Development of a Progressive Failure Finite Element Analysis For a Braided Composite Fuselage Frame

Daniel C. Hart

Thesis submitted to the Faculty of theVirginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Sciencein

Aerospace Engineering

Dr. Eric Johnson, ChairDr. Richard Boitnott

Dr. Rakesh K. Kapania

July 2002Blacksburg, Virginia

Keywords: Triaxial braid, J-section frame, postbuckling, delamination, progressive failure,

crashworthiness, fuselage frame

Development of a Progressive Failure Finite Element Analysis For a Braided Composite Fuselage Frame

Daniel C. Hart

(ABSTRACT)

Short, J-section columns fabricated from a textile composite are tested in axial compression to study the modes of failure with and without local buckling occuring.The textile preform architecture is a 2x2, 2-D triaxial braid with a yarn layup of 39.7% axial. The preform was resin transfer molded with 3M PR500 epoxy resin. Finite element analyses (FEA) of the test specimens are conducted to assess intra- and inter- laminar progressive failure models. These progressive failure models are then implemented in a FEA of a circular fuselage frame of the same cross section and material for which test data was available. This circular frame test article had a nominal radius of 120 inches, a forty-eight degree included angle, and was subjected to a quasi-static, radially inward load, which represented a crash type loading of the frame. The short column test specimens were cut from some of the fuselage frames. The branched shell finite element model of the frame included geometric nonlinearity and contact of the load platen of the testing machine with the frame. Intralaminar progressive failure is based on a maximum in-plane stress failure criterion followed by a moduli degradation scheme. Interlaminar progressive failure was implemented using an interface finite element to model delamination initiation and the progression of delamination cracks. Inclusion of both the intra- and inter- laminar progressive failure models in the FEA of the frame correlated reasonably well with the load-displacement response from the test through several major failure events.

0°18k 64°6k±⁄[ ]

Acknowledgments

First and foremost I would like to thank my parents, Dennis and Anita, my brother Justin, and

most importantly my wife Vanessa for their continued support in pursuit of my degrees. I

would also like to thank Dr. Eric Johnson, the committee chair, for his support throughout my

academic career and committee members Dr. Richard Boitnott and Dr. Rakesh K. Kapania.

While completing my graduate research I was aided by the Impact Dynamics Branch

at the NASA Langley Research Center in Hampton Virginia. I would like to thank Dr. Richard

Boitnott, who was not only on my committee but worked with me and helped orchestrate the

testing done at the facility. Also helping me complete the testing were the technicians of the

building. Operating the testing machine were George Palko, who likes to poke everyone’s

ribs, Nelson Seabolt, the West Virginia boy who keeps everyone in line, and Ricky Martin,

who puts up with those two on a daily basis. Helping with the data acquisition set up were Jim

Richardson, Ed Knode, and Sotiris Kellas all of whom I would like to thank for their

contributions. I would also like to thank Lisa Jones who was our NASA contact at the Impact

Dynamics Branch.

iii

Helping with the analysis I need to thank Vinay Goyal, Carlos Dávila, Navin Jaunky, and

Nicolas Chretien.

Thank you to everyone who helped me along the way, especially my close friends. Their

friendship throughout the years has allowed me to benefit from and enjoy my collegiate career. So

thank you, in no particular order, Todd Norell, Tony Reichel, Mark Nelson, Mike Henry, Kevin

Waclawicz, Trevor Wallace, Matt Short, Mike Elander, Henrik Pettersson, and Tony Zerante.

I must acknowledge the NASA grant numbers NAG-1-2309 & NAG-1-01123 for the

funding of this research effort, and both the Virginia Tech College of Engineering and NASA

LaRC for the use of their computing facilities.

iv

Table of Contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Chapter 1: Advancing The Analysis of Textile Composites For Crashworthy Structures

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Braided Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Composite Structure and Crashworthy Design . . . . . . . . . . . . . . . . . . . . . 2

1.3 Previous Fuselage Frame Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Chapter 2: Material Properties and Cross Section Anomalies . . . . . . . . . . . . . . . . . . . 9

2.1 Triaxial Braid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2 Epoxy Resin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

v

2.2 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Failure Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Manufacturing Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.3 RTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4.4 Inner Flange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4.5 Outer Flange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Chapter 3: Short Column Compression Tests, Design and Results . . . . . . . . . . . . . . . 17

3.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Preliminary Compression Testing and FEA . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Short Column Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.4 Specimen Numbering and Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.5 Instrumentation and Test Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.6 Testing Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.6.1 1.5-inch Specimen Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.6.2 Four-inch Specimen Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.6.3 Six-inch Specimen Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Chapter 4: Finite Element Analysis of Short Column Compression Tests . . . . . . . . . 38

4.1 ABAQUS Shell Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Finite Element Model Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.3 Element Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.4 Displacement Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.5 FEA Results and Test Data Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 43

vi

4.5.1 1.5-inch Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.5.2 Four-inch Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.5.3 Six-inch Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Chapter 5: Frame Segment Finite Element Analysis and Comparison . . . . . . . . . . . . 56

5.1 Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.2 Frame FEA Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Chapter 6: Interface Element and Progressive Failure Analysis . . . . . . . . . . . . . . . . . 61

6.1 Failure Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.2 Intralaminar Failure and Degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.3 Delamination Initiation and Progression . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.4 FEA Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.4.1 Short Column Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.4.2 Frame Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Chapter 7: Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

7.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

7.2 Finite Element Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.3 Short Column Test and FEA Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.4 Fuselage Frame FEA Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.5 Final Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

A.1 Strain Gage Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

vii

A.2 Specimen Strain Gage Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

a.2.1 1.5-inch Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

a.2.2 Four-inch Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

a.2.3 Six-inch Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

B.1 Sample ABAQUS Input File For Six-inch Column Model . . . . . . . . . . . 91

b.1.1 hdmesh6.inp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

b.1.2 Material Reduction Scheme For Progressive Failure . . . . . . . . . . . 98

Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

viii

List of Figures

Fig. 1.1 Sketch of the frame test apparatus [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Fig. 1.2 J-section fuselage frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Fig. 2.1 Geometric discontinuity in the web to outer flange junction created by the manufacturing process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Fig. 3.1 General specimen nomenclature along with strain gage locations for the six-inch specimens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Fig. 3.2 Two-inch short column specimen after failure. . . . . . . . . . . . . . . . . . . . . . . . . 19

Fig. 3.3 Short column specimens mounted in end fixtures with strain gages attached. Column gage lengths are 6, 4, and 1.5 inches. . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Fig. 3.4 Universal testing machine with six-inch specimen mounted between the cross head and loading platen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Fig. 3.5 Specimen #1, 1.5-inch column after failure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Fig. 3.6 Specimen #2 under load with local buckling of the front side outer flange visible.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

ix

Fig. 3.7 Specimen #2 after failure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Fig. 3.8 Load versus displacement data for specimen #5. . . . . . . . . . . . . . . . . . . . . . . . 30

Fig. 3.9 LVDT data for specimen #5. Numbers indicate LVDT locations at the mid height of the cross section shown on the right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Fig. 3.10 Strain response data for the outer flange of specimen #5. . . . . . . . . . . . . . . . . . 32

Fig. 3.11 Strain response of the axial filler material for specimen #5. . . . . . . . . . . . . . . . 33

Fig. 3.12 Strain response for the web and inner flange of specimen #5. . . . . . . . . . . . . . 34

Fig. 3.13 Specimen #3 showing local buckling of the outer flange. Noted are the approximate wave crest and node locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Fig. 3.14 Six-inch specimen after failure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Fig. 4.1 Comparison of the end shortening results using S4R and S4R5 shell elements. 40

Fig. 4.2 Geometry used to create short column models with the correct curvature. . . . . 41

Fig. 4.3 End shortening response for specimen #1, 1.5-inch column. . . . . . . . . . . . . . . 44

Fig. 4.4 Compressive strain response in the front side outer flange for specimen #1, 1.5-inch column. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Fig. 4.5 Compressive strain response in the inner flange of specimen #1, 1.5-inch column.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Fig. 4.6 ABAQUS linear buckling results for a four-inch column. On the right is a front on view of the outer flange, showing the symmetric buckling waves on the front and back side outer flange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Fig. 4.7 Finite element model of six-inch column. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Fig. 4.8 Load-shortening data for specimen #3 and FEA results. . . . . . . . . . . . . . . . . . . 50

Fig. 4.9 Axial strain response for in the front side outer flange of specimen #3 and FEA strain response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Fig. 4.10 Strain response of the filler material at the web to outer flange junction and FEA results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

x

Fig. 4.11 Axial strain response in the web and FEA results for the six-inch column. . . . 54

Fig. 4.12 Inner flange axial strain response and FEA results for the six-inch column. . . 55

Fig. 5.1 Refined shell element model of a 48 degree frame segment. . . . . . . . . . . . . . . 57

Fig. 5.2 Midspan displacement and force response plots from linear and nonlinear analysis with and without contact compared to test data of frame B. . . . . . . . . . . . . . . . 59

Fig. 6.1 Upper (S+) and lower (S-) surfaces of the interface element. . . . . . . . . . . . . . . 66

Fig. 6.2 Representative traction-stretching curve for the springs . . . . . . . . . . . . . . . . . . 67

Fig. 6.3 Load versus displacement response for the six-inch column from the test and FEA with progressive failure models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Fig. 6.4 Load displacement responses from analyses including intra- or inter- laminar progressive failure models compared to test data. . . . . . . . . . . . . . . . . . . . . . . . 72

Fig. 6.5 Load versus displacement responses for the test and FEA including both the intra- and inter- laminar progressive failure models. . . . . . . . . . . . . . . . . . . . . . . . . . 74

Fig. 6.6 Load displacement responses from the analysis including both the intra- and inter- laminar progressive failure models and the test. The domain of the intralaminar failure extended to web and inner flange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Fig. 6.7 Predicted element failures using the progressive failure model. . . . . . . . . . . . . 77

Fig. 6.8 Comparison of the element failures predicted by the progressive failure model and failures that occurred on frame B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Fig A1. Axial strain gage locations for the 1.5-inch specimens. All dimensions in inches.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Fig A2. Axial strain gage locations for the four-inch specimens. All dimensions in inches.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Fig A3. Axial strain gage locations for the six-inch specimens. All dimensions in inches.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

xi

List of Tables

Table 1.1 Frame B Dimensions And Cross-Sectional Data . . . . . . . . . . . . . . . . . . . . . 6

Table 2.1 Tri-Axial Braid Properties For Vf = 55.26% . . . . . . . . . . . . . . . . . . . . . . . . 12

Table 3.1 Local Buckling Results For Short J-Section Columns From ABAQUS . . . 22

Table 3.2 Test Set Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Table 5.1 Responses From Several Analyses Compared to The Test of Frame B . . . 60

Table 6.1 Reduction Factors For Intralaminar Material Degradation . . . . . . . . . . . . . 65

Table 6.2 Interfacial Strengths [15] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

xii

CHAPTER 1 Advancing The Analysis of Textile Composites For Crashworthy Structures

Composite materials are presently used in multiple industries including aerospace, marine,

automotive, and trucking. Structural components such as frame rails, stiffeners, skins, and

bulkheads fabricated from advanced composites can be found in lightweight flight, space, and

land vehicles. The architecture of these composites range from unidirectional tapes to weaves

and braids. The most recent advancements have been in two-dimensional (2D) and three-

dimensional (3D) weaves and braids, which are termed “textile” composites due to the

fabrication process. Textile composite materials are attractive because of their strength to

weight ratio, energy absorbing characteristics, and the possibility of mass producing

specialized parts. The present research is a continuation of a previous study, which will be

reviewed in this chapter along with an overview of composites in structural design.

1.1 Braided CompositesAdvancements in lightweight structures follows the development of new materials and new

fabrication processes. The subject material in this research is a textile composite consisting of

a preform of yarns, or tows, of graphite fibers interlaced in three in-plane directions, which is

subsequently impregnated with epoxy resin by a resin transfer molding (RTM) process. The

1

preform architecture for this research is a 2x2 2D triaxial braid, details of which will be discussed

in a subsequent chapter.

Textile composite materials have good energy absorbing characteristics because of their

multiaxial strengths, which is attractive for aircraft and automotive industries, to name a few.

Braided composites sacrifice some in-plane stiffness and strength to improve out-of-plane

strength and resistance to delamination with respect to tape laminates. This interlaminar strength

is derived from undulation of the yarns in the thickness direction and subsequent nesting of the

braided layers that occurs during the RTM manufacturing process. Nesting occurs during the

RTM process, pressure from the influx of resin forces layers to move around slightly adjusting the

orientation of some yarns. Yarns of coincident layers end up side by side in the matrix, thus

making a connection between the layers through the cured resin of the matrix.

Delamination in tape laminates is one reason they have poor energy absorbing

characteristics under lateral impact loading. Once delamination initiates there is nothing but the

brittle matrix to carry out-of-plane stresses, thus leading to separation of two layers and to

potential catastrophic failure. The braided architecture and fabrication leads to thickness direction

reinforcement and nesting as previously mentioned. Nesting offers an increased amount of

interlaminar interaction compared to unidirectional composites, which increases the strength in

the thickness direction. Energy absorbing characteristics of textile composites stems from the

material architecture and through-the-thickness strength [1].

1.2 Composite Structure and Crashworthy DesignIn the event of a crash, and without specifically incorporating energy absorbing concepts into

vehicle’s structure, most of the impact energy is transmitted through the structure to the occupants

2

and payload. It follows that the need for understanding the deformation and progressive failure

process of these new materials when subjected to crash loads is crucial in designing safe and

useful structures. Weight sensitive structural designs with laminated composites incorporate thin-

wall construction, which under compressive load can buckle. Assuming some postbuckling load

carrying capacity, these thin-walled, laminated components may begin failing by material failures

within a lamina (matrix cracks, fiber rupture, fiber-matrix debonding, etc.), or by delamination of

adjacent lamina. Structural components having postbuckling strength, albeit at reduced stiffness,

may be viewed as beneficial with respect to energy absorption, since finite loads can be carried

over large displacements; crumple zones in an automotive structure is one example. If the design

is to carry service loads without buckling then preventative measures can be used, for example the

addition of material layers. The issue becomes how to design a composite structure to carry

service loads without failure and yet under crash loads to fail in such a manner so as to absorb as

much energy as possible. To accomplish the latter, we must first understand the failure

mechanisms and predict the progressive failure sequence.

Consider a survivable crash scenario of a transport aircraft on an airport runway. The force

acting on the passenger due to deceleration of the aircraft must be limited while the kinetic energy

due to impact is absorbed. This kinetic energy is absorbed by stroking of landing gear, crushing of

the fuselage sub-structure below the passenger deck, and proper seat design. For crushing of the

structure below the passenger deck, it has been shown from drop tower tests of fuselage sections

that the fuselage frames play a very important role in the response and energy absorbing

characteristics [2]. Also it was found, for the limited vertical drop speeds of a survivable crash,

that the dynamic and static failure sequences are not that much different. Hence, it is instructive to

understand the fundamental mechanics of the progressive failure sequence of a quasi-statically

3

loaded fuselage frame under a crash-type load. In particular, the focus of this study is the response

and progressive failure analysis of fuselage frames fabricated from a triaxial braided composite

material. Tests of these frames were conducted in Ref. [3] and these tests are discussed in the next

section.

1.3 Previous Fuselage Frame TestsIn a previous study[3], circular braided composite fuselage frames segments with J cross sections

were subjected to quasi-static, radial inward loading until several major failure events were

recorded. A sketch of the frame mounted in a universal testing machine is shown Figure 1.1 .

Frame geometry is shown in Figure 1.2 , with dimensions of the frame denoted by B in Ref. 3

listed in Table 1.1. Response data from the tests were compared to corresponding results obtained

from a finite element analysis (FEA) of the frame using the ABAQUS/Standard [4] software

package. The open section curved beam element labeled B32OS in the ABAQUS library of

����������������������������������������������������������������������������������������������������������

�����������������������������������������������������������������������������������������������������������������������������������������������������

���������������

moveable table of the testing machine

fixed cross headplaten

braided frame

end blockend block

I-beam

Fig. 1.1 Sketch of the frame test apparatus [3].

4

elements was used in the analysis. FEA results yielded an initial frame stiffness within 1% of test

measurements.

α

riro

A

A

Fig. 1.2 J-section fuselage frame.Section A A–

h

wi

ti

wo

tw

to

ri

ro

5

The largest circumferential strains measured in the test were compressive and were

located at the center of the frame where the load was applied through contact with the platen of

the testing machine. However, compressive strains measured by electrical resistance strain gages

near the site of the first major failure event were about 40% lower than the theoretical

compressive failure strain of the material predicted by computer program Textile Composite

Analysis for Design, or TEXCAD [5].The deformation of the frame in the vicinity of the load

platen consisted of a local buckling and postbuckling response of the radially outboard flanges

and distortion of the cross section. Local postbuckling of the flanges reduces the direct

compressive load carried by the flanges at the expense of increased direct compression carried by

the junction between the flanges and web. The first major failure event in this local deformation

state can be due to a material compressive strength failure in the junction, or by delamination

initiating in the flange, or by a combination of both mechanisms. Delamination has been shown to

Table 1.1 Frame B Dimensions And Cross-Sectional Dataa

Inner Flange Width ( ) 1.2500 Web Thickness ( ) 0.1590

Inner Flange Thickness ( ) 0.2040 Opening angle ( )b

Outer Flange Width ( ) 2.7700 Cross Section Area in2 1.2168

Outer Flange Thickness ( ) 0.0885 Second Area Moment About 1-axis ( ) 3.9230 in4

Cross Section Height ( ) 4.8000 Second Area Moment About 2-axis ( ) 0.1914 in4

Radius of Inner Flange ( ) 117.85 Torsion Constant ( ) 0.0104 in4

Radius of Outer Flange ( ) 122.65 Height of Centroid From 2.4270

a. Dimensions in inches unless otherwise noted.b. For the frame mounted in the end blocks shown in Figure 1.1 .

wi tw

ti α 42°

wo

to I11h I22

ri J

ro ri

6

be the dominant failure mechanism in thin composite compression panels when the width to

thickness ratio, b/t, is between 10 and 20 [6]. The effective b/t ratio for the outer flange in the

cross section of frame B is 15.6.

Cross-sectional distortions and local buckling events cannot be modeled on the basis of

beam theory alone, since beam theory is based on the assumption that cross sections do not distort

in their own plane. Although the linear beam FEA can predict the initial structural stiffness, it

cannot be expected to account for cross-sectional distortions that precede the first major failure

event. To predict local buckling and postbuckling events in the vicinity of the load platen, we at

least need a branched shell FEA of frame B.

1.4 ObjectiveThe overall objective of this research is to improve the analysis for the response of the forty-eight

degree frame segments tested in Ref. [3], and to predict the failure sequence. To capture the

distortion of the cross section and local buckling events observed in the tests, a geometrically

nonlinear, branched shell finite element model is implemented in ABAQUS/Standard, which

includes contact modeling of the platen with the frame. In order to accomplish the prediction of

the failure sequence, it was decided to conduct short column compression tests of the J-section

textile composite frame, since failure in the forty-eight degree frame tests initiated under

compression in the outer flange at the location of the applied load. These short column tests

provide further information on the failure mechanisms that occur in the as fabricated J-section

under direct compression and under local postbuckling. Data obtained from short column tests is

then used to improve the finite element analysis of failure of the forty-eight-degree textile

composite fuselage frame.

7

An overview of the textile material is given in Chapter 2. Here the material architecture

will be discussed along with strength properties, and the cross-sectional characteristics of the J-

section resulting from the manufacturing process is presented. Following this is the short column

test design and test results are presented in Chapter 3, with a discussion of the finite element

models and FEA correlation with test data in Chapter 4.

The FEA of the forty-eight degree frame segment is presented in Chapter 5. Here the

model is discussed along with the results and how they correlated with test data.

Discussion of the progressive failure analysis (PFA) is presented in Chapter 6. PFA

includes intra- and inter- laminar failure. Interlaminar failure is accomplished via delamination

and intralaminar failure is based on maximum values of the in-plane stresses followed by a

stiffness reduction scheme. A special interface finite element is used to model delamination.

Chapter 7 contains with a brief summary and concluding remarks.

8

CHAPTER 2 Material Properties and Cross Section Anomalies

Architecture of the textile composite and geometry of the cross section are discussed in this

chapter.

2.1 Triaxial BraidThe preform of the 2x2 2D triaxial braid is produced on a braiding machine which consists of

yarn carriers that rotate around a cylindrical mandrel in circular paths, and this mandrel can

move in the axial direction. The rotational speed of the yarn carriers relative to the

translational speed of the mandrel controls orientation of these braider yarns. Fixed, straight

axial yarns are introduced at the center of the orbit of the yarns carriers, and the braider yarns

lock the axial yarns in the center of the fabric. A flat braided sheet is obtained by cutting the

cylindrical sheet from the mandrel and stretching it out flat. Triaxial braids offer strength in

three planer directions with braider yarns in symmetrical bias angles measured from the axial

yarn. The triaxial braid is called a quasi-laminar, or a 2D, composite since it has distinct

9

layers, which can be separated without breaking fibers prior to the resin transfer molding (RTM)

process. Modest volume fractions of through-the-thickness fibers provide delamination

resistance, but the majority of the fibers provide high in-plane stiffness and strength. The 2x2

pattern has two yarns following the same pattern, so in the braid there are two braider yarns

between cross over points [1]. Thickness is controlled by making multiple rounds about the

mandrel, essentially laying down nearly identical layers that have no mechanical connection.

Consolidation of the layers is achieved in the RTM process, which also causes some nesting of the

layers. During the RTM process pressure from the influx of resin can push the 2D braided layers

together causing yarns to intermingle creating a mechanical interaction between layers by locking

yarns from two coincident layers in the cured matrix.

Architecture definition and nomenclature for 2D triaxial braids lists bias braid angles, bias

and axial yarn size in thousands of fibers, and overall percentage of axial yarns in a unit cell. A

unit cell is defined as the smallest grouping of yarns that can be copied to make up the periodic

pattern. A 2x2 unit cell has a set of 2 + and 2 - bias yarns intersecting with an axial yarn on

either side of the intersection. For example, the architecture for the specimens of this project is

[0º18K/ 64º6K] 39% axial, which states that nominal bias yarns are at an angle of 64º measured

from the axial yarns and they contain 6,000 fibers per yarn and there are 18,000 fibers per axial

yarn and 39% of the unit cell volume is made up of axial yarns.

2.1.1 Fiber

The yarns consist of AS4 Gr/Ep fibers combined into tows of 18,000 and 6,000 fibers. Dry tows

are used, which means that there is no surface treatment of the fibers during the manufacturing

θ θ

10

process. Individual tows of 6000 fibers have a modulus of elasticity equal to psi and an

ultimate tensile strength of psi.[7]

2.1.2 Epoxy Resin

During the RTM process 3M’s PR500 epoxy resin is introduced into the mold using a vacuum.

The resin has the following properties, modulus of elasticity of psi, ultimate tensile

strength of 8,300 psi, and an ultimate flexure strength of 18,450 psi.[8]

2.2 Material PropertiesThe computer program Textile Composite Analysis for Design [5], or TEXCAD, was used to

predict material properties, which were partially verified with tensile coupon tests [9]. Other

properties include a yarn packing density of 0.75 and axial yarn spacing of 0.2087 in. (5.3mm)

TEXCAD input includes yarn and resin information, such as axial and bias yarn angles, number

of filaments in the yarns, and the dimensions of unit cell and yarns. Using micro-mechanical

models TEXCAD predicts the Young moduli, shear moduli, Poisson’s ratios, and failure

strengths. The TEXCAD predictions and tension test results are listed in Table 2.1 for a fiber

volume fraction %. This fiber volume fraction was determined by the density method

from coupons cut from the web of one the frames[9].

3.31 7×10

5.9 5×10

5.07 5×10

Vf 55.26=

11

2.3 Failure CriteriaFailure criteria specifically developed for triaxial braided materials are less common than criteria

developed for tape laminates due to the complex architecture of the triaxial braid. With undulating

Table 2.1 Tri-Axial Braid Properties For Vf = 55.26%

Properties TEXCAD[5] Tension Tests[3]Axial Modulus (E11,psi)

Transverse Modulus (E22,psi) N/A

Through Thickness Modulus (E33,psi) N/A

Poisson’s Ratio ( ) 0.231 0.26

Poisson’s Ratio ( ) 0.216 N/A

Poisson’s Ratio ( ) 0.298 N/A

In Plane Shear Modulus (G12,psi) N/A

Transverse Shear Modulus (G13,psi) N/A

Transverse Shear Modulus (G23, psi) N/A

Maximum Compressive Axial Stress (XC, psi) 71,000 N/A

Maximum Tensile Axial Stress (XT, psi) 91,370 76,880

Maximum Compressive Transverse Stress (YC, psi) 56,890 N/A

Maximum Tensile Transverse Stress (YT, psi) 73,140 N/A

Maximum In-Plane Shear Stress (SC, psi) 30,460 N/A

Tensile Failure Strain( T, ) 14071 10588

Compression Failure Strain ( , ) 10108 N/A

7.06 6×10 7.09 6×10

6.59 6×10

1.53 6×10ν12ν13ν23

1.91 6×10

0.601 6×10

0.645 6×10

ε1t µε

ε1c µε

12

braider yarns, and to some extent undulating axial yarns due the compaction of the RTM process,

the micromechanical analysis required to model the stresses and predict failure modes is difficult.

Approaches to predict failure in textile composites with periodic geometry are based on

unit cells. Spatially translated copies of a unit cell construct the entire textile composite. These

approaches for failure prediction can be based on failure loci for individual yarns and matrix in

terms of the local stress state in a unit cell, or be based on in-plane stresses averaged over the

volume of the unit cell. The micromechanical approach is used in computer program TEXCAD to

predict failure of a unit cell based on constituent stresses obtained from the isostrain assumption.

Several features in TEXCAD aid in estimating failure [1]. These features include: bending of the

undulation yarns modeled as the response of a curved beam on an elastic foundation, which

includes the effect of yarn splitting; the nonlinear shear response of impregnated yarns

represented by a power law relation; first order effects of geometric nonlinearity due to yarn

straightening or wrinkling; and, there is a stiffness reduction algorithm that is applied when local

damage is detected. As a result of these features in TEXCAD, fiber dominated failure of the yarns

is predicted using a maximum stress criterion for both tension and compression axial yarn stresses

(σ11). Matrix dominated failure within the yarns is predicted using a maximum stress criteria for

each fiber dominated failure mode: transverse tension (σ22, σ33), transverse shear (τ23), and

longitudinal shear (τ12, τ13). Interstitial matrix material failure is predicted by using two failure

criteria: a principal stress criterion (used in the absence of applied shear stresses), and a maximum

octahedral shear stress criterion (used in the presence of shear stresses). Composite failure is

predicted when (i) axial yarn failure is detected anywhere in the RUC, or (ii) all yarns fail in the

same failure mode and failure is detected in the interstitial matrix material [10]

13

Techniques designed for laminated composites involve a combination of failure criterion.

One of the most commonly used criterion accounts for four typical compressive failure modes in

unidirectional composites, matrix failure in tension or compression, fiber matrix shear failure,

fiber buckling, and delamination [11]. In comparison to textile composite failure, specifically

triaxially braided composites, the major failures are shear micro cracking between fiber bundles,

local delamination between plies under compression, fiber kink bands forming under

compression, and micro cracking around the bias rovings under axial tension [1]. Complex

geometry and fabrication anomalies make determination of failure types difficult.

The outputs from TEXCAD include the material properties of the given composite along

with the failure strengths. These strengths can be incorporated in a simple in-plane maximum

stress failure criterion which will be discussed subsequently.

2.4 Manufacturing ProcessComplex material architecture makes material property prediction difficult. Along with the

variables associated with material architecture, damage associated with the manufacturing

process occurs, damage happens during braiding where yarns may become over tensioned or tows

may be frayed. During the curing process often times yarns become crimped or misaligned

decreasing the strength at random locations in the part. Complexity of the part and the technique

used to manufacture the shape also plays a roll in the strength properties of the structure.

14

2.4.3 RTM

Resin transfer molding is a common manufacturing technique that uses a female mold to create

the hard form of the finished product and a vacuum process to pull the resin into the molded

preform and pull all gases out of the mold, creating a part with very few defects.

2.4.4 Inner Flange

The number of braided layers in the web and inner flange is the same, but, as can be seen from the

thicknesses listed in Table 1.1, the thickness of the radially inboard flange is greater than the

thickness of the web. Hence, because of the manufacturing process there is a reduced fiber

volume fraction in the radially inner flange. Reduction of the fiber volume fraction is due to an

increase in the volume of resin in the inner flange. The fiber volume fraction in the inner flange,

, was approximated by , here is the thickness of the web,

is the inner flange thickness, and is the fiber volume fraction in the web. According to

Naik[12], the relationship between the fiber volume fraction and the moduli are approximately

linear. These data from Ref. 6 are for a material with an architecture of [0°18k/± 67.46k], yarn

packing density of 0.75, and axial yarn spacing of 0.2094 in. (5.32 mm). Other than the 3.4°

difference in the braider angle this architecture matches that of the frames. Using slopes measured

from the plots in [12], the reduced moduli for the inner flange are psi and

psi. The variation in the shear moduli with fiber volume fraction is negligible,

so it and other property data for the inner flange are as listed for the web and outer flange in

Table 2.1.

Vf( )i Vf( )i twVfw( ) ti⁄ 0.4307= = tw

ti Vfw

E11 5.836×10=

E22 5.096×10=

15

2.4.5 Outer Flange

Production of the outer flange is done by dividing the layers of the web into two and folding them

over [13]. Eight layers of the web are split into a set of four layers, when folded over a void is

created due to the curvature of the folding process. At the point of splitting of the fabric, a V-

shaped void is created at the web-flange junction. This void was filled with a braided strand of

axial fibers run circumferentially and consolidated with the frame in the resin transfer molding

process as shown in Figure 2.1.

Braided filler strand

MatrixBraided fabric

Fig. 2.1 Geometric discontinuity in the web to outer flange junction created by the manufacturing process.

16

CHAPTER 3 Short Column Compression Tests, Design and Results

Quasi-static compression tests of short columns allows for the study of failure mechanisms

associated with the cross sectional shape of the fuselage frames. The goals of these tests are to

study the mechanisms of failure and to measure the compressive strength of the section with

and without local buckling occurring during the response. Fabrication details can affect the

compression strength. For example, one of the failure events observed in the full frame tests

was the separation from the frame of a ligament of the axial filler strand contained in the

junction of the outer flange and web [9]. In this chapter the design of the specimens and the

results from the testing will be discussed.

3.1 NomenclatureWhile discussing the results of testing, some nomenclature specific to the testing

configuration and cross section is helpful. In Figure 3.1 we define branches of the cross

section and give nominal locations of axial strain gages bonded to the six-inch columns.

17

Because of the frame curvature, the terms inner and outer refer to radial distances from the center

of curvature.

3.2 Preliminary Compression Testing and FEAFlat-end compression tests of unsupported two-inch columns, cut from the undamaged portions of

frame B, were loaded in compression until failure. Loads and end displacements were recorded in

a series of four tests with the fourth test specimen fitted with two sets of back-to-back axial strain

gages on the web and inner flange. Brooming of the column end initiated failure in the inner

flange, which progressed through the web to the outer flange as shown in Figure 3.2.

31 2

View From Front Side

z

x

321

4

Top Viewx

y

Back Side

Front Side

InnerFlange

Back Side Outer Flange

Front Side Outer Flange

11

6 5

10 96 5 11

10 9

Fig. 3.1 General specimen nomenclature along with strain gage locations for the six-inch specimens.

8

12

138 13

18

A finite element model was developed using S4R5 shell elements that included the frame

curvature, 3-D orthotropic material properties, and reduced moduli for the inner flange due to a

decrease in the fiber volume fraction. The buckling load determined from the finite element

analysis was within 2% of the maximum compressive load in the test of the two-inch-long

column. The correlation of the buckling load and the failure load may indicate that local bucking

occurred nearly simultaneously with end brooming failure.

3.3 Short Column DesignBecause a mixture of failure mechanisms were exhibited by the unsupported two-inch columns a

second series of tests with better end supports were designed. Buckling analyses of a linear

prebuckling equilibrium state under specified end shortening were undertaken on shell element

models of various column heights. The axial displacements at buckling were then specified in a

Brooming began here, inner flange.

Progression of failure followed green arrow.

Fig. 3.2 Two-inch short column specimen after failure.

19

separate equilibrium analysis to determine the load at buckling by summing up the nodal reaction

forces predicted by the equilibrium analysis.

Approximate failure displacements for the column heights were determine by the

following simple column strain-displacement relationship.

(3.1)

In Equation 3.1 is the compressive failure strain predicted by TEXCAD as listed

in Table 2.1, is the column height, and is the end-shortening displacement for the

compressive strength failure mode of the material.

When the displacement associated with material failure is less than the displacement at

buckling, a compressive material failure should be observed during testing. By comparing the

displacement buckling results and the displacement for material failure determine by Equation 3.1

a specimen height was chosen for compressive material failure. Analysis indicated that a longer

specimen was likely to be dominated by local buckling, so a reasonable column height was

chosen. To observe a mix of failure mechanisms a height between the material failure and

buckling failure was decided upon. Column heights chosen were 1.5, 4, and 6 inches, these

correspond respectively to compressive material failure, mixed failure modes, and a local

buckling failure. Specimen ends were supported in an epoxy potting mixture to prevent end

brooming and back-to-back strain gages were bonded to the flanges of the specimens in a pattern

to capture local bucking deformations. Axial gages were bonded near the junction of the web and

outer flange to capture the increase in compressive strains at the junction during postbuckling.

εfailure l⋅ ∆l=

εfailure

l ∆l

20

Three of the short column test specimens, one of each length, mounted in the end fixtures with

strain gages attached, are shown in the photograph of Figure 3.3.

Buckling displacements and loads for the chosen column heights are listed in Table 3.1.

For the material failure mode, the end shortening for the1.5-inch gage length specimen was 0.015

inches, which is less than the FEA predicted local buckling displacement of 0.019 inches. There

were two distinct results calculated by ABAQUS for the six-inch specimen, the results are listed

in the last two rows of Table 3.1. When the column was modeled with only the six inch gage

length, the buckling prediction is a sine wave in the radially outer flange. If the column is

modeled with the extra height to include the potting, the buckling shape becomes three half waves

with the central wave having the largest amplitude bordered by two smaller half waves of

Fig. 3.3 Short column specimens mounted in end fixtures with strain gages attached. Column gage lengths are 6, 4, and 1.5 inches.

21

opposite amplitude. The buckling shapes are negatives of each other for the front and back side of

the outer flange.

3.4 Specimen Numbering and OriginThere were three replicates for each height chosen for a total of nine specimens. When these

specimens were cut from the fuselage frames an extra two and a half inches of length was added

to the gage length to account for the potting and machining the specimens flat and parallel. Short

column specimens were cut from undamaged portions of previously tested fuselage frames A and

C [9]. There were three testing sets representing the three heights. Short column data for each

testing set represented two frames; for example, one 8.5 inch section was cut from frame A and

two specimens were cut from frame C to make up the six-inch gage length test set. Complete test

set information is listed in Table 3.2. Frame A was used for material coupons in the previous

frame tests and therefore was not subjected to damage, while frame C was previously loaded

through multiple failures. Specimens were extracted from portions of frame C as far from visible

Table 3.1 Local Buckling Results For Short J-Section Columns From ABAQUS

Gage Length (in)At Buckling

End-shortening (in) Compressive Force (lbs)1.5 0.0191 1091424 0.0168 39074

6 0.0235 34084

6a

a. Model includes extra length of the column potted in the end fixture.

0.0241 33491

22

damage zones as possible. It was assumed that damage was detectable by visible inspection of the

external surfaces, and that no internal damage was present in the sections deemed to be

undamaged. Specimen #3 cut from frame C was about eight inches away from a damage zone,

and #4 was about 4.5 inches away from a damage zone.

The production quality of frame A is suspect, with matrix rich and deprived regions,

surface voids, and misaligned braids and fiber tows. Since these fabrication imperfections are

likely to be present in specimens 7, 8, and 9 cut from frame A, and since the measured failure

loads were consistently around 5,000 lbs lower than failure loads of specimens cut from frame C,

it was determined that the test data for these specimens was not representative of the frame B

material. Hence, the data from tests of specimens 7, 8, and 9 will not be studied further.

3.5 Instrumentation and Test ProcedureSpecimens were fitted with up to thirteen electrical resistance strain gages oriented in the axial

direction. Back-to-back gages were bonded to the flanges of the specimens in a pattern to capture

local bucking deformations. Axial gages were bonded near the junction of the web and outer

flange to capture the increase in compressive strains at the junction during postbuckling. The six-

Table 3.2 Test Set Information

Test SetSpecimen Origin and Numbers

Frame A Frame C1.5” gage length 7 1 & 64” gage length 8 2 & 56” gage length 9 3 & 4

23

inch specimens have thirteen axial gages and the 1.5- and four-inch specimens have nine gages.

Detailed figures of strain gage locations are located in the Appendix A.

The short columns were loaded quasi-statically in compression using a 120 kip universal

testing machine at the NASA Langley Research Center. A photograph of a specimen mounted in

the test frame is shown in Figure 3.4. Specimen response was measured from strain gages and

linear variable displacement transducers (LVDT), and also recorded by digital video.

To insure uniform load distribution and alignment, the specimens were initially loaded

slowly to a level of 10 kips and the strain data was monitored. If non-uniform axial strains

occurred, then shims were inserted under the specimen to achieve a uniform initial compressive

strain. When the initial strain data indicated uniformity, the specimen was loaded until failure.

The testing machine was operated under load control using hydraulic pressure at an approximate

loading rate of 500-1000 lbs. per second. Loading was controlled manually, using fine and coarse

control valves in the hydraulic system. The cross head of the machine is positioned by two large

threaded columns, and these columns are fixed in part to the machine through two large springs.

For the large loads encountered at failure in these tests, the sudden increase in compliance of the

test specimen can cause a momentary dynamic loading condition possibly related to the release of

spring energy. This dynamic response of the load frame was noticeable in the responses

monitored by the instrumentation, and consisted of large measured displacement changes with

negligible amounts of load change.

24

Fig. 3.4 Universal testing machine with six-inch specimen mounted between the cross head and loading platen.

25

3.6 Testing Results

3.6.1 1.5-inch Specimen Results

Failure of the short columns occurred rapidly with little visual and only minimal audible

evidence. Prior to failure popping noises were audible, and small localized surface deformations

were seen in the web. Catastrophic failure of the specimen was confined to a small length along

the load axis in the gage section near one of the potted ends, and extended over the entire cross

section. In this failure zone, matrix fractures followed the bias yarns, plies delaminated, yarns

fractured, and in the web fabric appeared to broom out of plane. Interior layers of the inner flange

crushed and pushed outward causing the surface layers to delaminate.

The 1.5-inch column failed between 63 and 64 kips. Load-displacement response

remained approximately linear throughout the test. No buckling was evident, and the mode of

failure appears to be dominated by material compressive strength.In the video, the inner flange

fails just prior to specimen failure. Failure was dominated by localized crushing and delamination

as seen in Figure 3.5. Localized matrix failures were seen on the surface in 3-4 locations when

loading exceeded 45 kips

26

.Strain gage locations on the 1.5-inch specimen are similar to the six-inch specimen, gage

pairs 1and 2 and 3 and 4 are positioned back to back on the inner flange and web respectively. On

the outer flange, pairs 5 and 6 are on front side with 7 and 8 on the back side. Gages 6 and 8

mounted on the web side of the outer flange. Measuring the strain on the outer flange surface over

the junction is gage 9.

3.6.2 Four-inch Specimen Results

Failure responses for the four-inch columns varied between the specimens. They exhibited

combined failure modes consisting of local buckling of the outer flange and some compressive

material failure of the inner flange. Snap-through occurred in the outer flange of specimen #5

during its local postbuckling response, but did not occur in specimen #2. However, in specimen

#2 the front and back side outer flanges exhibited unsymmetrical bending modes.

Fig. 3.5 Specimen #1, 1.5-inch column after failure.

27

Local buckling of the front side outer flange occurred at a load level of around 38 kips for

both specimens. The buckling mode shape is slightly unsymmetrical and is shown in Figure 3.6.

The crest of the buckling wave appears to be just above the mid height of the gage length. From

video of the test, the back side outer flange buckles in the same shape but with its wave crest just

below the mid height. Localized material failures near the web to outer flange junction coincide

with changes in the flange displacement and shape. As observed from video of the tests, popping

is associated with increased bending of the outer flange. Failure in the outer flange consisted of

cracking and delamination. Prior to cross section failure there is failure and separation of the axial

strand of filler material at the outer flange junction. This leads to crack propagation across the

outer flange. The failure location coincides with a node in buckling wave for specimen #5, and at

a wave crest for specimen #2, as is shown in Figure 3.7.

28

Fig. 3.6 Specimen #2 under load with local buckling of the front side outer flange visible.

Wave CrestMid Height

Fig. 3.7 Specimen #2 after failure.

29

Failure loads were specimen dependent, and occurred at 57 kips and 53 kips for specimens

2 and 5, respectively. Except for some initial take up, and within a few thousand pounds of failure,

loading was very linear with respect to the end shortening displacement throughout the test, as is

shown in Figure 3.8. Near the initiation of local buckling, localized material failures can be seen

and heard as small distortions in the material surface and audible pops. As the load is increased

from initial buckling, the bending deformations in the outer flanges change shape from

unsymmetrical waves to a symmetric half wave. The unsymmetrical buckling shape may be

associated with the slight curvature of the specimen or with uneven support at the gage length

edges. Because the buckling shape was consistent between specimens, material imperfections in

the specimen do not appear to govern the buckling mode shapes.

0

10000

20000

30000

40000

50000

60000

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Lo

ad

(lb

s)

Fig. 3.8 Load versus displacement data for specimen #5.

30

The snap through occurring in specimen #5 is evident in both the LVDT displacement data

shown in Figure 3.9, and in the strain gage data shown in Figure 3.10. Data from LVDT # 2 and

LVDT # 3 in Figure 3.9, indicate that both sides of the outer flange are displacing radially outward

until snap through, and then the front side displaces toward the inner flange. On the outer flange

back-to-back strain gage pairs 5 and 6 are on front side with back-to-back gages 7 and 8 on the

back side. The axial strain reversal of gages 5 and 6 near the applied displacement of 0.050 inches

shown in Figure 3.10 is evidence of the snap through event of the front side flange. Snap through

was not observed with specimen #2

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.00 0.01 0.02 0.03 0.04 0.05 0.06

End Displacement (in)

Fla

ng

e D

isp

lac

em

en

t (i

n)

LVDT 1

LVDT 2

LVDT 3

1

2

3

23

1

Fig. 3.9 LVDT data for specimen #5. Numbers indicate LVDT locations at the mid height of the cross section shown on the right.

31

.

Axial strain measured on the surface of the filler material at the junction is linear with

respect to the end-shortening until snap through occurs at an approximate displacement of 0.05

inches. See Figure 3.11. When the bending response of the front outer flange changes direction

due to snap through, there is an abrupt increase in compressive strain in the filler material, which

precipitates its separation from the junction.

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Co

mp

res

siv

e S

tra

in %

Gage 5

Gage 6

Gage 7

Gage 8

5

6

7

8

Fig. 3.10 Strain response data for the outer flange of specimen #5.

32

Inner flange and web responses are essentially purely compressive until snap through of

the front side outer flange occurs, as indicated by the responses of strain gages 1-4 in Figure 3.12.

Back-to-back gages 1 and 2 are bonded to the surfaces of the inner flange, and back-to-back gages

3 and 4 are bonded to the surfaces at center of the web. When the bending response of the front

outer flange changes direction due to snap through, the amount of bending strain carried by the

web increases drastically as is shown by the responses from gages 3 and 4. The loss of rotational

restraint provided by outer flanges to the web due to snap through, results in the dramatic increase

in web bending. Gage 4 is on the back side of the web and is clearly going into tension in Figure

3.12.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Co

mp

res

siv

e S

tra

in %

Fig. 3.11 Strain response of the axial filler material for specimen #5.

33

3.6.3 Six-inch Specimen Results

The failure response of the six-inch column specimens were fairly uniform. Buckling initiated in

the six-inch columns around 33-35 kips and the columns failed around 50 kips. The load-

displacement response became slightly non linear near the buckling load predicted by FEA.

Buckling was predicted to occur around 34 kips, and during testing buckling of the outer flange

began between 33 and 35 kips. See Figure 3.1 for the nomenclature used to describe the cross-

sectional configuration. The out-of-plane deformation of the front side outer flange changed from

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Co

mp

res

siv

e S

tra

in %

Gage 1

Gage 2

Gage 3

Gage 41

2

4

3

Fig. 3.12 Strain response for the web and inner flange of specimen #5.

34

a single half wave to three half waves along the load axis. The larger amplitude wave in the

middle of the flange deflected toward the inner flange, and the two adjacent smaller amplitude

waves deflected in the opposite sense as shown by the photograph in Figure 3.13. The out-of-

plane displacement of the outer flange on the back side was a single half wave displacing away

from the inner flange, with the amplitude of this back side flange smaller than the amplitude of the

front side flange. The out-of-plane displacement of the web was toward the back side of the

section in a half wave along the load axis and a half wave perpendicular to this axis.

In the postbuckling response and prior to ultimate failure, both sides of the matrix,

surrounding the filler material at the junction of the web and outer flange, fracture along the load

axis. Subsequently the axial filler material failed and separated from the outer flange. Failure

progressed across the outer flange to the edges and through the web to the inner flange. The outer

flange of specimen #3 failed near the node line location of the local buckling mode as shown in

the photograph in both Figure 3.13 and Figure 3.14. However, specimen #4 failed near the

location of the large amplitude buckle crest in the outer flange.

35

Fig. 3.13 Specimen #3 showing local buckling of the outer flange. Noted are the approximate wave crest and node locations.

Wave Crest

Node

36

.

Failure response data for the short columns will be shown in comparison to FEA results in

a subsequent chapter.

Fig. 3.14 Six-inch specimen after failure.

37

CHAPTER 4 Finite Element Analysis of Short Column Compression Tests

Finite element modeling for the compression response of the short column test specimens is

discussed. The finite element analyses include geometric nonlinearity, but the material law is

assumed to remain linear elastic.

4.1 ABAQUS Shell ElementsTwo shell elements from the ABAQUS library were considered; these are elements S4R5 and

S4R [14]. The S4R5 element is a quadrilateral, small strain, thin shell element. Strain

measures are suitable for large rotations but small strains. There are five degrees of freedom at

each of the four nodes; the three displacements of the reference surface, and the two

projections of the change in the unit normal along orthogonal directions tangent to the

reference surface that measure transverse shear strains. To model classical shell theory,

Kirchhoff’s constraints are imposed numerically at a set of reduced integration points on the

reference surface; i.e., a discrete Kirchhoff constraint. The transverse shear stiffness acts as a

38

penalty that enforces the constraint of vanishing transverse shear strains at the set of reduced

integration points. The element formulation accepts the drilling degree of freedom, so that there

can be six degrees of freedom at a node, if six degrees of freedom are specified by the user at that

node, or if the node is in contact with an element containing six degrees of freedom per node.

When six degrees of freedom is indicated at a node, the extra rotational degree of freedom is

constrained locally by applying a small stiffness penalty to a strain measure representative of the

same rotation of the shell’s reference surface.

Element S4R is a quadrilateral, finite-membrane-strain, shell element for use with both

thin and thick shells. It has six degrees of freedom at each node of the four nodes. The shell theory

used depends on the thickness of the element. Thickness change as a function of the in-plane

deformation is allowed. For thick shells a first-order shear deformation theory is used. For thin

shells a discrete Kirchhoff constraint is imposed to reduce the transverse shear deformation.

A comparison of the S4R5 and S4R shell elements was made using the refined mesh

model of the six-inch short column, which will be discussed in more detail in Section 4.5.3 on

page 48. The load end-shortening response plot from the FEA of this specimen is shown in

Figure 4.1. The S4R element predicts a stiffer response in the nonlinear region of the response

plot than the S4R5 element.

Initial analyses of the short column specimens employed the S4R5 element. To improve

the correlation with the six-inch short column tests, element S4R was used as the mesh was

refined. As is depicted in Figure 4.1, the analysis with S4R resulted in a stiffer postbuckling

response, which correlated better with the test data. Also, the six degrees of freedom per node for

element S4R facilitated the use of the decohesion element to model delamination. The decohesion

39

element was implemented in the user-written subroutine UEL of ABAQUS to model progressive

failure, which is discussed in Chapter 6. The S4R element was used in the final analyses where

the element sizes were on the order of a sixteenth of an inch.

4.2 Finite Element Model GeometryCross-sectional dimensions used for finite element modeling are those listed in Table 1.1 for

frame B, which are taken from Ref. [9]. Using the radius of the inner flange, , and the radius of

the outer flange, from this table combined with the desired short column height , the half

5000

20000

35000

50000

0.00 0.02 0.04 0.06

Displacement (in)

Lo

ad

(lb

s)

S4R

S4R5

Fig. 4.1 Comparison of the end shortening results using S4R and S4R5 shell elements.

ri

r0 H

40

angle of the circular arc of the inner flange, , and the half angle of the arc of the outside flange,

, are determined. The basic geometry is specified in the finite element model using

as shown in Figure 4.2. Two cylindrical surfaces representing the flanges were created with radii

and . The area bounded by radii , , and the vertical height represented the flat surface

of the web. The three surfaces were meshed with quadrilateral elements, and then material

properties were assigned to the elements sets constituting these surfaces.

4.3 Element SizeThe element mesh was refined to accurately represent the local buckling witnessed in the front

side outer flange during testing. To capture the buckling deformation, it is usually required to

have about five nodes per half wave. The original element size was on the order of a half an inch,

which was then refined to a quarter of an inch to get improved results. Further refinement was

done to the elements using biased meshing techniques. With the bias meshing tool the initial

ai

a0 ri ai r0 a0, , ,

Mid Plane

Origin

ri

r0

ai

a0

H 2⁄

H 2⁄

Fig. 4.2 Geometry used to create short column models with the correct curvature.

ri r0 ri r0 H

41

element size and the final element size can be selected within a subdomain, then the meshing tool

automatically determines the number and varying element sizes to go from the initial to final

element size. Element sizes ranged from a sixteenth of an inch to a quarter of an inch in the

meshes used for the analyses.

4.4 Displacement ControlLoading was specified by controlled shortening. The node set making up the top edge of the

model was displaced in the negative 3-direction, corresponding to axial compression, and

restrained in all other degrees of freedom. The nodes making up the bottom of the column were

constrained in all degrees of freedom; i.e., clamped.

Both geometrically linear and nonlinear elastic analyses were performed. Linear analyses

were used to see if model fidelity was sufficient to match the initial column stiffness measured in

the tests, but linear analysis is not capable of predicting the shortening at buckling. To determine

the postbuckling load-shortening response, nonlinear analyses use an iterative solution procedure

within each incremental load step. Assuming equilibrium was established at the last load step,

Newton’s method is used to converge to a solution for the next load increment. Load step

increments are automatically determined by ABAQUS. An example of an ABAQUS input deck

for a nonlinear analysis, called hdmsh6.inp, is listed in Appendix B. The initial displacement load

increment is specified as 0.01 in this input deck and the maximum displacement is specified as

0.06. This value of the maximum displacement is specified for the 3-direction of the “DISP” node

set, which is the set of nodes at the top end of the model.

42

4.5 FEA Results and Test Data ComparisonOnly the 1.5- and six-inch columns are analyzed in detail. The 1.5-inch short columns failed

primarily in a material compressive strength mode, while the six-inch short columns failed in a

local postbuckling response mode. The failure of the four-inch short columns was more complex,

and appeared to exhibit combinations of both modes. Since the goal of the short column tests was

to study the mechanisms of compression failure with and without local buckling occurring during

the response, it was decided that the four-inch short column test was less important in assessing

criterion to use for each individual mode in the full frame analysis. Hence, the mixed mode failure

of the four-inch columns would not aid in achieving the goal of the current research and therefore

was not studied.

4.5.1 1.5-inch Column

The finite element model of the 1.5-inch column consisted of 304 S4R5 shell elements and 378

nodes, with element size on the order of a quarter of an inch. The load-shortening response plot

from the 1.5-inch specimen #1 is shown Figure 4.3. The response is nearly linear both in the test

and in the nonlinear FEA. The slope of the load-shortening test data is lbs/in and the

FEA predicts a slope lbs/in, which is a 14.3% discrepancy. The maximum shortening in

the test shown in the response plot is 0.0325 inches at a load of 64,700 lbs. At this same

shortening the FEA predicts at load of 78,000 lbs.

The axial strain responses from back-to-back gages bonded to the front side outer flange

of the 1.5-in. specimen are shown in Figure 4.4 along with the predictions from the FEA. The

2.1 6×10

2.4 6×10

43

strains predicted at these locations from the FEA are labeled as section points S.P.1 and S.P. 3 in

the plot. Section points refer to the location through the thickness of the element where the strains

and stresses are computed. Since the FEA model has one shell element comprising all the lamina

through the wall thickness, S.P. 1 and S.P. 3 are located nearest the external surfaces of the wall.

The strains predicted from FEA correlate very well with the strain gage data until an end

shortening of about 0.029 inches. At this shortening gage 6 reads 1.1% compressive strain and

gage 5 reads 0.55% compressive strain. The discontinuity in the gage responses at the shortening

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0.000 0.010 0.020 0.030 0.040

Displacement (in)

Lo

ad

(lb

s)

Test Data

FEA

Fig. 4.3 End shortening response for specimen #1, 1.5-inch column.

44

of 0.029 inches indicates an initiation of some failure event. The difference in these back-to-back

axial strains, or bending strain, is about 0.58%, and their average, or membrane strain, is about

0.84%. Gage 6 saturates as the shortening increases from 0.029 inches.

In contrast to the response of the outer flange, the bending in the inner flange is negligible

prior to the first major failure event, as is shown by the responses of back-to-back axial strain

gages 1 and 2 in Figure 4.5. The discontinuities in gage 1 and 2 responses occurs at shortening of

0

0.5

1

1.5

2

0.00 0.01 0.02 0.03 0.04

Displacement (in)

Co

mp

res

siv

e S

tra

in %

Gage 5

Gage 6

FEA Section Point 1

FEA Section Point 3

6

5

s.p. 1

s.p. 3

Fig. 4.4 Compressive strain response in the front side outer flange for specimen #1, 1.5-inch column.

45

0.0314 inches where the gages read a compressive axial strain of 0.69%. The axial strain

responses in the inner flange and the web are very similar, so for simplicity only the results for the

inner flange are shown. Video of the 1.5-inch column tests shows the inner flange failing prior to

the failure of the entire cross section, which is not the sequence seen for the six-inch specimens.

The compressive axial strain of 0.69% at the discontinuity in the gage responses is less than the

1% compressive failure strain predicted by TEXCAD for this material. The FEA predicts larger

compressive strains in the inner flange and web than what occurs in the test. At an end shortening

of 0.0314 inches FEA predicts a compressive strain of 0.94%. It is not clear why the correlation

between analysis and test is poorer in the inner flange and web with respect to the good

correlation achieved in the outer flange. The stiffer response of the FEA with respect to the test on

the load-shortening plot in Figure 4.3 correlates with the predictions of the axial strains in the

inner flange and web.

4.5.2 Four-inch Column

The only FEA completed on the four-inch column was a linear ABAQUS buckling analysis. This

analysis used 888 S4R5 shell elements with 950 nodes and an element size on the order of a

quarter of an inch. Boundary conditions and extra length representing the potting was included,

along with curvature and reduced inner flange properties. As can be seen in Figure 3.6 the local

buckling shape of the outer flange is a non symmetric half wave. ABAQUS predicts a symmetric

buckling pattern as shown in Figure 4.6. This discrepancy in the buckling wave pattern between

test and analysis maybe due to the support conditions in the test as idealized in the analysis. The

depth of the potting compound in the fixture varies around the specimen, and this variable depth is

not modeled in the FEA.Though a difficult task, perhaps more attention needs to be given in

46

making the potting resin cure evenly so that potting thickness does not vary around the cross

section of the specimen.

0

0.2

0.4

0.6

0.8

1

1.2

0.00 0.01 0.02 0.03 0.04

Displacement (in)

Co

mp

res

siv

e S

tra

in %

Gage 1

Gage 2

FEA

Fig. 4.5 Compressive strain response in the inner flange of specimen #1, 1.5-inch column.

47

4.5.3 Six-inch Column

Short column specimens 3 and 4 have a six-inch gage length. The FEA model contains 5698 S4R

shell elements and is shown in Figure 4.7. Element size in the model is on the order of a sixteenth

Fig. 4.6 ABAQUS linear buckling results for a four-inch column. On the right is a front on view of the outer flange, showing the symmetric buckling waves on the front and back side outer flange.

48

of an inch, and this refined mesh was developed primarily for the failure analysis to be discussed

in Chapter 6.

The load-shortening data from the test of the six-inch specimen #3 along with the FEA

predictions are shown in Figure 4.8. The analysis and test compare very well in the initial portion

of the response. The initial stiffness is lbs/in from the test data and lbs/in from

the FEA results, which is 3.6% discrepancy. The analysis begins to soften relative to the test data

as the load increases from 30 kips.

Fig. 4.7 Finite element model of six-inch column.

1.1 6×10 1.06 6×10

49

The axial strains responses from back-to-back gages 5 and 6 located on the front side of

the outer flange are shown in Figure 4.9. The strains predicted at these locations from the FEA are

labeled as section points S.P.1 and S.P. 3 in the plot. The FEA and test are in close agreement in

the initial portion of the response but begin to deviate in the postbuckling region. Fair correlation

0

10000

20000

30000

40000

50000

60000

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Lo

ad

(lb

s)

Test Data

FEA

Fig. 4.8 Load-shortening data for specimen #3 and FEA results.

50

is achieved in the postbuckling response regime. At an end shortening of about 0.045 inches gage

6 reads 0.89% compressive strain and gage 5 reads 0.11% compressive strain. As the shortening

increases from 0.045 inches, responses from gages 5 and 6 exhibit at small jump and then the

difference in the strains, or bending strain, begins to decrease.

0

0.2

0.4

0.6

0.8

1

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Co

mp

res

siv

e S

tra

in %

Test Data, Gage 5

Test Data, Gage 6

FEA, Section Point 1

FEA, Section Point 3

6

S.P. 3

5

S.P. 1

Fig. 4.9 Axial strain response for in the front side outer flange of specimen #3 and FEA strain response.

51

The axial strain response from gage #11, which is located on the external surface of the

outer flange just above the web junction, is shown in Figure 4.10. It is along this line that extra

filler material was added in the fabrication process. During fabrication, the eight plies of fabric in

the web of the preform were split into two four ply fabrics to form the outer flanges forming a

void shown in Figure 2.1. Post inspection of the failed specimens revealed fracture surfaces that

progressed in a direction parallel to the load axis in the matrix surrounding the filler material, and

in some instances the filler material separated from the junction. Gages 11 to 13 were located on

the line of filler material to a see if this structural feature influenced failure. As is shown in

Figure 4.10, at an end-shortening displacement about 0.045 in., which corresponds to strain of

0.54%, the gages exhibit a jump suggesting a failure initiating in the junction. Recall that gages 5

and 6 on the outer flange in Figure 4.9 also jumped at this end-shortening displacement. The

junction remains relatively straight during the local postbuckling response of the flange. In

postbuckling the flange carries proportionally less of the direct compression and the junction

carries proportionally more direct compression as the end-shortening increases. A large increase

in the bending response of the flanges between end-shortening displacements from 0.030- to

0.045-inches is evident in Figure 4.9.

52

Back-to-back axial strain gage data from the web indicates a small amounts of bending

occurring in the initial portions of the test as shown in Figure 4.11. The predictions of these strain

responses from the FEA are very good in the initial portions of the test, but the correlation

degrades in the postbuckling response. The FEA predicts a large amount of bending in

0

0.2

0.4

0.6

0.8

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Co

mp

res

siv

e S

tra

in %

Test Data, Gage 11

FEA

Fig. 4.10 Strain response of the filler material at the web to outer flange junction and FEA results.

53

postbuckling relative to the strain gage data. The analysis predicts the back side of the web going

into tension at a lower value of shortening than occurred in the test.

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Co

mp

res

siv

e S

tra

in %

Test Data, Gage 3

Test Data, Gage 4

FEA, Section Point 1

FEA, Section Point 33

S.P. 3

4

S.P. 1

Fig. 4.11 Axial strain response in the web and FEA results for the six-inch column.

54

The back-to-back axial inner flange strains from the test and FEA of the six-inch column

are shown in Figure 4.12. Correlation between the strain gage data and FEA is very good. through

most of the response.

Finite element analysis results for the short columns correlates well in the initial linear

region and fairly well once test data goes non linear. The load drops measured during testing were

not predicted. Further improvements to the analysis need to be implemented.

0

0.2

0.4

0.6

0.8

1

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Co

mp

res

siv

e S

tra

in %

Test Data, Gage 1

Test Data, Gage 2

FEA, Section Point 1

FEA, Section Point 3

S.P. 1

1

2

S.P. 2

Fig. 4.12 Inner flange axial strain response and FEA results for the six-inch column.

55

CHAPTER 5 Frame Segment Finite Element Analysis and Comparison

Finite element modeling for the response of the full 48-degree frame tested in Ref. [3] is

presented. Issues discussed include mesh development, FEA representations of the applied

load, and geometrically linear and nonlinear response analyses. The material law is assumed

to be linear elastic.

5.1 Finite Element ModelFinite element models of frame B [3] were developed in ABAQUS/Standard using the

dimensions listed in Table 1.1, material property data for the web and outer flange listed in

Table 2.1, reduced Young’s moduli as discussed in Section 2.4.4 on page 15, and shell