A technique for the numerical homogenization of plastic deformation of unidirectionally reinforced composites is developed. A modification of Prandtl–Reuss theory that takes into account the influence of the first invariant of stress tensor is used as governing relations for an equivalent orthotropic material. The isotropic hardening is described by a function depending on the work of plastic deformation. A micromechanical analysis is performed on a representative cell by the finite-element method for the general case of triaxial stress state. Deformation diagrams and yield surfaces for carbon fiber plastics with a square packaging scheme of fibers are given.
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References
R. Hill, The Mathematical Theory of Plasticity, Oxford: Oxford Univ. Press (1950).
M. Vogler, R. Rolfes, and P. P. Camanho, “Modeling the inelastic deformation and fracture of polymer. Part I: Plasticity model,” Mech. Mater, 59, 50-64 (2013).
K. Naumenko and H. Altenbach, “Modeling high temperature materials behavior for structural analysis. Part I: Continuum mechanics foundations and constitutive models,” Cham: Springer: Advanced Structured Materials, 28 (2016). DOI: 10.1007/978-3-319-31629-1.
A. R. Melro, P. P. Camanho, F. M. Andrade Pires, and S. T. Pinho, “Micromechanical analysis of polymer composites reinforced by unidirectional fibers. Part I: Constitutive modelling,” Int. J. Solids Struct., 50, 1897-1905 (2013).
A. R. Melro, P. P. Camanho, F. M. Andrade Pires, and S. T. Pinho, “Micromechanical analysis of polymer composites reinforced by unidirectional fibers. Part II: Micromechanical analyses,” Int. J. Solids Struct., 50, 1906-1915 (2013).
F. P. Van der Meer, “Micromechanical validation of a mesomodel for plasticity in composites,” Europ. J. Mech. A/Solids., 60, 58-69 (2016).
R. Bedzra, J. W. Reese, and J. W. Simon, “Meso-macro modeling of anisotropic metallic composites within the framework of multisurface plasticity,” Int. J. Solids Struct., 120, 186-198 (2017).
Y. J. Cho, W. J. Lee, and Y. H. Park, “Effect of boundary conditions on plasticity and creep behavior analysis of particle reinforced composites by representative volume element approach,” Comput. Mater. Sci., 100, Part A, 67-75 (2015).
C. Hoffarth, S. D. Rajan, R. K. Goldberg, D. Revilock, K. S. Carney, P. DuBois, and G. Blankenhorn, “Implementation and validation of a three-dimensional plasticity-based deformation model for orthotropic composites,” Composites: Part A, 91, 336-350 (2016).
Y. K. Khdir, T. Kanit, F. Zaїri, and M. Naїt-Abdelaziz, “Computational homogenization of elastic-plastic composites,” Int. J. Solids Struct., 50, 2829-2835 (2013).
T. Laux, K. W. Gan, J. M. Dulieu-Barton, and O. T. Thomsen, “A simple nonlinear constitutive model based on nonassociative plasticity for UD composites: Development and calibration using a modified arcan fixture,” Int. J. Solids Struct., 162, 135-147 (2019).
S. Marfia and E. Sacco, “Computational homogenization of composites experiencing plasticity, cracking and debonding phenomena,” Comput. Methods Appl. Mech. Eng., 304, 319-341 (2016).
G. J. Dvorak, “Transformation field analysis of inelastic composite materials,” Proc. R. Soc. London, Ser. A, 437, 311-327 (1992).
L. R. Meza, J. M. J. Schormans, J. J. C. Remmers, and V. S. Deshpande, “Shear response of 3D non-woven carbon fiber reinforced composites,” J. Mech. Phys. Solids., 125, 276-297 (2019).
B. Nedjar, “Plasticity-based modeling of fiber/matrix debonding in unidirectional composites,” Compos. Struct., 108, 41-48 (2014).
Z. Hashin, “On the elastic behaviour of fiber reinforced materials of arbitrary transverse phase geometry,” J. Mech. Phys. Solids., 13, No. 3, 119-134 (1965).
T. Mori and K. Tanaka, “Average stress in matrix and average elastic energy of materials with misfitting inclusions,” Acta Metall., 21, No. 5, 571-574 (1973).
H. Singh, M. Gupta, and P. Mahajan, “Reduced order multiscale modeling of fiber reinforced polymer composites including plasticity and damage,” Mech. Mater., 111, 35-56 (2017).
L. Zhang and W. Yu, “Variational asymptotic homogenization of elastoplastic composites,” Compos. Struct., 133, 947-958 (2015).
B. I. Miled, I. L. Doghri, L. Brassart, and L. Delannay, “Micromechanical modeling of coupled viscoelastic-viscoplastic composites based on an incrementally affine formulation,” Int. J. Solids Struct., 50, 1755-1769 (2013).
D. Tsalis, T Baxevanis., G. Chatzigeorgiou, and N Charalambakis, “Homogenization of elastoplastic composites with generalized periodicity in the microstructure,” Int. J. Plast., 51, 161-187 (2013).
Q.-C. He and Z.-Q. Feng, “Homogenization of layered elastoplastic composites: Theoretical results,” Int. J. Non Linear Mech., 47, 367-376 (2012).
A. F. Fedotov, “Hybrid model for homogenization of the elastoplastic properties of isotropic matrix composites,” Mech. Compos. Mater., 53, No. 3, 361-372 (2017).
R. M. Christensen, Mechanics of Composite Materials, John Wiley & Sons, New York-Chichester-Brisbane-Toronto (1979)
R. V. Mises, “Mechanik der plastischen Formänderung von Kristallen,” Z. Angew. Math. Mech., 8, 161-185 (1928). DOI: https://doi.org/10.1002/zamm.19280080302.
J. Małachowski, G. L’vov, and S. Daryazadeh, “Numerical prediction of the parameters of a yield criterion for fibrous composites,” Mech. Compos. Mater., 53, No. 5, 589-600 (2017).
P. J. Hine, R. A. Duckett, A. S. Kaddour, M. J. Hinton, and G. M. Wells, “The effect of hydrostatic pressure on the mechanical properties of glass fiber/epoxy unidirectional composites,” Composites: Part A, 36, No. 2, 279-289 (2005).
S Darya Zadeh. and G. I. L’vov, “Numerical procedure of determining the effective mechanical characteristics of an aligned fiber composite,” Strength Mater., 47, No. 4, 536-543 (2015).
G. I. Lvov and O. A. Kostromitskaya, “Two-level computation of elastic characteristics of woven composites,” Mech. Compos. Mater., 54, No. 5, 577-590 (2018).
A. Gilat, R. K. Goldberg, and G. D. Roberts, “Strain rate sensitivity of epoxy resin in tensile and shear loading,” NASA/TM-2005-213595. URL: https: // ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050179433.pdf
V. A. Il’in and E. G. Poznyak, Linear Algebra [in Russian], – M., Nauka (1999).
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 56, No. 1, pp. 3-26, January-February, 2020.
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L’vov, G.I., Kostromitskaya, O.A. Numerical Modeling of Plastic Deformation of Unidirectionally Reinforced Composites. Mech Compos Mater 56, 1–14 (2020). https://doi.org/10.1007/s11029-020-09856-8
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DOI: https://doi.org/10.1007/s11029-020-09856-8