FIBER REINFORCED UNI-DIRECTIONAL AND
PLAIN WOVEN COMPOSITES: MECHANICAL
JUNE 2020
LOW VELOCITY IMPACT STUDY ON BASALT
FIBER REINFORCED UNI-DIRECTIONAL AND
PLAIN WOVEN COMPOSITES: MECHANICAL
Submitted
in fulfilment of requirements for the degree of Doctor of Philosophy
to the
June 2020
Dedicated to
and my parents
i
CERTIFICATE
This is to certify that the thesis entitled, “Low Velocity Impact Study on Basalt Fiber
Reinforced Uni-Directional and Plain Woven Composites: Mechanical
Characterization and Numerical Modeling” submitted by Mr. Mohit Gupta for the
award of degree of Doctor of Philosophy to the Indian Institute of Technology Delhi is
a record of bonafide research work carried out by him under our guidance and supervision.
Mr. Mohit Gupta has fulfilled all the prescribed requirements and the thesis is, in our
opinion, worthy of consideration for the degree of Doctor of Philosophy in accordance with
the regulations of the Institute. The contents of this thesis have not been submitted in part
or in full to any other University or Institute for the award of any degree or diploma.
Place: New Delhi
Date: 30-06- 2020
iii
ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to my supervisors Prof. Puneet
Mahajan, Prof. Bent F. Sørensen and Dr. R.T. Durai Prabhakaran for their valuable
guidance, inspiration, consistent encouragement, motivation and support during my
research tenure. I admire their immense knowledge and fruitful discussions which helped
me to think and conduct research in a meaningful way without which the work would not
have been realized.
I was in continuous guidance under my research guru Prof. Puneet Mahajan for
the time spent with him was constructively meaningful to cultivate the essence of research
and strengthen my basics. I completely admire him for his patient and understanding nature
during our interactions. His unwavering support helped me a lot, both professionally as
well as on personal fronts.
I would like to thank my research committee comprising of members, Prof. Naresh
Bhatnagar, Prof. B.P. Patel and Prof. Maloy K. Singha for their valuable suggestions
during my presentations and one to one discussions. I am also thankful to Prof.
Alagirusamy for sharing his valuable knowledge in my research work and providing me
his assistance during my research tenure.
I would sincerely like to thank Dr. Harpreet Singh for his wonderful support in
many aspects of my research. He is a wonderful human with abundance of knowledge. I
will never forget all the constructive dialogues we shared that paved the way for my
research. I would like to thank Ashraf for helping me out in manufacturing of samples and
conducting experiments and Sriram for helping me in carrying out Micro-CT scans.
I was really fortunate to meet two really wonderful persons Anurag Kumar Singh
and Adnan Ahmed, for they have been my “brothers in trenches”. Their friendship and
iv
unconditional support under any circumstances made the time spent during research a really
wonderful and memorable one. I would like to thank Vishakha Kaushik for her unending
support. The hard time spent completely unruffled played a crucial role, for which I am
really thankful to Saurabh, Arzoo, Karnika and Aditya to be ever present for hangouts.
I am thankful to Dr. Sangeeta Khare for her valuable suggestions and great support
during my lab hours. I would like to thank my seniors Dr. Rajneesh, Dr. Kiran, Dr. Atul,
Dr. Chaman, Dr. Jitendra, Dr. Aswani and Dr. Praveen for their support and valuable
tips during my research. I also like to thank Amit Yadav for being a wonderful neighbour
both in lab and hostel and for his kind support. I would like to thank all my computational
lab members for providing a healthy environment in the lab for research. I am glad to have
friends like Mayank, Shitanshu and Gaurav for their wonderful support. A big thanks to
the lab staff members Mr. Rishi, Mr. Anil and Mr. Madan for preparing and helping me
in assisting me in conducting experiments in the labs of the department.
I would like to thank my brother Mudit and his wife Kanuj for their loving and
caring nature which has been a constant support system during my research.
Two amazing persons in my life, my parents, nothing can be compared to their
unconditional love and untiring support in all the dimensions of my life. They have done
so much more than they’ll ever know. I am completely blessed and grateful to have such
parents. My sincere gratitude to you both for all your love and blessings. Lastly I would
like to thank a very important person in our life, my spiritual guru Shri Kamal Singh
Yadav Ji for his blessings, thoughtful discussions and un-comparable motivation.
Mohit Gupta
v
ABSTRACT
Composites are made up of two or more constituent materials in order to utilize the
advantages of both the constituents to provide excellent properties like high specific
stiffness, high specific strength, good corrosion and fatigue resistance etc. However, their
sensitivity to impact damage arising due to tool drops, hail stones, bird strike etc. poses
serious threats as the damage is tough to detect from visual inspection. Besides impact use
of less environmental friendly fibers and matrix materials are also a cause of concern in use
of composites. Basalt, a mineral fiber obtained from rocks requires less chemicals during
processing compared to glass and carbon, but its composites are less explored in their
mechanical performance and low velocity impact (LVI) behavior. The present thesis
emphasizes on developing constitutive models for Uni-Directional (UD) and Plain Woven
(PW) lamina and their mechanical characterization for providing inputs to the proposed
models to simulate numerically the response under LVI cross-ply and PW laminates.
Tensile and compressive tests were conducted on UD and PW laminates to evaluate
the moduli and strengths of lamina in longitudinal and transverse directions. Intralaminar
fracture toughness in tension and compression were obtained using Compact Tension (CT)
and Compact Compression (CC) tests. The interlaminar fracture toughness energies were
determined in Mode-I and Mode-II testing configuration using double cantilever (DCB)
and end-notch flexural (ENF) tests to model the delamination between plies. Shear tests
were performed to measure the modulus, shear strength and the non-linear behavior arising
from both damage and plasticity. Cyclic off-axis tests were performed and using effective
stress concept damage was decoupled from the plasticity in the non-linear stress strain
curves under off-axis loadings to obtain the parameter of general quadratic yield function.
vi
Continuum Damage Mechanics (CDM) based elasto-plastic constitutive laws were
developed for both UD and PW lamina using a three-dimensional plastic potential function.
The elastic stiffness in different directions was degraded once damage initiation criteria
were satisfied. In UD lamina model damage was assumed in principal material directions
and damage variable in shear was a function of the damage variables in these directions. In
PW lamina variables independent shear damage variables and damage laws were used.
Exponential damage evolution laws used material softening parameter ‘m’ for a particular
mesh size was determined for principal directions in tension and compression its value was
related to the experimentally obtained intralaminar fracture toughness. Delamination
between plies was modeled using surface based cohesive zone modeling (CZM) for
predicting delamination damage between plies. Experimentally determined interlaminar
fracture energies were used in CZM. These constitutive models for UD and PW materials
were implemented in a user subroutine, VUMAT for ABAQUS/Explicit and used to predict
the force-time, displacement response of laminates of these materials under LVI.
LVI experiments at different impactor velocities were also performed on cross-ply
and PW laminates using drop weight impact tester. The force-time and displacement
response from the simulations matched with those obtained from experiments. The extent
of damage from simulations also matched well with damage measured using ultrasonic C
scan. The constitutive models for UD and PW lamina were thus validated.
vii

, ,

, , ,


,
,
(LVI)
- (UD) (PW)

LVI - PW


UD PW
(CT) (CC)
-I
- II () -
() ,
-
-
viii
-
()
- -
UD PW
, UD

PW
’m’



(CZM) CZM
UD PW
, VUMAT
(ABAQUS/Explicit) LVI -,

LVI - - PW
-

UD PW

ix
CONTENTS
1.2 Basalt as an alternative to glass 4
2.0 LITERATURE REVIEW 7
2.2 Damage and its mechanism in composites 8
2.2.1 Modeling strategies of failure in composites / Failure
initiation criteria’s in composites
10
2.4.2 Failure Mechanics due to LVI 17
2.4.3 LVI response of UD, cross-ply and PW laminates 20
2.5 Basalt Fiber 22
2.5.2 LVI on Basalt cross-ply and PW laminate 24
2.6 Gaps in literature 25
2.7 Research Objectives 26
2.9 Summary 28
LAMINATES
29
x
laminates
30
DIC
32
3.3.2 Experimental setup and test procedure 32
3.4 Determination of BFRP (Basalt Fiber Reinforced Polymer)
composite properties
3.4.4 Interlaminar Fracture toughness (Mode-I) 44
3.4.5 End Notch Flexure characterization (Mode-II) 46
3.4.6 Characterization of Intralaminar Fracture Toughness in
fiber direction
3.6 Summary 55
UNI-DIRECTIONAL AND PLAIN WOVEN LAMINATES
57
4.3.1 Intralaminar Damage propagation 66
4.3.2 Plasticity model for UD lamina 67
4.4 Intralaminar Failure Initiation criteria in PW lamina 71
4.4.1 Plasticity Model for PW lamina 74
4.4.2 Inter-Laminar damage using cohesive surfaces 81
4.5 Computational procedure 83
5.1 Drop weight impact tester 85
5.2 Digital Image Correlation (DIC) 89
xi
5.3.1 Explicit FE formulation 96
5.3.2 FE simulation model specifications of LVI 97
5.4 Summary 98
6.1 Comparison of Impact experiments for basalt/epoxy and
glass/epoxy cross-ply laminates
6.3 Impact response of BPW laminates 107
6.4 Discussions 116
6.5 Summary 118
7.0 CONCLUSIONS 119
7.3 Future scope of the work 122
REFERENCES 123
1.1 Percentage of total structural weight attributed to composites over
the years [A. safety 2011] 2
1.2 Typical testing pyramid for airframe structure development.
[MAAXIMUS 2010] 3
2.1 Schematic representation of individual failure modes in composite
(a) fiber fracture, (b) fiber pullout (c) fiber kinking (d) fiber-matrix
debond (e) matrix cracking
Cole 1999] 10
2.3 Accidental tool drop and a typical BVID curve 15
2.4 Classification of types of impacts for composites based on
penetration energy 16
2.5 Classification of types of impacts for composites based on impact
duration (Olsson 2000) 17
2.6 Types of matrix cracks (a) shear cracks (b) tension cracks [6] 18
2.7 (a) Pine tree pattern, (b) Inverse pine tree pattern of cracks in
impacted laminates [Abrate 1998] 18
2.8 Delaminations in Cross-ply Laminate [Alvarez 1998] 19
3.1 Schematic architecture and actual images of BUD and BPW fabrics
used for preparing laminates 30
3.2 Vacuum assisted resin infusion setup 31
3.3 Typical random black speckle pattern over white base paint 32
3.4 Experimental setup consisting of 3-D DIC and Zwick testing
machine setup 35
3.5 Failed longitudinal tension specimens 36
3.6 Stress-strain plots for longitudinal tension test of BUD and BPW. 36
3.7 Stress-strain plots for longitudinal tension of BUD specimen 37
3.8 Experimental setup consisting of 3D DIC and MTS testing machine
setup for compression tests. 38
xiv
3.9 Stress-strain plots for longitudinal compression for BUD and BPW
specimens 39
3.10 Stress-strain plots for transverse compression of BUD specimen 39
3.11 Specimen description for Iosipescu shear test 40
3.12 Iosipescu test setup showing shear test specimen under test on a
DAK UTM 41
3.13 Shear strain distribution obtained from DIC for a BPW specimen 41
3.14 Tested specimen of basalt laminate under shear for (a) BUD showing
splitting at notch roots (b) BPW showing no splitting due to fiber
interlacement
42
3.15 Average shear-stress shear-strain plots for BUD and BPW Iosipescu
shear specimen 43
3.16 (a): Schematic representation of DCB test specimen with total length
of the beam ‘L’, total beam thickness ‘2h’, initial crack length ‘a0’,
instantaneous crack length ‘a’ during tests. (b) BUD DCB test
specimen under progress with extended UTM display and
instantaneous crack growth being captured simultaneously.
45
3.17 Mode-I fracture toughness plots for (a) BUD and (b) BPW
specimens 45
3.18 Schematic representation of ENF test specimen 46
3.19 Setup for Compact Tension and Compact Compression on a DAK
UTM 47
3.20 (a) Schematic diagram showing the CT specimen dimensions. (b)
Instantaneous crack detection using DIC for CT specimen under
load.
48
3.21 R-curve for the tensile fracture toughness tests using CT specimens
of (a) BUD cutting across 0° fibers and (b) BPW cutting across warp
or weft fibers.
48
3.22 (a) Frctured surface of CT testwith a crack perpendicular to loading
direction. (b) 3D-reconstructed model from the Micro-CT scan
images of the CC tested specimen. The cut-section slice image shows
a 53.2° fractured plane formed due to compression.
49
xv
3.23 (a) Schematic diagram showing the CC test specimen dimensions.
(b) Instantaneous crack monitoring using DIC for a CC test. 50
3.24 R-curve for the compressive fracture toughness tests using CC
specimens of (a) BUD 0° and (b) BPW 0° fibers. 50
3.25 Experimental test setup for pure epoxy tension and compression
tests. 53
3.26 Tested specimens of pure epoxy under tension and compression. 54
3.27 Stress-strain curves for cyclic tests for pure epoxy specimens loaded
in (a) tension and (b) compression. 54
4.1 Schematic representation of effective configuration of material with
stiffness E and area A0 is equivalent to the damaged configuration
with modulus E and area (A0-AD)
59
4.2 Effect of damage on stress strain behaviour of material at various
strains when loaded and unloaded during damage propagation 60
4.3 A typical stress-strain response for a material showing elastic-plastic
regime. B- yield point, C- Damage initiation point (σS), F- failure
point with failure strain (εf). BC is the non-linear portion due to
plasticity only, CE unloading in absence of damage, DE unloading
in presence of damage.
4.4 Failure modes of a laminate subjected to LVI. 63
4.5 Stress states on a fracture plane inclined at an angle "θ" [Namala,
2013]. 64
4.6 Single ply of UD fabric showing coordinate directions 1, 2 and 3. 65
4.7 (a) Schematic depicting a loaded off-axis tensile specimen with
stresses at an element within at an angle φ, (b): Strain contours
showing from DIC for a 30° off-axis BUD specimen loaded in
tension.
70
4.8 (a) Stress vs Total strain for 20°, 30° and 40° off axis specimens. (b)
Effective Stress- effective plastic strain plots for a66=2.1 70
4.9 Single ply of PW fabric showing coordinate directions 1,2 and 3 71
4.10 Stress-strain curve for out of plane compression test 74
4.11 Yield surface shown in shear stress space 75
xvi
4.12 Cyclic (red) shear stress strain variation is used to find damage
variable, ‘D’ which is calculated using degraded stiffness. Effective
stress-strain curve (purple) is obtained from monotonic stress-strain
curve (blue) using the damage variable ‘D’ obtained via cyclic curve.
77
4.13 Strain contours εxx for 30° off-axis tensile test of BPW specimen 77
4.14 (a) Cyclic stress strain data (b). Monotonic with actual (with-
damage) and effective (without damage) stress-strain data for three
specimens subjected to tensile load in 20°, 30° and 40° to the fiber
direction.
78
4.15 Equivalent stress - equivalent plastic strain data for three off-axis
tests (20°, 30° and 40°) 79
4.16 Shear stress-shear strain experimental and effective curves and their
simulated curves 80
strain curves 80
procedure for an integration point 83
5.1 Impactor Tup with mounting head 86
5.2 (a) Schematic of velocity flag (b) Double edge velocity flag with
infrared beam source 87
5.3 Schematic showing how energy plots and force deflection plots are
obtained. 89
5.4 Details of extrinsic calibration parameters of stereo system (a)
Optical axis rotation (α) and stereo angle (β) (b) Tilt (γ) 90
5.5 (a) Schematic diagram of LVI tester with 3D DIC High speed camera
system (b) Camera positioning for imaging speckles on laminate and
tup simultaneously. (c) Front view of the impactor assembly with
various parts.
91
5.6 DIC analysis for (a) Velocity calculation of the tup during the impact
event (b) Deflection analysis of the plate during impact. 92
5.7 Complete setup of impact tester and high speed imaging using DIC
for deflection analysis on the laminate surface. 94
xvii
5.8 Assembly of tup attached to the falling mass, laminate and laminate
holder to manually grip the laminate 94
5.9 Velocity profile of the falling and rebounding impactor tup along the
force profile for a 10 J impact test 95
5.10 Contact force between deformable target and rigid impactor. 97
5.11 Boundary conditions and simulation model details used for impact
analysis 98
glass/epoxy laminates and (b) cross-ply basalt/epoxy and BPW
laminate for 10 J, 20 J and 30 J.
102
levels of impact energy. (a) force-time history and (b) impactor
energy-time history
levels of impact energy. (a) Central deflection-time history and (b)
Force-Deflection history
Ultrasonic C-scan of Basalt/Epoxy Laminates (c) Numerical
Simulation prediction of Basalt/epoxy laminates
105
6.6 Micro-CT scan of the impacted laminate at 30 J impact energy 106
6.7 Load-time and deflection-time plots for average of three experiments
each at 10 J, 20 J and 30 J. (square markers with continuous line
show load data, while circular dots with no connecting line show
deflection data).
108
6.8 Load versus time plots for (a) 10 J, (c) 20 J, (d) 30 J and absorbed
energy versus time plots for (b) 10 J, (c) 20 J, (f) 30 J impact energies 110
6.9 Deflection versus time plots for (a) 10 J, (c) 20 J, (e) 30 J and load
versus deflection plots for (b) 10 J, (c) 20 J, (f) 30 J impact energies 111
6.10 (a) Indent depth obtained from impact simulation (b) Micro-CT
scans of BPW specimen from 30 J impacted laminate showing
impact non-impact sides dent formation. (c) Sliced image of the cut
112
xviii
section of the dent from the middle with dent diameter and dent depth
dimensions (all dimensions in mm).
6.11 Comparison of DIC (experimental) deflection at 3 points marked P1,
P3 at 10 mm and 20 mm away from impactor tip with their
corresponding numerical plots of deflection-time at 30 J energy
level.
113
6.12 (a) Points A, B, C shown over the load-time and deflection-time plots
for 30 J impact simulation. (b) Stress and damage analysis of the
most critical element for 30 J impact simulation. (These stresses are
normalized by dividing the corresponding strength.) (c) Figure
showing the position of the critical element, 5th element from center
at a distance of 4 mm.
114
6.13 Comparison for in-plane and out-of plane plastic shear strains at point A
(t=3.7 ms). Contours below shows the superimposed out-of plane plastic
shear strains 13
& 23
at time interval A (t= 3.7 ms), B (t=5.2 ms) and C
(t=8.5 ms) during the impact event.
115
6.14 Damage area comparison between (a) Ultrasonic C-scan of BPW
Laminates (b) Numerical Simulation prediction of BPW laminates
(all dimensions in mm).
LIST OF TABLES
2.1 Properties of E-glass and basalt fibers [Fiore et. al. 2011] 23
3.1 Specimen specifications for different tests performed 34
3.2 Mechanical properties summary for BUD and BPW lamina 43
4.1 Characteristic lengths and their corresponding fracture energy values
for different intralaminar fracture modes 67
4.2 Off-axis test plasticity parameters for UD lamina 71
4.3 Plasticity parameters obtained from BPW off axis tests 78
5.1 Impact experiments specification 89
6.1 Comparison of impact data analysis for basalt/epoxy vs glass/epoxy 102
xxi
0 A Total cross section area
D Scalar damage variable
DE Effective modulus due to degradation of an isotropic material
0S Compliance tensor
11 22
33 Nominal stresses in longitudinal, transverse and out of plane direction
12 13
23 Shear stresses for in-plane and out of plane directions
Eij Young’s modulus
I Second order identity tensor
11D 22D 33D Damage variables in plane fiber, in plane transverse and out of plane
transverse directions
44D 55D 66D Damage variables for in-plane shear, and out of plane shear directions
11e 22e 33e Effective stresses in longitudinal, transverse and out of plane direction
12e 13e 23e Effective stresses for in plane transverse and out of plane transverse
directions
xxii
1CS Longitudinal Compressive strengths
2CS Transverse compressive strengths
R1C Longitudinal direction compression failure criterion
R2C Transverse direction compression failure criterion
3CR
Out-of plane direction compression failure criteria
n,l and t Refers to normal, longitudinal and tangential direction with respect to the
fracture plane direction
66a Single parameter plastic variable
e Effective equivalent stress
f Effective flow stress
(σ e ) xx
Effective applied stress
ε x p Plastic strain in the uniaxial direction of the specimen
yieldF Plastic potential function
p
e Napier’s constant
m Material softening parameter
transverse compression, out of plane compression.
xxiii
C Intralaminar fracture toughness
cL Characteristic length of the element for a particular damage mode
f
m
Total strain
DIC Digital image correlation
UTM Universal testing machine
DCB Double cantilever beam
ENF End notch flexure
ASTM American society for testing and material
LED Light-emitting diode
CCD Charge-coupled device