

6.7 (a) Load-indentation depth curves corresponding to pyramidal indentation

tests of the resin processed with cure cycles C-2 and C-3, displaying identical

behavior. (b) Array of indentations in one of the resin pockets is shown in

the 30× 30 µm SPM image. . . . . . . . . . . . . . . . . . . . . . . . . . . 116

6.8 (a) Load-fiber displacement curves corresponding to fiber push-in tests in

laminates processed with cure cycles C-2 and C-3. The arrow indicates the

critical load for interfacial debonding, which was the same in both cases. (b)

SPM image showing one fiber debonded from the matrix after the push-in

test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6.9 X-ray tomograms of the cross-section of coupons tested to measure the ILSS

for cure cycles C-1, C-2, C-3. . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.10 (a) Sketch of the DCB specimens to measure GIc. (b) Typical load-cross

head displacement curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

X

LIST OF FIGURES

6.11 Load-cross head displacement curves for GIc for cure cycle (a) C-1, (b) C-2

and (c) C-3 of the unidirectional AS4/8552 laminates. . . . . . . . . . . . . 121

6.12 Mode I interlaminar fracture toughness, GIc, of the unidirectional [0]10

AS4/8552 laminates as a function of void content. . . . . . . . . . . . . . . 121

6.13 (a) Sketch of the specimens to measure GIIc. (b) Typical load-cross head

displacement curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

6.14 Load-cross head displacement curves of the GIIc test of AS4/8552 laminates

(a) cycle C-1, (b) cycle C-2 and (c) cycle C-3. . . . . . . . . . . . . . . . . 124

6.15 Interlaminar fracture toughness GIIc of the unidirectional AS4/8552 lami-

nates as a function of void content. . . . . . . . . . . . . . . . . . . . . . . 124

6.16 Scanning electron micrograph of the fracture surface of coupons tested to

measure GIIc of unidirectional panels cured following cycle C-3. . . . . . . 125

6.17 Compression IITRI fixture. . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6.18 Compressive strength of the multiaxial AS4/8552 laminates as a function of

void content. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.19 (Fracture mechanisms in compression of multiaxial laminates manufactured

using curing cycle C-2. a) dispersed stacking sequence [45/0/-45/90]3s (b)

clustered stacking sequence [453/03/-453/903]s. . . . . . . . . . . . . . . . . 130

6.20 Drop weight apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.21 Load vs. time curves of multiaxial AS4/8552 laminates subjected to low

velocity impact (a) cure cycle C-1, (b) cure cycle C-2 and (c) cure cycle C-3. 133

6.22 Load vs. time curves of multiaxial [45/0/-45/90]3s AS4/8552 laminates sub-

jected to low velocity impact for curing cycles C-1, C-2 and C-3. . . . . . . 133

6.23 Load vs. time curves of multiaxial [453/03/-453/903]s AS4/8552 laminates

subjected to low velocity impact for curing cycles C-1, C-2 and C-3. . . . . 134

6.24 Results of the C-scan inspections of multiaxial AS4/8552 laminates sub-

jected to low-velocity impact: (a) [453/03/-453/903]s, (b) [45/0/-45/90]3s. . 135

XI

LIST OF FIGURES

6.25 Damage mechanisms of multiaxial laminates subjected to low velocity im-

pact. 3D view of the impacted area (a) stacking sequence [453/03/-453/903]s

and (b) stacking sequence [45/0/-45/90]3s. . . . . . . . . . . . . . . . . . . 137

6.26 Damage mechanisms of multiaxial laminates subjected to low velocity im-

pact. Cross-section under the impact (a) stacking sequence [453/03/-453/903]s

and (b) stacking sequence [45/0/-45/90]3s. . . . . . . . . . . . . . . . . . . 138

6.27 Conical distribution of delaminations within the laminate after low-velocity

impact (a) stacking sequence [453/03/-453/903]s and (b) stacking sequence

[45/0/-45/90]3s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

6.28 Compression after impact fixture. . . . . . . . . . . . . . . . . . . . . . . . 140

6.29 Compressive strength after impact of multiaxial AS4/8552 laminates with

different stacking sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

XII

List of Tables

1.1 Interlaminar delamination toughness for void free and voided laminates with

a volume fraction of voids of 5% Asp & Brandt (1997). . . . . . . . . . . . 8

3.1 Gel time of the AS4/8552 prepregs after consolidation following cure cycles

C-1, C-2 and C-3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 Residual heat of reaction, ∆Hres, degree of cure, α, and onset glass transition

temperature, Tg, of unidirectional AS4/8552 composite panels manufactured

with different curing cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.3 Constants of the Williams and Hubert kinetic model. . . . . . . . . . . . . 52

3.4 Lay up of the manufactured panels. . . . . . . . . . . . . . . . . . . . . . . 54

4.1 Final compaction and bleeding strains. . . . . . . . . . . . . . . . . . . . . 62

4.2 Paramenters A and B for Kenny’s model. . . . . . . . . . . . . . . . . . . . 65

4.3 Compaction strains of unidirectional [0]10 laminates subjected o different

curing cycles at 2 bars of pressure. . . . . . . . . . . . . . . . . . . . . . . 69

4.4 Simulation and experimental results of the vertical strain at the end of the

curing cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.5 Predicted and experimental mass loss for curing cycles C-1, C-2, C-3 . . . 72

5.1 Volume fraction of voids, Vf , void flatness ratio, f , and average distance

between sections with high porosity along the panel width (Y axis), ∆d, as

a function of the cure cycle for AS4/8552 unidirectional laminates. . . . . . 88

XIII

LIST OF TABLES

5.2 Volume fraction of voids, Vf , as a function of the cure cycle and ply-clustering

for AS4/8552 composite panels manufactured with different curing cycles. . 95

6.1 Interlaminar shear strength of [0]10 laminates. The average values and stan-

dard deviation were obtained from 5 tests for each condition. . . . . . . . . 111

6.2 Resin hardness, H, and critical load for fiber-matrix interfacial debonding,

Pc, as determined from nanoindentation tests. . . . . . . . . . . . . . . . . 116

6.3 Compressive modulus (Ec) and compressive strength (σc) of multiaxial lam-

inates processed using different curing cycles. . . . . . . . . . . . . . . . . . 128

6.4 Elastic and dissipated energies during low velocity impact of multiaxial

AS4/8552 panels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

6.5 Projected delamination areas of multiaxial AS4/8552 panels with different

lay-up after low velocity impact. . . . . . . . . . . . . . . . . . . . . . . . . 136

6.6 Compression after impact strength of multiaxial AS4/8552 laminates with

different stacking sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

XIV

Chapter 1

Introduction

1.1 Fiber-reinforced Polymer Composites

Fiber-reinforced polymer-matrix composites (FRPs) are nowadays extensively used in

structural elements due to their high specific stiffness and strength. FRPs are constituted

by high performance fibers (carbon, glass, aramid, etc.) embedded in a thermoset matrix

and they are normally provided in the form of prepregs semifinishied products. Prepreg

sheets consist of a fabric impregnated with resin maintained in a pre-gelled state. Laminates

are formed by stacking (manually or automatically) individual prepreg sheets that are

consolidated by the simultaneous application of pressure and temperature. The external

applied pressure impedes the growth of voids during curing and even leads to the collapse

of air bubbles, giving rise to materials with very low porosity and excellent mechanical

properties, as required by aerospace and sports industries. Traditionally, the consolidation

process is carried out in autoclave which is an expensive manufacturing route in terms

of capital investment and processing time, limiting the expansion of composite materials

to other industrial sectors. These limitations act as driving forces to look for alternative

out-of-autoclave processing routes (OOA), including, among others, the use of prepregs in

1

1.2 Manufacturing Defects in Composite Laminates

a standard resin transfer molding process (SQRTM), replacing pressurized gas by a fluid

with a high thermal inertia to reduce the curing time (QUICKSTEP) Griffiths & Noble

(2004), or the development of special low temperature cure prepregs that can be cured in

standard ovens. These techniques are able to produce composite parts faster but it should

be noted that they do not often obtained the mechanical properties achieved by autoclave

processing due to the lower fiber content and to the presence of voids.


Defects are introduced in the composite laminates in all manufacturing processes, al-

though the size and frequency of each type depends upon the processing cycle. Typical

defects found in thermoset composite parts as a result of the manufacturing conditions are:

• Porosity (voids) due to volatile resin components or to trapped air bubbles.

• Foreign bodies (for example backing paper of the prepreg sheets).

• Incorrect fibre volume fraction due to excess or insufficient resin. Slight local varia-

tions of volume fraction are always present but large differences from specifications

may be caused by inappropriate processing conditions.

• Bonding defects. Components may be bonded together (e.g. panels and stringers)

during manufacturing and defects in the bondline occur due to incorrect cure condi-

tions for the adhesive or contamination of the surfaces to be bonded.

• Fibre misalignment and fiber waviness. Waviness is detrimental for the mechanical

performance of the material (particularly in compression).

• Ply misalignment caused b errors during lay-up of the laminate plies. Ply misalign-

ment alters the overall stiffness and strength of the laminate and may cause warping

during cure.

• Incompletely cured matrix due to incorrect curing cycle or faulty material.

• Ply cracking. Thermally-induced cracks occur with certain ply lay-ups due to the

differences in the thermal expansion coefficient of the plies.

2


• Delaminations are planar defects usually at ply boundaries. They are not typical dur-

ing manufacturing but may be produced by contamination during lay-up, machining

or impact damage (e.g. tool drops).

• Fiber defects are one of the ultimate limiting factors in determining strength of

composites, and sometimes faulty fibers can be identified as the sites from which

damage was initiated.

The most important manufacturing defect in composite laminates is porosity. Many

of the other defects occur more rarely and always lead to porosity formation. Resin flow

governed by pressure gradients in the laminate play a critical role in void formation and

migration. Understanding the flow-compaction mechanisms during manufacturing is the

key to control the porosity of composite parts.

The control of thermoset prepregs manufacturing require the understanding of the resin

rheological properties during curing as well as of the cure kinetics. The final quality of the

laminate will depend on the competion of resin flow and cure reactions. Low viscosity of

the resin is required to impregnate adequately the fiber preform and this is favored by an

adequate temperature cycle design. Increasing temperature accelerates the cure reactions

and hinders the void migration mechanisms. Rheological analysis has been used to study

the cure process of epoxy resins Berglund & J.M. Kenny (1991), Wang et al. (1997) and

epoxy prepregs Simon & Gillham (1993) and is essential for the optimization of composite

processing.

The mechanics of prepreg compaction in autoclave was pioneered by Springer and co-

workers Loos & Springer (1983), Tang et al. (1987) starting from the consolidation theory

developed for soil mechanics Terzaghi (1943). These authors described the resin flow

through the composite following Darcy’s flow theory in a porous medium, and determined

the laminate compaction sequence. The external pressure was first supported by the resin

and pressure was transferred to the fiber bed as bleeding progressed through the laminate

surfaces. This process continued until the composite reached the maximum compaction of

the reinforcement and all the resin excess was expelled.

Air bubbles are always present in the raw prepreg due to deficient fiber impregnation

during prepreg manufacturing. In addition, voids are also introduced during the prepa-

ration of the laminate kit. The stability of voids as a function of the temperature and

3

1.3 Effect of Defects on Mechanical Performance

pressure has been extensively studied by Kardos et al. Kardos et al. (1986), who consid-

ered the effects of the resin viscosity and of the resin-void surface tension. They developed

a model for void growth which was successfully applied to predict the evolution of voids

in thermoset composites Ledru et al. (2010), Grunenfelder & Nutt (2010). Although these

models provide the essentials of the mechanics of void growth in polymers, they are re-

stricted to small spherical voids embebed in a viscous resin. Their validity is not proved

for long cylindrical voids, the standard morphology observed unidirectional fiber reinforced

composites. In addition, although there are many references in the scientific literature re-

garding the detrimental effect of voids on the mechanical performance of composites Bowles

& Frimpong (1992), Costa et al. (2001), Wisnom et al. (1996), there is still a lack of infor-

mation regarding the influence of curing conditions on the actual volume fraction, shape

and spatial distribution of voids within the laminate.


The effect of voids on the mechanical properties of composites has been the object

of many investigations. The results show that fiber-dominated mechanical properties are

not significantly influenced by voids Olivier et al. (1995), Bureau & Denault (2004), while

matrix-dominated properties are strongly dependent on their presence. Reduction in in-

terlaminar shear strength Olivier et al. (1995), Wisnom et al. (1996), Costa et al. (2001),

compressive strength Suarez et al. (1996), Cinquin et al. (2007) tensile transverse strength

Olivier et al. (1995), Varna et al. (1995), bending Olivier et al. (1995), Hagstrand et al.

(2005), fatigue Bureau & Denault (2004), Almeida & Nogueira Neto (1994), Chambers

et al. (2006) and fracture toughness Asp & Brandt (1997), Rizov (2006) have been re-

ported in the literature.

The effect of void content on interlaminar shear strength (ILSS) was investigated by

Wisnom et al. (1996) using glass/epoxy and carbon/epoxy UD laminates and by Costa

et al. (2001) using carbon/epoxy and carbon/bismaleimide woven laminates. Both studies

reported a reduction between 8% and 33% depending on the void content ranging from

1.1 to 5.6%, Fig. 1.1 and 1.2. The reduction in the interlaminar shear strength with the

void content was justified in both cases on the basis that crack nucleation starts from

the voids, according to Scanning Electron Microscopy (SEM) observations on the broken

4


samples. SEM observations showed that the void location was strongly dependent on the

specific matrix system. In the case of epoxy resin, the voids were preferentially located at

the crossing point of the woven fibre tows, while they were typically found at interface of

woven fibre tows in the carbon/bismaleimide laminates.

1 2 3 4 5 65 0

5 5

6 0

6 5

7 0

7 5

8 0

ILSS (

MPa)

V o i d s c o n t e n t ( % )Figure 1.1: Interlaminar shear strength as a function of void content for carbon fab-

ric/epoxy laminates Costa et al. (2001).

Olivier et al. (1995) analyzed the effect of curing cycle pressure on the porosity of

carbon/epoxy UD laminates and reported a similar reduction in the ILSS with void contents

in the range 0.3 and 10%. The effect of voids on the longitudinal and transverse tensile

properties were also investigated by these authors. They noticed that the longitudinal

modulus as well as the longitudinal tensile strength (fiber-dominated properties) were not

affected by the porosity, Fig. 1.3. However, the transverse properties (which are matrix-

controlled) were found to be extremely sensitive to the presence of defects with a reduction

of 10% and 30%, respectively, for a void contents of 0.3 and 10% respectively, Fig. 1.3. The

shape and size of the voids was characterized by means of optical microscopy and image

analysis for different curing cycles. Void shape was assessed from three different sections of

the same void obtained from at least three parallel cut planes spaced ≈ 10 µm apart. For a

given void content, the specimens with the largest voids showed a reduction in the bending

5


1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 55 5

6 0

6 5

7 0

7 5

8 0ILS

S (MP

a)

V o i d s c o n t e n t ( % )Figure 1.2: Interlaminar shear strength as a function of void content for carbon fab-

ric/bismaleimide laminates Costa et al. (2001).

modulus three times larger (15%) than those with small defects (5%). The influence of

void content on the bending properties was also investigated by Hagstrand et al. (2005)

for UD glass fibre reinforced polypropylene composites. As in case of Olivier et al. (1995),

they found a reduction in both flexural modulus and bending strength of 20% and 28%,

respectively, for a void content of 14%.

Suarez et al. (1996) investigated the effect of void content on the compressive strength

of UD carbon/epoxy laminates. They found a roughly linear correlation between void

content and compressive strength, with a reduction of about 40% for a volume fraction

of 4% of voids. Lower influence of porosity was found by Cinquin et al. (2007) for quasi

isotropic carbon/epoxy laminates with a the reduction in the compressive strength of 14%

for a void content of 11%.

Asp & Brandt (1997) investigated the effects of pores and voids on the interlaminar

delamination toughness of carbon/epoxy laminates, by means of static Mode I, Mode II

and mixed mode fracture tests, Table 1.1. The results were inconclusive due to the large

scatter.

6


0 2 4 6 8 1 0 1 2

7 0

8 0

9 0

1 0 0 C o m p o s i t e A C o m p o s i t e B

( b )

Transv

erse te

nsile s

trengt

h (%)

V o i d c o n t e n t ( % )

0 2 4 6 8 1 0 1 28 5

9 0

9 5

1 0 0Lo

ngitu

dinal

tensile

stren

gth (%

)

V o i d c o n t e n t ( % )

C o m p o s i t e A C o m p o s i t e B

( a )

Figure 1.3: Influence of the void content on the (a) longitudinal and (b) transverse

tensile strength for [0]16 unidirectional carbon/epoxy composites T2H 132 300 EH (A)

(Hexcel) and R922 12K (Ciba) (B) Olivier et al. (1995).

7


GC (J/m2) GC (J/m2)

Test method Void free laminate Voided laminate

Mode I 229.0± 17.8 239.8± 9.7

Mode II 883.1± 117.5 811.3± 57

Mixed Mode 478.8± 43.7 454.5± 70.3

Table 1.1: Interlaminar delamination toughness for void free and voided laminates with

a volume fraction of voids of 5% Asp & Brandt (1997).

Olivier et al. (1995) found that Mode I fracture toughness depend very much on the

void volume fraction. They reported a reduction of 22% in GIC for a void content of 5%.

Fatigue properties were in general more affected by the void content than static prop-

erties. Almeida & Nogueira Neto (1994) carried out four-point bending tests on [0/90]12

carbon/epoxy laminates and found that the static strength was not influenced by a void

content of 3% but had a detrimental effect on fatigue strength. Cyclic bending results Bu-

reau & Denault (2004) for continuous glass fibre/polypropylene woven composites showed

that different void contents led to a shift of the S-N curves without changing their slope,

indicating a reduction of fatigue life with increasing void content. The damage evolution

under bending fatigue was also investigated by Chambers et al. (2006) for UD carbon fibre

composites. They noticed that the fatigue life changed from 2000 to 106 cycles by varying

the void content from 1.6% to 3.1%, Fig. 1.4. The authors concluded that the voids played

a fundamental role in the fatigue life when they were located in the inter-ply region where

delamination occurred.

Rizov (2006) investigated the influence of voids on the Mode I fatigue behavior of glass

fiber reinforced polypropylene plates manufactured by injection molding. An increase in the

void content resulted in higher crack propagation rates. A limited influence was, however,

reported for void volume fractions below 1%, whereas higher void contents (up to 7%)

induced significant reductions in the fatigue crack propagation threshold and fatigue crack

growth resistance.

8

1.4 Objectives

Figure 1.4: Effect of vacuum pressure on void volume fraction and fatigue life at σmax =

0.8 Chambers et al. (2006).

1.4 Objectives

Traditionally, the manufacturing of high performance polymer-matrix composites is

carried out by means of autoclave systems using prepreg tapes stacked and consolidated

under the simultaneous application of pressure and temperature. High autoclave pres-

sures prevent the growth of bubbles and promote the collapse of air entrapments in the

laminate, controlling the final porosity and ensuring the high performance of the compo-

nents. However this manufacturing method is expensive in terms of capital investment and

processing time and hence is not cost-effective for other industries. This fact has driven

an increasing demand of alternative out-of-autoclave processing routes (OOA). However,

these techniques usually are not able to produce composite parts with equivalent mechan-

ical properties in comparison with components manufactured using autoclave due to the

lower fiber volume fraction and higher porosity contents. A deeper understanding of the

effect of the processing conditions (pressure and temperature) on prepreg consolidation

would allow to improve the quality of the components manufactured by means of out-of-

autoclave processing routes. According to this, the main goal of this thesis was to assess

the effect of the curing cycle on the development of voids during consolidation of prepreg at

low pressure. The proper design of the temperature curing cycle, based on the rheological

9

1.4 Objectives

and thermal characterization of the prepregs, led to the manufacture of unidirectional and

multiaxial panels with controlled void content. The void volume fraction, shape and spatial

distribution were also analyzed in detail by means of X-ray computed microtomography

and the results were discussed in the light of the processing conditions. This information

is critical to optimize processing parameters and to provide inputs for virtual testing and

virtual processing tools. In addition, the matrix-controlled mechanical properties of the

panels were measured in order to establish the effect of the voids on the mechanical perfor-

mance of the laminates. Finally, the effect of the processing conditions on the compaction

behavior of unidirectional AS4/8552 panels manufactured by compression molding was

simulated using the finite element, as a first approximation to more complex and accurate

models for out-of-autoclave curing and consolidation of composite laminates.

10

Chapter 2Consolidation and Curing of

Thermoset Fiber-Reinforced

Composites

2.1 Experimental Evidences

Processing of thermoset composites takes place by the simultaneous exposition of the

material to heat and pressure for a given period of time. The resulting cure cycle is

therefore a combination of temperature and pressure profiles. The temperature leads to

the initiation of the crosslinking chemical reactions. It also reduces the viscosity of the

resin favoring the impregnation of the fibers while the excess of resin and vapor bubbles

are squeezed out from the material. Pressure and temperature are the driving forces to

bleed the laminate, consolidate individual plies and reduce the void content.

During consolidation of prepreg materials, resin flow can be dominant in the direction

perpendicular to the laminate (Fig. 2.1.a), parallel to the laminate (Fig. 2.1.b) or in both

directions (Fig. 2.1.c). Depending on the width to thickness ratio, the first case is repre-

11


Figure 2.1: Possible resin flow patterns, Dusi et al. (1987): a) Normal to the laminate,

b) Parallel to the plies, c) Mixed flow.

sentative of the compaction process under hydrostatic pressure which occurs in autoclave

consolidation while the second type of flow is representative of the behavior under hot press

conditions.

The typical compaction mechanisms in porous media are percolation and shear flow.

The resin flows through the pores between the fibers when percolation flow is dominant and

the resin excess is squeezed-out allowing the compaction of the material which attains the

maximum fiber volume fraction. The percolation mechanism is typically used to describe

resin flow within the laminates in thermoset matrix composites. Under shear flow, fiber and

matrix experience a homogeneous solid-like deformation and the material behavior under

compaction is similar to that of a soft solid. Shear flow is usually observed in thermoplastic

matrix composites in which the high viscosity of polymer prevents percolation flow.

The compaction and the arrangement of individual plies during consolidation are con-

trolled by the prevailing flow patterns associated to each manufacturing route (Fig. 2.2).

Under through-thickness flow, compaction occurs sequentially and the thickness of each in-

dividual ply decreases gradually from the top of the tool surface to the bottom, (Fig. 2.2).

The resin is squeezed out from the gap between the first and second ply and then it is

again squeezed-out from the second gap due to the movement of the two first layers. This

process is repeated up to the final compaction of the laminate. However, in case of resin

flow parallel to the laminate, the thickness reduction of all plies is simultaneous. Com-

paction came out as a result of both mechanisms in the case of mixed flow (parallel and

perpendicular to the plies).

The mechanics of autoclave prepreg compaction was pioneered by Springer and co-

workers, Springer (1982), starting from the consolidation theory developed for soil mechan-

12


Figure 2.2: Compaction processes. a) resin flow normal to the laminate. b) Resin flow

parallel to the plies. c) Mixed resin flow normal and parallel to the plies.

ics. Their experiments verified the wavelike nature of the compaction process described

above by analyzing the relative motion of a suspension of a rod network in a viscous liq-

uid. Subsequently, Cambell et al. (1985) found an analogous mechanism of compaction

in thick graphite-epoxy laminates. In this case, the thickness of each layer was measured

using photomicrographs of laminates cured at different pressures in autoclave. The results

are shown in Fig. 2.3. As expected, the compacted layers were located at the top of the

laminate (bag surface) and the number of fully compacted plies increased with the applied

13

2.2 Governing Equations

pressure. Resin flow occurs only through regions with pressure gradients and ends when

they are relieved during the process.

Figure 2.3: Thickness of individual plies of AS4/3501-6 laminates after autoclave curing.

nc stands for the final number of compacted plies Cambell et al. (1985).


The optimum curing conditions for a given composite system can be determined once

the fundamental physical and chemical mechanisms involved are well understood. Obvi-

ously, the optimum cure cycle can be established empirically by means of expensive trial

and error experimental campaigns, but the whole approach can be more efficient by means

of mathematical models representing the underlying physics of the compaction phenom-

ena. A suitable model for simulating the curing process should be supported by a set of

submodels based on the governing equations describing the physico-chemical phenomena

occurring during processing (i.e. cure kinetics, resin flow, ply compaction, heat transfer,

residual stresses, etc.). Such kind of approaches could considerably reduce the number of

experimental trials to reach an optimum cure cycle. The following sections are devoted

14


to summarize the governing equations controlling the compaction phenomena in standard

thermoset prepreg manufacturing.

2.2.1 Resin Cure Kinetics

Cure of thermoset resins occurs via the incorporation of curing agents that trigger the

curing reactions -by addition or condensation chemical mechanisms- leading to a three

dimensional cross-linked network of polymeric chains. During the process, the resin expe-

riences a number of changes which depend on time and temperature: gelation, vitrification

and cure. These phenomena are usually represented in time-temperature-transformation

diagrams (Fig. 2.4). Regions in the diagram represent different physical states of a given

thermoset polymer: liquid, gel-gummy, gel-glassy and vitreous-ungelled. The gel point is

defined as the instant at which the three-dimensional network reaches an infinite molecular

weight due to an irreversible process. The initial stages of the resin curing will be more

likely dominated by purely viscous effects but the resin will behave increasingly as a vis-

coelastic solid as the crosslinking reactions progress, and particularly near to the gel point.

Above the gel point, the polymer behaves as a solid and the resin no longer needs the

mold or the die to maintain its final shape so the part can be demolded. After gelification,

vitrification may occur when the curing process takes place under non-isothermal condi-

tions if the glass transition temperature, Tg, rises the cure temperature leading to a drastic

reduction of the cure rate due to the restriction of mobility between neighbor polymeric

chains. The reduction in the cure rate at vitrification is believed to be caused by a shift

in the rate-controlling mechanism from kinetics (dependent on temperature and reactants

concentration) to diffusion as a result of the reduction in the resin free-volume and the

molecular mobility that accompanies this transition, Montserrat (1992) and Berglund &

J.M. Kenny (1991).

Three critical temperatures are highlighted on the temperature axis: Tg0, the glass

transition temperature for completely uncured resin, gelTg, the temperature at which vit-

rification and gelation occurs simultaneously, and Tg∞, is the glass transition temperature

of the fully-cured material.

In order to understand in more detail the cure reactive process, it is necessary to exam-

ine the reaction kinetics for a given temperature-time profile. The curing kinetics can be

15


Figure 2.4: Representative curing time-temperature-transformation diagram of a ther-

moset polymer, Berglund & J.M. Kenny (1991).

analyzed from a double perspective: the microscopic models based on mechanistic kinetic

approaches and the macroscopic phenomenological models, Van Overbeke et al. (2001).

The former analyze the kinetic mechanisms associated with each of the reactions involved

in the process resulting in very complex models coupled with sophisticated experimental

techniques for measuring the concentration of all chemical species. The latter phenomeno-

logical methods analyze the overall process from a single reaction which is selected to

represents the global curing process. Such models are semi-empirical and do not provide

a clear description of the individual chemical reactions involved in the process but they

do not require very sophisticated experimental techniques for parameter identification and

can provide very accurate results.

The phenomenological models are developed from the concept of the reaction rate in-

ferred from the heat generated during the crosslinking reaction. For instance, let us assume

two reactive groups A and B present in a given resin system whose initial concentrations,

C0A and C0

B, are known. The reaction rate of components A and B depends on the curing

temperature and concentration of the reactants (kinetic control): the higher the concen-

16


tration of A and B, the higher the reaction probability between them. The reaction rate,

vreac, is defined as the time derivative of the variation of concentration of the reagent,

vreac =dα

dt(2.1)

where α is the degree of cure defined as,

α =C0A − CAC0A

(2.2)

where CA is the concentration of the component A at time t and C0A the initial concen-

tration. The value of α ranges from 0 at the initial stage to 1 when the material is fully

cured.

The general kinetic equation expressing the variation of the cure rate with temperature

T and concentration of the reactants is expressed mathematically by Van Overbeke et al.

(2001).

dα

dt= κ(T )f(α) (2.3)

where f(α) is a function which depends on the current reactant concentration and κ(T ) is

a thermally-activated rate constant defined by an Arrhenius-type equation as,

κ(T ) = A exp

(−EaRT

)(2.4)

where A is a proportionality constant, Ea the activation energy, and R the ideal gas

constant. Substituting Equation 2.4 into Equation 2.3 yields the time derivative of the

degree of cure as,

dα

dt= A exp

(−EaRT

)f(α) (2.5)

Several expressions for f(α) have been proposed in the past to fit experimental results,

Keenan (1987), Mijovic et al. (1984), Moroni et al. (1986) and Dusi et al. (1987). Most

epoxy-amine systems show an autocathalytic behavior during the cure and, the term f(α)

can be expressed in such cases as Yang et al. (1999),

17


f(α) = αm(1− α)n (2.6)

where m and n are the orders of cure reaction. Notice that f(0) = 0 and f(tfullcure) = 1.

Substituting Equation 2.7 into Equation 2.3 and rearranging terms yields the typical

expression of the autocatalytic model for the dynamic curing process without diffusion,

also known as Borchardt and Daniels equation, Borchardt & Daniels (1956),

dα

dt= A exp

(−EaRT

)αm(1− α)n (2.7)

This expression is strictly valid up to the point where the reaction becomes kinetically

controlled. While this is usually true for early stages of the cure process, other factors

may come into play as reactants are consumed and a macromolecular polymer network is

formed. Borchardt and Daniels approach was modified by Johnston and Hubert (1995),

Hubert et al. (1995), to take into account reduction in the curing rate at the last stages of

cure as a result of the change in mechanism from kinetics to diffusion when Tg reaches the

cure temperature. Mathematically, the cure rate can be expressed as follows,

dα

dt=

A exp [−Ea/RT ]αm(1− α)n

1 + exp [C(α− (αC0 + αCTT ))](2.8)

where m, n, A, C, αC0 and αCT stand for model constants to be determined experimentally.

The diffusion mechanisms are included by adding the term [1/[1+exp [C(α− (αC0 + αCTT ))]]]

to Equation 2.8.

2.2.2 Resin Viscosity

For a Newtonian fluid, the applied shear stress necessary to deform a fluid, τ , is pro-

portional to the shear velocity gradient, γ, according to

τ = ηγ (2.9)

where η is the viscosity of the resin and γ stands for the velocity gradient perpendicular to

the fluid motion. It is given by ∆v/h, where ∆v is the velocity difference (relative velocity)

and h is the distance between adjacent layers.

18


Matrix resin flow during prepreg compaction is induced by the pressure gradient neces-

sary to remove the excess of resin from the laminate, promote adequate bonding between

plies, and collapse most of voids within the laminate. The rheological behavior of ther-

moset resins is governed by two main physical mechanisms. On the one hand, the viscosity

decreases with temperature as a result of the higher mobility of the polymer chains. On

the other hand, cross-linking reactions, which are thermally activated, lead to an increase

of viscosity. The resin viscosity can be modeled also by empirical equations assuming that

the temperature, T , and degree of cure, α(t), are known at any time during the curing

process.

Several approaches can be found in the literature assuming uncoupled effects of tem-

perature and degree of cure (i.e. Lee et al. (1982), Dusi et al. (1987), Ciriscioli et al. (1992)

and Kenny (1992)). Such approaches are based on a general constitutive equation in which

both phenomena are described separately as, Flory (1953) (Fig. 2.5).

η(T, α) = Φ(T )χ(α) (2.10)

where η is the resin viscosity and Φ(T ) and χ(α) functions of the temperature and the

degree of cure, respectively. This expression leads to a minimum of viscosity over the time

that can be used to define the processing window of the material.

Figure 2.5: Evolution of viscosity as a function of α and temperature

Stolin et al. (1979) and lately Lee et al. (1982), Dusi et al. (1987) and Ciriscioli et al.

(1992) proposed uncoupled models based on the following equation,

19


η(T, α) = η0 exp

(−URT

)+ κα (2.11)

where U is the activation energy associated with viscous flow and κ a constant accounting

for the effect of the chemical reaction on the resin viscosity. It was also assumed that U

is independent of α and therefore it only leads to a constant shift in the viscosity under

isothermal conditions.

Alternative models were developed by Kenny (1992), Kim & Kim (1994) in an attempt

to predict the rheological behavior of the resin more accurately for cure degrees close to

the gelification point by incorporating the parameter αg, which is related with the degree

of cure at gel point as,

η(T, α) = Aη exp

(−EηRT

)[αg

(αg − α)

](a+bα)

(2.12)

where Aη, Eη, a, b and αg are model parameters. Equation 2.12 is also an Arrhenius-type

relation in which temperature and degree of cure are uncoupled.

2.2.3 Fiber Bed Permeability and Elasticity

The consolidation of thermoset FRPs is a complex process involving coupled mecha-

nisms such as the resin rheology and cure behavior. Other mechanisms controlling the

compaction phenomena are related with the fiber bed architecture, namely permeability

and elasticity.

• Fiber bed permeability

Permeability characterizes the permeation of a fluid through a porous medium. As

discussed previously, the resin has to be squeezed-out during the composite consolidation

to achieve the maximum fiber volume fraction, to remove voids and to favor fiber impreg-

nation. The resin flow through the channels of the fiber preform can be easily described

by Darcy’s law by means of the permeability parameter which establishes the relationship

between the flow rate and the pressure gradient necessary to drive the flow. This law

was originally developed for the flow of Newtonian fluids through porous media made up

of granular particles. Gebart (1992) validated Darcy’s law for low flow rate processes as

20


the one ocuring during composite compaction. The generalized form of Darcy’s law is

expressed as,

~u = −K

ηgradP (2.13)

where u is the volume averaged flow velocity, η the viscosity of the fluid, gradP the pressure

gradient, and K the permeability tensor of the fiber preform. The three-dimensional form

of Darcy’s law can be expressed in matrix form as,

ux

uy

uz

= −1

η

Kxx Kxy Kxz

Kyx Kyy Kyz

Kzx Kzy Kzz

∂P∂x∂P∂y

∂P∂z

(2.14)

where ux, uy, uz are the resin velocity components and Kij the permeability tensor compo-

nents. Kij = 0 for i 6= j when the orthotropic axes of the fabric are used as the reference

frame.

The motion of the resin through the fiber preform is usually modeled as the flow through

a porous medium constituted by the fiber network. As a result, the resin mobility decreases

as the fiber volume fraction increases during compaction. Other factors, such as the fiber

architecture and sizing of the fibers, can also affect the permeability of the fiber bed.

Hence, the permeability factors of the fiber bed should be determined experimentally from

the relation between the pressure drop and the flow rate through the fiber network or

estimated by means of empirical models.

Many empirical models based on the physics of lubrication flow or flow through capillar-

ity tubes have been developed to describe this relationship. The Carman-Kozeny equation

(Equation 2.15), developed by adopting the capillary models from the soils mechanics lit-

erature, is one of the most widely accepted for calculating the permeability of fiber beds.

It considers the porous medium as a system of parallel capillaries with diameters estimated

in terms of the hydraulic radius of the system,

KK =r2f

4kK

(1− Vf )3

Vf(2.15)

21


where rf is the fiber radius, Vf is the fiber volume fraction, KK the permeability in the

flow direction and kK the Kozeny constant which has to be determined experimentally.

However, several shortcomings of this model should be indicated. The resin flow and

therefore the value of Kozeny constant, kK , will depend on fluid type, fiber packing and

porosity. Experiments carried out by Lam & Kardos (1989) indicated that the permeability

was dependent on the permeating liquid due to deviations from Newtonian fluid behavior

and on fiber arrangements due to deviations from the assumed regular patterns. Moreover,

the experimental values of kK determined for high porosities cannot be used to describe

low porosity scenarios. In conclusion, Equation 2.15 fails to predict the permeability over

the total porosity range of the fiber beds, Skartsis et al. (1992), Gebart (1992) and Astrom

et al. (1992). Gutowski and coworkers, Gutowski et al. (1987b), found that Equation 2.15

could give a good fit to the axial permeability of unidirectional reinforcements, while there

were certain discrepancies for the transverse permeability as the model was not able to

capture the absence of flow when the fibers touch each other blocking any transverse flow.

Despite all the above limitations, the Carman-Kozeny equation seems to be valid for

slow Newtonian flow through porous media over moderated porosity ranges. For these

situations, the proportionality between flow rate and pressure drop is retained and Darcy’s

law is valid Carman (1956), Durst et al. (1987), Gebart (1992), Dullien (1979).

Alternative constitutive equations were developed to overcome these shortcomings Gebart

(1992), Bruschke & Advani (1993) and Gutowski et al. (1987b) but there is no universal

able to predict accurately the permeability of fiber beds within the whole porosity range.

The particular feature of each composite manufacturing process should be taken into ac-

count when dealing with physically-based simulations.

• Fiber bed elasticity

For technologically relevant materials, the fiber volume fraction is within the range

50-70% and therefore inter-fiber spacing becomes very small, of the order of microns or

smaller, leading to multiple fiber-to-fiber contacts when consolidation forces are applied

during processing. The external pressure is initially supported by the resin and, as bleed-

ing progresses, pressure is transferred to the fiber bed. This process continues until the

composite reaches the maximum compaction of the fibers for the applied external pressure

22


and no more resin can be squeezed-out. The load carried by the fibers becomes appreciable

for fiber volume fractions in the range 60 to 70%, Gutowski et al. (1986) (Fig. 2.6).

Figure 2.6: Pressure carried by the fibers as a function of the fiber volume fraction,

Gutowski et al. (1986).

The effective stress theory, originally developed to study soil consolidation, Terzaghi

(1943) and Biot (1941), was applied by Gutowski et al. (1987a,b) and Dave et al. (1987)

to study the compaction of fiber beds. The partition of the stress tensor between fibers

and resin can be expressed as,

σij = σ′ij − Prδij (2.16)

where σij is the total Cauchy stress tensor, σ′ij stands for the effective stress carried by the

fiber bed, Pr is the resin pressure and δij the Kronecker delta (δij = 1 for i = j and δij = 0

for i 6= j).

The fiber bed effective stress tensor can be related to the strain tensor through the

following elastic constitutive equation,

εij = Sijσ′ij (2.17)

23


where Sij is the fiber bed effective compliance matrix. This elastic compliance can be

expressed for an orthotropic elastic solid as,

ε11

ε22

ε33

γ12

γ13

γ23

=

1E1

−ν21E2

−ν31E3

0 0 0−ν12E1

1E2

−ν32E3

0 0 0−ν13E1

−ν23E2

1E3

0 0 0

0 0 0 1G12

0 0

0 0 0 0 1G13

0

0 0 0 0 0 1G23

σ′11

σ′22

σ′33

τ ′12

τ ′13

τ ′23

(2.18)

where Ei and νij stand for the Young’s moduli and the Poisson’s ratios, respectively. The

subindex 1 corresponds to the fiber direction. Other constitutive laws assume that the

shear response of the material is independent of the normal strains and controlled by the

viscosity of the resin Dillon & Gutowski (1992).

These linear elastic models do not account for the stiffening phenomena observed during

compaction. Gutowski et al. (1987b,a) and Dave et al. (1987) proposed an analytical

relationship between the transverse effective stress carried by the fiber bed, σ′, and the fiber

volume fraction (depending on the deformation), as an attempt to develop an equation for

composite compaction processes, Equation 2.19,

σ′ =A0V0

Vf

1−√

VfV0

16π3

β2

E

√VaVf

(√VaVf− 1

)3 (2.19)

where Ef is the flexural modulus of the fiber, β the average waviness ratio of the fiber (which

is defined as the length of the wavy portion of the tow to the total fiber tow length), V0

the initial fiber volume fraction, Vf the current fiber volume fraction, Va the maximum

fiber volume fraction achievable and A0 the initial cross-sectional area perpendicular to

the applied load.

The parameters of the Gutowsky equation should be fitted from compaction tests car-

ried out at different fiber volume fractions. The fiber bed compaction curve (i.e. the

variation of effective stress vs. strain through the thickness direction) is a critical material

property and it is very difficult to measure for prepreg systems. The principal difficulty

24


Figure 2.7: Normalized effective stress σ′/[A0/(16π3

β2

E )] (Equation 2.19) vs. fiber volume

fraction for different maximum fiber volume fraction, Va, Gutowski et al. (1986).

is to isolate the response of the fiber bed from the whole mechanical response of the

prepreg. Typically, the fiber bed behavior is measured by compaction tests carried out on

dry preforms Kim et al. (1991) or by impregnating the fiber preform with silicone oil after

dissolving the polymer matrix to minimize the viscous effects caused by the fluid flowing

out from the sample, Gutowski et al. (1986). Hubert & Poursartip (2001) measured the

compaction curve directly in a prepreg using the load-hold method in which the fiber bed

compaction curve is obtained directly from the total load-displacement curve. The load-

hold method is based on transversely compressing a prepreg laminate to different strain

levels. The strain is kept in each step constant until the load is fully relaxed. Assuming

that the composite material behaves as a simple viscoelastic system, the final relaxed load

should correspond with the elastic response of the fiber bed after the resin pressure is re-

leased. By loading the specimen to different strains, the complete fiber bed compaction

curve can be extracted (Fig. 2.8). The method was found very accurate when resin flow

25

2.3 Flow-compaction modeling

dominates the compaction process but less precise for other deformation mechanisms such

as compaction of entrapped air bubbles.

Figure 2.8: Load-displacement curve for the load-hold test method for AS4/3501-6

composite prepreg, Hubert & Poursartip (2001).


This section devoted to summarize the different approaches in the literature to solve the

compaction phenomena of FRPs by means of the combination of the governing equations

described above.

Work in flow-compaction modeling was pioneered by Loss and Springer who devel-

oped the sequential compaction model, based on their experimental observations, Loos &

Springer (1983). The model predicts the laminate mass loss and the thickness variation

during the cure cycle assuming pressure gradients in both vertical (through thickness) and

horizontal (parallel to the fibers) directions, but computing the flow separately in each

direction. The vertical flow in the laminate is described in terms of Darcy’s law while

the flow along the fibers and parallel to the tool plate was characterized as a viscous flow

26


between two close parallel plates. The model assumed that the resin alone supported the

applied pressure. Loos et al. (1985) determined the resin flow from laminates with different

ply thicknesses, dimensions and ply stacking sequences using this model and found good

agreement with the experimental data. The experiments indicated that the ply stacking

sequence did not affect significantly the total resin mass loss in flat laminates.

An effective stress formulation was developed simultaneously by Gutowski et al. (1987a,b)

and Dave et al. (1987). They assumed that the resin squeezed (percolate) through the

fibers, leading to visco-elastic load sharing between resin and fiber bed. Smith & Poursar-

tip (1993) demonstrated that the sequential model was a particular case of the effective

stress formulation. They concluded that the effective stress model describes more accu-

rately the entire laminate compaction process.

In this thesis, the effective stress model will be applied to investigate the compaction

behavior of unidirectional flat laminates manufactured by compression molding to assess

the effect of curing cycle during consolidation. The composite material was idealized as

a void-free fiber bed fully saturated with a thermoset resin. During the compaction, the

composite part is compressed through the thickness (z direction), and the local displace-

ment can be described using a new variable ξ = w+z, Gutowski & Dillon (1997), in a local

deformation coordinate system, where w is the local displacement in the consolidation di-

rection and z is the position of the control composite volume V extracted from the original

composite panel (Fig. 2.9). This procedure allows to convert a moving boundary problem

to a fixed domain problem. The fiber continuity allows to relate the new coordinate with

the current volume fraction of fiber, Vf , since the volumetric deformations of the composite

are due to the flow of the resin out of the laminate,

∂ξ

∂z=V0

Vf(2.20)

The mass continuity for the resin can be established using the mass balance principle,

Suresh et al. (2002). Considering the flow of a fluid with density ρ = ρ(x, y, z, t) within a

region with velocity u, the mass of the fluid within any arbitrary fixed control volume ν at

any time is calculated as M =∫νρdV . The rate of increase of M is calculated as,

dM

dt=

∫ν

∂ρ

∂tdV (2.21)

27


Figure 2.9: Schematic showing the geometry and the deforming coordinate system of

a control volume.

The rate at the which fluid mass enters in the control volume ν through its boundary

surface S is the flux integral, q, which can be expressed according to the Gauss’ divergence

theorem as

q =

∫S

ρ~n · ~u dA =

∫ν

div(ρ~u) dV (2.22)

where ~n is the normal unit vector outward to S.

The rate of mass increase within ν is equal to the rate at which mass enters in the

control volume through its boundary surface S, minus the rate at which mass is lost. The

rate of mass loss due to bleeding can be expressed as

dMloss

dt=

∫ν

s dV (2.23)

where s is the sinking rate which is assumed uniform and constant in time.

Therefore the balance of mass can be written,

dM

dt= −

∫ν

div(ρ~u) dV −∫ν

s dV (2.24)

28


rearranging Equation 2.24, it leads to,

∫ν

[∂ρ

∂t+ div(ρ~u) + s

]dV = 0 (2.25)

since the shape of the considered control volume is arbitrary, Equation 2.25 leads to,

∂ρ

∂t+ div(ρ~u) = −s (2.26)

which takes the following form in a Cartesian coordinate system,

∂ρ

∂t+

∂

∂x(ρux) +

∂

∂y(ρuy) +

∂

∂z(ρuz) = −s (2.27)

where ux, uy, uz are the scalar components of the velocity vector ~u.

The density of the fluid is replaced by ρb, which is the ratio between resin mass and

the control volume to take into account the presence of the fibers,

ρb = (1− Vf )ρr (2.28)

where ρr is the resin density. Replacing Equation 2.28 and Equation 6.8 into Equation 2.27

yields the final continuity equation,

∂

∂x

(uxV0

Vf

)+

∂

∂y

(uyV0

Vf

)+∂uz∂z

+∂

∂t

[(1− Vf )

V0

Vf

]= 0 (2.29)

At this point, the flow velocities can be replaced in terms of pressure gradients in the

continuity equation using the Darcy’s law leading to Equation 2.30,

Kxx

Vf

∂2Pr∂x2

+Kyy

Vf

∂2Pr∂y2

+1

V 20

∂

∂z

(VfKzz

∂Pr∂z

)= η

∂

∂t

(1− VfVf

)(2.30)

The equilibrium equation resulting of the force balance between the applied pressure

during consolidation (P Tij ) and the stress carried by the fibers (effective stress, σ′ij) and by

the resin (Pr) on the prepreg can be expressed as,

P Tij = σ′ij − Prδij (2.31)

29


The load borne by the fibers (fiber bed effective stress tensor, σ′ij), can be related to

the strain tensor through,

εij = Sijσ′ij (2.32)

To illustrate the compaction process, an unidimensional example is solved for the typ-

ical material properties found for thermoset prepregs. This unidimensional problem is

representative of the autoclave consolidation for prepregs when resin flow occurs along the

through-thickness direction from the tool to the bag surface.

Figure 2.10: Boundary conditions and material properties inputs for run R1

When resin bleeding is constrained through-thickness (ux = uy = 0), Equation 2.30 can

be simplified to,

∂

∂z

(VfV0

Kzz

η

∂Pr∂z

)+V0

V 2f

∂Vf∂t

= 0 (2.33)

and Equation 2.33 can be rewritten using the void ratio e =1−VfVf

as variable for simplicity,

yielding to,

30


1

V0

∂

∂z

(Kzz

η(1 + e)

∂Pr∂z

)=∂e

∂t(2.34)

where V0 = 1/(1 + e0) are the initial fiber volume fraction and void ratio. Finally, taking

into account that the applied autoclave pressure PT is constant, and the chain derivative

rule ∂Pr

∂z= −∂σzz

∂e∂e∂z

, Equation 2.34 can be expressed as,

(1 + e0)2 ∂

∂z

(Kzz

η(1 + e)

∂σzz∂e

∂e

∂z

)=∂e

∂t(2.35)

where ∂σzz∂e

represents the fiber bed equation in terms of the void ratio. For uniaxial strain

along the thickness direction and a linear elastic material with Young Modulus E, the

relation between fiber bed stress and void ratio can be expressed as σzz = E(1− (1 + e))V0

and ∂σzz∂e

= −V0E.

The boundary problem represented by this equation can be solved for autoclave condi-

tions assuming impermeable and permeable flow at tool (z = 0) and bag (z = H) surfaces.

Initially, the fiber volume fraction is set to V0 corresponding to a stress free state on the

fiber preform.

Equation 2.35 has to be solved numerically by means of the Runge-Kutta method

for arbitrary values of the material constants and consolidation process: typical autoclave

pressure, PT = 7 bar, initial fiber volume fraction, V0 = 0.574, permeability factor, Kzz = 5·10−13m2, resin viscosity η = 1000 Pa s and fiber bed elasticity, E = 7 MPa. The integration

was performed along the laminate thickness, H = 5 mm, during the consolidation time.

The Mathematica input used to solve the equation is presented in Appendix A.

Different resin pressure distributions through the thickness are plotted in Fig. 2.11.a as

a function of consolidation time. Initially, the resin pressure corresponded to the autoclave

pressure but, as soon as consolidation started, the applied pressure was transfered to the

fiber bed relieving the pressure from the resin. The pressure relief wave propagates through

the thickness from the bag surface to the tool surface until the consolidation process ends

when all the resin pressure is transfered to the fiber bed, Fig. 2.11.b.

31


0 . 0 2 . 0 x 1 0 - 1 4 . 0 x 1 0 - 1 6 . 0 x 1 0 - 1 8 . 0 x 1 0 - 10 . 0 0 0

0 . 0 0 1

0 . 0 0 2

0 . 0 0 3

0 . 0 0 4

0 . 0 0 5 t = 0 s

t = 4 0 5 6 st = 2 4 5 6 s

t = 6 5 6 s

M a t h e m a t i c a A b a q u s

Thick

ness p

osition

(m)

E f f e c t i v e s t r e s s ( M P a )

t = 5 0 s

( b )

0 . 0 2 . 0 x 1 0 5 4 . 0 x 1 0 5 6 . 0 x 1 0 5 8 . 0 x 1 0 50 . 0 0 0

0 . 0 0 1

0 . 0 0 2

0 . 0 0 3

0 . 0 0 4

0 . 0 0 5

0 . 0 0 6t = 0 s

t = 4 0 5 6 s

t = 2 4 5 6 s

t = 6 5 6 s

M a t h e m a t i c a A b a q u s

Thick

ness p

osition

(m)

P o r e p r e s s u r e ( P a )

t = 5 0 s

( a )

Figure 2.11: Simulation results for (a) resin pressure evolution and (b) fiber effective

stress as a function of consolidation time.

32


Additionally, the same equation was solved by means of the porous fluid flow module

of the Abaqus Standard finite element program. Again, the input used in the example is

presented in Appendix B. The agreement between both integration methods is fairly good

although the ability of Abaqus Standard to incorporate different material properties and

boundary conditions, etc., is preferred.

Finally, the compaction displacement is presented in Fig. 2.12 as a function of time.

Initially, the displacement is zero as the external pressure is supported by the incompressible

resin, and grows monotonically until total consolidation is attained.

The final thickness, Hf can be computed by assuming logarithmic compressive strains

and the linear elastic behavior of the fiber bed elasticity when total consolidation is reached,

ε = − ln

(Hf

H0

)⇒ Hf = H0 exp

[−PTE

](2.36)

Figure 2.12: Evolution of compaction displacement as a function of time.

33

Chapter 3Materials and Cure Cycle Definition

The effect of processing conditions on the void population was studied in carbon/epoxy

prepregs consolidated by compression molding. In addition, the relationship between the

curing cycle and the mechanical performance was established. To this end, three different

curing cycles were carefully designed following the rheological and thermal analysis of the

raw prepregs. The chapter presents the characteristics of the materials, the manufacturing

route and the processing parameters.

3.1 AS4/8552 prepreg system

Unidirectional carbon/epoxy AS4/8552 prepreg sheets were purchased from Hexcel

composites. The 8552 epoxy resin is a blend of a high functionality epoxy resin TGMDA

(Tetraglycidyl methylenedianiline), a lower functionality epoxy resin TGpAP (Triglycidyl

p-aminofenol) and 4,4’-diaminodiphenylsulfone (DDS) and 3,3’-diaminodiphenylsulfone amines

as curing agents. The epoxy system has been modified by the supplier with the incorpora-

tion of thermoplastic particles in order to enhance the fracture toughness and the impact

35

3.2 Cure Cycles Definition

performance Hexcel (2010b). The AS4 carbon fiber was manufactured from polyacryloni-

trile (PAN), Hexcel (2010a). Carbon reinforcement in the prepregs was unidirectional. The

nominal prepreg areal weight was 194 g/m2.


3.2.1 Rheology

The evolution of the resin viscosity during curing is an essential parameter to design

the curing cycle and provides the experimental data required to calibrate the empirical

viscosity models.

The rheological behavior of the prepreg was measured under oscillatory mode using a

parallel plate rheometer (AR200EX, TA Instruments) with disposable plates. A prepreg

raw sample of 25 mm in diameter was placed between the plates of the rheometer and

subjected to an oscillatory shear strain of constant amplitude and frequency under a given

temperature history. The dynamic viscoelastic response of the composite prepreg is given

by the storage and the loss moduli, G′ and G′′, respectively, which change with time as

a result of cross-linking reactions. The complex modulus G∗ = |G′ + iG′′| stands for the

resistance of the material to be deformed while tan δ = G′′/G′ expresses the ratio between

the storage and loss moduli. The evolution of the complex viscosity η∗ (modulus of real

and imaginary parts) can be determined as,

η∗ =|G′ + iG′′|

ω(3.1)

where ω is the frequency of the imposed oscillatory strain. δ is a frequency-dependent

function which represents the angle between the viscous stress and the shear stress.

Two set of experiments were performed under isothermal and dynamic conditions to

characterize the rheology of the prepreg.

36


3.2.2 Isothermal Viscosity Profiles

Isothermal viscosity profiles were generated at frequencies of 10, 5.5 and 1 Hz with an

oscillatory shear strain amplitude (γ) of 0.05% at dwell temperatures of 110, 120, 140,

160, 170 and 180C. Two experiments were performed for each temperature using prepreg

raw samples of 25 mm in diameter and four plies were placed between the plates of the

rheometer. Storage and loss moduli were determined from the shear stress-time curves,

G′ =τ

γcos δ (3.2)

G′′ =τ

γsin δ (3.3)

where τ is the shear stress. The corresponding complex viscosity modulus was calculated

according to Equation 3.1.

The gel point was assumed to be reached when tan δ = G′′/G′ was independent of

applied frequency, according to the criterion developed by Winter and Chambom Winter

& Chambon (1986), Fig. 3.1. This criterion provides the gel time avoiding the G′ and G′′

”intersection” criterion, commonly used for neat resins. The presence of the fibers in the

prepreg increases the friction between the parallel plates of the rhometer geometry and the

higher storage component of the shear modulus makes impossible to establish the gel point

through the ”intersection” criterion because G′ and G′′ curves never cross each other (i.e.

Fig. 3.2).

The influence of temperature on the minimum complex viscosity, η∗min, and on the

gelation time under isothermal conditions is plotted in Fig. 3.3. The initial viscosity of the

polymeric resin decreases with increasing temperature because the higher the reaction rate

for a given system, the shorter the time required to reach the gel point.

37


0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 00 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

t g e l = 1 7 1 m i n

1 0 H z 5 . 5 H z 1 H z

tan δ=

G’/G’’

C u r e t i m e ( m i n u t e s )

( b )

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 00 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6( a ) 1 0 H z 5 . 5 H z 1 H z

tan δ=

G’/G’’


t g e l = 2 2 6 m i n

38


0 1 0 2 0 3 0 4 0 5 00 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5( d )

t g e l = 2 4 m i n

1 0 H z 5 . 5 H z 1 H z

tan δ=

G’/G’’


0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 00 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8( c )

t g e l = 7 5 m i n

1 0 H z 5 . 5 H z 1 H z

tan δ=

G’/G’’


39


0 5 1 0 1 5 2 0 2 5 3 00 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5( e )

t g e l = 1 8 m i n

1 0 H z 5 . 5 H z 1 H z

tan δ=

G’/G’’


0 5 1 0 1 5 2 00 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

t g e l = 1 2 m i n

1 0 H z 5 . 5 H z 1 H z

tan δ=

G’/G’’


( f )

Figure 3.1: Gel point of the AS4/8552 prepreg under isothermal conditions at (a)

110C, (b) 120C, (c) 140C, (d) 160C, (e) 170C and (f) 180C.

40


0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 01 0 4

1 0 5

1 0 6

1 0 7

G ’Sto

rage m

odulu

s, G’

(MPa

)

C u r e t i m e ( m i n u t e s )1 0 4

1 0 5

1 0 6

1 0 7

G ’ ’

Loss

modu

lus, G

’’ (MPa

)

Figure 3.2: Storage (G′) and loss moduli (G′′) of AS4/8552 prepreg at 120C.

1 0 0 1 2 0 1 4 0 1 6 0 1 8 01 0 3

1 0 4

1 0 5

Minim

um co

mplex

visco

sity, η

∗ min (P

a s)

M i n i m u m C o m p l e x v i s c o s i t y

0

1 0 0

2 0 0

3 0 0Ge

l time (

minu

tes)

G e l T i m e

Figure 3.3: Minimum complex viscosity, η∗min, and gel time, tgel, under isothermal

conditions for the AS4/8552 prepreg.

41


Fig. 3.4 shows the evolution of the complex viscosity under isothermal conditions. The

plateau of constant viscosity was shorter at higher temperatures leading to shorter gel

times and lower minimum viscosities. From the viewpoint of composite processing, low cure

temperatures (≈ 110−120C) favor long processing windows -the low viscosity region before

gelification- but the elevated value of the minimum viscosity hinders fiber impregnation.

Moreover, it also makes difficult to squeeze out of the panel the air bubbles within the

prepreg as well as the air entrapped between prepreg plies. High cure temperatures (≈ 160−180C) lead to lower minimum viscosities in the resin but the gelation time is dramatically

reduced. Therefore, the curing cycle should be designed in such a way that a minimum

viscosity is attained during the time necessary to allow the voids to migrate and bleed out

or dissolve before gelation.

0 5 0 1 0 01 0 3

1 0 4

1 0 5

1 0 6

1 0 7

Co

mplex

visco

sity, η

∗ (Pa s

)

C u r e t i m e ( m i n u t e s )Figure 3.4: Isothermal viscosity profiles of AS4/8552 prepreg.

3.2.3 Dynamic Viscosity Profiles

Dynamic viscosity profiles were generated at 1 Hz of frequency and a shear strain

amplitude of 0.05% at constant heating rate of 5, 8 and 10C/min, Fig. 3.5. The complex

viscosity decreased slightly at the begining due to the higher mobility between polymer

42


chains induced by temperature. Before reaching the minimum viscosity, the slope changed

slightly as a result of the linear growth of the polymer chains and the beginning of the

crosslinking reactions. After the minimum, the viscosity increased sharply because of the

gelification of the resin. Higher heating rates shifted the minimum viscosity towards higher

temperatures, decreasing the absolute value of the minimum viscosity and leading to longer

gel times. As a result, manufacturing routes with higher heating rates lead to wider process

windows and lower minimum viscosities.

5 0 1 0 0 1 5 0 2 0 0 2 5 01 0 4

1 0 5

1 0 6

Comp

lex vis

cosity

, η∗ (P

a s)

Figure 3.5: Dynamic complex viscosity profiles of the AS4/8552 prepregs at different

heating rates.

The viscosity profile of the neat 8552 epoxy resin was compared with the equivalent

prepreg viscosity profile in order to evaluate the effect of the fiber reinforcement on the

rheological properties, Fig. 3.6 Boswell (2000). The viscosity profile of the neat resin and

of the prepreg presented similar trends but the fiber reinforcement induced a dry friction

which increased the storage component of the shear modulus G∗. This effect was taken

into account in the modeling of flow in the compaction models applying a correction factor.

43


0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 01 0 2

1 0 3

1 0 4

1 0 5

1 0 6

1 0 7

1 0 8

1 0 9

1 0 1 0

1 0 1 1

η∗


2 5

5 0

7 5

1 0 0

1 2 5

1 5 0

1 7 5

2 0 0

Figure 3.6: Viscosity measurements of 8552 epoxy resin and of S2/8552 prepregs Boswell

(2000).

3.2.4 Definition of Cure Cycles

Based on the previous considerations, three curing cycles were designed to manufacture

the composite panels, Fig. 3.7. The pressure was held constant and equal to 2 bars. The

temperature profile was different in each cycle in order to ascertain its influence on the void

volume fraction, shape and spatial distribution. The simplest cycle, C-1, consisted on a

heating ramp at a constant rate up to 180C, Fig. 3.7.a. Cycle C-2 (Fig. 3.7.b), was similar

to C-1 but the heating ramp was interrupted at 130C and the prepreg was held at this

temperature for 10 min. This modification was intended to maintain the material longer

in the low viscosity regime, so void transport and resin infiltration were easier. Finally,

cycle C-3 (Fig. 3.7.c) presented a ramp until 180C. This initial flash temperature peak was

intended to reduce the minimum viscosity and facilitate the impregnation of fibers and the

transport of the voids. The temperature was immediately reduced after the peak to 130C,

held at this temperature for 10 min and finally increased up to 180C. All the heating and

44


cooling ramps were carried out at 8C/min - 10C/min based on preliminary rheological

experiments. The evolution of the complex viscosity during each cycle is plotted together

with the temperature profile in Fig. 3.7. These curves show that final gelation did not

take place in any cycle before the maximum temperature of 180C was attained for the

second time. This guarantees enough time for resin flow and void evacuation leading to

panels with low porosity (<3%). The gelation time corresponding to each cure cycle was

computed using the Winter and Chambom criterion, Fig. 3.8, and the corresponding gel

times are shown in Table 3.1. The final hold at 180C ensured that the parts were fully

cured and presented adequate mechanical properties.

Cycle Gel time (min)

C-1 17

C-2 28

C-3 36

Table 3.1: Gel time of the AS4/8552 prepregs after consolidation following cure cycles

C-1, C-2 and C-3.

0 1 0 2 0 3 0 4 0 5 01 0 4

1 0 5

1 0 6

1 0 7

η

( a )

0

5 0

1 0 0

1 5 0

2 0 0

45


0 1 0 2 0 3 0 4 0 5 01 0 4

1 0 5

1 0 6

1 0 7

5 0

1 0 0

1 5 0

2 0 0

η

η

( c )

0 1 0 2 0 3 0 4 0 5 01 0 4

1 0 5

1 0 6

1 0 7

η

0

5 0

1 0 0

1 5 0

2 0 0

( b )

Figure 3.7: Temperature profile of the cure cycles used to process AS4/8552 composite

prepregs and the corresponding evolution of the complex viscosity, η∗, during the (a)

cycle C-1, (b) cycle C-2 and (c) cycle C-3.

46


0 5 1 0 1 5 2 0 2 5 3 0 3 50 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2

1 . 4

t g e l = 2 8 m i n

1 0 H z 5 . 5 H z 1 H z

tan δ=

G’/G’’


C y c l e C - 2( b )

0 5 1 0 1 5 2 0 2 50 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2

t g e l = 1 7 m i n

1 0 H z 5 . 5 H z 1 H z

tan δ=

G’/G’’


C y c l e C - 1( a )

0 5 1 0 1 5 2 0 2 50 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2

t g e l = 1 7 m i n

1 0 H z 5 . 5 H z 1 H z

tan δ=

G’/G’’


C y c l e C - 1( a )

47


0 5 1 0 1 5 2 0 2 5 3 00 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2( c )

t g e l = 3 6 m i n

1 0 H z 5 . 5 H z 1 H z

tan δ=

G’/G’’


C y c l e C - 3

Figure 3.8: Gel point of the AS4/8552 prepreg subjected to different cure cycles (a)

cycle C-1, (b) cycle C-2 and (c) cycle C-3.

3.2.5 Thermal Characterization

Differential scanning calorimetry (DSC) was used to determine the degree of curing,

α, and the glass transition temperature, Tg, for each cure cycle. DSC was also used to

generate the experimental data necessary to fit the kinetic model.

The calorimetric experiments were carried out using a modulated differential scanning

calorimeter (MDSC Q200, TA Instruments). Raw prepreg samples (10 mg) were placed

onto the Al pan of the DSC apparatus and subjected to the corresponding temperature

cycle. Variations in the enthalpy or heat capacity of the reactive sample led to temperature

gradients with respect to the reference sample and therefore to a heat flow. The gradient

is recorded and the corresponding heat released by the sample is determined.

The heat released during the exothermic curing process of a thermoset resin is pro-

portional to the degree of cure of the resin, α. It can be computed by means of DSC

48


Figure 3.9: MDSC Q200 (TA Instruments).

by measuring the heat flow exchanged between the reactive sample of prepreg and the

reference sample (reaction enthalpy) according to,

α =∆Htot −∆HR

∆Htot

(3.4)

where ∆Htot stand for the total heat of reaction (maximum heat achievable for the prepeg

system) and ∆HR is the residual heat measured after curing.

The total reaction heat ∆Htot was obtained by averaging the total enthalpy measured

from room temperature up to 300C at 5, 8 and 10C/min, Fig. 3.10, yielding ∆Hdin =

∆Htot = 176.20± 0.48 J/g.

The residual reaction heat, ∆HR, Fig. 3.11, and the glass transition temperature, Tg,

Fig. 3.12, were measured by means of modulated DSC tests at 5C/min with ±2C ampli-

tude of temperature modulation and 100 seconds of period after the sample was subjected

to the corresponding cure cycle. The glass transition occurs by the breaking of secondary

bonds which increases the mobility of the polymeric chains and hence the heat capacity of

the sample. Variations in the heat capacity of the sample lead to changes in the heat flow

which can be detected by DSC.

49


0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0- 8

- 6

- 4

- 2

0

2

4

6Dy

nami

c Hea

t Flow

, ∆H din

(w/g)

Figure 3.10: Heat flow of the AS4/8552 prepreg as a function of temperature and

heating rate (5, 8 and 10C/min).

3 0 3 5 4 0 4 5 5 0 5 5

- 0 . 4

- 0 . 3

- 0 . 2 C y c l e C - 1 C y c l e C - 2 C y c l e C - 3

Resid

ual H

eat fl

ow, ∆

H R (w/g)

T i m e ( m i n )Figure 3.11: Residual reaction heat of AS4/8552 prepreg after curing cycles C-1, C-2,

C-3.

50


Figure 3.12: Glass transition temperature of AS4/8552 prepreg after curing cycles C-1,

C-2, C-3 at onset.

The residual reaction heat, ∆HR, the final degree of cure, α, and the glass transition

temperature, Tg for each curing cycle are summarized in Table 3.2.

Cycle ∆Hres (J/g) α Tg (C)

C-1 19.1 0.891 207.6

C-2 18.4 0.895 210.4

C-3 18.3 0.896 210.6

Table 3.2: Residual heat of reaction, ∆Hres, degree of cure, α, and onset glass tran-

sition temperature, Tg, of unidirectional AS4/8552 composite panels manufactured with

different curing cycles.

Tg and α were very similar for all cycles and equivalent to other data reported in the

literature Hubert & Poursartip (2001); Sun (1993). They indicate that a high cross-linking

degree was reached in the thermoset resin during curing, leading to similar mechanical

properties of the resin in all the cycles.

The evolution of α as function of cure time α(t) was determined experimentally for cycle

C-1 by measuring the reaction heat released during curing ∆Ht according to Equation 3.5,

51


α(t) =∆Ht(∆Htot −∆HR)

∆Htot∆Ht=ttotal

(3.5)

where ∆Ht=ttotal is the reaction heat released at the end of the curing (t = ttotal). Due to the

complexity of the curing cycles C-2 and C-3, which result in a combination of temperature

ramps and holds, α(t) could not be obtained accurately by DSC experiments. In such cases,

isothermal-dynamic transitions are not adequately detected with DSC by the limitations

of the technique itself. The evolution degree of cure with the cure time (cure rate) was

studied with the aid of the kinetic model developed by Johnston and Hubert Hubert et al.

(1995) described previously. The kinetics parameters of this model (Equation 2.8) were

obtained by means of the non-linear regression based on weighted least-squares fitting of

the curve α(t) determined experimentally for cycle C-1 and are summarized in Table 3.3.

This method allowed to estimate the evolution of degree of cure for a given cure cycle.

The predictions of the Johnston and Hubert model are depicted in Fig. 3.13. It is shown

that the modifications introduced in cycles C-2 and C-3 with respect to cycle C-1 hindered

the curing of the resin, leading to a lower viscosities in the initial stages of the cycle.

Kinetic constants

Ea = 63242 J/mol

A = 40000 s−1

m = 0.30

n = 1.196

Cr = 25.08

αC0 = 0.051

αCT = 0.001766 K−1

Table 3.3: Constants of the Williams and Hubert kinetic model.

52

3.3 Manufacturing of Composite Laminates

0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 00 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

Degre

e of C

ure, α

(t)

T i m e ( s )

W & H m o d e l C y c l e C - 1 W & H m o d e l C y c l e C - 2 W & H m o d e l C y c l e C - 3 E x p e r i m e n t a l C y c l e C - 1

Figure 3.13: Evolution of the degree of cure of the AS4/8552 prepreg. Predictions

from Williams and Hubert model for curing cycles C-1, C-2, C-3 and experimental results

of curing cycle C-1.


Square unidirectional and multiaxial panels were manufactured by compression molding

from AS4/8552 prepregs (Fontijne Grotnes LabPro400). The prepreg plies were stacked

according to the sequence indicated in Table 3.4 and placed between polytetrafluoroethy-

lene sheets for adequate release after the consolidation, Fig. 3.14. No previous vacuum

debulking of the laminate prepreg kit was performed and a constant pressure of 2 bars

was applied immediately after placing the kit between the press plates. Three curing cy-

cles were applied based on the thermo-rheological studies performed for the raw AS4/8552

prepregs.

Panel examination after processing revealed resin bleeding on all faces for multiaxial

laminates while bleeding was limited to the faces perpendicular to the fiber direction in

the unidirectional panels. This indicates that the resin flow was anisotropic and mainly

occurred along the fiber direction due to the higher prepreg permeability in this direction.

53


Figure 3.14: Staking and packing process of unidirectional laminates.

Panel class Staking sequence Dimensions (mm3) Cured ply thickness (mm)

Unidirectional [0o]5s 200× 200× 2 0.2

Multiaxial[45o/0o/-45o/90o]3s 320× 320× 4.6 0.19

[45o

3/0o

3/-45o

3/90o

3 ]s 320× 320× 4.6 0.19

Table 3.4: Lay up of the manufactured panels.

As far as multiaxial panels is concerned, resin bleeding was the result of the resin flow

following different fiber orientation (0, +45, 90, -45).

3.3.1 Thermogravimetric Measurements

The volume fraction of carbon fiber was measured using thermogravimetric experiments

performed in a vertical thermobalance (model Q50, TA Instruments). The samples were

heated from room temperature up to 1000C at 10C/min in N2 atmosphere up to 500C

and in laboratory air at higher temperature and the mass loss associated with thermal

degradation of the epoxy resin was measured. The nominal fiber volume fraction of the

composite panels was determined according to the ASTM-D3171 (2011) standard from the

densities of carbon (1.79 g/cm3) and epoxy resin (1.3 g/cm3) without considering the initial

void volume fraction.

The fiber volume fraction, Vf , obtained with this methodology was ≈ 59% for unidi-

rectional panels, Fig. 3.15, and ≈ 60% to multiaxial panels, Fig. 3.16.

54


0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 00

2 5

5 0

7 5

1 0 0

C o m b u s t i o n o f c a r b o n f i b e r

C y c l e C - 1 C y c l e C - 2 C y c l e C - 3

Mass

loss (

%)

T h e r m a l a n d o x i d a t i v e d e g r a d a t i o n o f R e s i n

Figure 3.15: Mass loss of AS4/8552 unidirectional laminates a function of temperature.

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 00

2 5

5 0

7 5

1 0 0( a )


Mass

loss (

%)

T h e r m a l a n d o x i d a t i v e d e g r a d a t i o n o f r e s i n


55


0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 00

2 5

5 0

7 5

1 0 0


Mass

loss (

%)

T h e r m a l a n d o x i d a t i v e d e g r a d a t i o n o f r e s i n


( b )

Figure 3.16: Mass loss of AS4/8552 multiaxial clustered laminates as a function

of temperature (a) dispersed laminate [45o/0o/-45o/90o]3s and (b) clustered laminate

[45o3/0

o3/-45

o3/90

o3 ]s.

The first loss in mass, shown in Fig. 3.15 and Fig. 3.16, occurred in an inert atmosphere

and was due to the thermal degradation of the polymeric resin. After air was introduced,

there was a second mass loss of resin at 500C by oxidation. Finally, carbon fibers com-

busted when the temperature attained was ≥ 600C. The initial Vf0 of the AS4/8552

prepreg was also measured by thermogravimetric analysis of the raw prepreg. The average

initial fiber volume fraction was 57%.

56

Chapter 4Simulation of the Compaction

Process

This chapter is focused in the development of a model to analyze the compaction process

of AS4/8552 unidirectional composite laminates manufactured by compression molding.

The model accounts for the different physical phenomena involved in the process. The

resin flow through the fiber preform was modeled using the Darcy’s flow in a porous media

while the compaction process was controlled by the non-linear response of the fiber bed.

The combination of resin flow, the load transfer from the resin to the fibers, and the

deformation of the fiber bed gave rise to a set of partial differential equations that can

be solved by the finite element method. This model was used to analyze the compaction

process of unidirectional AS4/8552 prepregs subjected to different cure cycles.

4.1 Bidimensional Finite Element Model

The analysis of resin flow can be simplified for certain manufacturing processes of com-

posites, such as compression molding. Transverse flow in the through-thickness direction

57


is rather small as the in-plane dimensions of the laminate are typically two or three orders

of magnitude larger than the thickness. The experimental evidence provided in this the-

sis by the compression molding of unidirectional panels revealed extensive resin bleeding

along the fiber direction while the transverse flow was negligible in comparison, Fig. 4.1.

This result is in agreement with the large differences in the permeability factors of a uni-

directional fiber preform between both directions. As a result, three dimensional panels

can be simplified into two dimensional geometries from the viewpoint of flow analysis,

which are representative of the primary directions of resin flow. This simplification reduces

significantly the computational power required and the complexity of the analysis.

Figure 4.1: Resin bleeding during compression molding of a unidirectional panel. Fibers

run horizontally and resin bleeding only occurred along the borders perpendicular to the

fibers .

These observations led to the analysis of the compaction process of the unidirectional

panel by means of the finite element analysis of a plane strain representative section of the

laminate along the fiber direction, Fig. 4.2. Due to the symmetries of the problem, only

one half of the section was analyzed (L/2 being L the total length of the square panel). The

panel thickness was H and the fibers were oriented along the z-axis. The general governing

equations of flow and deformation were reported in chapter 2, and they are basically a

combination of the Terzaghi, Darcy and continuity equations for a porous elastic media.

For the sake of clarity, they are presented here for the case of resin flow in the z-x plane.

The following non-linear partial derivative equation was obtained,

58


Figure 4.2: Sketch and representative section of the panel for the finite element model.

Kzz

Vf

∂2Pr∂z2

+1

V 20

∂

∂y

(VfKxx

∂Pr∂x

)= η∗

∂

∂t

(1− VfVf

)(4.1)

where σ′f +Pr = PT stands for the Terzaghi equation relating the stress carried by the fiber

bed, σ′f , and the resin pressure, Pr, to the total applied external pressure PT , η∗ is the resin

viscosity and Kzz and Kxx the permeability factors along the z and x directions. It should

be noted that the fiber bed elasticity and the permeability factors are highly dependent

on the applied deformation as the fiber-to-fiber contacts increase during the compaction

process. Additionally, the viscosity evolves with time as a consequence of the changes in

temperature during the cure cycle. This partial derivative equation is, therefore, highly

non-linear and was solved in the time and spatial domains by means of the implicit finite

element method using the commercial software Abaqus Standard Abaqus (2012).

Prescribed symmetry displacement conditions, uz = 0, were imposed at the center of

the panel (z = L/2) while stress free conditions were set at the opposite end (z = 0) which

corresponds to the free edge of the laminate. Top and down surfaces (x = 0, x = H) were

treated as non deformable and frictionless surfaces. To this end, the vertical displacement

of the lower tool surface (x = 0) was set to ux = 0, while the vertical displacement of the

upper surface (x = H) was given by ux = δ and depended on the total pressure applied to

the laminate. The geometry was discretized with 4-node bilinear displacement and pore

pressure quadrilateral elements (CPE4P in Abaqus). These elements, formulated under

plane strain conditions in the z-x plane, contain independent degrees of freedom for the

59


pore fluid pressure and are traditionally used to analyze consolidation in problems governed

by Darcy’s flow in Terzaghi’s porous solids. Eight elements were used in the discretiza-

tion through the thickness of the laminate to capture the pressure gradient between the

tool surfaces. A total of 5000 elements was used to ensure a good discretization of the

bidimensional problem.

The following sections are devoted to describe the constitutive behavior of the material

in terms of the fiber bed elasticity and of the permeability.

4.1.1 Fiber bed constitutive equation

During the compaction process, the applied deformation increases the volume fraction

of reinforcement in the laminate. Therefore, fibers become progressively into contact and

the fiber-to-fiber interactions led to a non-linear mechanism of load transfer. Many at-

tempts have been carried out in the past to derive simple, analytical constitutive equations

for the fiber bed such as, for instance, the fiber in a box model developed by Gutowski

Gutowski et al. (1986). Other authors were able to measure the compaction curve on the

AS4/8552 prepreg system by means of the load-hold method Hubert & Poursartip (2001).

In both cases, the fiber bed constitutive equation, σ′f (Vf ), only represents the response of

an unidirectional composite material subjected to deformation perpendicular to the fibers

and, therefore, only provides a part of a more complex behavior including the presence and

flow of the resin. This behavior can be represented adequately by means of an orthotropic

elastic material in the z − x plane according to the following assumptions:

• The elastic modulus of the unidirectional composite material in the fiber direction, Ez,

is independent of the compaction process and depends only on the fiber longitudinal

elastic modulus. The contribution of the fluid resin can be neglected.

• The transverse elastic modulus of the unidirectional composite material, Ex, is con-

trolled by the fiber bed constitutive equation. This behavior can be modeled in

Abaqus assuming that the elastic modulus depends on the fiber volume fraction, and

therefore, on the compaction strain or thickness reduction.

• The in-plane Poisson is ratio, νzx, was assumed to be zero so no coupling between

the longitudinal and transverse behavior is taken into account.

60


• The in-plane shear response of the material is controlled by the shear modulus Gzx

which was set arbitrarily to one half of the transverse modulus assuming an isotropic

behavior.

The fiber bed compaction curve of the AS4/8552 prepreg was estimated by means of

a simple set of compaction tests carried out at different temperatures. Unidirectional [0]10

square specimens of 77.5 × 77.5 mm2 were cut, packed together with a Teflon/glass fiber

cloth and consolidated under constant load in an Instron 3384 electromechanical testing

machine. The load was maintained constant during the consolidation process with an av-

erage compaction pressure of 2 bars which was applied to the laminate kit by means of

two steel compression plates, Fig. 4.3.a. The testing rig was introduced in an Instron en-

vironmental chamber and the temperature was measured with standard K thermocouples

in contact with the laminate. The specimens were first placed between the compression

plates followed by an immediate preload at 2 bars during 45 minutes to remove air en-

trapped between adjacent layers of the laminate (debulking operations). Afterwards, a

constant temperature ramp of 10C/minute was applied until the desired temperature

(120, 140, 160 or 180C) was attained. This temperature was maintained during 2.5 h. It

should be mentioned that the evolution of the temperature in the composite laminate was

different from the thermal cycle imposed to the environmental chamber as a consequence of

the large thermal inertia of the whole fixture, Fig. 4.3.b. The initial slope was the same in

all cases corresponding to the maximum rate allowed by the thermal controller but deviate

rapidly from linearity until the fully stationary regime was attained.

The vertical strain, εx, was obtained from the initial and final laminate thickness and is

summarized in Table 4.1 for the four temperatures. The compaction of the laminates was

similar, around 20%, and independent of the temperature. The total compaction time was

large enough in all the cases to attain the maximum compaction (or the maximum volume

fraction) corresponding to an applied external pressure of 2 bars.

In addition, the resin bleeding strain was estimated by measuring the mass loss after

the compaction of the laminate. The bleeding strain was computed as

εbleeding =Mf −M0

ρrW0L0H0 (4.2)

61


Figure 4.3: a) Testing rig used for the compaction tests, b) Evolution of the laminate

temperature.

Temperature Cycle εx εbleeding

I-120C 0.193± 0.017 0.0839± 0.0072

I-140C 0.197± 0.007 0.0906± 0.0061

I-160C 0.191± 0.019 0.0914± 0.0097

I-180C 0.194± 0.017 0.0954± 0.0056

Table 4.1: Final compaction and bleeding strains.

where W0, L0 and H0 are, respectively, the initial width, length and thickness of the lam-

inate (assuming that the weight loss by bleeding is fully compensated by the thickness

change). Resin bleeding was obtained by measuring the initial mass of the laminate M0

and the final mass Mf , which was obtained after carefully trimming the excess of resin

of the edges of the plate. The results are also summarized in Table 4.1 and compared

with the total final strain. It should be noted that these values are very different, and

the bleeding strains accounted for less than 50% of the total strain. The percolation flow

mechanism leading to resin bleeding is not the only mechanism responsible for the final

thickness and the discrepancies could be attributed to debulking operations. The effect of

debulking during the preparation of the laminate kit and the method of removal the excess

of air entrapped between adjacent layers during lamination could play an important role

62


in the compaction process and influences systematically the compaction curve. This fact

limited the accuracy of the modelization of compaction as debulking and air entrapped be-

tween adjacent layers are highly dependent on the operator experience. For these reasons,

an initial strain offset, εx,debulk, due to debulking was introduced to obtain an adequate

prediction of the final thickness. The final compaction curve used for the simulations of

consolidation for the curing cycles C-1, C-2 and C-3 is plotted in Fig. 4.4 where the initial

strain offset due to debulking has been included. The values of εx,T (the maximum strain

corresponding to the applied load of 2 bar), and εx,debulk were fitted using the data from

compaction experiments I-120, I-140, I-160, I-180.

0 . 0 0 . 1 0 . 20 . 0

0 . 1

0 . 2

0 . 3

εx , d e b u l k εx T

r e s i n f l o w

Stres

s (MP

a)

S t r a i n ( % )

E x p e r i m e n t a l d a t a G u t o w s k i ’ s M o d e l

d e b u l k i n g p h a s en o f l o w

P T

Figure 4.4: Estimated compaction curve for the AS4/8552 prepreg.

4.1.2 Fiber Bed Permeability

Resin was squeezed out from the laminate during the compaction process until the

maximum volume fraction of reinforcement was attained. Resin flow in porous media is

traditionally modeled by means of Darcy’s equation that relates the fluid velocity to the

pressure gradient through the permeability factors and the fluid viscosity, equation 1.13.

63


The intrinsic permeability or hydraulic conductivity tensor of an orthotropic preform, K,

can be expressed as

K =γ

η∗

[Kzz 0

0 Kxx

](4.3)

where z is the fiber direction and x the direction perpendicular to the fibers, and γ and

η∗ the specific weight and the dynamic viscosity of the resin, respectively. Kzz and Kxx

stand for the permeability coefficients of a orthotropic porous media measured in units of

square length. The hydraulic conductivity K was obtained from Equation 4.3 taking into

account that Kzz was the permeability in the flow direction (z-direction) and is a function

of the fiber volume fraction and of the viscosity. Kxx was ≈ 0 by assuming no flow in the

direction perpendicular to the fibers (x direction).

The dependence of the permeability Kzz with the fiber volume fraction was introduced

by means of the Carman-Kozeny equation 2.15 according to

Kzz =r2f

4k

(1− V 3f )

Vf(4.4)

where rf is the fiber radius (≈ 3− 4 µm for AS4 carbon fibers) and k the Carman-Kozeny

constant. This constant mainly determines the time necessary to achieve the maximum

compaction and was set to k = 0.006 so that the total compaction strain εx,T result obtained

by means of the finite element simulation was equal to the compaction experiments I-120,

I-140, I-160, I-180 for the same total curing time.

The viscosity is the other parameter necessary to obtain the hydraulic conductivity.

The viscosity of the resin is strongly dependent on the temperature during the prepreg

consolidation and the viscosity profiles of the AS4/8552 prepreg material were obtained

from the dynamic rheological experiments carried out in section 3.2.4. The viscosity

of the resin was fit to the analytical model developed by Kenny (1992), Equation 2.12.

This model includes the dependency of the viscosity on the temperature and the cure

degree. The Jonhson and Huber autocatalytic model (presented in equation 2.8, and used

in section 3.2.5) was used to determine the degree of cure.

The rheological characterization described in section 3.2.2 and section 3.2.3 provided

the experimental data required to determine the constants for the viscosity model of the

64


AS4/8552 prepreg. The identification of the parameters of the model was performed se-

quentially. Firstly, Equation 2.12 was rewritten in logarithmic form as follows:

ln η∗(T, α) = lnAµ +EµRT

+ (A+Bα) ln

(αg

αg − α

)(4.5)

This expression can be simplified for the case of a negligible degree of cure (α ≈ 0) as

ln η∗(T, 0) = lnAµ +EµRT

(4.6)

and the linear fit by the least squares method of the logarithm viscosity vs. the inverse of

the temperature, Equation 4.6, provided the initial viscosity Aµ and the activation energy

Eµ, Fig. 4.5. The average values obtained from dynamic runs carried out at 8 and 10C/min

were Aµ = 3894 Pa s and Eµ = 7214 J/mol.

The remaining parameters controlling the effect of the degree of cure in the viscosity.

The parameters A and B were obtained by means of the weighted-square non-linear re-

gression method from isothermal runs at 130 and 160C, Fig. 4.6 and the corresponding

average values are presented in Table 4.2. The degree of cure associated with the gel point,

αg, was set to 0.8 according to the viscosity tests and the corresponding curve of degree of

cure vs. cure time (section 3.2.5).

Temperature A B

130C 1.09 2.00

160C 1.13 1.85

Table 4.2: Paramenters A and B for Kenny’s model.

For comparison purposes, the results of the model are plotted together with the exper-

imental viscosity measurements carried out at 120, 140, 160 and 180C in Fig. 4.7. The

results were in good agreement and demonstrate the ability of Kenny’s model Kenny (1992)

to capture the influence of temperature and degree of cure in the viscosity of the AS4/8552

prepreg.

65


0 . 0 0 2 4 0 . 0 0 2 6 0 . 0 0 2 8 0 . 0 0 3 01 0 . 0

1 0 . 2

1 0 . 4

1 0 . 6

1 0 . 8

1 1 . 0

1 1 . 2

Ln co

mplex

visco

sity

1 / T ( K - 1 )Figure 4.5: Linear fit according to Equation 4.6 of the logarithmic viscosity vs. 1/T at

8C/min and 10C/min.

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8

4 . 0 x 1 0 5

8 . 0 x 1 0 5

1 . 2 x 1 0 6

1 . 6 x 1 0 6

2 . 0 x 1 0 6

Comp

lex vis

cosity

, η∗ (P

a s)

D e g r e e o f c u r e , α

Figure 4.6: Non-linear fit according to Equation 2.12 of the viscosity vs. degree of cure

α at 130 and 160C.

66


0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0

1 0 5

1 0 6

K e n n y ’ s m o d e l I - 1 4 0 E x p e r i m e n t a l I - 1 4 0

Comp

lex vis

cosity

, η∗ (P

a s)

C u r e t i m e ( s )

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0

1 0 5


Comp

lex vis

cosity

, η∗ (P

a s)


( a )

( b )

67


0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0

1 0 5

1 0 6



Comp

lex vis

cosity

, η∗ (P

a s)

( c )

0 2 0 0 0 4 0 0 0 6 0 0 0

1 0 5

1 0 6


Comp

lex vis

cosity

, η∗ (P

a s) K e n n y ’ s m o d e l I - 1 8 0

E x p e r i m e n t a l I - 1 8 0

( d )

Figure 4.7: Evolution of the complex viscosity with cure time: a) 120C, b) 140C, c)

160C and d) 180C.

68


4.1.3 Effect of the Temperature Cycle on the Compaction

The consolidation process of unidirectional flat laminates was simulated using the finite

element approximation for the flow-compaction model for the curing cycles C-1, C-2 and

C-3 in order to asses the effect of the processing conditions on the compaction of unidi-

rectional flat AS4/8552 panels manufactured by compression molding. Consolidation was

only considered in the vertical direction and the applied pressure was held constant at 2

bar. The non-linearity of the fiber bed permeability was considered using the compaction

curve described in Fig. 4.4. The viscosity profiles were computed using Kenny’s model.

The experimental and Kenny’s model viscosity profiles during compaction for curing cycles

C-1, C-2 and C-3 are shown in Fig. 4.8. The agreement between the model predictions and

the experiments was excellent.

For comparison, unidirectional [0]10 square specimens with dimensions 200× 200 mm2

were packed in teflon/glass fiber fabric and consolidated at 2 bar by means of hot pressing.

They were preloaded during 45 minutes at 2 bar before between the compression plates at

room temperature and were consolidated using curing cycles, C-1, C-2 and C-3. The total

vertical strain εx was determined by measuring the dimensions of the samples before and

after the test. The strain caused by the resin bleeding out of the panel was obtained from

the mass loss of resin (εbleeding). The measured displacements are summarized in Table 4.3.

Curing Cycle εx εbleeding

C-1 0.089±0.042 0.0242±0.0071

C-2 0.116±0.028 0.0304±0.0069

C-3 0.123±0.032 0.0249±0.0069

Table 4.3: Compaction strains of unidirectional [0]10 laminates subjected o different

curing cycles at 2 bars of pressure.

The variation of the vertical strain as a function of the curing time for the tree curing

cycles is plotted in Fig. 4.9. As expected, the consolidation strain εx was a function of the

processing conditions. The total thickness reduction was mainly due to percolation flow

and debulking. The experimental results were in ”good” agreement with the numerical

simulations and both are shown in Table 4.5.

69


1 0 5

1 0 6

K e n n y ’ s m o d e l E x p e r i m e n t a l

Comp

lex vis

cosity

, η∗ (P

a s)

C - 1( a )

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0C u r e t i m e ( s )

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0

1 0 5

1 0 6

Comp

lex vis

cosity

, η∗ (P

a s)


C - 2 K e n n y ’ s m o d e l E x p e r i m e n t a l

( b )

70


1 0 5

1 0 6

K e n n y ’ s m o d e l E x p e r i m e n t a l

C - 3

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0

( c )Co

mplex

visco

sity, η

∗ (Pa s

)

C u r e t i m e ( s )Figure 4.8: Viscosity profiles for curing cycle (a) C-1, (b) C-2 and (c) C-3.

0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0- 0 . 1 6

- 0 . 1 2

- 0 . 0 8

- 0 . 0 4

0 . 0 0 C y c l e C - 1 C y c l e C - 2 C y c l e C - 3

Strain

, ε x

t i m e ( s )

r e s i n f l o w

d e b u l k i n g p h a s en o f l o w

Figure 4.9: Numerical simulation of compaction strain as a function of the curing time

for curing cycles C-1, C-2 and C-3

71


Cure cycles Experimental Simulation

C-1 0.089 0.119

C-2 0.116 0.139

C-3 0.123 0.135

Table 4.4: Simulation and experimental results of the vertical strain at the end of the

curing cycle

During the compaction process, the resin was squeezed out the laminate with a velocity

u(x, t). The rate of mass change (dMr/dt) in the composite can be computed as function

of the resin velocity distribution through the thickness in the edge at z = 0 (permeable

edge) using the law of conservation of mass Springer (1982),

dMr

dt= −ρr

∫ −H/2H/2

u(x, t)dx (4.7)

where H is the thickness of the laminate and ρr the density of the resin. The total mass

loss can be obtained by integrating Equation 4.7,

Mr = −ρr∫ t

0

∫ −H/2H/2

u(x, t)dxdt (4.8)

and the resin mass loss for the 200× 200 mm2 predicted by the model was compared with

the experimental results in Table 4.5.

Cure cycles Experimental (g) Simulation (g)

C-1 1.8 1.38

C-2 2.2 1.65

C-3 2.1 1.62

Table 4.5: Predicted and experimental mass loss for curing cycles C-1, C-2, C-3

The predicted mass loss differed by about 25% from the experimental results, a 5%

higher than the differences in the vertical strain. These differences could be attributed to

the experimental error to meaure the experimental mass loss, which was determined by

removing the resin from the edges of the laminate.

72


Figure 4.10 show the evolution of the hydraulic conductivity γKη∗

for each cure cycle. The

hydraulic conductivity increased up to a maximum which coincides with the gel point of the

resin. Afterwards, the hydraulic conductivity decreased as the degree of curing increased

until the resin flow stopped. The time when the resin is able to flow in the composite is a

good estimation of the processing window.

The evolution of the effective stress (stress supported by the fiber bed) along the width

of the laminate and the pore pressure (pressure supported by the resin) are plotted for

curing cycle C-2 in Figure 4.11 (plots of curing cycles C-1 and C-3 are very similar and not

included for the sake of brevity). The load transferred to the fiber bed was maximum at

the permeable edge (z = 0) and decreased towards the central region. The pore pressure

(Pr) in this region was zero so all the load was transfered almost instantaneously to the

fabric perform. From this point, the pressure is gradually transferred to the fibers as the

resin was squeezed out of the laminate so the fiber bed was less compressed. Pr increased

from z = 0 due to the presence of the resin which supported part of the applied load.

0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 00 . 0

2 . 0 x 1 0 - 7

4 . 0 x 1 0 - 7

6 . 0 x 1 0 - 7

8 . 0 x 1 0 - 7

1 . 0 x 1 0 - 6

1 . 2 x 1 0 - 6

H y d r a u l i c c o n d u c t i v i t y

T i m e ( s )

( a )C y c l e C - 1

2 5

5 0

7 5

1 0 0

1 2 5

1 5 0

1 7 5

2 0 0

T e m p e r a t u r e

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

D e g r e e o f c u r e

α

73


0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 00 . 0

2 . 0 x 1 0 - 7

4 . 0 x 1 0 - 7

6 . 0 x 1 0 - 7

8 . 0 x 1 0 - 7

1 . 0 x 1 0 - 6

1 . 2 x 1 0 - 6

1 . 4 x 1 0 - 6


T i m e ( s )

( c )C y c l e C - 3

2 5

5 0

7 5

1 0 0

1 2 5

1 5 0

1 7 5

2 0 0


0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0


α

0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 00 . 0

2 . 0 x 1 0 - 7

4 . 0 x 1 0 - 7

6 . 0 x 1 0 - 7

8 . 0 x 1 0 - 7

1 . 0 x 1 0 - 6

1 . 2 x 1 0 - 6

1 . 4 x 1 0 - 6


T i m e ( s )

( b )C y c l e C - 2

2 5

5 0

7 5

1 0 0

1 2 5

1 5 0

1 7 5

2 0 0


0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0


α

Figure 4.10: Numerical predictions of the evolution of the hydraulic conductivity as a

function of the curing time for curing cycles (a) C-1, (b) C-2 and (c) C-3, element 501

74


Figure 4.11: Evolution of the (a) pore pressure (Pr) and (b) effective stress (σ′) along

width of the laminate for curing cycle C-2

75

Chapter 5X-ray Computed Tomography

Characterization of Defects

X-ray computed tomography (XTC) was used to characterize the void population of the

unidirectional and quasi-isotropic composite panels manufactured by means of compression

molding. Different panels were studied corresponding to the three curing cycles defined in

Chapter 3. XCT enables the straightforward determination of the volume fraction, shape

and spatial distribution of voids within the panels. The chapter begins with a review of

the main non-destructive evaluation techniques used for composite materials, followed by

a brief description of the fundamentals of XTC. The results of the void population analysis

are presented at the end of the chapter.

5.1 Non-Destructive Evaluation Techniques

The microstructural characterization of composite materials is necessary to understand

the main physical phenomena that occur during manufacturing or service of the material.

Conventionally, composite materials characterization is performed in 2D, which is often

77

5.1 Non-Destructive Evaluation Techniques

linked to image analysis to provide quantitative information of the microstructural features.

Sometimes, 3D information can be obtained by expansion of 2D measurements DeHoff &

Rhines (1953) but:

• The number of objects per surface area cannot be related to the 3D number of objects

per unit volume because 2D section objects might appear separated whereas they are

connected in 3D.

• The size distribution of the phases with complex shape cannot be obtained from a

2D section.

• The connectivity of the phases cannot be obtained from 2D measurements.

Furthermore, sample preparation for 2D observations may lead to experimental arte-

facts. For instance, observation of pores is not always accurate since polishing might create

artificial voids by extracting hard phases (such as carbon fibers) from the material or elim-

inating voids in a soft material by refilling them.

The traditional 2D techniques for composite inspection are optical or electron mi-

croscopy (SEM), X-ray radiography, ultrasonics, etc. and not all of them are useful for the

analysis of the porosity or void population. Since voids produce strong scattererings of the

elastic waves, ultrasonic attenuation has been commonly used to determine the porosity.

Mechanical tests were correlated with ultrasonic attenuation to predict the stiffness and

residual strength of porous composites Stone & Clarke (1975), Rubin & Jerina (1993),

Hsu & Nair (1987). Jeong & Hsu (1995) measured the ultrasonic attenuation in carbon

fiber-reinforced composites and found that the attenuation slope (slope of attenuation co-

efficient vs. frecuency curve) correlated with the void content. They also observed that

both attenuation and attenuation slope were particularly sensitive to the pore morphol-

ogy. Moreover, the use of ultrasonic backscatter and Lamb wave modes to characterize

anomalies in composites has received considerable interest in recent years. Cohen & Crane

(1982) applied the polar backscatter technique to examine fiber misalignment, cracks and

porosity. The leaky Lamb waves were used as a nondestructive tool for detecting different

discontinuities in composites, including porosity P.McIntire (1991) and transverse cracks

Dayal & Kinra (1991). Finally, Jeong (1997) established a correlation between ultrasonic

attenuation slope and interlaminar shear strength as well as void content for carbon/epoxy

78

5.2 X-ray Computed Tomography Fundamentals

unidirectional and quasi-isotropic composites and carbon/polyimide woven laminates for a

void content up to 11%.

In comparison with all these thecniques, X-ray computed microtomography (XCT)

is one of the most versatile 3D nondestructive evaluation techniques. It provides three-

dimensional visualization mapping of the X-ray absorption coefficient within the object

yielding the possibility of a three-dimensional characterization. The basis of X-ray tomog-

raphy is X-ray radiography: an X-ray beam is sent through a sample and the transmitted

beam is recorded on a detector. The resulting image contains the superimposed informa-

tion (projection) of a volume onto a plane and 3D information can be obtained from a

large number of radiographs while rotating the sample between 0 and 360. X-ray tomog-

raphy has many applications in material science i.e: cell size distributions in PVC foams

Elmoutaouakkil et al. (2003) or metal foams Olurin et al. (2002), characterization of cel-

lular materials Maire et al. (2007), analysis of damage in fiber reinforced composites Sket

et al. (2012), P.J. Schilling et al. (2005), Fidan et al. (2012), Moffat et al. (2008), Centea

& Hubert (2011) and Enfedaque et al. (2010).

In this thesis, the volume fraction, shape and spatial distribution of voids were analyzed

in detail by means of X-ray computed microtomography, which has been demonstrated to

be a very powerful technique for analyzing the microstructural features of composites.


XCT is a non-destructive imaging method in which the 3D reconstruction of an object

can be obtained from X-ray images collected at many different angles. Figure 5.1 shows

the principle of operation of X-ray tomography. X-rays are generated by the acceleration

of electrons from a filament towards a target material, normally made of a heavy element,

such as tungsten or molybdenum. The electrons extracted from the filament (cathode)

are focused and centered by electromagnets and travel inside the vacuum tube towards

the anode at the end. The collision of the electrons from the filament against the target

generate X-rays by photoelectric and Compton effects and als, but less importantcohernt

scattering. The sample is positioned in between the X-ray source and the detector. The X-

rays traveling through the sample are attenuated depending on the absorption coefficient

of the material and the energy of the incident X-ray beam reaching the detector which

79


records a radiography. During a tomographic scan a set of radiographies is recorded at

different angle positions.

Figure 5.1: Schematic of a X-ray tomography system.

The sample can be modeled as a two or three-dimensional distribution of the X-ray

attenuation coefficient, µ(x, y), which is a property that characterizes the ability of the

material to absorb X-ray from the beam source. The radiation intensity, I, transmitted

through a layer of material, Figure 5.2, is related to the incident intensity, I0 according to

Lambert-Beer’s law, Equation 5.1. This equation relates the total attenuation p(t) (ratio

of transmitted to incident intensity of radiation) through the X-ray absorption coefficient

of the material, µ(x, y).

p(t) = lnI

I0

= exp

[∫Γ

µ(x, y)ds

](5.1)

where the line integral represents the total attenuation suffered by the X-ray beam traveling

along a straight path s(x, y) through the cross-section of the object and t is the distance

from each ray of parallel beam to the center of rotation, Figure 5.2. The procedure for

the reconstruction of a sample volume from the radiographies collected at different angles

θ of rotation is summarized briefly, and explained on a parallel beam configuration for

simplicity. During radiography collection, sample rotates around the z-axis (perpendicular

80


to the paper). The cross-section of the sample is described by the function f(x, y). The

X-ray beam is assumed to be formed by parallel rays. When each ray passes through the

sample, part of the radiation is absorbed and the attenuated intensity, p(t, θ), is collected

in the detector. The attenuation will depend on the absorption coefficient of the material

crossed and on the length of the path, s, through the sample.

Figure 5.2: Principle of tomography and illustration of the Fourier slice theorem.

Once the different projections are recorded for a set of rotation angles, the next step is to

obtain the tomographic reconstruction of the original object. The object is reconstructed

by means of the projection-slice theorem Herman (1980), Kak & Slaney (1987). This

theorem establishes that the reconstruction of the object f(x, y) is possible from the X-ray

attenuation projections acquired at infinite rotation angles, p(t, θ). This function p(t, θ) is

also known as the Radon transform. The projection-slice theorem states that it is possible

reconstruct the cross-section of the object by f(x, y) finding the inverse Radon function of

p(ω, θ) (Fourier inverse transform). By stacking up a series of cross-sections a volume of

the object is obtained. Unfortunately, the inverse Radon transform is extremely unstable

with respect to noisy data. In practice, a stabilized and discretized version of the inverse

Radon transform (known as the Filtered Back Projection algorithm) Herman (1980), Kak

& Slaney (1987) is used. The idea of the back projection is to assign to each point of

the object the average intensity of all the projections that pass through that point. The

81

5.3 Characterization of Void Population

back projected image is, however, a blurred version of the original object. To overcome

this effect, the reconstructed object is filtered using a high pass filter. Finally, the object

is reconstructed by means of specific interpolation techniques. All the samples studied

in this work were reconstructed using the algorithm based on the filtered back-projection

procedure.


The distribution of voids in the raw prepregs and in the consolidated laminates was

studied by means of XCT using a Nanotom 160NF tomograph (Phoenix, Inc.), Figure 5.3.

The tomograms were collected at 50 kV and 350 µA using a Molybdenum target. Typical

acquisition time for each tomogram was around 5 h.

Figure 5.3: Nanotom 160NF tomograph.

The analysis of the reconstructed volumes was targeted to characterize the geometrical

features and spatial distribution of the voids. Voids were extracted by identifying the voxels

of the tomograms belonging either to a void or to the bulk composite material based on

their grey level. The threshold used for void segmentation was based on the local variance

method from Sauvola applied to each slice, adapting the threshold according to the mean

82


and standard deviation of the peak of the histogram (more details can be found in Yan

et al. (2005)). Only voids larger than 2× 2× 2 connected voxels were considered. Smaller

voids can be artifacts from noise and were neglected in this work. The binary images were

used to compute the quantitative values of the volume fraction, spatial distribution and

geometry of voids using Matlab routines.

5.3.1 Unidirectional Laminates

The resolution of most measurements was set to 11 µm/voxel but a few analyses were

carried out with a resolution of 4 µm/voxel. Prismatic samples of 20 × 20 × 2 mm3

in thickness were extracted from the central part of the laminates for the tomographic

inspections.

A X-ray microtomography section perpendicular to the fiber tows of the raw prepreg

(not cured) is shown in Figure 5.4. The fiber content in the prepreg was lower than that of

the final laminate and the average distance between fiber tows was 804±120 µm. Porosity

in the prepreg was limited and it was mainly concentrated within the tows, although

isolated rounded pores in the matrix were also found.

Figure 5.4: X-ray microtomography cross-section of the raw prepreg perpendicular to

the fiber tows. Matrix appears as light gray regions, fibers tows as dark gray regions and

pores are black.

So far, experimental studies on processing-associated porosity in polymer-matrix com-

posites were carried out from optical or scanning microscopy analysis of cross-sections. In

order to understand the results that will be presented later, results provided by optical

microscopy (OM) and X-ray computed tomography (XCT) were compared. For instance,

Figure 5.5.a shows a montage of 10 optical micrograph of a cross-section perpendicular to

the fibers of a panel manufactured with cure cycle C-1.

83


Figure 5.5: (a) OM montage of a cross-section of the composite panel manufactured

with cure cycle C-1. (b) XCT slice of the same cross-section with 4 µm/voxel resolution.

(c) Idem as (b) with 11 µm/voxel resolution. (d) Average of all the slices along the

fiber direction with 4 µm/voxel resolution. (e) Idem as (d) with 11 µm/voxel resolution.

Regions with a large volume fraction of interply voids are marked with an ellipse.

Three well-defined regions can be distinguished in the OM picture: fiber-rich regions

(light gray), resin-rich regions (in gray, normally located around the fiber tows and showing

an undulated behavior along the laminate) and porosity (dark gray) which was sometimes

filled with resin during polishing, hindering pore evaluation. The same cross-sectional

84


area was also visualized by XCT with a resolution of 4 µm/voxel in Fig. 5.5.b and 11

µm/voxel in Fig. 5.5.c. The void area fractions determined from these micrographs were

1.9% (OM), 2.1% (CT, 4 µm) and 2.0% (CT, 11 µm). The differences between OM and

XCT arose probably from the pores filled with resin during polishing operations while the

void area fraction determined by XCT with 11 µm/voxel resolution was slightly lower than

that measured with 4 µm/voxel because the smallest pores were not detected at lower

resolution. Nevertheless, their overall contribution to the total area fraction was of the

same order of the error associated to the experimental measurement.

XCT allows the straightforward determination of the area fraction of pores along the

fiber direction, a very time-consuming task with OM. For instance, the analysis of 1500

slices along the fiber direction showed that the porosity varied between 2.0% and 4.1%,

along the fiber direction in laminate C-1 the average being 2.9%. The drawback of XCT

slices is that it is not possible to distinguish between the resin matrix and the carbon fibers

due to the similarities in the X-ray absorption coefficient of both materials. However, this

limitation was overcome in the present case because the microstructure remains relatively

constant along the fiber direction. Thus, it was possible to enhance the microstructural

features (i.e. emphasize the differences between matrix-rich and fiber-rich regions) by

averaging the gray levels along the fiber direction over all the slices. The results are

shown in Fig. 5.5.d and Fig. 5.5.e for the XCT obtained with 4 µm/voxel and 11 µm/voxel

resolution, respectively. Resin bands were clearly visible under these conditions and, in

addition, it was possible to observe the regions where the pores were concentrated (marked

by the ellipsoids). These observations seem to indicate that most of the porosity came

from air entrapment between laminas during the lay-up. Light gray areas surrounding the

resin bands correspond to high fiber density regions. This effect was observed in the XCT

with both 4 µm/voxel and 11 µm/voxel resolution.

XCT images with 11 µm/voxel resolution were used to obtain information about the

void shape and spatial distribution within the panels, as shown in Fig. 5.6.a, in which

carbon fibers and resin were set to semi-transparency to reveal the voids.

85


Figure 5.6: (a) X-ray microtomography of void spatial distribution in the uniaxial

composite panels manufactured according to the curing cycles C-1, C-2 and C-3. (b)

Typical rod-like void together with its equivalent cylinder.

5.3.1.1 Geometry

Voids were elongated in shape with the major axis parallel to the fiber axis (Z axis).

Each individual void was fitted to an equivalent cylinder of elliptical section whose volume,

centroid and moments of inertia were equal to those of the void. Fig. 5.6.b shows the

voxel reconstruction of a typical void, where the rod-like shape is clearly visible, and the

corresponding equivalent cylinder is also shown for comparison.

Voids were closely aligned with the fiber direction and the maximum misalignment was

below ≈ 1.5(angle between the fiber direction and the principal axis of the equivalent

cylinder). Information about the void shape was obtained from the statistical analysis

of the dimensions of the equivalent cylinders. The cross-section of voids perpendicular

to the fiber direction (Z axis) was characterized by the flatness ratio, f , Fig. 5.7, which

stands for the ratio between the semiaxes of the ellipsoidal section, as shown in Table 5.1.

86


The flatness ratio was approximately f ≈ 1.5, regardless of the cure cycle, and this result

points to the dominant effect of the applied external pressure on the transversal shape of

the voids. More interesting is the analysis of the elongation factor, Fig. 5.7, defined as the

ratio between the major axis and the average transversal axis (average of the minor X-axis

and medium Y-axis), which is plotted in Fig. 5.8 as a function of the void volume.

Figure 5.7: Definition of the elongation factor and flatness ratio of individual voids.

The results for all the cure cycles are consistent and the larger the void, the longer the

elongation. This is indicative of two different void origins. The smaller ones, with more

rounded shape, could come from internal voids within the prepreg, either present before

the consolidation (gas bubbles from resin mixing operations, broken fibers) or generated

by diffusion of water during the cure cycle. Long, elongated voids were the result of air

entrapment and wrinkles created during lay-up and presented larger volume. Interestingly,

the evolution of the elongation with the void volume is grouped into two sets. Laminates

manufactured following cure cycles C-1 and C-2 present higher elongations (by a factor of

2) than those processed with cycle C-3.

87


0 . 0 8 . 0 x 1 0 5 1 . 6 x 1 0 6 2 . 4 x 1 0 6 3 . 2 x 1 0 6 4 . 0 x 1 0 6

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0 C y c l e C 1 C y c l e C 2 C y c l e C 3

Elong

ation

facto

r

V o i d v o l u m e ( µm 3 )Figure 5.8: Elongation factor of individual voids for the different cure cycles.

Cycle Vf (%) f ∆d (µm)

C-1 2.9 1.45 973± 286

C-2 0.4 1.49 1075± 374

C-3 1.1 1.52 1276± 330

Table 5.1: Volume fraction of voids, Vf , void flatness ratio, f , and average distance

between sections with high porosity along the panel width (Y axis), ∆d, as a function of

the cure cycle for AS4/8552 unidirectional laminates.

Panel examination after processing revealed resin bleeding on the faces perpendicular

to the fiber direction but not on the faces parallel to the fibers. This fact indicates that

resin flow was anisotropic and mainly occurred along the fiber direction, in agreement with

the higher permeability factor in this direction. The dominant resin flow along the fibers

led to the formation of a channel-type structure (also reported in previous studies Loos &

Springer (1983), Tang et al. (1987) and facilitated the transport and coalescence of voids

along the fibers. In addition, the cross-section of the elongated voids was reduced as a

result of the compaction pressure and many of them eventually collapsed, leading to panels

with very low porosity.

88


5.3.1.2 Void Volume Fraction

The volume fraction of voids, Vf , was obtained directly from the tomograms by numer-

ical integration of the individual volume of all the voids, and it is reported in Table 5.1.

The composite panels manufactured following curing cycle C-1 contained the highest vol-

ume fraction of pores (2.9%), while curing cycle C-2 led to the minimum residual porosity

(0.4%). For discussion purposes, the dynamic viscosity profiles in the low viscosity region

previously presented in Fig. 3.7 are now replotted together in Fig. 5.9. The low viscosity

region corresponds to the processing window where consolidation takes place and this in-

formation is very reliable to establish the connection between the processing conditions and

void volume fraction and spatial distribution. Low viscosity values (in the range 3−5×105

Pa s) were attained 10 min after the beginning of cure and were maintained for another 10

min in all cycles.

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 01 0 4

1 0 5

1 0 6

Comp

lex vis

cosity

, η* (P

a s)

T i m e ( s )

C y c l e C 1 C y c l e C 2 C y c l e C 3

Figure 5.9: Dynamic evolution of the complex viscosity, η∗, of unidirectional AS4/8552

composite prepreg at the processing window region.

The viscosity increased sharply afterwards for the cycle C-1, and the processing window

of this cycle was the shortest one. The time available for migration and/or diffusion of the

air bubbles was limited and this led to the panel with the highest volume fraction of voids.

89


On the contrary, the lowest porosity was attained with the cure cycle C-2. The low viscosity

region(< 5.0×105 Pa s) was maintained during 30 min up to the final gelation, facilitating

the migration/diffusion of air bubbles and reducing porosity significantly. The viscosity

profile in the processing window of cycle C-3 was initially similar to C-1 but the processing

window was longer, leading to an intermediate porosity level between cycle C-1 and C-2.

This result shows that small variations in the processing conditions may lead to noticeable

changes in the final void population.

5.3.1.3 Void Spatial Distribution

X-ray tomograms, Fig. 5.6.a, showed that the voids tended to be grouped in channels

parallel to the fibers. In order to quantitatively evaluate this effect, the volume fraction

of voids was integrated along the fiber (Z axis) and the laminate thickness (X axis) to

obtain the distribution of porosity across the width of the laminate (Y axis). The results

are plotted in Fig. 5.10, which shows that the voids were not distributed homogeneously

across the width of the laminate but were periodically concentrated in sections along the

laminate width. The porosity of these sections was much higher than the average and,

for instance, the panel manufactured with cycle C-1 (with an average porosity of 2.9%)

presented zones with maximum porosities of up to 9% while other sections were almost

free of voids (< 1%). The average distance between the high porosity regions, ∆d, (shown

in Table 5.1) was determined from the average distance between the peaks in void volume

fraction distribution along Y direction, Fig. 5.10. It was around 1 mm in all samples, which

is of the same order as the average distance between fiber tows in the raw prepreg, Fig. 5.4.

More detailed information about the actual location of the high porosity regions can

be found in Fig. 5.12, which shows the X-ray absorption of the composite panel along the

fiber axis. This image was obtained by averaging the gray values of parallel slices along the

Z axis and takes advantage of the concentration of voids in channels parallel to the fibers

and of the differences in density (and, thus, in X-ray absorption coefficient) between voids,

resin and fibers, Fig. 5.11. Black zones stand for low density sections which contain very

high porosity. White zones represent high fiber density sections while gray zones are either

low fiber density or resin-rich regions. Porosity was mainly concentrated within resin-rich

tubular cells, which were separated by a skeleton of fiber-rich zones.

90


0 2 4 6 8 1 0 1 2 1 4 1 6 1 80

2

4

6

8

1 0 C y c l e C 1 C y c l e C 2 C y c l e C 3

Void

Volum

e frac

tion (

%)

L a m i n a t e w i d t h , Y ( m m )

Figure 5.10: Distribution of porosity across the width (Y axis) of the AS4/8552 unidi-

rectional laminates.

Figure 5.11: Averaging gray values of X-ray absorption of the composite panel along

the fiber axis.

This peculiar distribution of the porosity within the laminate is the result of a process

of inhomogeneous consolidation. Upon the application of pressure, most of the load is

transferred through a continuous skeleton of fiber-rich regions. The higher pressure in

these regions leads to the migration of resin as well as voids into the cells formed by the

91


skeleton. The pressure in these regions is lower, facilitating the nucleation and/or growth

of voids. In addition, resin flow along the fibers facilitated the coalescence of voids, so the

elongation factor of individual voids increased with its volume, Fig. 5.8. The fact that the

average distance between the high-porosity regions, ∆d, is similar to the average distance

between fiber tows in the raw prepreg supports this mechanism of consolidation.

Figure 5.12: Average X-ray absorption of composite panel along the fiber (Z axis).

Black zones stand for low density sections (pores), while white zones represent high

density sections (fibers). Gray zones stand for matrix-rich regions.

These observations are very relevant from the viewpoint of understanding and simulat-

ing void formation during consolidation, because most of the models for void nucleation

and growth during cure of thermoset-based composites assumed that voids develop within a

homogeneous medium, Grunenfelder & Nutt (2010), Kardos et al. (1986), Loos & Springer

(1983). Nevertheless, Fig. 5.12 clearly demonstrates that inhomogeneities resulting from

the formation of preferential percolation paths for load transfer during consolidation may

alter significantly the pressure distribution within the laminate and modify the volume

fraction, size and spatial location of the voids.

Finally, the porosity distribution through the thickness of the laminate (X axis) was

also obtained from the tomograms and is plotted in Fig. 5.13. The porosity was maximum

in the middle and minimum (and close to zero) near to the upper and lower surfaces. These

facts, together with the bell shape of the porosity distribution, are indicative that the voids

located near the surfaces migrated easily under the application of pressure.

92


0 2 5 0 5 0 0 7 5 0 1 0 0 0 1 2 5 0 1 5 0 0 1 7 5 00

1

2

3

4

5

6

7 C y c l e C 1 C y c l e C 2 C y c l e C 3

Void

volum

e frac

tion (

%)

L a m i n a t e t h i c k n e s s , X ( µm )

Figure 5.13: Void distribution through the thickness of the laminate (X axis).

5.3.2 Multiaxial Laminates

Quasi-isotropic laminates with dispersed ([45/0/-45/90]3s) and clustered ([453/03/-453/903]s)

stacking sequences were consolidated to study the effect of the lay-up in the void popula-

tion (Table 3.4). Prismatic samples of 20×20×4.6 mm3 were extracted from the laminates

for the tomographic inspections. The resolution of the tomograms was set to 9 µm/voxel

in this case.

The void distribution and orientation within the panels is shown in Fig. 5.14, in which

carbon fibers and resin were set to semi-transparency to reveal the voids which were elon-

gated and oriented along the fiber direction 0, +45, 90, -45 in each ply.

93


Figure 5.14: X-ray microtomography of void spatial distribution in the quasi-isotropic

[453/03/-453/903]s composite panel manufactured following the curing cycle C-3.

In order to obtain quantitative information about the void orientation, shape and spatial

distribution, a binarized volume from the original volume was used to fit each individual

void to an equivalent cylinder of elliptical section whose volume, centroid and moments of

inertia were equal to those of the void as in the case of the unidirectional panels.

5.3.2.1 Void Volume Fraction

The volume fraction of voids, Vf , was obtained directly from the tomograms by nu-

merical integration of the individual volume of all the voids within the panels. The void

volume fraction of each quasi-isotropic laminate cured following the cycles C-1, C-2 and

C-3 is shown in Table 5.2, together with data obtained for uniaxial laminates [0]10. The re-

lationship between the processing window and the porosity is evident from these data. The

minimum porosity was attained with cycle C-2, while cycle C-1 led to the highest porosity

because there was not enough time for the evacuate the voids from the laminate and they

did not collapse in the absence of the high hydrostatic pressure provided by the autoclave.

Cycle C-3 also led to low porosities but the volume fraction of voids was consistently higher

than that obtained with cycle C-2.

94


Cycle Vf [45/0/-45/90]3s (%) Vf [453/03/-453/903]s(%) [0]10 (%)

C1 1.78 1.30 2.9

C2 0.12 0.24 0.4

C3 0.60 0.26 1.1

Table 5.2: Volume fraction of voids, Vf , as a function of the cure cycle and ply-clustering

for AS4/8552 composite panels manufactured with different curing cycles.

5.3.2.2 Void Orientation and Spatial Distribution

Regardless of stacking sequence, voids were elongated and the major axis oriented in

each ply parallel to the fibers (0, +45, 90, -45) as shown in Fig. 5.15 which presents

the void density (number of voids per mm3) as a function of the orientation of the major

axis of the equivalent ellipsoid for the dispersed and clustered lay-ups. Void orientation

was independent of the cure cycle and of the lay-up.

0 4 5 9 0 1 3 5 1 8 00 . 00 . 10 . 20 . 30 . 40 . 50 . 60 . 70 . 80 . 91 . 0

[ 4 5 / 0 / - 4 5 / 9 0 ] 3 sC y c l e C 1C y c l e C 2C y c l e C 3

Numb

er of

voids

per m

m3

( a )

95


C y c l e C 1C y c l e C 2C y c l e C 3

0 4 5 9 0 1 3 5 1 8 00 . 0

0 . 3

0 . 6

0 . 9

1 . 2

1 . 5Nu

mber

of vo

ids pe

r mm3

[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s

( b )

Figure 5.15: Void density (expressed as the number of voids per mm3) as a function

of the orientation of the major axis of the equivalent ellipsoid for the (a) [45/0/-45/90]3s

dispersed quasi-isotropic laminates and (b) [453/03/-453/903]s clustered quasi-isotropic

laminates processed with different cure cycles.

The volume fraction of voids was integrated along the laminate fiber direction (Z axis)

and the laminate thickness (X axis) to obtain the distribution of porosity along the width

of the laminate (Y axis) for the dispersed and clustered laminates, as is shown in Fig. 5.16.a

and Fig. 5.16.b , respectively. The inhomogeneity of the void distribution along the width

was very limited in the multiaxial panels, contrary to the behavior found in the unidi-

rectional laminates, and this is in agreement with the homogeneous in-plane flow in the

multiaxial panels. However, the same inhomogeneities appeared at the ply level in the mul-

tiaxial panels. Fig. 5.17.a shows the distribution of porosity along the width (Y axis) in a

single cluster of plies with fibers oriented along the Z axis in the [453/03/-453/903]s panel

manufactured with cycle C-3. These results show that the porosity was inhomogeneously

distributed along the width of each ply, following an approximately periodic pattern with

peaks of high porosity (in the range 3 to 10%) separated by valleys with zero porosity.

96


0 2 4 6 8 1 0 1 2 1 4 1 60

1

2

3

4Vo

id Vo

lume f

ractio

n (%)


( a )C y c l e C 1C y c l e C 2C y c l e C 3

[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s

0 2 4 6 8 1 0 1 2 1 4 1 60

1

2

3

4

Void

Volum

e frac

tion (

%)


( b )C y c l e C 1C y c l e C 2C y c l e C 3

[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s

Figure 5.16: Distribution of porosity along the width (Y axis) for AS4/8552 multiaxial

panels (a) dispersed ([45/0/-45/90]3s), (b) clustered ([453/03/-453/903]s).

97


More information can be obtain from Fig. 5.17.b, which shows the X-ray absorption of

the same cluster of plies along the fiber axis. This image was obtained by averaging the gray

values of parallel tomograms along the Z axis and takes advantage of the concentration

of voids in channels parallel to the fibers and of the differences in density (and, thus,

in X-ray absorption) between voids, resin and fibers. Black zones stand for low density

sections which contain very high porosity. White zones represent high fiber density sections

while gray zones are either low fiber density or resin-rich regions. Porosity was mainly

concentrated within resin-rich tubular cells, and this spatial distribution was also found in

unidirectional laminates Hernandez et al. (2011) as a result of a process of inhomogeneous

consolidation during cure. Upon the application of pressure, most of the load is transferred

through a continuous skeleton of fiber-rich regions. The higher pressure in these regions

leads to the migration of resin as well as voids into the cells formed by the skeleton. The

pressure in these regions is lower, facilitating the nucleation and/or growth of voids. Thus

resin flow in each ply was anisotropic and mainly occurred along the fiber direction, in

agreement with the higher permeability factor in this direction. The dominant resin flow

along the fibers led to the formation of a channel-type structure also reported in previous

studies (Loos & Springer (1983), Tang et al. (1987)) and facilitated the transport and

coalescence of voids along the fibers.

The spatial distribution of the voids through the laminate thickness (X axis) is shown

in Fig. 5.18.a and Fig. 5.18.b for the [45/0/-45/90]3s and [453/03/-453/903]s laminates,

respectively. The porosity was zero close to the laminate surfaces in all cases because

voids in these areas could easily migrate outside of the panel. Porosity increased with

the distance to the surfaces and two different distributions were found depending on the

laminate sequence. In the case of the dispersed laminate (Fig. 5.18.a), the porosity was -on

average- constant through the thickness while it reached a maximum value at approximately

1 mm from the surfaces1 in the clustered laminates and then decreased rapidly to a plateau

in the central region (Fig. 5.18.b). Overall, the porosity profile was similar in dispersed

and clustered laminates but it differed from the one measured in unidirectional [0]10 panels

Hernandez et al. (2011), which is shown in Fig. 5.13. The porosity increased from the

surfaces towards the interior of the panel in this case and the void volume fraction in

the center of the panel for unidirectional laminates was much higher than that found in

multiaxial panels subjected to the same cure cycle.

98


Figure 5.17: (a) Distribution of porosity along the width (Y axis) in a single cluster

of three plies with fibers parallel to Z direction in the [453/03/-453/903]s laminate man-

ufactured according curing cycle C-3. (b) Average X-ray absorption of composite panel

along the fiber (Z axis) of a single cluster of plies.

These results seems to indicate that interplies between lamina with different fiber orien-

tation also acted as pathways for void migration during consolidation. Thus, the porosity

of multiaxial laminates was lower than that of unidirectional panels for identical cure condi-

tions (Table 5.2). Panel examination after processing revealed resin bleeding on all faces in

the multidirectional laminates while only on the faces perpendicular to the fiber direction

in the unidirectional panels.

99


0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 00

1

2

3

Void

volum

e frac

tion (

%)


( a )C y c l e C 1C y c l e C 2C y c l e C 3

[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 00

1

2

3

Void

volum

e frac

tion (

%)


( b )[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s


Figure 5.18: Void distribution through the thickness of the multiaxial panels (a) dis-

persed ([45/0/-45/90]3s), (b) clustered ([453/03/-453/903]s).

100


5.3.2.3 Geometry

Information about the void shape was obtained from the statistical analysis of the

dimensions of the equivalent cylinders. The average length of the major, medium and

minor axes of the equivalent ellipsoid are plotted as a function of the void volume in

Fig. 5.19 and Fig. 5.20 for dispersed and clustered laminates, respectively. These data

show that the void length increased rapidly with the void volume, indicating that the voids

grew along the fiber direction in each ply. Although the cure cycle influenced the void

volume fraction, Table 5.2, it did not change the morphology of the voids and the length of

the axes of the equivalent ellipsoid were independent of the cure cycle. The comparison of

Fig. 5.19 and Fig. 5.20 also indicated that the void morphology depended on the laminate

lay-up.

0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 6

2 0 0

4 0 0

6 0 0

8 0 0C y c l e C 1C y c l e C 2C y c l e C 3

[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s

Avera

ge m

ajor a

xis (µ

m)

V o i d v o l u m e ( µm 3 )

( a )

101


0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 65

1 0

1 5

2 0

2 5

3 0

Avera

ge m

inor a

xis (µ

m)


( c )C y c l e C 1C y c l e C 2C y c l e C 3

[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s

0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 6

1 0

2 0

3 0

4 0

5 0

6 0

7 0

[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s


Avera

ge me

dium a

xis (µ

m)


( b )

Figure 5.19: Dimensions of (a) major axis, (b) medium axis and (c) minor axis of

individual voids for dispersed panels [45/0/-45/90]3s manufactured with curing cycles

C-1, C-2 and C-3.

102


0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 6

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0C y c l e C 1C y c l e C 2C y c l e C 3

Avera

ge m

ajor a

xis (µ

m)


( a )[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s

0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 6

1 0

2 0

3 0

4 0

5 0

6 0( b )

Avera

ge m

edium

axis (

µm)



[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s

103


0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 6

1 0

2 0

3 0C y c l e C 1C y c l e C 2C y c l e C 3

( c )Av

erage

mino

r axis

(µm)


[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s

Figure 5.20: Dimensions of (a) major axis, (b) medium axis and (c) minor axis of

individual voids for clustered panels [453/03/-453/903]s manufactured with curing cycles

C-1, C-2 and C-3.

This is more evident in Fig. 5.21, Fig. 5.22 and Fig. 5.23 which show the evolution of

the average elongation factor, e = 2b1/(b2 + b3), of the flatness ratio, f = b2/b3, and axes

of the equivalent cylinders, as function of the void volume for the clustered, dispersed and

unidirectional laminates cured following cycle C-3. Similar results were also found for cure

cycles C-1 and C-2. It is worth noting that the elongation factor increased with the degree

of clustering and this indicates that void migration along the fiber direction was favored by

thicker plies, leading to more elongated pores. The flatness ratio, depicted in Fig. 5.21, was

equivalent in the unidirectional and clustered laminates and slightly higher in the dispersed

laminate. These differences were not significant and indicate that the shape of the pore

section was mainly controlled by the consolidation pressure.

104


0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 6

1

2

3

4

5[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s[ 0 ] 1 0

Avera

ge fla

tness

ratio

V o i d v o l u m e ( µm 3 )Figure 5.21: Flatness ratio as a function of the void volume for different laminate ply

clustering stacking sequences cured using cycle C-3.

0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 6

1 0

2 0

3 0

4 0

5 0[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s[ 0 ] 1 0

Avera

ge el

onga

tion f

actor

V o i d v o l u m e ( µm 3 )Figure 5.22: Elongation factor as a function of the void volume for different laminate

ply clustering stacking sequences cured using cycle C-3.

105


0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 6

1 0

2 0

3 0

4 0

5 0

6 0

7 0[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s[ 0 ] 1 0

Avera

ge m

edium

axis (

µm)


( b )

0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 6

1 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 0

[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s[ 0 ] 1 0

Avera

ge m

ajor a

xis (µ

m)

V o i d v o l u m e ( µm ) 3

( a )

106


0 . 0 5 . 0 x 1 0 5 1 . 0 x 1 0 6 1 . 5 x 1 0 6 2 . 0 x 1 0 65

1 0

1 5

2 0

2 5

3 0[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s[ 0 ] 1 0


Avera

ge m

inor a

xis (µ

m)

( c )

Figure 5.23: (a) Major axis, (b) medium axis and (c) minor axis dimensions of individ-

ual voids for panels manufactured with curing cycle C-3 and different laminate lay-ups:

multiaxial dispersed ([45/0/-45/90]3s), multiaxial clustered ([453/03/-453/903]s) and uni-

directional ([0]10).

107

Chapter 6

Mechanical Behavior

It has been well established in previous studies that porosity leads to a marked reduction

in the composite mechanical properties, particularly in those dominated by the matrix such

as the interlaminar shear strength and the transverse tensile strength Bowles & Frimpong

(1992), Davies et al. (2007). In this work, several of the main matrix-controlled mechan-

ical properties were measured in order to establish the relationship between processing

conditions and mechanical performance. The interlaminar shear strength (ILSS) and the

interlaminar toughness (GIc and GIIc) were selected to evaluate the effect of porosity on

the mechanical performance of the unidirectional panels. Additionally, plain compression,

low velocity impact and compression after impact (CAI) tests were performed on multiaxial

panels to address the effect of processing conditions on these properties.

109

6.1 Unidirectional Laminates


6.1.1 Interlaminar Shear Strength (ILSS)

The interlaminar shear strength test was measured according to the ASTM D2344

standard ASTM-D2344 (2000). Prismatic [0]10 specimens of 20 × 10 × 2 mm3 (length ×width × thickness) were machined from the center of the composite panels and tested under

three point bending with 10 mm of loading span. Five tests were performed under stroke

control at a crosshead speed of 1 mm/min using an electromechanical universal testing

machine (Instron 3384), Fig. 6.1.

Figure 6.1: Three point bending fixture.

The load was continuously measured during the test with a 30 kN load cell. The applied

load and the cross-head displacement was recorded and the maximum load, Pmax, attained

during the test was used to compute the interlaminar shear strength (ILSS) according to,

τILSS =3Pmax

4bh(6.1)

where b and h stand, respectively, for the width and depth of the beam cross section. This

expression correspond to the maximum shear stress obtained in rectangular cross sections

subjected to three point bending. The ILSS results are summarized in Table 6.1 and

representative load-displacement curves corresponding to each curing cycle are plotted in

Fig. 6.2.

110


Cycle ILSS (MPa) Vf (%)

C-1 95.05± 3.9 2.9

C-2 101.40± 4.6 0.4

C-3 108.37± 4.9 1.1

Table 6.1: Interlaminar shear strength of [0]10 laminates. The average values and

standard deviation were obtained from 5 tests for each condition.

0 . 0 0 . 2 0 . 4 0 . 6 0 . 80

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

2 5 0 0

3 0 0 0

Load

(N)

C r o s s - h e a d d i s p l a c e m e n t ( m m )


Figure 6.2: ILSS load-displacement curves.

The ILSS of the unidirectional laminates manufactured according to the cure cycles

C-1, C-2 and C-3 is plotted as a function of the void content in Fig. 6.3. As expected,

the ILSS decreased with the porosity and the laminates with the highest porosity (C-1)

showed the lowest ILSS, while those with the minimum volume fraction of voids (C-2 and

C-3) presented the highest ILSS. The effect of porosity on the interlaminar strength of the

laminate could be rationalized in terms of net-section models which assumed cylindrical

voids arranged in a regular square pattern. The reduction in the ILSS due to reduction in

the composite net section is given by,

τILSS(Vf ) = τILSS(0%)

(1−

(4Vfπ

)1/2)

(6.2)

111


where τILSS(0%) is the theoretical ILSS for the void-free laminate, Wisnom et al. (1996).

This expression was fitted by the least squares method to the experimental results, leading

to an ILSS for the void free laminate of 116 MPa, and it is plotted in Fig. 6.3, together

with the experimental data. Although the general trends were well captured by the net

section analysis, the model overestimated the ILSS of the composite C-2 that presented the

lowest void volume fraction (0.4%). These discrepancies may be due to the fact that the

ILSS could be insensitive to the void volume fraction below certain void thershold (≈ 1%),

Costa et al. (2001). As it was shown in Table 3.2, the degree of cure, α, attained with the

different cure cycles was very similar and it was therefore expected that the shear strength

of the epoxy matrix, which is one of the key factors controlling ILSS, should be similar for

all cure cycles. This extreme was confirmed by nanoindentation experiments carried out

to measure the hardness of the epoxy in the laminates subjected to curing cycles C-2 and

C-3, as it will be shown later.

Figure 6.3: Interlaminar shear strength of the unidirectional AS4/8552 composite lam-

inates as a function of void content.

The fracture surfaces of the ILSS coupons corresponding to laminates C-2 and C-3

were examined in the scanning electron microscope (EVO MA15, Zeiss) to ascertain any

112


possible differences in the fracture mechanisms. Representative fractography surfaces are

shown in Fig. 6.4 and Fig. 6.5 where the typical cusp structures were observed (Fig. 6.6),

indicative of fracture by shear along the fiber direction Greenhald (2009). Cusps are formed

as successive, parallel microcracks initiated by shear in the epoxy matrix at an angle of

45 with the fiber direction, (Fig. 6.6). The microcracks propagate at this angle until they

are stopped at the fiber-matrix interface. At this point cusps are formed as the inclined

microcracks coalesce with the main crack running along the fiber direction direction. The

fracture micromechanisms were essentially equivalent in both laminates but the height and

size of the cusps were larger in laminate C-3 indicative of a tougher matrix, a stronger

interface or a change in the coalescence mechanism due to the different shape of the voids

as indicated by the elongation factor (Fig. 6.5). This latter effect could be operative as

the elongation factor was larger for laminate C-2. When the fiber-matrix bond quality is

good, very small microcracks occurring in the area of contact between the cusp and the

fiber called serrated feet are observed, Fig. 6.4. Such structures were only found in the

fractography of the laminate C-3.

Figure 6.4: Scanning electron micrograph of the fracture surface of a coupon tested to

measure the ILSS; showing serrated feet for the laimate cured using cycle C-3.

113


Figure 6.5: Scanning electron micrographs of the fracture surfaces of coupons tested to

measure the ILSS. (a) Cure cycle C-2. (b) Cure cycle C-3.

114


Figure 6.6: Cusp formation mechanism Greenhald (2009)

In order to understand better the differences in ILSS and fracture morphology between

laminates C-2 and C-3, a thorough micromechanical characterization of the resin and the

matrix/fiber interface was performed by means of instrumented nanoindentation (Hysitron

TI950). Nanoindentation tests with a pyramidal tip were carried out in appropriate areas of

the laminate cross-sections where resin pockets were formed to study the matrix behavior.

At least 10 indentations were performed in each sample with a maximum load of 0.7 mN.

The hardness was quantified using the Oliver and Pharr (OP) method, Oliver & Pharr

(1992) and the results are summarized in Table 6.2. Irrespectively of the appropriateness

of the OP method to calculate the hardness in polymers, the hardness of the resin after

both curing cycles was the same, as expected from their identical degree of curing and

glass transition temperature. This is also shown in Fig. 6.7.a in which two representative

load-displacement curves were plotted (one for each laminate). The insert in Fig. 6.7.b

corresponds to a scanning probe microscopy (SPM) image showing a resin pocket and the

array of indentations performed. Only those indentations in the resin that were sufficiently

far away from the surrounding fibers (further than 10 times the indentation depth, as a

rule of thumb) were used to calculate the hardness in order to avoid any constraint effects

induced by the fibers.

115


Cycle H (MPa) Pc

C-2 410± 30 24± 2

C-3 420± 20 24± 1

Table 6.2: Resin hardness, H, and critical load for fiber-matrix interfacial debonding,

Pc, as determined from nanoindentation tests.

Figure 6.7: (a) Load-indentation depth curves corresponding to pyramidal indentation

tests of the resin processed with cure cycles C-2 and C-3, displaying identical behavior.

(b) Array of indentations in one of the resin pockets is shown in the 30 × 30 µm SPM

image.

In the case of the interface strength, the differences were analyzed by means of push-in

tests as it has been suggested that the cure cycle could modify this parameter, Davies

et al. (2007). Push-in tests were carried out by using a flat punch (with a diameter of 3.5

µm) to push individual fibers on the cross-section of a bulk specimen Kalinka et al. (1997),

Molina Aldargeguia et al. (2011). The tests the advantage that they can be performed

i-situ on the current laminates without complex sample preparation.

116


Figure 6.8: (a) Load-fiber displacement curves corresponding to fiber push-in tests in

laminates processed with cure cycles C-2 and C-3. The arrow indicates the critical load

for interfacial debonding, which was the same in both cases. (b) SPM image showing one

fiber debonded from the matrix after the push-in test.

The initial load-fiber displacement response is linear, Fig. 6.8.a, corresponding to the

elastic deformation of the fiber and the matrix, and it was shown that the departure from

linearity at the critical load Pc coincides with the onset of interfacial debonding, Molina Al-

dargeguia et al. (2011), Rodriguez et al. (2012). The actual value of the interface strength

can be determined from, Pc, from the elastic properties of matrix and fibers as well as

the constraining effect of the surrounding fibers. In the case of isotropic glass fibers, good

results have been obtained through the application of the shear-lag model while more

sophisticated computational analysis are required for anisotropic materials, Molina Al-

dargeguia et al. (2011), Rodriguez et al. (2012). In the particular case of the laminates

considered here, the interfacial strength can be considered approximately proportional to

the critical loads, which were identical and are marked with an arrow in the load-fiber dis-

placement curves plotted in Fig. 6.8.a. Up to 10 push-in tests were performed in each case

and the average critical loads, reported in Table 6.2, indicate that the interfacial strength

of laminates C-2 and C-3 was equivalent. Thus, neither the resin nor the interface strength

117


can explain the slight differences in ILSS observed between the laminates manufactured

following cure cycles C-2 and C-3, which were very likely due to the changes in the void

morphology.

In order to elucidate this point, X-ray computed tomography of the broken samples was

performed to ascertain the fracture mechanisms. X-ray tomographies of the cross-sections

are shown in Fig. 6.9. They show that the proximity of large, elongated voids favors the

growth of the cracks leading to lower values of ILSS. The coupons manufactured using

the curing cycle C-1 show multiple interconnected cracks and this fracture mechanism is

favored by the high level of porosity. In principle, the larger and more elongated voids

found in panels manufactured using cycle C-2 contributed to the crack propagation more

than the shorter voids corresponding to cycle C-3 and this fact could be explain the lower

ILSS of the panels cured using cycle C-2 as compared to C-3 panels.

Figure 6.9: X-ray tomograms of the cross-section of coupons tested to measure the

ILSS for cure cycles C-1, C-2, C-3.

6.1.2 Mode I and II Interlaminar Toughness

Interlaminar fracture toughness tests in mode I and II were performed according to

ASTM D5528 standard, ASTM-D5528 (2007).

118


Double cantilever prismatic specimens [0]10 of 250 × 25 × 3 mm3 (length × width

× thickness) were machined from the unidirectional composite panels to determine GIc,

Fig. 6.10.a. A 0.003 mm Teflon film (PTFE) was inserted at the mid plane to act as crack

starter. Five DCB specimens were loaded continuously until a crack of approximately 100

mm in length was propagated. Tests were performed under stroke control at a crosshead

speed of 10 mm/min using an electromechanical universal testing machine (Instron 3384).

The load was continuously measured during the test with a 30 kN load cell (Instron).

The mode I interlaminar fracture toughness, GIc, was calculated from the propagated

crack length and the energy dissipated, which was determined from the load-cross head

displacement plot according to,

GIc =A

aw(6.3)

where a and w stand, respectively, for the propagated crack length and the width of the

specimen, and A is the energy neccesary to propagate the crack (integration of the area

under the load-displacement curve according to Fig. 6.10.b).

Figure 6.10: (a) Sketch of the DCB specimens to measure GIc. (b) Typical load-cross

head displacement curve.

The corresponding curves obtained from GIc test are plotted in Fig. 6.11 (only one

representative curve of each cure cycle was plotted for the sake of brevity). No significant

119


differences were observed within the experimental scatter among the different laminates

Fig. 6.12, and it can be concluded that porosity did not influence this property.

0 2 4 6 8 1 0

1 4 0

1 6 0

1 8 0

2 0 0

2 2 0

2 4 0

2 6 0( b ) C y c l e C - 2

Load

(N)

D i s p l a c e m e n t ( m m )

a 0

a 1

a 2

a 3a 4

0 2 4 6 8 1 0

1 4 0

1 6 0

1 8 0

2 0 0

2 2 0

2 4 0

2 6 0( a ) C y c l e C - 1

a 4

a 3

a 2

a 1

Load

(N)


a 0

120


0 2 4 6 8 1 08 0

1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

2 0 0( c )Lo

ad (N

)


C y c l e C - 3

a 0

a 1

a 2

a 3a 4

Figure 6.11: Load-cross head displacement curves for GIc for cure cycle (a) C-1, (b)

C-2 and (c) C-3 of the unidirectional AS4/8552 laminates.

0 1 2 3 40 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

C 1C 3

InterL

amina

r frac

ture e

nergy

, GIc (k

J/m2 )

V o i d v o l u m e f r a c t i o n ( % )

C 2

Figure 6.12: Mode I interlaminar fracture toughness, GIc, of the unidirectional [0]10

AS4/8552 laminates as a function of void content.

121


The interlaminar fracture toughness in mode II, GIIc was obtained according to EN6034

standard EN-6034 (1995). The test specimens were cut from the GIc specimens tested

previously. In this case, prismatic specimens [0]10 of 110 × 25 × 3 mm3 (length × width

× thickness) were used (Fig. 6.13). Five specimens were tested under three point bending

with 100 mm of loading span. The tests were performed under stroke control at a crosshead

speed of 1 mm/min. Fig. 6.14 show representative load-displacement curves of GIIc test

for the material cured with different cycles.

Figure 6.13: (a) Sketch of the specimens to measure GIIc. (b) Typical load-cross head

displacement curve.

The interlaminar fracture toughness GIIc was computed according to,

GIIc =9Pa2δ

2w(1/4L3 + 3a3)(6.4)

where δ is the crosshead displacement at the delamination onset, P is the load at this point,

a the initial crack length, w the specimen width and L the specimen effective length.

122


0 1 2 3 40

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0( b )

Flexu

re loa

d, P (

N)

D i s p l a c e m e n t , δ ( m m )

C y c l e C - 2

0 1 2 3 40

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0Fle

xure

load,

P (N)


C y c l e C - 1( a )

123


0 1 2 3 40

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0Fle

xure

load,

P (N)


C y c l e C - 3( c )

Figure 6.14: Load-cross head displacement curves of the GIIc test of AS4/8552 lami-

nates (a) cycle C-1, (b) cycle C-2 and (c) cycle C-3.

0 1 2 3 40 . 6

0 . 7

0 . 8

0 . 9

1 . 0

C 1C 3

C 2

InterL

amina

r frac

ture e

nergy

, GIIc

(kJ/m

2 )

V o i d v o l u m e f r a c t i o n ( % )Figure 6.15: Interlaminar fracture toughness GIIc of the unidirectional AS4/8552 lam-

inates as a function of void content.

124

6.2 Multiaxial Laminates

The corresponding values of GIIc are plotted in Fig. 6.15. The same trends observed in

the interlaminar shear tests are reproduced here: the laminate with the highest porosity

level C-1 showed the lowest GIIc while toughness of C-2 and C-3 cycles were equivalent

within the experimental scatter. The fracture surfaces of the tested coupons were ex-

amined by scanning electron microscopy (EVO MA15, Zeiss) to ascertain the dominant

fracture mechanisms. As expected, the fractographic images of these tests revealed failure

mechanisms similar to those observed in the ILSS specimens.

Figure 6.16: Scanning electron micrograph of the fracture surface of coupons tested to

measure GIIc of unidirectional panels cured following cycle C-3.


6.2.1 Plain Compression

Plain compression tests of the multiaxial composite panels were carried out according

to ASTM D3410 ASTM-D3410 (2003). Two stacking sequences were used in the analysis

of the multiaxial panels in order to address the effect of lay-up configuration on laminate

mechanical properties. The first stack configuration results of the homogeneous distribution

125


of plies with different orientation through the thickness [45/0/-45/90]3s. The second one

corresponds to a clustered distribution in which three layers with the same fiber orientation

are placed together. Prismatic [453/03/-453/903]s and [45/0/-45/90]3s coupons of 145 × 20

× 4.6 mm3 were tested, corresponding to clustered and dispersed configurations. Specimens

were protected with glass fiber tabs to prevent premature failure in the grip area. The load

was applied to the specimen during the test through shear loading by means of wedge grips,

Fig. 6.17. A gage length of 10 mm was used to prevent compressive buckling. The tests

were performed at a crosshead speed of 1.5 mm/min using an electromechanical universal

testing machine (Instron 3384). The load was monitored during the test with a 150 kN

load cell and the longitudinal strain along the loading axis was measured with two standard

resistive strain gages (350Ω) attached to both lateral surfaces of the specimen.

Figure 6.17: Compression IITRI fixture.

The compressive strength (σc) was determined according to,

σc =PmaxA

(6.5)

126


where Pmax and A correspond, respectively, to the maximum load and the area of the cross

section of specimen.

The strain was computed by averaging the readings of both strain gages while the per-

centage of bending, indicative of the non-homogeneous stress distribution in the specimen

was given by,

Bending =ε1 − ε2ε1 + ε2

× 100 (6.6)

where ε1 and ε2 stand, respectively, for the gage readings. Bending should be below 10%

in valid tests. The compressive modulus was obtained from the slope of the stress-strain

curve between 1000 and 3000 µε The corresponding values of compressive modulus and

strength are sumarized in Table 6.3 for the two laminate configurations and subjected to

different cure cycles. The influence of the porosity on the compressive strength is depicted

in Fig. 6.18.

0 . 0 0 . 4 0 . 8 1 . 2 1 . 6 2 . 04 0 0

4 5 0

5 0 0

5 5 0

6 0 0

6 5 0

C 1

C 3C 2

C 1

C 3

[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s

Comp

ressiv

e stre

ngth

(MPa

)

V o i d v o l u m e f r a c t i o n ( % )

C 2

Figure 6.18: Compressive strength of the multiaxial AS4/8552 laminates as a function

of void content.

The compressive modulus and strength decreased with the porosity independently of the

laminate stacking sequence. However, the influence of the porosity on the elastic modulus

127


[45/0/-45/90]3s [453/03/-453/903]s

Cycle Vf (%) σc (MPa) Ec (GPa) Vf (%) σc (MPa) Ec (GPa)

C-1 1.78 478± 32 46.0± 0.4 1.30 477± 27 45.7± 0.4

C-2 0.12 556± 38 47.4± 0.7 0.24 509± 29 46.0± 0.7

C-3 0.60 589± 15 47.9± 0.6 0.26 519± 20 46.5± 0.8

Table 6.3: Compressive modulus (Ec) and compressive strength (σc) of multiaxial lam-

inates processed using different curing cycles.

was very small, as it could be expected from the low porosity levels in the laminates.

Similarly, the modulus of the laminates with a dispersed lay-up was marginally higher but

neither factor was relevant. This was not the case in the compressive strength, in which

both factors did influence the mechanical performance. The compressive strength of the

laminates processed following cycle C-1 (with a porosity in the range 1.3-1.8%) was smaller

(by ≈ 50 MPa in the clustered lay-up and by 100-150 MPa in the dispersed laminate) than

that of the plates processed following cycles C-2 and C-3, whose porosity was below 0.6%.

These results point out the importance of designing an optimum cure cycle as limited

porosity levels (below 2%) led to a noticeable reduction in the compressive strength and

this effect will be amplified for higher void volume fractions. This behavior is identical to

the one found for ILSS and GIIc in the unidirectional panels which were mainly controlled

by the shear behavior of the porous matrix material. These results could be qualitatively

explained in terms of the compressive strength model of Budiansky, Budiansky (1993).

Assuming that the compressive response of the angle ply laminate is controlled by the load

carried by the 0 layers of the laminate, and neglecting the effect of the off-axis plies at

±45 and 90, the laminate strength is given by,

σmaxc = βXc (6.7)

where β is a proportionality constant which depends on the laminate stacking sequence

and Xc is the compressive strength of the 0 layers. Budiansky’s model assumed that the

ply compressive strength was controlled by a fiber kinking mechanisms occurring at the

microscale according to,

128


Xc =G12

1 + Φγy

(6.8)

where G12 is the in-plane shear modulus, Φ the fiber misalignment angle and γy the in-plane

shear yield strength of the composite which is highly dependent on the plastic behavior of

the porous matrix. Therefore, the higher the strength of the matrix due to the absence of

voids, the lower the effects of local fiber kinking and the higher the compressive strength.

The results in Fig. 6.18 also show that dispersed laminates presented higher compressive

strength than clustered ones for equivalent values of the void volume fraction. Fracture

occurred catastrophically in both materials and optical micrographs of the broken speci-

mens showed that it was accompanied by delamination between plies with different fiber

orientation (Fig. 6.19). Thus, delamination was concentrated in a few planes in the clus-

tered laminates (Fig. 6.19.b). The effect of ply clustering on the compressive strength

of quasi-isotropic laminates was studied by Lee & Soutis (2007). Laminates with dis-

persed ([45/90/-45/0]ns) or clustered ([45n/90n/-45n/0n]) lay up and different thickness

(n = 2, 4, 8) were tested in compression and no differences in the compressive strength were

found in the case of n = 2 and 4. In the case of the thicker laminates (n = 8), clustered

laminates were significantly weaker but this behavior was attributed to pre-existing matrix

cracking damage induced during machining in the thick plies. Our results do show an

effect of ply-clustering for equivalent void content and it should be noted that this latter

variable was not controlled in Lee & Soutis (2007). The differences in the compressive

strength between clustered and dispersed laminates can be rationalized in terms of the

critical stress necessary to trigger microbuckling in the 0 plies. Assuming that the fiber

orientation was independent of the ply thickness, this stress depends on the confinement

provided by the contiguous plies with different fiber orientation and drops rapidly once

interply delimitation occurs. It is well known that interply delamination occurs at lower

stresses in clustered laminates because they are prone to matrix cracking and there is more

elastic energy stored in the ply to promote delamination Lee & Soutis (2007). Thus, early

interply delamination is expected in clustered materials and will trigger catastrophic failure

at lower stresses.

129


Figure 6.19: (Fracture mechanisms in compression of multiaxial laminates manufac-

tured using curing cycle C-2. a) dispersed stacking sequence [45/0/-45/90]3s (b) clustered

stacking sequence [453/03/-453/903]s.

6.2.2 Low Velocity Impact

The damage resistance of the multiaxial composite panels was obtained by means of

a drop-weight impact test according to ASTM D7136 ASTM-D7136 (2005). Rectangular

specimens of 150 × 100 × 4.6 mm3 were machined from the two sets of quasi-isotropic

AS4/8552 composite panels manufactured according to the two stacking sequences: dis-

perse [45/0/-45/90]3s and clustered [453/03/-453/903]s. Tests were carried out using an

Instron Dynatup 8250 drop weight testing machine, Fig. 6.20. The specimens were simply

supported by the fixture and hold at the corners with a clamping tweezers, leading to a

free impact area of 125 × 75 mm2. Guiding pins were placed to position the specimen

centered. This configuration minimizes the fixture interferences with the impactor. The

impacts were performed by releasing the impactor with a selected mass from a chosen

height, which dropped freely. The impact mass was set to 4.98 Kg and the drop height

to 64 cm to achieve an impact energy of 30.8 J. A hemispherical-shaped steel tup of 12.7

mm diameter was used as impactor. The tup was instrumented with an accelerometer to

measure the impact load and the tup displacement and velocity.

130


Load vs. time curves of the impacted specimens are shown in Fig. 6.21, Fig. 6.22 and

Fig. 6.23. All the curves showed similar trends. The first part of the curves correspond

to the elastic regime of the impact process and is common for all laminates. Damage

began with the propagation of delaminations leading to a sudden load drop (indicated by

arrows). The only notable difference between dispersed and clustered laminates was the

presence of large ocillcilations in the dispersed ones. The porosity level did not have any

noticeable effect on the impact behavior of the panels probably because the small differences

in porosity was masked by the effect of other macroscopic defects as delaminations due to

the high impact energy.

Figure 6.20: Drop weight apparatus.

131


0 2 4 6 80

3

6

9 [ 4 5 / 0 / - 4 5 / 9 0 ] 3 s [ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s

F c l u s td

Load

(kN)

T i m e ( m s )

F d i s pd

( a )C y c l e C - 1

0 2 4 6 80

3

6

9( b )

Load

(kN)

T i m e ( m s )

C y c l e C - 2 [ 4 5 / 0 / - 4 5 / 9 0 ] 3 s [ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s

F d i s pd

F c l u s td

132


0 2 4 6 80

3

6

9

Load

(kN)

T i m e ( m s )

C y c l e C - 3 [ 4 5 / 0 / - 4 5 / 9 0 ] 3 s [ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s

( c )

F d i s pd

F c l u s td

Figure 6.21: Load vs. time curves of multiaxial AS4/8552 laminates subjected to low

velocity impact (a) cure cycle C-1, (b) cure cycle C-2 and (c) cure cycle C-3.

0 2 4 6 80

3

6

9

Load

(kN)

T i m e ( m s )


[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s

Figure 6.22: Load vs. time curves of multiaxial [45/0/-45/90]3s AS4/8552 laminates

subjected to low velocity impact for curing cycles C-1, C-2 and C-3.

133


0 2 4 6 80

3

6

9Lo

ad (k

N)

T i m e ( m s )

[ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s C y c l e C 1 C y c l e C 2 C y c l e C 3

Figure 6.23: Load vs. time curves of multiaxial [453/03/-453/903]s AS4/8552 laminates

subjected to low velocity impact for curing cycles C-1, C-2 and C-3.

The elastic and dissipated energies during the impact are summarized in Table 6.4.

The absorbed energy was very similar in all cases regardless of the cure cycle (and, thus,

of porosity) and of the lay-up configuration.

[45/0/-45/90]3s [453/03/-453/903]s

Cycle Elastic (J) Dissipated (J) Elastic (J) Dissipated (J)

C1 9.55± 0.87 20.90± 0.15 8.7± 3.2 22.0± 3.8

C2 10.59± 0.67 19.54± 0.31 8.4± 3.0 22.3± 2.6

C3 11.20± 1.30 18.83± 0.72 8.8± 2.7 21.5± 2.0

Table 6.4: Elastic and dissipated energies during low velocity impact of multiaxial

AS4/8552 panels.

The impact led to permanent indentation, matrix cracking, fiber breakage and delami-

nations around the impact area. These damage mechanisms dissipate the majority of the

impact energy (dissipated energy). The remaining impact energy is absorbed and recovered

by elastic deformation of the panel.

134


The impacted panels were inspected by C-scan and X-ray computed tomography. Fig. 6.24

shows the results of the ultrasonic C-scan inspections of the impacted laminates. Again

Ply-clustering reduced the number of interfaces available for delamination leading to large

projected delamination areas, Table 6.5.

Figure 6.24: Results of the C-scan inspections of multiaxial AS4/8552 laminates sub-

jected to low-velocity impact: (a) [453/03/-453/903]s, (b) [45/0/-45/90]3s.

135


Cycle [453/03/-453/903]s [45/0/-45/90]3s

cm2 cm2

C-1 52.88 28.56

C-2 50.06 27.45

C-3 54.58 27.06

Table 6.5: Projected delamination areas of multiaxial AS4/8552 panels with different

lay-up after low velocity impact.

It is neccesary to point out that the delamination areas were probably affected by the

boundary conditions. The ASTM-D7136 (2005) standard establishes that the delamination

diameter should be lower than half of the specimen width in order to eliminate boundary

effects in the delamination progress. In our case, this condition was not fulfilled and the

effect of boundaries and clamping system should be taken into account. Nevertheless, the

differences in the delaminated area between dispersed and clustered lay-ups are clearly

observable.

The proper interpretation of the through-thickness location of the delaminations de-

pends on the inspections performed, since delaminations close to the impact surface could

mask the existence of deeper delaminations when using ultrasound techniques. To this end,

more detailed inspections based on X-ray tomography were carried out to obtain more in-

formation about the damage mechanisms in clustered and dispersed multiaxial laminates,

Fig. 6.25 and Fig. 6.26. The tomograms of the cross-section below the impactor show that

the main damage mechanisms were interply delamination as well as intraply failure. De-

laminations occurred between plies with different orientation. They were evenly distributed

through the thickness and had similar length in the dispersed laminates (Fig. 6.26.b), while

fewer though much longer delaminations were found in the clustered material (Fig. 6.26.a)

and the residual crack openings were wider. Moreover, intraply damage in the form of

crushing below the impact was higher in the clustered material. These observations are in

agreement with the curves in Fig. 6.21. The critical load for delamination was smaller in

the clustered material but delaminations were localized in a limited number of interplies

and grew longer, leading to a high delaminated area. As a result, the stiffness of the clus-

tered material decreased rapidly after the development of interply decohesion leading to a

reduction in the peak load and to a longer time response.

136


Figure

6.25:

Dam

age

mec

hanis

ms

of

mu

ltia

xia

lla

min

ates

sub

ject

edto

low

velo

city

imp

act.

3Dvie

wof

the

imp

acte

d

are

a(a

)st

ack

ing

sequ

ence

[45 3/0

3/-

453/9

0 3] s

and

(b)

stac

kin

gse

quen

ce[4

5/0/

-45/

90] 3s.

137


Figure

6.26:

Dam

age

mech

anism

sof

mu

ltiaxial

lamin

atessu

bjected

tolow

velocity

imp

act.C

ross-sectionund

erth

e

impact

(a)

stack

ing

sequen

ce[45

3 /03 /

-45

3 /903 ]s

and

(b)

stackin

gseq

uen

ce[45/

0/-45/90]3

s .

138


The distribution of the through-thickness delaminations of the impacted laminates are

shown in Fig. 6.27. The largest delaminations appeared at the opposing surface of the

impact forming the typical conical structure.

The non-destructive inspections performed by means of C-scan ultrasounds and X-ray

computed tomography did not revealed any significant differences in the size and the shape

of the delamination areas due to the curing cycle. This was probably a consequence of the

smaller differences in the porosity which were masked by longer defects induced by impact.

Figure 6.27: Conical distribution of delaminations within the laminate after low-

velocity impact (a) stacking sequence [453/03/-453/903]s and (b) stacking sequence

[45/0/-45/90]3s.

6.2.3 Compression After Impact (CAI)

The residual compressive strength after impact of the laminates was measured accord-

ing to ASTM D7137 ASTM-D7137 (2005). To this end, the impacted specimens were

139


subjected to in-plane compression to evaluate the residual compressive strength after im-

pact. Tests were carried out using an electromechanical universal testing machine (Instron

3384), Fig. 6.28. The fixture incorporates adjustable side plates to accommodate the thick-

ness variations and to prevent specimen buckling. The specimen was simply supported at

the four edges, and the compression load was applied directly to the top fixture plate

by a platen installed in the cross-head of the testing machine. The load was continuously

measured during the test with a 150 kN load cell. The instrumentation of the specimens in-

cluded four back-to-back strain gages (350 Ω HBM) to detect evidence of specimen bending

during the test. They were located at 25 mm from each edge, Fig. 6.28.

Figure 6.28: Compression after impact fixture.

The test starts with a pre-load of 450 N to ensure that all surfaces are in contact

and to align the plates. The test is performed at a compression rate of 1 mm/min until

approximately 10% of the estimated ultimate compressive load. The recorded strain gage

data is reviewed at this point to evaluate specimen bending. The bending percent at

maximum load should be less than 10% for a valid test and can be determined from,

PB =εSG1 − εSG3

εSG1 + εSG3

(6.9)

140


where εSG1 and εSG3 are the strains from the gages on opposite faces, respectively. After

the preload, the load is reduced to 150 N and then the system is balanced. If the bending

is low enough, the specimen is compressed until failure.

Table 6.6 summarizes the results of the compression after impact tests. Curing cycle

(and porosity) did not influence the mechanical behavior while ply clustering had an im-

portant influence. The average compressive strength after impact obtained from 5 tests

(together with the corresponding standard deviations) is plotted in Fig. 6.29 for all the

laminates. All specimens failed catastrophically at the maximum load. These results show

that damage induced during impact overcame the effect of porosity on the compressive

strength and that the residual strength of clustered laminates was consistently lower than

that of plates with a dispersed lay-up. These data are in agreement with the damage

patterns presented in Fig. 6.26.a and Fig. 6.26.b, which showed longer and wider delam-

inations in the clustered laminate. They should facilitate micro buckling of the 0 plies

under compression.

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

[ 4 5 / 0 / - 4 5 / 9 0 ] 3 s [ 4 5 3 / 0 3 / - 4 5 3 / 9 0 3 ] s

Comp

ressiv

e stre

ngth

after

impa

ct (M

Pa)

C 2 C 3C 1

C 2 C 3 C 1

0 2 4 6 8 1 0V o i d s v o l u m e f r a c t i o n ( % )

Figure 6.29: Compressive strength after impact of multiaxial AS4/8552 laminates with

different stacking sequence.

141


Cycle [45/0/-45/90]3s [453/03/-453/903]s

MPa MPa

C-1 173.4± 4.4 147± 20

C-2 176.90± 0.37 138± 20

C-3 180± 12 140± 10

Table 6.6: Compression after impact strength of multiaxial AS4/8552 laminates with

different stacking sequence.

In conclusion, the effect of porosity in the low velocity impact and in the after impact

strength was negligible. The detrimental effect of porosity was only observed in the plain

compression strength while in case of low velocity impact and CAI was masked by the

damage mechanisms induced by the impact. Ply clustering decreased the compressive

strength after impact and the in-plane compressive strength of the multiaxial laminates.

142

Chapter 7Conclusions and Future Work

7.1 Conclusions

The main goal of this thesis was to assess the effect of the temperature curing cycle on

the development of voids during consolidation by compression molding of prepregs and the

effect of voids on the mechanical properties of laminates. The main conclusions obtained

are the following:

• It has been demonstrated that it is possible manufacture composite panels with low

porosity and good mechanical properties by means of compression molding under low

pressure (2 bars). This was achieved by a careful design of the temperature cycle

leading to wide processing windows in which the resin has low viscosity.

• Multiaxial laminates presented lower porosities than the unidirectional ones. This

result was attributed to the presence of two main path ways for void migration:

along the fibers in each ply and along the interpies between laminas with different

fiber orientation.

143

7.1 Conclusions

• A compaction model was developed to analyze the consolidation process in AS4/8552

unidirectional composite laminates manufactured by compression molding. The model

included the effect of the stress transfer between resin and the fiber bed and the

macroscopic flow of the resin through the fiber preform including the changes in

viscosity induced by temperature and curing. The model parameters were obtained

from the rheological and thermo-mechanical experiments carried out in raw prepreg

samples. The predictions of the thickness change were in reasonable agreement with

the experimental results.

• Rod-like voids were observed and the elongation factor (length/average diameter)

increased with void size. Most of the voids were the result of air entrapment and

wrinkles created during lay-up. They were oriented parallel to the fibers and concen-

trated in channels along the fiber orientation. XTC analysis along the fiber direction

in unidirectional panels showed the presence of a cellular-like structure with an ap-

proximate cell diameter of ≈ 1 mm. The cell walls were fiber-rich regions and porosity

was localized at the center of the cells. This porosity distribution within the lami-

nate was the result of inhomogeneous consolidation. Upon the application of pressure,

most of the load was predominantly transferred through the continuous skeleton of

these fiber-rich regions. The higher pressure in these regions led to the migration of

resin as well as of voids into the resin cells. In addition, the pressure within the cells

was lower, facilitating the nucleation and/or growth of voids. Resin flow along the

fibers facilitated the coalescence of voids in this direction, so the elongation factor of

individual voids increased with its volume.

• The consolidation in multiaxial panels was the result of the combination of the resin

flow along each fiber orientation 0, +45, 90, -45 leading to a multidirectional

network of flow channels.

• The interlaminar shear strength (ILSS) of unidirectional laminates was strongly af-

fected by the porosity. The results followed the predictions of simple net-section

analysis, which assumed cylindrical voids arranged in a regular square pattern. It

was found that large and elongated voids favored the growth of the cracks leading to

the reduction of ILSS. The same trends were observed in the case of GIIc while GIc

was insensitive to the void volume fraction.

144

7.2 Future Work

• The compressive strength of the laminates decreased as the void volume fraction

increased. Dispersed laminates presented higher compressive strength than clustered

ones for equivalent levels of porosity. This result was attributed to the early onset

of delamination upon loading in the laminate with thicker plies. Similarly, lower

peak loads and delamination thresholds as well as more extended delaminations were

found in clustered laminates subjected to low-velocity impact. In addition, they

showed lower compression after impact strength. Porosity did not influence either the

low-velocity impact behavior or the compression after impact as defects introduced

during impact overcame the influence of porosity on the failure mechanisms.

7.2 Future Work

• Laminates were manufactured under constant pressure of 2 bar to reduce the number

of variables. Experiments with pressures in the range 1 to 7 bar (from vacuum bagging

to autoclave conditions) will provide complementary information of the effect of the

applied pressure on the volume fraction, shape and spatial distribution of voids.

• Extension of the experiments to other fabric architectures will provide information

about the effect of the type of fabric on the preferential flow paths of the resin in the

laminate.

• Differences in the flow behavior were observed between unidirectional and multiaxial

laminates. The extension of the compaction compaction model to multiaxial lami-

nates using a three-dimensional configuration will lead to a better understanding of

the compaction and flow process of multiaxial laminates.

• Design a comprehensive method to improve the fiber bed compaction curve depending

on the fiber architecture, fluid type, etc. will enhance the mechanical predictions of

the flow compaction model

• Flow-compaction model only takes into account the distributed porosity. Inclusion

of large voids in the compaction model, using micro-scale models, could provide very

interesting information about the behavior of individual voids during consolidation.

The analysis of an elongated void embebed in the material will lead to a better

understanding of the evolution of void shape and size during the consolidation process.

145

Appendices

147

Appendix AMathematica Input for

Unidimensional Compaction

INTEGRACIONCOMPACTACIONUNIDIMENSIONAL;INTEGRACIONCOMPACTACIONUNIDIMENSIONAL;INTEGRACIONCOMPACTACIONUNIDIMENSIONAL;

"Fraccion Volumetrica Inicial";"Fraccion Volumetrica Inicial";"Fraccion Volumetrica Inicial";

Vo = 0.574;Vo = 0.574;Vo = 0.574;

"Viscosidad (Pa.s)";"Viscosidad (Pa.s)";"Viscosidad (Pa.s)";

m = 1000;m = 1000;m = 1000;

"Presion Total Aplicada (Pa)";"Presion Total Aplicada (Pa)";"Presion Total Aplicada (Pa)";

pT = 0.7 ∗ 10∧6;pT = 0.7 ∗ 10∧6;pT = 0.7 ∗ 10∧6;

"Espesor Total (m)";"Espesor Total (m)";"Espesor Total (m)";

h = 0.01;h = 0.01;h = 0.01;

"Modulo Elastico (Pa)";"Modulo Elastico (Pa)";"Modulo Elastico (Pa)";

El = 7.0 ∗ 10∧6;El = 7.0 ∗ 10∧6;El = 7.0 ∗ 10∧6;

"Coeficiente de Poisson";"Coeficiente de Poisson";"Coeficiente de Poisson";

ν = 0.33;ν = 0.33;ν = 0.33;

szz = −El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + e[z, t])Vo− 1);szz = −El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + e[z, t])Vo− 1);szz = −El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + e[z, t])Vo− 1);

149

dszz = −El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ Vo;dszz = −El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ Vo;dszz = −El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ Vo;

"Permeabilidad Karman-Kozeny(m∧2)";"Permeabilidad Karman-Kozeny(m∧2)";"Permeabilidad Karman-Kozeny(m∧2)";

Az = 10∧ − 12;Az = 10∧ − 12;Az = 10∧ − 12;

Kzz = Az(1 + e[z, t])2(

1− 11+e[z,t]

)3

;Kzz = Az(1 + e[z, t])2(

1− 11+e[z,t]

)3

;Kzz = Az(1 + e[z, t])2(

1− 11+e[z,t]

)3

;

"Permeabilidad Constante(m∧2)";"Permeabilidad Constante(m∧2)";"Permeabilidad Constante(m∧2)";

Kzz = 6.45 ∗ 10∧ − 13;Kzz = 6.45 ∗ 10∧ − 13;Kzz = 6.45 ∗ 10∧ − 13;

eo = (1− Vo)/Vo;eo = (1− Vo)/Vo;eo = (1− Vo)/Vo;

"Variables del problema";"Variables del problema";"Variables del problema";

T = 1;T = 1;T = 1;

Vf=.;Vf=.;Vf=.;

t=.;t=.;t=.;

z=.;z=.;z=.;

NullNullNull

"Busqueda de Compactacion Final esup";"Busqueda de Compactacion Final esup";"Busqueda de Compactacion Final esup";

solution = FindRoot[szz == pT, e[z, t], 0.8eo];solution = FindRoot[szz == pT, e[z, t], 0.8eo];solution = FindRoot[szz == pT, e[z, t], 0.8eo];esup = solution[[1, 2]];esup = solution[[1, 2]];esup = solution[[1, 2]];

"Integracion Ecuacion Diferencial en e(z,t) (la exponencial se utiliza para"Integracion Ecuacion Diferencial en e(z,t) (la exponencial se utiliza para"Integracion Ecuacion Diferencial en e(z,t) (la exponencial se utiliza para

aplicar el salto de la aplicacion de la presion exterior)";aplicar el salto de la aplicacion de la presion exterior)";aplicar el salto de la aplicacion de la presion exterior)";

solution2 =solution2 =solution2 =

NDSolve[(1 + eo)∧2 ∗D[−Kzz/(m ∗ (1 + e[z, t])) ∗ dszz ∗D[e[z, t], z], z]==D[e[z, t], t],NDSolve[(1 + eo)∧2 ∗D[−Kzz/(m ∗ (1 + e[z, t])) ∗ dszz ∗D[e[z, t], z], z]==D[e[z, t], t],NDSolve[(1 + eo)∧2 ∗D[−Kzz/(m ∗ (1 + e[z, t])) ∗ dszz ∗D[e[z, t], z], z]==D[e[z, t], t],

e[z, 0] == eo, e[0, t] == esup + (eo− esup) ∗ Exp[−100t], e[h, t] == esup + (eo− esup) ∗ Exp[−100t],e[z, 0] == eo, e[0, t] == esup + (eo− esup) ∗ Exp[−100t], e[h, t] == esup + (eo− esup) ∗ Exp[−100t],e[z, 0] == eo, e[0, t] == esup + (eo− esup) ∗ Exp[−100t], e[h, t] == esup + (eo− esup) ∗ Exp[−100t],e[z, t], z, 0, h, t, 0, 6000T]e[z, t], z, 0, h, t, 0, 6000T]e[z, t], z, 0, h, t, 0, 6000T]

"Plot e(z,t)";"Plot e(z,t)";"Plot e(z,t)";

Plot3D[solution2[[1, 1, 2]], z, 0, h, t, 0, 6000T,PlotRange→ eo, esup,Plot3D[solution2[[1, 1, 2]], z, 0, h, t, 0, 6000T,PlotRange→ eo, esup,Plot3D[solution2[[1, 1, 2]], z, 0, h, t, 0, 6000T,PlotRange→ eo, esup,PlotPoints→ 50]PlotPoints→ 50]PlotPoints→ 50]

150

−SurfaceGraphics−

"Plot Vf(z,t)";"Plot Vf(z,t)";"Plot Vf(z,t)";

Plot3D[1/(1 + solution2[[1, 1, 2]]), z, 0, h, t, 6000T, 0,PlotPoints→ 50,Plot3D[1/(1 + solution2[[1, 1, 2]]), z, 0, h, t, 6000T, 0,PlotPoints→ 50,Plot3D[1/(1 + solution2[[1, 1, 2]]), z, 0, h, t, 6000T, 0,PlotPoints→ 50,

PlotRange→ Vo, 1/(1 + esup)]PlotRange→ Vo, 1/(1 + esup)]PlotRange→ Vo, 1/(1 + esup)]

151


"Plot Presion de Resina";"Plot Presion de Resina";"Plot Presion de Resina";

Plot3D[−El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + solution2[[1, 1, 2]])Vo− 1), z, 0, h,Plot3D[−El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + solution2[[1, 1, 2]])Vo− 1), z, 0, h,Plot3D[−El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + solution2[[1, 1, 2]])Vo− 1), z, 0, h,t, 6000T, 0,PlotPoints→ 50,PlotRange→ 0, pT]t, 6000T, 0,PlotPoints→ 50,PlotRange→ 0, pT]t, 6000T, 0,PlotPoints→ 50,PlotRange→ 0, pT]

152


PlotPresiondefibras;PlotPresiondefibras;PlotPresiondefibras;

Plot3D[pT + El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + solution2[[1, 1, 2]])Vo− 1),Plot3D[pT + El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + solution2[[1, 1, 2]])Vo− 1),Plot3D[pT + El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + solution2[[1, 1, 2]])Vo− 1),

z, 0, h, t, 6000T, 0,PlotPoints→ 50,PlotRange→ 0, 2pT]z, 0, h, t, 6000T, 0,PlotPoints→ 50,PlotRange→ 0, 2pT]z, 0, h, t, 6000T, 0,PlotPoints→ 50,PlotRange→ 0, 2pT]

153


t = 1;t = 1;t = 1;

pressureIntegrate = pT + El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + solution2[[1, 1, 2]])Vo− 1);pressureIntegrate = pT + El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + solution2[[1, 1, 2]])Vo− 1);pressureIntegrate = pT + El ∗ ((1− ν)/(1− ν − 2 ∗ ν∧2)) ∗ ((1 + solution2[[1, 1, 2]])Vo− 1);

Plot[pressureIntegrate, z, 0, h/2,PlotRange→ 0, pT]Plot[pressureIntegrate, z, 0, h/2,PlotRange→ 0, pT]Plot[pressureIntegrate, z, 0, h/2,PlotRange→ 0, pT]

−Graphics−

table = Table[−z + h/2, pressureIntegrate, z, 0, h/2, 0.0001]table = Table[−z + h/2, pressureIntegrate, z, 0, h/2, 0.0001]table = Table[−z + h/2, pressureIntegrate, z, 0, h/2, 0.0001]

SetDirectory["C:\Temp\Silvia"];SetDirectory["C:\Temp\Silvia"];SetDirectory["C:\Temp\Silvia"];

OpenWrite["datos"];OpenWrite["datos"];OpenWrite["datos"];

Export["datos", table, "CSV"]Export["datos", table, "CSV"]Export["datos", table, "CSV"]

Close["datos"]Close["datos"]Close["datos"]

154

Appendix BAbaqus Input for Unidimensional

Compaction

*Heading

*Preprint, echo = NO, model = NO, history = NO, contact = NO

**

** PARTS

**

*Part, name = Part− 1

*Node

1, 0., 0.

2, 0.000500000024, 0.

3, 0., 0.000500000024

4, 0.000500000024, 0.000500000024

5, 0., 0.00100000005

6, 0.000500000024, 0.00100000005

7, 0., 0.00150000001

8, 0.000500000024, 0.00150000001

9, 0., 0.00200000009

10, 0.000500000024, 0.00200000009

11, 0., 0.00249999994

155

12, 0.000500000024, 0.00249999994

13, 0., 0.00300000003

14, 0.000500000024, 0.00300000003

15, 0., 0.00350000011

16, 0.000500000024, 0.00350000011

17, 0., 0.00400000019

18, 0.000500000024, 0.00400000019

19, 0., 0.00449999981

20, 0.000500000024, 0.00449999981

21, 0., 0.00499999989

22, 0.000500000024, 0.00499999989

*Element, type = CPE4P

1, 1, 2, 4, 3

2, 3, 4, 6, 5

3, 5, 6, 8, 7

4, 7, 8, 10, 9

5, 9, 10, 12, 11

6, 11, 12, 14, 13

7, 13, 14, 16, 15

8, 15, 16, 18, 17

9, 17, 18, 20, 19

10, 19, 20, 22, 21

*Nset, nset = PickedSet2, internal, generate

1, 22, 1

*Elset, elset = PickedSet2, internal, generate

1, 10, 1

** Section: Section-1

*Solid Section, elset = PickedSet2, material = Material − 1

1.,

*End Part

**

**

** ASSEMBLY

156

**

*Assembly, name = Assembly

**

*Instance, name = Part− 1− 1, part = Part− 1

*End Instance

**

*Nset, nset = PickedSet4, internal, instance = Part− 1− 1, generate

1, 22, 1

*Elset, elset = PickedSet4, internal, instance = Part− 1− 1, generate

1, 10, 1

*Nset, nset = PickedSet5, internal, instance = Part− 1− 1

1, 2

*Elset, elset = PickedSet5, internal, instance = Part− 1− 1

1,

*Nset, nset = PickedSet7, internal, instance = Part− 1− 1

21, 22

*Elset, elset = PickedSet7, internal, instance = Part− 1− 1

10,

*Elset, elset = PickedSurf6S3, internal, instance = Part− 1− 1

10,

*Surface, type = ELEMENT , name = PickedSurf6, internal

PickedSurf6S3, S3

*Nset, nset = pickedSet7PP , internal, instance = Part− 1− 1

21, 22

*End Assembly

**

** MATERIALS

**

*Material, name = Material − 1

*Elastic

7e+06, 0.33

*Permeability, specific = 11760

6.64188e-13,4.32507e-01

157

8.91092e-13,4.82507e-01

1.15873e-12,5.32507e-01

1.46881e-12,5.82507e-01

1.82284e-12,6.32507e-01

2.22215e-12,6.82507e-01

2.66789e-12,7.32507e-01

3.16112e-12,7.82507e-01

3.70276e-12,8.32507e-01

4.29364e-12,8.82507e-01

4.93450e-12,9.32507e-01

5.62600e-12,9.82507e-01

5.88000e-12,1.00000e+00

**

** BOUNDARY CONDITIONS

**

** Name: BC-1 Type: Symmetry/Antisymmetry/Encastre

*Boundary

PickedSet4, XSYMM

** Name: BC-2 Type: Symmetry/Antisymmetry/Encastre

*Boundary

PickedSet5, YSYMM

*Initial Conditions, type=ratio

PickedSet4,1.0

** —————————————————————-

**

** STEP: Step-1

**

*Step, name = Step− 1, unsymm = Y ES

*Soils, consolidation, end = PERIOD, utol = 2e+ 06

1e-06, 1.0e-6

**

** LOADS

**

158

** Name: Load-1 Type: Pressure

*Dsload

PickedSurf6, P, 700000.

**

** OUTPUT REQUESTS

**

*Restart, write, frequency = 0

**

** FIELD OUTPUT: F-Output-1

**

*Output, field, variable = PRESELECT

**

** HISTORY OUTPUT: H-Output-1

**

*Output, history, variable = PRESELECT

*End Step

** —————————————————————-

**

** STEP: Step-2

**

*Step, name = Step− 2, unsymm = Y ES, nlgeom = yes, inc = 1000

*Soils, consolidation, end = PERIOD, utol = 7.0e5

0.001, 6000., 1e-05, 10.,

**

** BOUNDARY CONDITIONS

**

** Name: BC-3 Type: Pore pressure

*Boundary

PickedSet7PP , 8, 8

**

** OUTPUT REQUESTS

**

*Restart, write, frequency = 0

159

**

** FIELD OUTPUT: F-Output-1

**

*Output, field, variable = PRESELECT

**

** HISTORY OUTPUT: H-Output-1

**

*Output, history, variable = PRESELECT

*End Step

160

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