Calculation of Stress-Strain Curves of Fabric Reinforced Composite Materials using the Endochronic Theory of Plasticity

The article gives a brief overview of mathematical models of orthotropic materials’ nonlinear deformation. We propose an endochronic model of nonlinear deformation of fabric reinforced composite material in plane stress state. Experimental results made it possible to find three unrelated deformation mechanisms - deformation in warp direction, deformation in weft direction and inplane shear. We give mathematical expressions and describe procedure of calculating model parameters. The study also shows the simulation results of nonlinear deformation of different fabric reinforced composites.

References

[1] Wu H.-C. Continuum mechanics and plasticity. Chapman & Hall/CRC Press, 2005. 684 p.

[2] Tong W. A plane stress anisotropic plastic flow theory for orthotropic sheet metals. International Journal of Plasticity, 2006, vol. 22, no. 3, pp. 497-535.

[3] Valanis K.C. A theory of viscoplasticity without a yield surface. Arch. of Mech., 1971, vol. 23, no. 4, pp. 517-551.

[4] Bondar’ V.S., Danshin V.V. Theory of inelasticity without loading surface and associated flow rule. Vestnik PNIPU. Mekhanika [PNRPU Mechanics Bulletin], 2015, no. 1, pp. 43-57 (in Russ.). DOI: 10.15593/perm.mech/2015.1.04 Available at: http://vestnik.pstu.ru/mechanics/archives/?id=&folder_id=4460

[5] Kadashevich Yu.I., Pomytkin S.P. Investigation of uniaxial and biaxial loadings of softening materials in endochronic theory of inelasticity. Vestnik SamGTU. Ser. Fiz.-mat. Nauki, 2012, no. 1(26), pp. 110-115 (in Russ.). DOI: 10.14498/vsgtu1007 Available at: http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=vsgtu&paperid=1007&option_lang=rus

[6] Kucher N.K. A version of the endochronic theory of plasticity to describe the asymmetrical cyclic loading of materials. Strength of Materials, 1999, vol. 31, no. 13, pp. 13-17. DOI: 10.1007/BF02509735 Available at: https://link.springer.com/article/10.1007/BF02509735

[7] Pindera M.J., Herakovich C.T. An endochronic model for the response of unidirectional composites under off-axis tensile load. In: Mechanics of Composite Materials. Recent advances. New York, Pergamon Press, 1983. Pp. 367-381.

[8] Zinov’yev P.A., Sarbaev B.S. Endochronic theory of fiber composite non-elastic deformation. Mekhanika kompozitnykh materialov, 1985, no. 3, pp. 423-430 (in Russ.).

[9] Sarbaev B.S. Endochronic theory of anisotropic continuum plasticity. Izvestiya RAN. Mekhanika tverdogo tela, 1991, no. 2, pp. 106-116 (in Russ.).

[10] Sarbayev B.S. An endochronic theory of plastic deformation of fibrous composite materials. Computational Materials Science, 1995, vol. 4, no. 3, pp. 220-232. DOI: 10.1016/0927-0256(95)00039-S Available at: http://www.sciencedirect.com/science/article/pii/092702569500039S

[11] Bobrov A.V., Sarbaev B.S., Shirshov Yu.Yu. Nonlinear deformation of carbide-derived carbon composite material. Journal of Machinery Manufacture and Reliability, 2014, vol. 43, no. 4, pp. 287-293. DOI: 10.3103/S1052618814040025 Available at: https://link.springer.com/article/10.3103/S1052618814040025

[12] ASTM D 5379/D 5379M-98. Standard test method for shear properties of composite materials by the V-notched beam method.