Effective pressure-sensitive elastoplastic behavior of particle-reinforced composites and porous media under isotropic loading. (English) Zbl 1130.74039
Summary: The composite under investigation consists of an elastoplastic matrix reinforced by elastic particles or weakened by pores. The material forming the matrix is pressure-sensitive. The Drucker-Prager yield criterion and a one-parameter non-associated flow rule are employed to formulate the yield behavior of the matrix. The objective is to estimate the effective elastoplastic behavior of the composite under isotropic tensile and compressive loadings. To achieve this objective, we use the composite sphere assemblage model of Z. Hashin [J. Appl. Mech. 29, 143–150 (1962; Zbl 0102.17401)]. Exact solutions are thus derived as estimations for the effective secant and tangent bulk moduli of the composite. The effects of loading modes and phase properties on the effective elastoplastic behavior of the composite are evaluated analytically and numerically.
MSC:
| 74Q15 | Effective constitutive equations in solid mechanics |
| 74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74E30 | Composite and mixture properties |
Citations:
Zbl 0102.17401References:
| [1] | Aboudi, J.: Micromechanical analysis of composites by the method of cells – update, Appl. mech. Rev. 49, S84-S91 (1996) |
| [2] | Aboudi, J.; Pindera, M. J.; Arnold, S. M.: Linear thermoelastic higher-order theory for periodic multiphase materials, J. appl. Mech. 68, 697-707 (2001) · Zbl 1110.74305 · doi:10.1115/1.1381005 |
| [3] | Bansal, Y.; Pindera, M. J.: Finite-volume direct averaging micromechanics of heterogneous materials with elastic – plastic phases, Int. J. Plasticity 22, 131-157 (2006) · Zbl 1177.74065 · doi:10.1016/j.ijplas.2005.04.012 |
| [4] | Bardella, L.: An extension of the secant method for the homogenization of the nonlinear behavior of composite materials, Int. J. Eng. sci. 41, 741-768 (2003) · Zbl 1211.74176 · doi:10.1016/S0020-7225(02)00276-8 |
| [5] | Berveiller, M.; Zaoui, A.: An extension of the self-consistent scheme to plastically-flowing polycrystals, J. mech. Phys. solids 26, 325-344 (1979) · Zbl 0395.73033 · doi:10.1016/0022-5096(78)90003-0 |
| [6] | Bousshine, L.; Chaaba, A.; De Saxcé, D.: Softening in stress – strain curve for Drucker – Prager non-associated plasticity, Int. J. Plasticity 17, 21-46 (2001) · Zbl 1004.74016 · doi:10.1016/S0749-6419(00)00017-6 |
| [7] | Chaboche, J. L.; Kruch, S.; Maire, J. F.; Pottier, T.: Towards a micromechanics based inelastic and damage modeling of composites, Int. J. Plasticity 17, 411-439 (2001) · Zbl 0988.74006 · doi:10.1016/S0749-6419(00)00056-5 |
| [8] | Chaboche, J. L.; Kanouté, P.; Roos, A.: On the capabilities of mean-field approches for the description of plasticity in metal matrix composites, Int. J. Plasticity 21, 1409-1434 (2005) · Zbl 1229.74150 · doi:10.1016/j.ijplas.2004.07.001 |
| [9] | Chadwick, P.: The quasi-static expansion of a spherical cavity in metals and ideal soils, Quart. J. Mech. appl. Math 12, 52-71 (1959) · Zbl 0085.38701 · doi:10.1093/qjmam/12.1.52 |
| [10] | Chen, W. F.; Han, D. J.: Plasticity for structural engineers, (1988) · Zbl 0666.73010 |
| [11] | Chu, T. Y.; Hashin, Z.: Plastic behavior of composites and porous media under isotropic stress, Int. J. Eng. sci 9, 971-994 (1971) · Zbl 0228.73043 · doi:10.1016/0020-7225(71)90029-2 |
| [12] | Doghri, I.; Tinel, L.: Micromechanical modeling and computation of elasto-plastic materials reinforced with distributed-orientation fibers, Int. J. Plasticity 21, 1919-1940 (2005) · Zbl 1154.74310 · doi:10.1016/j.ijplas.2004.09.003 |
| [13] | Doghri, I.; Tinel, L.: Micromechanics of inelastic composites with misaligned inclusions: numerical treatment of orientation, Comp. meth. Appl. mech. Eng. 195, 1387-1406 (2006) · Zbl 1130.74036 · doi:10.1016/j.cma.2005.05.041 |
| [14] | Dvorak, G.: Transformation field analysis of inelastic composite materials, Proc. R. Soc. lond. 437, 311-327 (1992) · Zbl 0748.73007 · doi:10.1098/rspa.1992.0063 |
| [15] | Dvorak, G.; Bahei-El-Din, Y.; Wafa, A.: The modeling of inelastic composite materials with the transformation field analysis, Model. simul. Mater. sci. Eng. 2, 571-586 (1994) · Zbl 0835.73038 |
| [16] | Fish, J.; Shek, K.: Computational plasticity and viscoplasticity for composite materials and structures, J. compos. B 29, 613-619 (1998) |
| [17] | Fotiu, P. A.; Nemat-Nasser, S.: Overall properties of elastic-viscoplastic periodic composites, Int. J. Plasticity 12, 163-190 (1996) · Zbl 0858.73054 · doi:10.1016/S0749-6419(96)00002-2 |
| [18] | Gonzalez, C.; Segurado, J.; Llorca, J.: Numerical simulation of elasto-plastic deformation of composites: evolution of stress microfields and implications for homogenization models, J. mech. Phys. solids 52, 1573-1593 (2004) · Zbl 1103.74020 · doi:10.1016/j.jmps.2004.01.002 |
| [19] | Gurson, A. L.: Continuum theory of ductile rupture by void nucleation and growth I: Yield criteria and flow rules for porous ductile media, ASME J. Eng. mater. Technol. 99, 2-15 (1977) |
| [20] | Hashin, Z.: The elastic moduli of heterogeneous materials, ASME J. Appl. mech. 29, 143-150 (1962) · Zbl 0102.17401 · doi:10.1115/1.3636446 |
| [21] | Hashin, Z.; Rosen, B. W.: The elastic moduli of fiber-reinforced materials, J. appl. Mech. 31, 223-232 (1964) |
| [22] | Hashin, Z.; Shtrikman, S.: A variational approach to the theory of the effective magnetic permeability of multiphase materials, J. appl. Phys. 33, 3125-3131 (1962) · Zbl 0111.41401 · doi:10.1063/1.1728579 |
| [23] | Hashin, Z.; Shtrikman, S.: A variational approach to the theory of the elastic behavior of multiphase materials, J. mech. Phys. solids 11, 127-140 (1963) · Zbl 0108.36902 · doi:10.1016/0022-5096(63)90060-7 |
| [24] | He, Q. -C.; Le Quang, H.; Feng, Z. -Q.: Exact results for the homogenization of elastic fiber-reinforced solids at finite strain, J. elasticity 83, 153-177 (2006) · Zbl 1103.74049 · doi:10.1007/s10659-006-9049-1 |
| [25] | He, Q. -C.; Le Quang, H.: Uniform strain fields and exact results in an elastoplastic fibre-reinforced composite, CR mech. 332, 547-555 (2004) · Zbl 1223.74012 · doi:10.1016/j.crme.2004.03.001 |
| [26] | Huang, Z. P.; Wang, J.: Nonlinear mechanics of solids containing isolated voids, ASME appl. Mech. rev. 59, 210-229 (2006) |
| [27] | Hu, G. K.: A method of plasticity for general aligned spheroidal void or fiber-reinforced composites, Int. J. Plasticity 12, 439-449 (1996) · Zbl 0884.73035 · doi:10.1016/S0749-6419(96)00015-0 |
| [28] | Kaminski, M.: Homogenization-based finite element analysis of unidirectional composites by classical and multiresolutional techniques, Comp. meth. Appl. mech. Eng. 194, 2147-2173 (2005) · Zbl 1137.74440 · doi:10.1016/j.cma.2004.07.030 |
| [29] | Li, G.; Castañeda, P.: The effect of particle shape and stiffness on the constitutive behavior of metal – matrix composites, Int. J. Solids struct. 30, 3189-3209 (1993) · Zbl 0817.73036 · doi:10.1016/0020-7683(93)90109-K |
| [30] | Liu, X.; Hu, G.: A continuum micromechanical theory of overall plasticity for particulate composites including particle size effect, Int. J. Plasticity 21, 777-799 (2005) · Zbl 1112.74315 · doi:10.1016/j.ijplas.2004.04.014 |
| [31] | Masson, R.; Zaoui, A.: Self-consistent estimates for the rate-dependent elastoplastic behaviour of polycrystalline materials, J. mech. Phys. solids 47, 1543-1568 (1999) · Zbl 0976.74010 · doi:10.1016/S0022-5096(98)00106-9 |
| [32] | Mcclintock, F. A.: A criterion for ductile fracture by growth of holes, ASME J. Appl. mech. 35, 363-371 (1968) |
| [33] | Michel, J. C.; Suquet, P.: Nonuniform transformation field analysis, Int. J. Solids struct. 40, 6937-6955 (2003) · Zbl 1057.74031 · doi:10.1016/S0020-7683(03)00346-9 |
| [34] | Milton, G. W.: The theory of composites, (2002) · Zbl 0993.74002 |
| [35] | Milton, G. W.; Serkov, S. K.: Bounding the current in nonlinear conducting composites, J. mech. Phys. solids 48, 1295-1324 (2000) · Zbl 0991.78019 · doi:10.1016/S0022-5096(99)00083-6 |
| [36] | Molinari, A.; Houdaigui, F. E.; Tóth, L. S.: Validation of the tangent formulation for the solution of the non-linear eshelby inclusion problem, Int. J. Plasticity 20, 291-307 (2004) · Zbl 1145.74328 · doi:10.1016/S0749-6419(03)00038-X |
| [37] | Mulhern, J. F.; Rogers, T. G.; Spencer, A. J. M.: Cyclic extension of an elastic fibre with an elastic – plastic coating, J. inst. Maths. appl. 3, 21-40 (1967) |
| [38] | Narasimhan, R.: Analysis of indentation of pressure sensitive plastic solids using the expanding cavity model, Mech. mater. 36, 633-645 (2004) |
| [39] | Needleman, A.: Void growth in an elastic – plastic medium, ASME J. Appl. mech. 39, 964-970 (1972) |
| [40] | Oskay, C.; Fish, J.: Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials, Comp. meth. Appl. mech. Eng. 196, 1216-1243 (2007) · Zbl 1173.74380 · doi:10.1016/j.cma.2006.08.015 |
| [41] | Paley, M.; Aboudi, J.: Micromechanical analysis of composites by the generalized method of cells, Mech. mater. 14, 127-139 (1992) |
| [42] | Pierard, O.; Doghri, I.: An enhanced affine formulation and the corresponding numerical algorithms for the mean-field homogenization of elasto-viscoplastic composites, Int. J. Plasticity 22, 131-157 (2006) · Zbl 1089.74043 · doi:10.1016/j.ijplas.2005.04.001 |
| [43] | Pindera, M. -J.; Freed, A. D.; Arnold, S. M.: Effects of fiber and interfacial layer morphologies on the thermoplastic response of metal matrix composites, Int. J. Solids struct. 30, 1213-1238 (1993) |
| [44] | Pindera, M. -J.; Salzar, R. S.; Williams, T. O.: An evaluation of a new approach for the thermoplastic response of metal matrix composites, Compos. eng. 3, 1185-1201 (1993) |
| [45] | Pindera, M. -J.; Arnold, S. M.; Williams, T. O.: Thermoplastic response of metal matrix composites with homogenized and functionally graded interfaces, Compos. eng. 4, 129-145 (1994) |
| [46] | Pindera, M. -J.; Freed, A. D.: The effect of matrix microstructure on thermally-induced residual stresses in sic/titanium aluminide composites, ASME J. Eng. mater. Technol. 116, 215-221 (1994) |
| [47] | Castañeda, P. Ponte: Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I – theory, J. mech. Phys. solids 50, 737-757 (2002) · Zbl 1116.74412 · doi:10.1016/S0022-5096(01)00099-0 |
| [48] | Castañeda, P. Ponte; Suquet, P.: Nonlinear composites, Advances in applied mechanics 34, 171-302 (1998) · Zbl 0889.73049 |
| [49] | Qui, Y. P.; Weng, G. J.: A theory of plasticity for porous materials and particle-reinforced composites, J. appl. Mech. 59, 261-268 (1992) · Zbl 0825.73037 · doi:10.1115/1.2899515 |
| [50] | Rice, J. R.; Tracey, D. M.: On the ductile enlargement of voids in triaxial stress fields, J. mech. Phys. solids 17, 201-217 (1969) |
| [51] | Torquato, S.: Random heterogeneous materials: microstructure and macroscopic properties, (2001) · Zbl 0988.74001 |
| [52] | Tvergaard, V.: Material failure by void growth to coalescence, Advances in applied mechanics 27, 83-151 (1990) · Zbl 0728.73058 · doi:10.1016/S0065-2156(08)70195-9 |
| [53] | Walker, K. P.; Freed, A. D.; Jordan, E. H.: Thermoviscoplastic analysis of fibrous periodic composites by the use of triangular subvolumes, Compos. sci. Technol. 50, 71-84 (1994) |
| [54] | Williams, T. O.; Pindera, M. -J.: TMF modeling of advanced metal matrix composites in the presence of microstructural details, Mater. sci. Eng. 200, 156-172 (1995) |
| [55] | Williams, T. O.; Pindera, M. -J.: An analytical model for the inelastic axial shear response of unidirectional metal matrix composites, Int. J. Plasticity 13, 261-289 (1997) · Zbl 0893.73039 · doi:10.1016/S0749-6419(97)00011-9 |
| [56] | Yvonnet, J.; He, Q. -C.: The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains, J. comp. Phys. 223, 341-368 (2007) · Zbl 1163.74048 · doi:10.1016/j.jcp.2006.09.019 |
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