Multi-inclusion unit cell models for metal matrix composites with randomly oriented discontinuous reinforcements

Nguyen Thanh, 1995, Microstructure and compression behavior in the semisolid state of short-fibre-reinforced A356 aluminium alloys, Mater. Sci. Engng., A196, 33, 10.1016/0921-5093(94)09680-5 Wu, 2000, The mechanical and thermal expansion behavior of an Al–Si alloy composite reinforced with potassium titanate whiskers, Compos. Sci. Technol., 60, 2873, 10.1016/S0266-3538(00)00160-3 Allen, 1990, The effective thermoelastic properties of whisker-reinforced composites as functions of material forming parameters, 17 Eshelby, 1957, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. R. Soc. London A, 241, 376, 10.1098/rspa.1957.0133 Ponte Castañeda, 1998, Nonlinear composites, 171 Tandon, 1984, The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites, Polym. Compos., 5, 327, 10.1002/pc.750050413 Withers, 1989, The application of the Eshelby method of internal stress determination to short fibre metal matrix composites, Acta Metall., 37, 3061, 10.1016/0001-6160(89)90341-6 Li, 1993, The effect of particle shape and stiffness on the constitutive behavior of metal matrix composites, Int. J. Solids Struct., 30, 3189, 10.1016/0020-7683(93)90109-K Lagoudas, 1991, Elastoplastic behavior of metal matrix composites based on incremental plasticity and the Mori–Tanaka averaging scheme, Comput. Mech., 8, 193, 10.1007/BF00372689 Lorca, 1991, An analysis of the effects of matrix void growth on deformation and ductility in metal ceramic composites, Acta Metall. Mater., 39, 2317, 10.1016/0956-7151(91)90014-R Böhm, 1993, Some simple models for micromechanical investigations of fiber arrangement effects in MMCs, Comput. Mater. Sci., 1, 177, 10.1016/0927-0256(93)90010-K Levy, 1991, Elastoplastic finite element analysis of short-fiber-reinforced SiC/Al composites. Effects of thermal treatment, Acta Metall. Mater., 39, 2255, 10.1016/0956-7151(91)90008-O Ingber, 1997, A parallel-supercomputing investigation of the stiffness of aligned short-fiber-reinforced composites using the boundary element method, Int. J. Num. Meth. Engng., 40, 3477, 10.1002/(SICI)1097-0207(19970930)40:18<3477::AID-NME225>3.0.CO;2-B Walpole, 1966, On bounds for the overall elastic moduli of inhomogeneous systems––I, J. Mech. Phys. Sol., 14, 151, 10.1016/0022-5096(66)90035-4 Willis, 1977, Bounds and self-consistent estimates for the overall moduli of anisotropic composites, J. Mech. Phys. Sol., 25, 185, 10.1016/0022-5096(77)90022-9 Benveniste, 1987, A new approach to the application of Mori–Tanaka’s theory in composite materials, Mech. Mater., 6, 147, 10.1016/0167-6636(87)90005-6 Takao, 1982, Effective longitudinal Young’s modulus of misoriented short fiber composites, J. Appl. Mech., 49, 536, 10.1115/1.3162509 Pettermann, 1997, Some direction dependent properties of matrix–inclusion type composites with given reinforcement orientation distributions, Composites, 28B, 253, 10.1016/S1359-8368(96)00055-8 Mlekusch, 1999, Thermoelastic properties of short-fibre-reinforced thermoplastics, Compos. Sci. Technol., 59, 911, 10.1016/S0266-3538(98)00133-X Bhattacharyya, 1994, The elastoplastic behavior of a class of two-phase composites containing rigid inclusions, Appl. Mech. Rev., 47, S45, 10.1115/1.3122821 Dunn, 1997, Elastic–plastic behavior of textured short-fiber composites, Acta Mater., 45, 3327, 10.1016/S1359-6454(96)00401-6 Benveniste, 1990, Some remarks on three micromechanical models in composite media, J. Appl. Mech., 57, 474, 10.1115/1.2892016 Ferrari, 1991, Asymmetry and the high concentration limit of the Mori–Tanaka effective medium theory, Mech. Mater., 11, 251, 10.1016/0167-6636(91)90006-L Ponte Castañeda, 1995, The effect of spatial distribution on the effective behavior of composite materials and cracked media, J. Mech. Phys. Sol., 43, 1919, 10.1016/0022-5096(95)00058-Q Hori, 1993, Double-inclusion model and overall moduli of multi-phase composites, Mech. Mater., 14, 189, 10.1016/0167-6636(93)90066-Z Kuster, 1974, Velocity and attenuation of seismic waves in two-phase media: I. Theoretical formulation, Geophysics, 39, 587, 10.1190/1.1440450 Berryman, 1996, Critique of two explicit schemes for estimating elastic properties of multiphase composites, Mech. Mater., 22, 149, 10.1016/0167-6636(95)00035-6 Hu, 2000, The connections between the double-inclusion model and the Ponte Castañeda–Willi, Mori–Tanaka, Mori–Tanaka, and Kuster–Toksoz models, Mech. Mater., 32, 495, 10.1016/S0167-6636(00)00015-6 Berryman, 1980, Long-wavelength propagation in composite elastic media, II. Ellipsoidal inclusions, J. Acoust. Soc. Am., 68, 1820, 10.1121/1.385172 Hashin, 1963, A variational approach to the theory of the elastic behavior of multiphase materials, J. Mech. Phys. Sol., 11, 127, 10.1016/0022-5096(63)90060-7 Fukuda, 1974, On Young’s modulus of short fiber composites, Fibre Sci. Technol., 7, 207, 10.1016/0015-0568(74)90018-9 Jayaraman, 1996, Correction to the Fukuda–Kawata Young’s modulus theory and the Fukuda–Chou strength theory for short fibre-reinforced composite materials, J. Mater. Sci., 31, 2059, 10.1007/BF00356627 Halpin, 1969, The laminate approximation for randomly oriented fibrous composites, J. Compos. Mater., 3, 720, 10.1177/002199836900300416 Fu, 1998, The elastic modulus of misaligned short-fiber-reinforced polymers, Compos. Sci. Technol., 58, 389, 10.1016/S0266-3538(97)00129-2 Courage, 1992, Effective material parameters for composites with randomly oriented short fibers, Comput. Struct., 44, 1179, 10.1016/0045-7949(92)90361-3 Ghosh, 1997, Tesselation-based computational methods for the characterization and analysis of heterogeneous microstructures, Compos. Sci. Technol., 57, 1187, 10.1016/S0266-3538(97)00042-0 Böhm, 2001, Comparisons between three-dimensional and two-dimensional multi-particle unit cell models for particle reinforced MMCs, Modell. Simul. Mater. Sci. Engng., 9, 47, 10.1088/0965-0393/9/2/301 Dong, 1997, Prediction of mechanical behavior of short fiber reinforced MMCs by combined cell models, Comput. Mater. Sci., 9, 121, 10.1016/S0927-0256(97)00066-9 Sørensen, 1992, Three-dimensional analysis of creep in a metal–matrix composite, Mater. Sci. Engng., A158, 129, 10.1016/0921-5093(92)90001-H Banerjee, 1992, Elastic analysis of three-dimensional solids with fiber inclusions by BEM, Int. J. Sol. Struct., 29, 2423, 10.1016/0020-7683(92)90001-A Bush, 1992, An investigation of two- and three-dimensional models for predicting the elastic properties of particulate- and whisker-reinforced composite materials, Mater. Sci. Engng., A154, 139, 10.1016/0921-5093(92)90339-3 Böhm, 1999, Modeling of phase arrangement effects in high speed tool steels, 147 Han, 2001, Three-dimensional multi-particle arrangement effects on the mechanical behavior and damage initiation of particle reinforced composites, Compos. Sci. Technol., 61, 1581, 10.1016/S0266-3538(01)00061-6 Gusev, 2000, Fiber packing and elastic properties of a transversely random unidirectional glass/epoxy composite, Compos. Sci. Technol., 60, 535, 10.1016/S0266-3538(99)00152-9 Rintoul, 1997, Reconstruction of the structure of dispersions, J. Colloid Interf. Sci., 186, 467, 10.1006/jcis.1996.4675 T. Antretter, Micromechanical Modeling of High Speed Steel, VDI–Verlag, Reihe 18, Nr. 232, Düsseldorf, 1998 LLorca, 1998, Microstructural factors controlling the strength and ductility of particle reinforced metal matrix composites, J. Mech. Phys. Sol., 46, 1, 10.1016/S0022-5096(97)00038-0 H.J. Böhm, A Short Introduction to Basic Aspects of Continuum Micromechanics, CDL–FMD Report 3–1998, TU Wien, Vienna, 1998 Weibull, 1951, A statistical distribution function of wide applicability, J. Appl. Mech., 18, 293, 10.1115/1.4010337 Wallin, 1987, Fracture of brittle particles in a ductile matrix, Int. J. Fract., 32, 201, 10.1007/BF00018353 Zimmerman, 1992, Hashin–Shtrikman bounds on the Poisson ratio of a composite material, Mech. Res. Comm., 19, 563, 10.1016/0093-6413(92)90085-O Torquato, 1991, Random heterogeneous media: Microstructure and improved bounds on effective properties, Appl. Mech. Rev., 44, 37, 10.1115/1.3119494 Christensen, 1979, Solutions for effective shear properties in three phase sphere and cylinder models, J. Mech. Phys. Sol., 27, 315, 10.1016/0022-5096(79)90032-2 Gusev, 1997, Representative volume element size for elastic composites: A numerical study, J. Mech. Phys. Sol., 45, 1449, 10.1016/S0022-5096(97)00016-1 Zohdi, 1999, A model for simulating the deterioration of structural-scale material responses of microheterogeneous solids, 91 Drugan, 1996, A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites, J. Mech. Phys. Sol., 44, 497, 10.1016/0022-5096(96)00007-5 Bao, 1991, Particle reinforcement of ductile matrices against plastic flow and creep, Acta Metall. Mater., 39, 1871, 10.1016/0956-7151(91)90156-U Povirk, 1992, Thermally and mechanically induced residual stresses in Al–SiC composites, Acta. Metall. Mater., 40, 2391, 10.1016/0956-7151(92)90158-B