年間 6 号発行
ISSN 印刷: 1543-1649
ISSN オンライン: 1940-4352
Indexed in
Modeling of Viscoelastic Behavior of Ballistic Fabrics at Low and High Strain Rates
要約
Ballistic fabrics are made from high-performance polymeric fibers such as Kevlar®, Twaron®, and Spectra® fibers. These fibers often behave viscoelastically. The Kelvin-Voigt and Maxwell rheological (viscoelasticity) models have been used to characterize stress-strain relations of such fabrics at different strain rates. However, these two-parameter models have been found to be inadequate and inaccurate in some applications. As a result, three-parameter rheological models have been utilized to develop constitutive relations for viscoelastic polymeric fabrics. In this article, a generalized Maxwell (GM) model and a generalized Kelvin-Voigt (GKV) model, which are both three-parameter viscoelasticity models, are proposed to describe the viscoelastic behavior of a ballistic fabric, Twaron® CT716, at the strain rates of 1 s-1 and 495 s-1. The GM model consists of a Maxwell element (including a viscous dashpot and a spring in series) and a second spring in parallel to the Maxwell element, while the GKV model is an assembly of a Kelvin-Voigt (KV) element (containing a viscous dashpot and a spring in parallel) and a second spring in series with the KV element. The predictions by the GM and GKV models are compared with existing experimental data, which reveals that the GKV model gives more accurate results at the low strain rate, whereas the GM model performs better at the high strain rate while still providing accurate predictions for the low strain rate responses.
-
David, N. V., Gao, X.-L., and Zheng, J. Q., Ballistic resistant body armor: Contemporary and prospective materials and related protection mechanisms. DOI: 10.1115/1.3124644
-
Brinson, H. F. and Brinson, L. C., Polymer Engineering Science and Viscoelasticity: An Introduction. DOI: 10.1007/978-0-387-73861-1
-
Tan, V. B. C., Shim, V. P.W., and Zeng, X., Modelling crimp in woven fabrics subjected to ballistic impact. DOI: 10.1016/j.ijimpeng.2005.06.008
-
Cheng, M. and Chen, W., Modeling transverse behavior of Kevlarr<sup>®</sup> KM2 single fibers with deformation-induced damage. DOI: 10.1177/1056789506060733
-
Tan, V. B. C. and Ching, T. W., Computational simulation of fabric armour subjected to ballistic impacts. DOI: 10.1016/j.ijimpeng.2005.05.006
-
Yang, H. H., Aramid Fibers.
-
Kalantar, J. and Drzal, L. T., The bonding mechanism of aramid fibres to epoxy matrices: Part 1. A review of the literature. DOI: 10.1007/BF00581071
-
Shim, V. P. W., Lim, C. T., and Foo, K. J., Dynamic mechanical properties of fabric armor. DOI: 10.1016/S0734-743X(00)00038-5
-
Termonia, Y. and Smith, P., Theoretical study of the ultimate mechanical properties of poly(p-phenyleneterephthalamide) fibres. DOI: 10.1016/0032-3861(86)90170-9
-
Shim, V. P. W., Lim, C. T., and Tay, T. E., Modelling deformation and damage characteristics of woven fabric under small projectile impact. DOI: 10.1016/0734-743X(94)00063-3
-
Yeh, W. Y. and Young, R. J., Molecular deformation processes in aromatic high modulus polymer fibres. DOI: 10.1016/s0032-3861(98)00308-5
-
Smith, J. C., Blandford, J. M., and Towne, K. M., Stress-strain relationship in yarns subjected to rapid impact loading: Part VIII. Shock waves, limiting breaking velocities and critical velocities.
-
Naik, N. K. and Shrirao, P., Composite structures under ballistic impact. DOI: 10.1016/j.compstruct.2004.05.006
-
Morye, S. S., Hine, P. J., Duckett, R. A., Carr, D. J., and Ward, I. M., Modelling of the energy absorption by polymer composites upon ballistic impact. DOI: 10.1016/S0266-3538(00)00139-1
-
Boyce, M. C., Socrate, S., and Llana, P. G., Constitutive model for the finite deformation stress-strain behavior of poly(ethylene terephthalate) above the glass transition. DOI: 10.1016/S0032-3861(99)00406-1
-
Koh, C. P., Shim, V. P. W., Tan, V. B. C., and Tan, B. L., Response of a high-strength flexible laminate to dynamic tension. DOI: 10.1016/j.ijimpeng.2007.04.010
-
Karim, M. R., and Hoo Fatt, M. S., Ratedependent constitutive equations for carbon fiber-reinforced epoxy. DOI: 10.1002/pc.20221
-
Roylance, D., Ballistics of transversely impacted fibers.
-
Lim, C. T., Shim, V. P. W., and Ng, Y. H., Finite-element modeling of the ballistic impact of fabric armor. DOI: 10.1016/S0734-743X(02)00031-3
-
Christensen, R. M., Theory of Viscoelasticity.
-
Averyanov, A. A., Botchenko, O. K., and Fil’bert, D. F., Rheological properties of polycaproamide in uniaxial extension with necking. DOI: 10.1007/BF00551213
-
Ellyin, F., Vaziri, R., and Bigot, L., Predictions of two nonlinear viscoelastic constitutive relations for polymers under multiaxial loadings. DOI: 10.1002/pen.20731
-
David N. V., Gao X.-L., Zheng J. Q., Stress Relaxation of a Twaron®/Natural Rubber Composite, Journal of Engineering Materials and Technology, 133, 1, 2011. Crossref
-
David* N. V., Gao X.-L., Zheng J. Q., Constitutive Behavior of a Twaron®/Natural Rubber Composite, Mechanics of Advanced Materials and Structures, 17, 4, 2010. Crossref
-
Gogineni S., Gao X. -L., David N. V., Zheng J. Q., Ballistic Impact of Twaron CT709® Plain Weave Fabrics, Mechanics of Advanced Materials and Structures, 19, 6, 2012. Crossref
-
Luan Kun, Sun Baozhong, Gu Bohong, Ballistic impact damages of 3-D angle-interlock woven composites based on high strain rate constitutive equation of fiber tows, International Journal of Impact Engineering, 57, 2013. Crossref
-
Kulkarni S.G., Gao X.-L., Horner S.E., Zheng J.Q., David N.V., Ballistic helmets – Their design, materials, and performance against traumatic brain injury, Composite Structures, 101, 2013. Crossref
-
David N. V., Gao X.-L., Zheng J. Q., Creep of a Twaron®/Natural Rubber Composite, Mechanics of Advanced Materials and Structures, 20, 6, 2013. Crossref