Abstract
In this study, a phase-field model is introduced to model the damage evolution, due to particle cracking in reinforced composites in which matrix deformation is described by an elastic-plastic constitutive law exhibiting linear hardening behavior. In order to establish the viability of the algorithm, the simulations are carried out for crack extension from a square hole in isotropic elastic solid under the complex loading path, and composites having the same volume fraction of reinforcements with two different particle sizes. The observed cracking patterns and development of the stress-strain curves agree with the experimental observations and previous numerical studies. The algorithm offers significant advantages to describe the microstructure and topological changes associated with the damage evolution in comparison to conventional simulation algorithms, due to the absence of formal meshing.
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References
Aranson IS, Kalatsky VA, Vinokur VM (2000) Continuum field description of crack propagation. Phys Rev Lett 85: 118. doi:10.1103/PhysRevLett.85.118
Biner SB (1990) Growth of fatigue cracks emanating from notches in SiC–Al composite. Fatig Fract Eng Mater Struc 13: 637. doi:10.1111/j.1460-2695.1990.tb00633.x
Biner SB (1994) The role of interfaces and secondary void nucleation on the ductile fracture process of discontinuous fiber reinforced composites. J Mater Sci 29: 2893. doi:10.1007/BF01117598
Bohm HJ, Han W (2001) Comparisons between three-dimensional and two-dimensional multi-particle reinforced metal matrix composites. Model Simul Mater Sci Eng 9: 47. doi:10.1088/0965-0393/9/2/301
Chawla N, Chawla KK (2006) Metal matrix composites. Springer, New York
Chen LQ, Shen J (1998) Applications of semi-implicit Fourier-spectral method to phase field equations. Comput Phys Commun 108: 147. doi:10.1016/S0010-4655(97)00115-X
Drabek T, Bohm HJ (2006) Micromechanical finite element analysis of metal matrix composites using nonlocal ductile failure models. Comput Mater Sci 37: 29. doi:10.1016/j.commatsci.2005.12.032
Frigo FM, Johnson SG (2005) The design and implementation of FFTW3. Proc IEEE 93: 216. doi:10.1109/JPROC.2004.840301
Ghosh S, Bai J, Raghavan P (2007) Concurrent multi-level model for damage evolution in microstructurally debonding composites. Mech Mater 39: 241. doi:10.1016/j.mechmat.2006.05.004
Griffith AA (1921) Phenomena of rupture and flow in solids. Philos Trans R Soc A 221: 163. doi:10.1098/rsta.1921.0006
Gungor MN, Liaw PK (eds) (1991) Fundamental relationship between microstructure and mechanical properties of metal matrix composites. TMS Warrendale, PA
Guo XH, Shi SQ, Ma XQ (2005) Elastoplastic phase field model for microstructure evolution. Appl Phys Lett 87: 221910. doi:10.1063/1.2138358
Gurson AL (1975) PhD thesis. Brown University
Hu SY, Chen LQ (2001) A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta Mater 49: 1879
Hu SY, Baskes MI, Stan M (2007) Phase-field modeling of microvoid evolution under elastic-plastic deformation. Appl Phys Lett 90: 081921. doi:10.1063/1.2709908
Jin YM, Wang YU, Khachaturyan AG (2001) Three-dimensional phase field microelasticity theory and modeling of multiple cracks and voids. Appl Phys Lett 79: 3071. doi:10.1063/1.1418260
Karma A, Kessler DA, Levine H (2001) Phase field model of mode-III dynamic fracture. Phys Rev Lett 87: 045501. doi:10.1103/PhysRevLett.87.045501
Khachaturyan AG, Semenovskaya S, Tsakalakos T (1995) Elastic strain energy of inhomogeneous solids. Phys Rev B 52: 15909. doi:10.1103/PhysRevB.52.15909
Llorca J, Needleman A, Suresh S (1991) An analysis of the effects of matrix void growth on deformation and ductility in metal-ceramic composites. Acta Metall Mater 39: 2317. doi:10.1016/0956-7151(91)90014-R
Llorca J, Gonzalez C (1998) Microstructural factors controlling the strength and ductility of particle-reinforced metal-matrix composites. J Mech Phys Solids 46: 1. doi:10.1016/S0022-5096(97)00038-0
Michel JC, Moulinec H, Suquet P (1999) Effective properties of composite materials with periodic microstructures: a computational approach. Comput Methods Appl Mech Eng 172: 109. doi:10.1016/S0045-7825(98)00227-8
Moulinec H, Suquet P (1998) A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput Methods Appl Mech Eng 157: 69. doi:10.1016/S0045-7825(97)00218-1
Needleman A, Tvergaard V (1987) An analysis of ductile rupture modes at a crack tip. J Mech Phys Solids 35: 151. doi:10.1016/0022-5096(87)90034-2
Needleman A (1990) An analysis of decohesion along an imperfect interface. Int J Fract 42: 21. doi:10.1007/BF00018611
Salac D, Lu W (2006) Controlled nanocrack patterns for nanowires. J Comp Theor Nanoscience 3: 263
Segurado J, Llorca J (2006) Computational micromechanics of composites: The effect of particle spatial distribution. Mech Mater 38: 873. doi:10.1016/j.mechmat.2005.06.026
Spatschek R, Hartmann M, Brener E, Muller-Krumbhaar H, Kassner K (2006) Phase-field modeling of fracture and composite materials. Phys Rev Lett 96: 015502. doi:10.1103/PhysRevLett.96.015502
Spatschek R, Muller-Gugenberger C, Brener E, Nestler B (2007) Phase field modeling of fracture and stress-induced phase transitions. Phys Rev E Stat Nonlinear Soft Matter Phys 75: 066111. doi:10.1103/PhysRevE.75.066111
Suresh S, Mortensen A, Needleman A (eds) (1993) Fundamentals of metal matrix composites. Butterworth, Stoneham, MA
Tang F, Anderson IE, Biner SB (2003) Microstructure and mechanical properties of pure Al matrix reinforced by Al–Cu–Fe particles. Mater Sci Eng A A 363: 20. doi:10.1016/S0921-5093(03)00433-7
Tvergaard V, Needleman A (1995) Effects of nonlocal damage in porous plastic solids. Int J Solids Struct 32: 1063. doi:10.1016/0020-7683(94)00185-Y
Tyrus JM, Gosz M, De Santiago E (2007) A local finite element implementation for imposing periodic boundary conditions on composite micromechanical models. Int J Solids Struct 44: 2972. doi:10.1016/j.ijsolstr.2006.08.040
Wang YU, Jin YM, Khachaturyan AG (2002) Phase field microelasticity theory and simulation of multiple voids and cracks in single crystals and polycrystals under applied stress. J Appl Phys 91: 6435. doi:10.1063/1.1471389
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Biner, S.B., Hu, S.Y. Simulation of damage evolution in discontinously reinforced metal matrix composites: a phase-field model. Int J Fract 158, 99–105 (2009). https://doi.org/10.1007/s10704-009-9351-6
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DOI: https://doi.org/10.1007/s10704-009-9351-6