Computational simulation of woven fabric subjected to ballistic impacts

Fabric deformation of Twaron® CT716 clamped on all sides for impact Figure 10.. Fabric deformation of Twaron® CT716 clamped on all sides for impact Figure 11.. Fabric deformation of Twar

COMPUTATIONAL SIMULATION OF WOVEN FABRIC SUBJECTED TO BALLISTIC IMPACTS

CHING TUAN WOON (B.Eng.(Hons.), NUS)

A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

ACKNOWLEDGEMENTS

I will like to thank my supervisor, Dr Vincent Tan BC, for his most wonderful guidance throughout my project His patience and willingness to accommodate me

as a part-time student is very much appreciated Thanks, Dr Tan

Special thanks too to Eng Kit, Dr Yuan JM, and others, for without their experimental results, there wouldn’t be anything for me to validate my numerical model with I’ll also like to thank Xuesen for his most valuable help regarding numerical modelling of woven fabric

Will also like to thank the staff of LSTC for providing me with an academic license

of LS-DYNA for me to start my simulation work, as well as being so helpful in answering my technical queries concerning the software

Thanks too to Alvin and Joe, for all the help ever rendered to me in the Impact Laboratory

And finally, a big thank you to the people of the Impact Laboratory, without whom the time I spent in the laboratory will be dreadful and boring Here’s wishing all of you the best in your future endeavours!

TABLE OF CONTENTS

ACKNOWLEDGEMENTS i

TABLE OF CONTENTS ii

SUMMARY iv LIST OF TABLES v LIST OF FIGURES vi

6 DISCUSSION 71

SUMMARY

This project proposes a novel numerical method to simulate the ballistic impact of woven fabric by small projectiles The model takes into account various yarn and fabric properties that affects the performance of fabric armour These properties include the rate-dependent property of the yarns, the fabric woven structure and crimp, as well as inter-yarn friction The model also takes into account projectile-yarn friction, and can simulate oblique impacts and different projectile geometries The model uses only 1D elements for the modelling of the fabric, and allows for multiple plies of fabric to be modelled The spacing between the plies of the fabric can also be adjusted The model runs on a commercially available finite-element analysis software

Agreement with experimental results was achieved for 2 different types of woven fabric Insights to the influences of various parameters to the woven fabric penetration process were also obtained

LIST OF TABLES

Table 1 Nominal material properties of Twaron® CT716 14

Table 2 Values of viscoelastic model parameters of Twaron® CT716 15

Table 3 Measured material properties of Kevlar® 218440 19

Table 4 Values of viscoelastic model parameters of Kevlar® 218440 19

Table 5 Numerical Results for Twaron® CT716 clamped on all sides 30

Table 6 Numerical Results for Twaron® CT716 clamped on 2 sides 36

Table 7 Ballistic Limits Obtained For Different Projectile-Yarn COF 42

Table 8 Ballistic Limits Obtained For Different Yarn-Yarn COF 42

Table 9 Numerical Results for 4x4 twill weave Twaron® CT716 clamped on all

sides 45 Table 10 Comparisons of projectile displacement and velocities for clamped-on-

Table 11 Numerical Results for 4x4 twill weave Twaron® CT716 clamped on 2

sides 49 Table 12 Comparisons of projectile displacement and velocities for clamped-on-

Table 14 Numerical Results for Kevlar® 218440 clamped on 2 sides 63

Table 15 Numerical Results for Kevlar® 218440 clamped on all sides 68

Table 16 Numerical Results for 2-ply Kevlar® 218440 clamped on all sides 69

Table 17 Numerical Results for 3-ply Kevlar® 218440 clamped on 2 sides 70

LIST OF FIGURES

Figure 2 Fabric fully clamped on all sides (from [35]) 13

Figure 4 Axial force (N) against time (ms) graph showing relaxation behaviour

Figure 5 Axial force (N) against strain graph showing response of Twaron®

Figure 9 Fabric deformation of Twaron® CT716 clamped on all sides for impact

Figure 10 Fabric deformation of Twaron® CT716 clamped on all sides for impact

Figure 11 Pyramidal shape deformation of fabric (from [34]) 27

Figure 13 Residual velocity (ms-1) against impact velocity (ms-1) for Twaron®

Figure 14 Energy absorbed (J) against impact velocity (ms-1) for Twaron® CT716

Figure 15 Fabric deformation of Twaron® CT716 clamped on 2 sides for impact

Figure 16 Fabric deformation of Twaron® CT716 clamped on 2 sides for impact

Figure 17 Deformation of fabric clamped on 2 sides (from [34]) 34

Figure 18 “Yarn pull-out” effect of fabric (from [34]) 34

Figure 19 Unravelling of yarns at the free edges of fabric (from [9]) 34

Figure 20 Residual velocity (ms-1) against impact velocity (ms-1) for Twaron®

Figure 24 Percentage improvement in perforation time (ms) against impact

velocity (ms-1) for the clamped-on-2-sides model 39 Figure 25 Fabric deformation of Twaron® CT716 for impact velocity = 110ms-1

Figure 26 Ballistic limit (ms-1) against projectile-yarn COF 41 Figure 27 Ballistic limit (ms-1) against yarn-yarn COF 42 Figure 28 Residual velocity (ms-1) against impact velocity (ms-1) for different

Figure 29 Energy absorbed (J) against impact velocity (ms-1) for different fabric

Figure 30 Deformation plot for different fabric weaves for clamped-on-all-sides

model at impact velocities of 110ms-1 (at 0.2ms) 46 Figure 31 Deformation plot for different fabric weaves for clamped-on-all-sides

model at impact velocities of 400ms-1 (at 0.05ms) 47 Figure 32 Residual velocity (ms-1) against impact velocity (ms-1) for different

Figure 33 Energy absorbed (J) against impact velocity (ms-1) for different fabric

Figure 34 Deformation plot for different fabric weaves for clamped-on-2-sides

model at impact velocities of 200ms-1 (at 0.14ms) 51 Figure 35 Deformation plot for different fabric weaves for clamped-on-2-sides

model at impact velocities of 400ms-1 (at 0.05ms) 51

Figure 38 Sequence of fabric deformation for Twaron® CT716 3-ply stacked

system 54 Figure 39 Sequence of fabric deformation for Twaron® CT716 3-ply system with

Figure 40 Residual velocity (ms-1) against impact velocity (ms-1) for different ply

systems 56 Figure 41 Fabric deformation of Kevlar® 218440 clamped on 2 sides for impact

Figure 47 Residual velocity (ms-1) against impact velocity (ms-1) for Kevlar®

Figure 48 Energy absorbed (J) against impact velocity (ms-1) for Kevlar® 218440

Figure 49 Sequence of fabric deformation for Kevlar® 218440 2-ply system with

Figure 50 Sequence of fabric deformation for Kevlar® 218440 2-ply system with

Figure 51 Disintegration of the Twaron® CT716 fabric with actual dimensions 74

Figure 52 Modifications made for Twaron® CT716 fabric 75

Figure 53 “Wedge-through” effect for 2nd modification model 76

Figure 54 Residual velocity (ms-1) against impact velocity (ms-1) for both

Figure 55 Energy absorbed (J) against impact velocity (ms-1) for both modified

models 77

Figure 56 Refined mesh density 78

LIST OF SYMBOLS

σ Fabric yarn stress

ε Fabric yarn strain

K1, K2 Stiffness parameters of 3-element linear viscoelastic model

μ Viscosity parameter of 3-element linear viscoelastic model

K0 Initial stiffness of 3-element linear viscoelastic model

K∞ Long-term stiffness of 3-element linear viscoelastic model

β Decay constant of 3-element linear viscoelastic model

1 INTRODUCTION

The use of body armour by man for protection from injury in combat has been prevalent since ancient times The type of materials used to make such body armour has progressed with the advancement of technology from animal skins in ancient times to metals in the Middle Ages, and to composites made from various types of materials (natural and man-made) in modern times

Aromatic polyamide fibres, better known as Aramid fibres, is one example of made materials that is commonly used in making today’s body armour Details of

man-this fibre is described by Chiao et al in [1] Kevlar® and Twaron® are 2 examples of such fibres These fibres are used to make yarns which are then woven into fabric Woven fabric is commonly used in today’s body armour due to their excellent impact resistance, high strength-to-weight ratio and drapability

It has been determined that the deformation and perforation process of the woven fabric during ballistic impact are influenced by various yarn and fabric properties A review of these properties is given by Cheeseman and Bogetti [2] The design of protective clothing to optimize these properties is typically based on extensive ballistic impact tests These tests consist of firing projectiles of various shapes and sizes into clamped specimens of the fabric The impact and exit velocities of the projectile are measured, and the deformation of the fabric is captured with high-speed cameras

There have also been numerous attempts, noticeably in the last decade, to numerically model the ballistic impact of woven fabric by small projectiles The effects of the yarn and fabric properties on the ballistic impact performance of woven fabric have also been numerically studied These have been made possible with the great advancement made in computing technology

The present study proposes a novel method of numerically modelling the ballistic impact of woven fabric by small projectiles using a commercially available software This method allows for various important yarn and fabric properties that affect the penetration process of the woven fabric to be modelled while using only simple 1D elements for the fabric Various other parameters that affect the penetration process can also be included

Numerical models of 2 types of woven fabrics with different weaving patterns were investigated and compared with experimental results Having successfully validated the models, some parameters were then varied to study their effects on the penetration process

2 LITERATURE REVIEW

2.1 Yarn And Fabric Properties

A brief description of some of the yarn and fabric properties that past researchers have found to influence the deformation and perforation process of woven fabric during ballistic impact is reported in this section

2.1.1 Yarn Material Properties

Shim et al [3,4] performed high-speed tensile tests on Twaron® yarns to investigate their response to dynamic loads The experimental results indicate that Twaron®yarns are highly strain-rate dependent A 3-element linear viscoelastic constitutive model (Figure 1) was found to describe the experimental stress-strain response

reasonably well This constitutive model was also used by Lim et al [5] in the

numerical modelling of Twaron® fabric

Figure 1 3-element linear viscoelastic model

The stress-strain response of this model can be described by

KK

)K

K

2 1

2 + & = + &

where K1, K2 (both representing spring stiffness) and μ (representing viscosity) are

constants pertaining to the yarn material

The stiffness varies in the following manner

t)(exp)K(KK

KKK

KKK

KKK

1 0 2 1

2

=

=+

=

∞

where K∞ is the long-term stiffness, K0 is the initial stiffness, and β is the decay

constant

As explained by Shim et al [3], this 3-element linear viscoelastic constitutive model

is able to represent the primary bond of the fabric fibres with the K1 spring, and the

secondary bond of the fabric fibres with the K2 spring and dashpot As the extension

of the K2 spring is affected by the dashpot, its behaviour during high strain rate

loading will be very limited Thus at high strain rate loading, the behaviour of this

3-element linear viscoelastic constitutive model will be governed mostly by the K1

spring, while the K2 spring will also influence the behaviour of the 3-element linear

viscoelastic constitutive model at low strain rate loading

The strain-rate dependent properties of Kevlar® yarns were also investigated by

Wang and Xia [6,7]

2.1.2 Fabric Woven Structure

Several important effects obtained during the deformation and perforation process of the woven fabric are dependent on its woven structure The type of weave of a fabric was found to affect the performance of the fabric by Cunniff [8] He found that an unbalanced weave resulted in an asymmetric transverse deflection of the fabric This resulted in less material being strained in the fabric, and a corresponding decrease in its performance The plain cross woven structure is commonly used in the construction of the fabric of protective clothing This woven structure will result in the fabric being orthotropic, with the principal directions in the warp and weft directions

Cheeseman and Bogetti [2] noted a “wedge-through” effect during the fabric penetration process During this process, some yarns are pushed aside while some are broken by the projectile, allowing the projectile to slip through The formation of

a hole smaller than the projectile diameter, obtained in experiments done by Shim et

al [3], Tan et al [9], and others bears claim to this effect Cheeseman and Bogetti

[2] attribute the yarn mobility to be a cause of this “wedge-through” effect, with loosely woven fabric being more susceptible to it

The “yarn pull-out” effect, also mentioned by Cheeseman and Bogetti [2], is the pulling out of the yarns from the free edges by the projectile This happens to fabric specimens that are clamped on only 2 sides It was noted that this also resulted in more energy absorption by the fabric This effect was observed to occur in different

degrees with projectiles of different shapes by Tan et al [9] In particular, conical

and ogival projectiles gave rise to the least yarn pull-out, compared to hemispherical and flat-head projectiles

Crimp is the undulation of the yarns due to their interlacing in the woven structure The straightening and realignment of these yarns during ballistic impact will result

in higher fabric deflection, as mentioned by Shim et al [3,4] It was mentioned by Zeng et al [10] that the warp and weft yarns have different degrees of crimp due to

the weaving process, as higher tension is applied to the weft yarns then

2.1.3 Friction

Experiments done by Tan et al [9] showed that frictional effects are more prominent

at lower impact velocities Small patches of fibre breakage at the yarn crossover points could be seen near the impact region for lower impact velocities compared to the cleaner breakage for higher impact velocities It was thought that this was due to more yarns being broken on contact for higher impact velocities Frictional effects are also dependent on the shape of the projectile Three fabric failure mechanisms – fibrillation (the splitting of fibres along its length), flattening and rupturing of the fibres, were also identified

Bazhenov [11] found a decrease in ballistic impact performance for wet Aramid laminates A projectile could successfully perforate a wet 20-ply laminate, but not a dry 14-ply laminate It was noticed that less energy was transferred to yarns away from the impact zone and the width of the yarn pull-out zone was very much reduced for wet laminates It was thought that the presence of water led to a

reduction of friction between the projectile and fabric, resulting in the sliding of the projectile between the fabric yarns

In a study of the effects of inter-yarn friction on ballistic performance of fabric, Tan

et al [12] varied the inter-yarn friction of their fabric samples by impregnating them

with varying concentrations of silica-water suspension It was found that the ballistic limits of their fabric ply systems increased when the concentrations of silica-water suspension was increased, up till a certain weight concentration

2.1.4 Boundary Conditions

Zeng et al [10] investigated how different types of boundary conditions of fabric

targets will affect their ballistic impact response They found that fabrics that were clamped only on 2 opposing sides showed better energy absorption (up to 90%) than fabrics clamped on all sides for lower impact velocities This is due to the large amount of kinetic energy transferred to the fabrics clamped only on 2 opposing sides, brought about by the “yarn pull-out” effect However, for higher impact velocities, the fabrics clamped on all sides could absorb more energy than fabrics that were clamped on 2 opposing sides This is because nearly as much kinetic energy as well as much more strain energy was transferred to the fabrics clamped on all sides at such high velocities They attribute the shorter perforation time of fabrics clamped on all sides to the faster failure of yarns brought about by the reflection of stress waves from the clamped boundaries

2.1.5 System Effects Of Multiple Plies

The system effects of a 2-ply system were investigated by both Cunniff [8] and Lim

et al [13] Cunniff [8] found that a spaced system armour would absorb more

energy than a plied system armour Lim et al [13] found that the response of these 2

systems varied with different projectile geometries and impact velocities In particular, a spaced system absorbed more energy than a plied system at high impact velocities for a spherical projectile

2.2 Analytical Models

Analytical models for predicting the ballistic impact response of fabric have been developed by a number of researchers [14–17] General continuum mechanics equations are typically used in these models for the study of penetration mechanics These models typically make a number of simplifications and assumptions While the simplicity of these models makes them very attractive, such models typically predict only the ballistic limit of the fabric for a given configuration These models very often do not or cannot take into account all the factors that affect ballistic impact

The model of Parga-Landa and Hernandez-Olivares [14] does not include effects of the fabric material during impact It also does not take into account projectile geometry, and accounts for fabric woven structure by making the wave velocity of the fabric a fixed fraction of the wave velocity in a single fibre The model of Walker [15] models fabric as an extended system of linear elastic springs

rate-While it takes into account the mass of the projectile and number of fabric layers, it does not model projectile geometry, friction, and interaction between fabric layers It also assumes no slippage between the fibres Similarly, the model of Billion and Robinson [16] neglects friction and interaction between fabric layers The model of

Gu [17] models fabric as crossed non-woven yarns Although this model does consider strain-rate effects, it does not consider friction nor projectile geometry

2.3 Numerical Models

The Finite Element Method (FEM) is a mathematical tool developed by academic and industrial researchers during the 1950s and 1960s It is used for simulating the response of a physical system when the system is subjected to a set of loads and boundary conditions For this method, the system is discretized into small elements that are connected to each other by nodal points, and their behaviour is represented

by a system of equations For simulation of dynamic cases, the equations are solved incrementally at each time-step Various results, such as displacement and stress, are then derived from the solution The real system with infinite unknowns is thus approximated with a finite number of unknowns With the advance of computing power, FEM has become a powerful design tool Today’s personal computer is able

to solve some practical problems within minutes New capabilities have also been added to the method Today’s FEM software are able to solve structural, thermal, fluid flow, electromagnetic, and even coupled-field problems It has also been used for the simulation of ballistic impact by several researchers

A popular method of modelling fabric with finite elements is to represent them as

networks of 1D elements Shim et al [3], Roylance et al [18], Ting et al [19], and

Cunniff and Ting [20] modelled yarns using such elements pin-jointed at the nodes

Crimp was represented by Shim et al [3] by discounting a fraction of the total strain

of the elements as due to the straightening of the yarns The model of Roylance et al

[18] accounts for crimp and fabric weave structure by providing a means to scale the mass of the fibre elements accordingly Multiple plies were also represented by increasing the numerical density of the fabric, although it was admitted that this approach ignores the interaction between different plies The projectile geometry was also not considered as the projectile impact velocity was applied only to a node

Ting et al [19] and Cunniff and Ting [20] modelled the 1D elements in a

non-coplanar fashion with kinks to represent crimped yarns The nodes of the warp and

weft yarns are coupled together with spring elements in their models Ting et al [19]

modelled multiple plies by coupling different plies with compression elements Their model assumes the plies to be laterally uncoupled, and does not check for

contact between consecutive plies The models of Shim et al [3], Roylance et al [18], Ting et al [19], and Cunniff and Ting [20] do not account for the slippage of yarns Johnson et al [21] and Shahkarami et al [22] also used pin-jointed 1D

elements to model the yarns of the fabric They used shell elements to provide contact surfaces for interactions between the projectile and different fabric layers

Johnson et al [21] modelled crimp by using a bilinear stress-strain relation for the

1D elements

The simple idealization of fabrics as 2D shells or membranes were done by Lim et

al [5], Simons et al [23], Brueggert and Tanov [24], and Tabiei and Ivanov [25,26]

A disadvantage of using these types of elements is the inability to account for the slippage and unravelling of yarns Inter-yarn friction, as well as crimp, could also not be represented

Detailed full-scale discretization of the yarns with solid elements was done by

Shockey et al [27], Blankenhorn et al [28], Borovkov and Voinov [29], Gu [30], and Duan et al [31,32] The advantage of modelling the yarns with solid elements is

that the orthotropic material properties of fabric, inter-yarn friction and crimp can be

realistically modelled However, as acknowledged by Blankenhorn et al [28], the

increased cost due to the large numbers of elements required is a major drawback of this method

The software used by a number of researchers [5,22–32] for their simulations is DYNA (Hallquist [33]) LS-DYNA is a commercially available non-linear, explicit, finite-element analysis software It has been used to successfully simulate various types of impact phenomena

LS-3 METHODOLOGY

Two different types of woven fabric made from different Aramid fibres, Twaron®CT716 and Kevlar® 218440, were modelled in this project The Twaron® CT716 woven fabric is a product of Teijin Twaron, while the Kevlar® 218440 woven fabric

is a product of Barrday

3.1 Experimental Details

The numerical models are based on actual ballistic tests done on 1-ply Twaron®CT716 woven fabric specimens (Tham [34]); as well as 1-ply, 2-ply and 3-ply systems for the Kevlar® 218440 woven fabric (Yuan and Tan [35])

The fabric specimen is constrained in 2 different ways during the ballistic tests It is either fully clamped on all sides (Figure 2) or fully clamped only on 2 opposing sides (Figure 3) The fabric specimens had dimensions of 120mm by 120mm, and the projectile was a steel sphere of diameter 12mm and mass 7g The projectile is propelled normally onto the centre of the fabric target by a high-pressure gas gun, with impact velocities ranging from 80ms-1 to 520ms-1 The experimental setup is

similar to that of Shim et al [3]

Figure 2 Fabric fully clamped on all sides (from [35])

3.2 Woven Fabric Material Properties

The present study uses the 3-element linear viscoelastic constitutive model used

previously by Shim et al [3,4] and Lim et al [5] to model the strain-rate dependent

properties of both types of woven fabric For the modelling performed in this project, this constitutive model is adopted using one of LS-DYNA’s constitutive material model for discrete springs and dampers (*MAT_SPRING_MAXWELL)

3.2.1 Twaron ® CT716 Woven Fabric

The nominal material properties of Twaron® CT716 are listed in Table 1 The values

of the 3 different parameters of the viscoelastic model used in this study for Twaron® CT716 are listed in Table 2

Table 1 Nominal material properties of Twaron® CT716

Specific density (g/mm3) 1.44e-3

(MPa) 9e4 Fibre modulus

(N/dtex) 6.25

Count (warp / weft) (dtex) 1100 / 1100

Density (warp / weft) (ends/mm) 1.22 / 1.22

(1 dtex = 1e-7 g/mm)

Table 2 Values of viscoelastic model parameters of Twaron® CT716

ends/mm22

.1N/strain6875

K

N/strain6875

dtex1100N/dtex 6.25

modulusYarn

The relationship between K∞ and K0 was derived from Equation (2) with the values

of K1 and K2 (which had similar values) used by Shim et al [3]

4193.8N/mm

K21

K21

KK

KKK

0 1

2 1

2 1

Equation (2) was also used to estimate the value of β from the constants used by

Shim et al [3] The derivation of β is as follows

4.62/ms

ms/mm

N 3000

N/mm6930N/mm

where the values of K1, K2 and μ are used by Shim et al [3]

The following figures (Figures 4 and 5) demonstrate the response of the 3-element

linear viscoelastic constitutive model used to model Twaron® CT716

Figure 4 shows the relaxation behaviour of Twaron® CT716 This figure shows how

the force required to extend a unit length of Twaron® CT716 by a constant strain of

1 will decrease exponentially from 8386N to a constant value of 4194N

Figure 5 shows the response of Twaron® CT716 subjected to varying strain rates It

can be seen that for very high strain rates, the stiffness of Twaron® CT716

(represented by the gradient of the curves) remains fairly constant As the strain

rates decreases, there is an increase in the rate at which the stiffness decreases The

stiffness of Twaron® CT716 will thus be lowest for the smallest strain rate

Figure 4 Axial force (N) against time (ms) graph showing relaxation behaviour of Twaron® CT716

3.2.2 Kevlar ® 218440 Woven Fabric

The measured material properties of Kevlar® 218440 [35] are listed in Table 3 The

values of the 3 different parameters of the viscoelastic model used in this study for

Kevlar® 218440 are listed in Table 4

Table 3 Measured material properties of Kevlar® 218440

Density (warp / weft) (ends/mm) 0.9 / 0.9

ends/mm9

.0N/strain12616

The value of K∞ is also estimated to be ½K0, and the value of β is estimated simply

as a rounded-up value of that used for Twaron® CT716

3.3 Finite Element Model

The 3-element linear viscoelastic constitutive model found in LS-DYNA (*MAT_SPRING_MAXWELL) is for discrete springs and dampers elements, and models only the stress-strain response The mass and volume of the fabric yarns are accounted for by using truss elements modelled using a null material model This type of 1D element has 3 degrees of freedom at each node and carries only an axial force It was used as it was deemed the most appropriate for modelling fabric yarns The truss elements were assigned a circular cross-sectional area as the fabric yarns were simplified as being cylindrical in shape

Every fabric yarn element modelled thus consists of a truss element superimposed onto a discrete springs and dampers element The truss element will account for the mass and contact surface of the fabric yarns, while the discrete springs and dampers element will account for the strain-rate dependent stiffness

The warp and weft yarns of the fabric are not tied to each other, and are free to interact and slide along one another Another important reason for using LS-DYNA

to model the ballistic impact of fabric (besides it having the 3-element linear viscoelastic constitutive model) is that one of its contact algorithms checks the entire length of 1D elements for penetration This feature allows yarns to be modelled by 1D elements efficiently, and is extensively used in this study

The fabric yarn elements are modelled using a length consistent with the actual spacing of the fabric yarns The nodes of the warp and weft yarns elements will thus

be vertically aligned at the crossover points of the fabric This length was used as it

is the longest length that can still accurately account for the fabric structure The

horizontal spacing of the fabric yarn elements is also similar to that used by Shim et

al. [3] A total of 84680 1D elements (42340 discrete springs and dampers elements and 42340 truss elements) were used to model the fabric

The Twaron® CT716 woven fabric has a plain cross woven structure, as can be seen

in Figure 6 The Kevlar® 218440 woven fabric has a more complicated woven structure, that of a 4x4 twill A diagram of the fabric mesh for the Kevlar® 218440 woven fabric can be found in Figure 7

0.828mm

Figure 6 Mesh of Twaron® CT716 woven fabric

1.15mm

1.11mm

Figure 7 Mesh of Kevlar® 218440 woven fabric

As can be seen in both Figures 6 and 7, the fabric yarn elements are modelled in a non-coplanar manner with kinks to represent crimp It was assumed that the crimp in the warp and weft directions are the same The thickness of the actual Kevlar®

218440 woven fabric is 0.6mm Hence the yarns were modelled with cylindrical truss elements of 0.15mm radius This meant that the yarns at the crossover points will initially be in contact with one another Given that the weave density is 0.9x0.9 ends/mm, the length of each yarn segment between crossover points shown in Figure

7 works out to be 1.11mm for the straight elements and 1.15mm for the kinked elements

A similar way of modelling the Twaron® CT716 woven fabric shown in Figure 6 was attempted The Twaron® CT716 woven fabric has a thickness of 0.4mm and weave density of 1.22x1.22 ends/mm Hence it was initially modelled with

cylindrical truss elements of 0.1mm radius, so that the yarns at the crossover points will also initially be in contact with one another However, this model seemed to display an extremely “brittle” characteristic, with the fabric disintegrating in a very unrealistic manner on impact Two other models with modified dimensions were subsequently generated and tried The model that was eventually chosen has cylindrical truss elements of 0.05mm radius with crossover points initially in contact with one another The length of each yarn segment between crossover points works out to be 0.828mm More details of these Twaron® CT716 woven fabric numerical models can be found in Section 6.2

It should be noted that the densities of the fabric yarns for both woven fabrics were adjusted to account for the correct fabric mass

In order to allow for fabric perforation, the truss elements were modelled with individual nodes joined together with spot-weld constraints These constraints were defined to fail when the truss elements of the fabric experience a tensile strain of 5%

in the axial direction of the fabric yarns No shear failure was defined This type of constraint allows the truss elements to rotate freely about the constrained nodes The failure strain of 5% was based on the fabric fibres primary bond failure strain used

by Shim et al [3] The fabric fibres primary bond failure strain, which is equivalent

to the high strain rate failure strain as explained in Section 2.1.1, was chosen as it

was found by Shim et al [3] to be the cause of fabric fibres failure during ballistic

impact due to the high strain rates experienced

Friction was introduced between the projectile and fabric, as well as between the warp and weft yarns of the fabric A value of 0.2 was used for the coefficient of friction between yarns as well as the coefficient of friction between fabric and steel for both types of yarns This value is an estimate of the friction coefficient based on the measured value of 0.22 for the friction coefficient of Kevlar® 49 yarns [36]

Two different sets of boundary conditions were used for the simulations One set has the fabric perfectly clamped on all sides, while the other set has the fabric perfectly clamped on 2 opposing sides

The projectile was simply modelled as a rigid sphere, and assigned the mechanical properties of steel The projectile was modelled to impact the centre of the fabric in

a normal direction A plan view picture of the entire numerical model is shown in Figure 8

Figure 8 Entire numerical model

4 TWARON® CT716 WOVEN FABRIC RESULTS

4.1 Single Ply Model

4.1.1 Clamped-On-All-Sides Model

The deformation plots of the clamped-on-all-sides model subjected to impacts at velocities of 110ms-1 and 400ms-1 can be found in Figures 9 and 10 These 2 velocities are chosen because they represent low impact velocity and high impact velocity loading respectively The impact velocity is considered low if the transverse wave reached the fixed edges prior to complete penetration, as can be seen in Figure

9, while it is considered high if complete penetration of the fabric was achieved before the transverse wave could reach the fixed edges, as can be seen in Figure 10

The plots also show that the pyramidal shape deformation observed in high-speed photographs of the ballistic impact experiment (Figure 11) is also obtained by the numerical model It can be seen that for both impact velocities, tearing of the fabric yarns occurs only at the projectile impact region

for impact velocity = 110ms-1

0.03ms

0.05msFigure 10 Fabric deformation of Twaron® CT716 clamped on all sides

for impact velocity = 400ms-1

The deformation plots of Figure 12 show that as the projectile penetrates the fabric, some of the yarns are broken while some are pushed aside by the projectile It can be seen that the pushing aside of the yarns allows the projectile to slip pass through The “wedge-through” effect can clearly be seen in this numerical model

Figure 12 “Wedge-through” effect

Figure 13 shows a plot of the residual velocity of the projectile against its impact velocity This plot also includes experimental data (Tham [34]) A similar plot, for energy absorbed by the fabric (calculated by the loss in kinetic energy of the

projectile) against impact velocity of the projectile, can be found in Figure 14 The results are listed in Table 5

Figure 13 Residual velocity (ms-1) against impact velocity (ms-1)

for Twaron® CT716 clamped on all sides

Figure 14 Energy absorbed (J) against impact velocity (ms-1)

for Twaron® CT716 clamped on all sides