A Numerical Investigation into the Effects of 3D ...

SECOND WORLD CONFERENCE ON 3D FABRICS AND THEIR APPLICATIONS April 6-7, 2009, Greenville, South Carolina, USA

A Numerical Investigation into the Effects of 3D Architecture on the Impact Response of Flexible Fabrics Gaurav Nilakantan a,b, Michael Keefe a,d, John W. Gillespie Jr. a,b,c,* Travis A. Bogetti e, Rob Adkinson e a

Center for Composite Materials Department of Materials Science and Engineering c Department of Civil and Environmental Engineering d Department of Mechanical Engineering University of Delaware, DE 19716, USA b

e

US Army Research Laboratory Aberdeen Proving Ground, MD 21005, USA

ABSTRACT In this study, the impact response of 3D fabrics consisting of layers of in-plane unidirectional tows in the warp and fill directions that are interlaced with tows in the thickness direction (z-tows) are studied. Specifically, the role of z-tows on momentum transfer, energy dissipation, transverse wave propagation, dynamic deflection, and separation of warp and fill layers will be considered. Computational modeling and simulation of flexible 3D fabrics using a finite element analysis is challenging because of the complexity of the tow geometry and three dimensional architecture. In this paper, we consider the architecture of a 3D 100 oz 3WEAVETM S2 fabric from 3TEX, Inc. A finite element (FE) model that incorporates the actual geometry and undulations of the warp, fill, and z-tows obtained from micrographs is presented. The FE model is used to simulate a series of transverse impact tests and is implemented in the commercial code LS-DYNA®. The role of z-tows is studied by varying its angle of inclination. The results obtained are compared against an equivalent three layer 2D plain weave fabric system, both with and without through-thickness stitching that holds the layers together. A special inhouse FE preprocessor DYNAFAB is used to automatically generate the entire finite element mesh of the 2D and 3D fabrics. The user can easily customize the various parameters of the yarn and tow geometry as well as the fabric architecture. Insights gained from this study will prove extremely useful in further material and architectural studies that will ultimately lead to optimization of the z- tows for improved structural reinforcement and energy dissipating capabilities of these 3D fabrics. Keywords: 2D fabric, plain weave, stitching 3D fabric, z-tows, transverse impact, architectural effect, energy absorption, finite element analysis, LS-DYNA _______________ *

Corresponding author. Tel.: +1(302)831-8149 (John W. Gillespie Jr.) Email address: [email protected]

INTRODUCTION 2D and 3D fabrics respectively comprised of high strength continuous filament yarns or tows, made from materials such as Kevlar, Twaron, Vectran, and S2-glass are used in applications that require impact and penetration resistance against incident high energy projectiles. Applications include body armor, spall liners, turbine fragment containment, ceramic tile backing, and structural reinforcements. Table (1) displays the typical properties of some high strength materials used in 2D and 3D fabrics. The fabrics may be used in a dry flexible form without any resin, or used in a partial to fully impregnated form. In the former case, energy dissipation is mainly due to tensile elongation of the yarns of tows while in the latter case, other additional energy dissipating modes are present such as delamination and fiber-matrix debonding. Trademark Name Kevlar KM2 Twaron S2 glass Vectran UM Spectra 1000 Kevlar 49 M5

Filament Material Aramid Aramid Glass LCP UHMWPE Aramid PIPD

Density, ρ 3 (g/cm ) 1.44 1.44 2.47 1.40 0.97 1.45 1.77

Modulus, E11 (GPa) 64 75 88 103 113 120 330

Strength, σfail (GPa) 3.20 3.50 4.70 3.00 3.25 2.76 5.00

Table 1. Commonly used high strength filament materials The two major parameters that govern the energy dissipating capability or performance of a dry fabric are the material and architecture. The performance is assessed through parameters such as projectile velocity time history and residual velocity, dynamic deflection or back face deformation, momentum transfer between projectile and fabric, energy dissipation, and percentage of broken tows. There are a few distinct advantages of a 3D fabric over a 2D fabric. The first is that 3D fabrics have no tow crimp yielding higher in-plane tensile properties and a faster initial deceleration of the projectile, since in a 2D fabric the yarns will first need to straighten out or decrimp before tensile elongation. The second is that when used in an impregnated system, z-tows provide higher interlaminar shear and tensile strength leading to reduced delamination type failure. The third is that they can be packed very tightly leading to high areal densities. In this study 2D fabrics are studied as our baseline to understand the role of the z-tows in 3D fabrics. The generic 2D fabric architecture selected comprises of 3 layers of a plain weave fabric both with and without stitching, while the generic 3D fabric architecture selected is similar to TM that of the 100 oz 3WEAVE S2 fabric from 3TEX, Inc. The geometry and material properties of the chosen 2D and 3D fabric architectures have been so defined such that they are equivalent fabric systems with the same areal densities allowing them to be qualitatively and quantitatively compared.

SETUP OF THE 2D PLAIN WEAVE FABRIC Figure (1) displays a micrograph of a generic plain weave fabric showing the undulations and cross section of the warp and fill yarns respectively. To initially demonstrate the role that through thickness stitching plays on the 2D fabric performance under impact, two cases are set up. The first case consists of three layers of a plain weave fabric.

Fig. 1. Micrograph of a generic 2D plain weave fabric

The geometrical parameters with respect to Figure (1) are assumed as follows: (s) 3.0 mm (w) 2.2 mm (t) 0.458 mm. It is assumed that both warp and fill yarns have the same cross section and undulations. As will be seen later, the geometrical parameters were so chosen so as to enable a comparison with the 3D fabric architecture used in this study. The in-plane dimensions of the fabric are 101.6 mm x 50.8 mm. The total fabric thickness is 2.748 mm. Figure (2) displays the FE model of the fabric meshed using only solid elements (case #1). Because of symmetry, only one quarter of the FE mesh needs to be modeled.

Fig. 2. FE model of the 2D plain weave fabric (2D-Case #1) The orthotropic material properties of the 2D fabric yarns are assigned as follows: Longitudinal modulus (E11) of 80 3 GPa, Density (ρ) of 3.56 g/cm . This density was chosen so that the areal density of this 2D fabric matches that of the 3D fabric described in a later section. Yarn failure via element erosion is incorporated in LS-DYNA using a maximum principal stress failure criterion (σfail) of 3.5 GPa

Fig. 3. FE model of the stitched 2D plain weave fabric (2D-Case #2) Dry yarns have very little initial resistance to transverse compression or shear because of the filament level architecture, wherein individual filaments simply redistribute themselves under load. For this reason, the transverse elastic moduli (E22 and E33) and shear moduli (G12 , G23, and G31) are assumed to be one-tenth the longitudinal elastic modulus. This is also a reasonable assumption when modeling a yarn as a homogenized continuum neglecting filament level detail, wherein the predominant material property is the longitudinal modulus. For computational stability reasons, small non-zero Poisson ratios of 0.01 are used. The second 2D fabric case is similar to the first case, with the addition of through thickness stitching that runs parallel to the warp yarns and passes through each gap in-between the yarn cross-over locations. Figure (3) displays the FE mesh of the fabric with stitching (case #2). The material properties of the stitching remain the same as that of the warp and fill yarns

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of case #1 with the exception of the density which is chosen as 1.31 g/cm . In order to maintain the same areal 3 density as the fabric of case #1, the density of the warp and fill yarns in case #2 is reduced to 3.18 g/cm .

SETUP OF THE 3D FABRIC Figure (4) displays micrographs of the 3D fabric. Dark overlay lines are used to clarify the cross sectional shapes of the warp, fill, and z-tows. The 3D fabric consists of five layers of warp and fill tows that are interlaced with z-tows that run parallel to the warp tows. Figure (4a) displays the undulations of the z-tows along with the cross sectional profiles of the fill tows. As can be seen, the top and bottom fill tows are semi-elliptical in shape while the middle fill tows transition along their length between two trapezium shapes which are vertical mirror images of each other. Figure (4b) displays the cross sectional profiles of the z-tows and warp tows which are rectangular in shape. As can be seen, the tight packing causes the warp tows to be pushed aside by the z-tows. The angle of inclination (θ) of the z-tows with respect to the horizontal is around 67.7°. The dimensions assigned to the tows of the corresponding FE model are as follows - Warp tow: (s) 2.5 mm, (t) 0.55 mm, (w) 2.2mm; Fill tow: (s) 3 mm (t) 0.56 mm; and z-tow (s) 2.5 mm (t) 0.25 mm (w) 1.166, where 's', 't', and 'w' are the span, thickness, and width respectively. The middle layer fill tow with the trapezium cross sectional shape has a longer side of 2.96 mm and a shorter side of 2.5 mm. The upper and lower layer fill tows with the semi-elliptical cross sectional shapes have a semi-major axis of 1 mm and a semi-minor maxis of 0.26 mm.

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Fig. 4. Micrographs of the 3D fabric Figure (5) displays the FE mesh of the 3D fabric (case #1) corresponding to the micrographs in Figure (4). Solid elements are used in the mesh to model the tows. The in-plane dimensions of the fabric are 101.6 mm x 50.8 mm. The total fabric thickness is around 2.78 mm. The orthotropic material properties of the 3D fabric warp, fill, and z3 tows are assigned as follows: Longitudinal modulus (E11) of 80 GPa, Density (ρ) of 2.43 g/cm , and a failure stress (σfail) of 3.5 GPa. Again, the transverse elastic moduli and shear moduli are one-tenth of the longitudinal modulus, and Poisson ratios of 0.01 are used. In order to study the effect of the z-tow inclination, a second 3D fabric case is set up, where the angle of z-tow inclination (θ) is set at 90°. To enable a comparison with the first 3D fabric case, all geometric and material parameters are kept the same with the exception of the upper and lower layer fill tows that now have a wider and thinner semi-elliptical shape as follows: semi-major axis of 1.375 mm and a semi-minor maxis of 0.4072 mm. Figure (6) displays the FE mesh of case #2 of the 3D fabric.

Fig. 5. FE model of the 3D fabric with θ=67.7° (3D-Case #1)

Fig. 6. FE model of the 3D fabric with θ=90° (3D-Case #2)

SETUP OF THE PROJECTILE A rigid cylindrical projectile of mass 17.83 gm, diameter 10.4 mm, and height 12.4 mm modeled using shell elements is used in the impact simulations. Figure (7) displays the cylindrical projectile. When used with the 2D fabric model, it spans approximately 7 warp yarns, 7 fill yarns, and 8 stitching yarns. When used with the 3D fabric model, it spans approximately 8 warp tows, 7 fill tows, and 9 z-tows.

Fig. 7. Rigid cylindrical projectile

COMPARISON OF FABRIC MASSES Figure (8) compares the total fabric masses of all four models, the mass of the projectile, as well as the mass of each fabric component. The mass fraction of the z-tows in 3D fabric case #1 and case #2 are 11.21 and 8.75% respectively, while the mass fraction of the stitching in the 2D fabric case #2 is 8.02%. The areal densities of all four 2 fabric models are approximately the same, at 5.115 kg/m .

Fig. 8. Summary of masses

RESULTS AND DISCUSSION - 2D FABRIC An impact simulation is set up in the dynamic FE code LS-DYNA using both the 2D fabric models (case #1 - no stitching, and case #2 - with stitching) and the cylindrical projectile discussed earlier. The fabric is gripped on all four sides and impacted at the center with a velocity of 60 m/s. This corresponds to a non-penetrating velocity. A static frictional coefficient of 0.23 is prescribed between the projectile and fabric, and 0.18 between yarns. Figures (9-10) compare the deformation profiles of both cases taken at various time instants during the first 75 µs of the impact event. These deformation profiles consist of the contours of vertical fabric displacement of the topmost layer as seen from the top view and vertical displacement of all layers as seen from the side view. In case #1, both separation between the projectile and fabric, as well as between the layers is evident at the time instants of 45 µs and 55 µs. After the fabric layers separate from the impacting projectile, they elastically rebound to contact the projectile again. This is seen at the time instant of 75 µs, where the layers are in contact with the projectile again. This process of projectile-fabric and inter-layer separation followed by rebounding continues during the impact process leading to steps and oscillations in the time history data displayed in Figure (11). In contrast, the deformation profiles of case #2 display no evident projectile-fabric separation. Also there is no inter-layer separation as the stitching is holding the layers together. From Figure (11a), there is a steep reduction in the projectile velocity during initial impact for case #1, followed by the first plateau which corresponds to the time interval when the layers have first separated from the projectile and then begin to rebound back. Upon reestablishing contact with the projectile again, there is another steep reduction in the projectile velocity until the next plateau. However the deceleration is more or less uniform in case #2 as the stitching ensures that the entire fabric structure deforms as a whole while maintaining contact with the projectile without inter-layer separation. This is further confirmed from the fabric dynamic deflection history in Figure (11b) and the projectile-fabric contact force history in Figure (11f) for case #1, which show large oscillations and peaks. Figure (11c) compares the fabric internal or elastic strain energy in both cases. For case #2, the component of internal energy absorbed by only the stitching yarns is also displayed. Clearly the stitching by itself contributes only to a small percentage of the total internal energy, however its presence significantly affects the overall deformation profile and total energy

absorption and contribution of each layer, leading to case #2 arresting the projectile at around 186 µs, well before case #1 as seen from Figure (11a).

Fig. 9. Deformation profiles of the 2D fabric, Case #1


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Fig. 11. Time history results of the 2D Fabric cases (a) Projectile velocity (b) Fabric dynamic deflection (c) Fabric internal energy (d) Fabric kinetic energy (e) Vertical component of fabric momentum (f) Projectile-fabric contact force

RESULTS AND DISCUSSION - 3D FABRIC An impact simulation identical to the 2D fabric case is set up in the dynamic FE code LS-DYNA using both the 3D fabric models (Case #1 - Z tows at 67.7°, and Case #2 - Z tows at 90.0°) and the cylindrical projectile discussed earlier. The fabric is gripped on all four sides and impacted at the center with a velocity of 60 m/s. This once again corresponds to a non-penetrating velocity. A static frictional coefficient of 0.23 is prescribed between the projectile and fabric, and 0.18 between yarns. Figures (12-13) compare the deformation profiles of both cases taken at various time instants during the first 75 µs of the impact event. These deformation profiles consist of the contours of vertical fabric displacement of the topmost layer as seen from the top view and vertical displacement of all layers as seen from the side view, and can be compared against Figures (9-10) of the 2D fabric cases.



It is evident that in both 3D fabric cases, there is no inter-layer separation as the z-tows do not fail during the impact event and hold the warp and fill tows together. However there is projectile-fabric separation followed by the fabric rebounding. This is seen from the peaks in the fabric dynamic deflection history in Figure (14b) and the projectile to fabric contact force history in Figure (14f). The fabric response is almost identical in both cases up to around 75-90 µs. After this the response of case #1 deviates from case #2. Upon close examination it is observed that during this time interval about eight to ten fill tows around the impact region fail in case #1 compared to just four to six fill tows in case #2. No warp or z-tows fail at any time during the entire impact event.

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Fig. 14. Time history results of the 3D Fabric cases (a) Projectile velocity (b) Fabric dynamic deflection (c) Fabric internal energy (d) Fabric kinetic energy (e) Vertical component of fabric momentum (f) Projectile-fabric contact force

Since the areal density and material properties assigned to all tows in both cases are identical, it is evident that the angle of inclination of the z-tows is affecting the extent to which the fill tows are deformed and stressed, causing them to reach the failure stress of 3.5 GPa earlier in case #1. This can be explained by considering the angle of inclination of the z-tows which determines their path length to be analogous to yarn crimp. Case #2 which has a 90° z-tow inclination has a longer z-tow and consequently greater 'crimp' compared to case #1 which has a 67.7° ztow inclination. During transverse impact and fabric deformation, the z-tows begin to straighten out. However the straightening of the z-tows exerts stress on the fill tows since the z-tows pass over and under the top and bottom fill tows respectively. Thus the straightening of the z-tows attempts to induce bending and crimp in the fill tows, which is resisted by fill tows since they are also gripped at both ends. Since there is greater z-tow crimp in case #2, the stresses induced by the z-tows in the central fill tows are smaller, or occur at a slower rate compared to case #1, explaining why more number of fill tows in case #1 fail at an earlier time instant. This results in case #2 arresting the projectile at around 153 µs, well before case #1 as seen from Figure (14a).

RESULTS AND DISCUSSION - 2D Vs. 3D FABRIC Figure (15) compares the results between the 2D and 3D cases. The 3D case #2 arrests the projectile the fastest amongst all cases as seen from Figure (15a). As seen from Figure (15c) there is a greater dissipation of frictional sliding energy between tows in the 3D fabric case #2 compared to that between the yarns in the 2D fabric cases. This is probably due to the tighter packing of the 3D fabric and greater normal forces between the tows since the warp and fill tows do not posses any crimp and have flatter surfaces. Of all the cases, only the 2D case #2 i.e. fabric with stitching displays a smoothly increasing dynamic deflection indicating no inter-layer or projectile-fabric separation. However the total dynamic deflection at the time of projectile arrest was the least in the 3D case #2. Also, as seen from Figure (15d), the internal energy absorption was the highest in the 3D case #2. Interestingly the magnitudes and rates of internal energy absorption of just the stitching yarns in 2D case #2 and just the z-tows in both 3D fabric cases are around the same, however when viewed as a fraction of the respective total fabric internal energy absorption, the z-tows in 3D case #2 proved most effective. Due to space restrictions, the impact case of a penetrating spherical projectile could not be presented in this paper. However a paragraph describing the salient results would be beneficial in putting the current results in perspective and providing further insight into the effect of 3D architecture. Consider the case of a spherical projectile of mass 1.140 gm and diameter 5.55 mm impacting the same 2D and 3D fabrics at 200 m/s, with the material properties and boundary conditions kept the same. The projectile is able to penetrate through the fabric with an average residual velocity of 108 m/s for the 3D fabric cases. The diameter of the projectile spans around three z-tows, however because of the spherical shape, only the central z-tow is deformed under impact to the greatest extent and fails first. Once this z-tow fails, if the warp and fill tows around the impact center haven't already failed, they simply get pushed aside by the penetrating projectile. The frictional energy dissipated by intertow sliding in the 3D fabrics is much greater than yarn sliding in the 2D fabrics. Also, because of the nature of the ztow inclination, the frictional energy is greater for 3D case #1 compared to 3D case #2. In terms of residual velocity, the stitched 2D fabric compares well with both 3D fabrics, with 3D case #1 having a slightly lower residual velocity compared to 3D case #2. The 2D case #1 fabric however performs poorly with a residual velocity of around 144 m/s. Also interesting in this particular impact case is that the orientation of the central or impacted z-tow significantly affects the instant of failure and consequently the residual projectile velocity. Here orientation refers to whether that portion of the z-tow directly underneath the projectile interlaces the fabric at the top or bottom. In the former case, the z-tow would be the first tow to get impacted. In the 2D case #1, once the projectile penetrates through the first layer, the first layer no longer significantly contributes to slowing down the projectile, and simply flaps freely. However in 2D case #2, even after the first layer has been penetrated, the stitching ensures the first layer remains connected to the other layers, and the first layer continues to deform and absorb significant amounts of internal energy, even greater than that of the other layers. The inter-yarn frictional sliding energy is also much greater for the 2D case #2 compared to 2D case #1. Finally the difference in residual projectile velocity between both 2D cases is almost 35 m/s highlighting the important contribution of the stitching yarns to the overall fabric performance under impact.

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Fig. 15. Time history results of the 3D Fabric cases (a) Projectile velocity (b) Fabric dynamic deflection (c) Inter-yarn and inter-tow frictional energy (d) Fabric internal energy

CONCLUSIONS For the impact study presented in this paper, 3D fabrics were shown to outperform 2D fabrics both with and without stitching. The angle of inclination of the z-tows affects the 3D fabric response to impact. A z-tow angle of inclination of 90° proved better than the lower angle of 67.7° for this non-penetrating impact case. Using stitching in the 2D fabrics greatly improved the performance over 2D fabrics without stitching, and led to greater energy absorption and a faster arresting of the projectile. The stitching also imparted greater structural rigidity to the fabric and significantly reduced inter-layer and projectile-fabric separations that led to oscillations in the results of the 2D fabric case without stitching. In the 3D fabric, the z-tows prevented inter-layer separations, however there still was a degree of projectile-fabric separation. This preliminary investigation into the effects of 3D architecture on the impact response of flexible fabrics has already yielded important insight that will help improve performance. However there still are many variables that need to be parametrically studied, that could have a significant effect on the performance. Clearly the velocity, size, and shape of the projectile makes a difference. The boundary conditions would also play a significant role, and a fabric gripped on four corners or two sides would

respond quite differently from a fabric gripped on all four sides, since different modes of deformation and energy dissipation become activated. Other z-tow inclination angles will need to be studied in order to establish a reliable trend. In this study, while changing the z-tow inclination angle, the span of the fill tows was kept constant, however it is possible to increase the inclination angle while also decreasing the fill tow width and span leading to a larger number of fill tows. This could affect the trends and results. Thus the effects of cross sectional shape, size, and span of the warp, fill, and z-tows also need to be explored. Other variables include material properties. This would help answer questions of whether it is beneficial to have a stiffer and stronger z-tow compared to the warp and fill tows, or whether a more compliant z-tow would prove effective. These exploratory paths could also be applied to the 2D fabrics with stitching. There are other important practical aspects that need to be incorporated into the study and two examples would be the statistical nature of tow strength due to the inherent presence of defects and weaving strength degradations. Nilakantan et al. [1] have investigated the statistical strength distributions of, and effects of weaving degradations on, Kevlar KM2 yarns and 2D plain weave Kevlar S706 fabrics. Abu-Obaid et al. [2] have investigated similar degradations in 3D S-2 glass fabrics. Nilakantan et al. [3] have presented a methodology to incorporate these statistical distributions of constituent tow material properties into a FE impact simulation. This makes the FE simulation more realistic and predictive in nature. Some examples of weaving process parameters that affect the fabric impact performance are the curvature of z-tows which could induce kink bands in the filaments, while abrasion between tows during the weaving process could break monofilaments or disorder the crystalline structure of some of the high performance materials leading to a loss in tensile strength. Thus through better weaving processes and the use of hybrid materials with improved kink-band, damage, and abrasion resistance, the performance of 3D fabrics could be improved. This also requires further investigation. To conclude, a significant amount of work still needs to be undertaken to fully understand the role of material and architecture on the impact response of 2D and 3D fabrics. 3D fabrics have many advantages over 2D fabrics in impact and penetration resistance applications. Insights provided by this study are the first step towards optimizing the performance of these 3D fabrics through further material and architectural modifications.

ACKNOWLEDGEMENTS The financial support of the US Army Research Laboratory at the Aberdeen Proving Grounds, MD, USA, and the Center for Composite Materials at the University of Delaware, DE, USA is gratefully acknowledged. CCM interns Mr. Cameron Showell and Mr. Allan Burleigh are also acknowledged for their assistance in preparing micrographs of the 2D and 3D fabrics.

REFERENCES [1] Gaurav Nilakantan, Michael Keefe, John W. Gillespie Jr., Eric D. Wetzel, Travis A. Bogetti, Rob Adkinson, "An experimental and numerical study of the impact response (V50) of flexible plain weave fabrics: Accounting for statistical distributions of yarn strength", The 1st Joint American-Canadian International Conference on Composites and the 24th Annual ASC Technical Conference, University of Delaware, Newark, DE 19711, USA, September 15-17, 2009. [2] Ahmad Abu-Obaid, Steve M. Andersen, John W. Gillespie, Jr., B. Dickenson, A. Watson, G. Chapman, R. A. Coffelt, "Effects of weaving on S-2 glass tensile strength distributions", TEXCOMP 9, University of Delaware, Newark, DE, USA, October 13-15, 2008. [3] Gaurav Nilakantan, Michael Keefe, John W. Gillespie Jr., Travis A. Bogetti, "Modeling the material and failure response of continuous filament fabrics for use in impact applications", TEXCOMP 9, University of Delaware, Newark, DE, USA, October 13-15, 2008.