×

zbMATH — the first resource for mathematics

Simulation of damage evolution in discontinuously reinforced metal matrix composites: a phase-field model. (English) Zbl 1400.74099
Summary: 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.

MSC:
74R99 Fracture and damage
74E30 Composite and mixture properties
Software:
FFTW
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aranson IS, Kalatsky VA, Vinokur VM (2000) Continuum field description of crack propagation. Phys Rev Lett 85: 118. doi: 10.1103/PhysRevLett.85.118 · doi:10.1103/PhysRevLett.85.118
[2] 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 · doi:10.1111/j.1460-2695.1990.tb00633.x
[3] 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 · doi:10.1007/BF01117598
[4] 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 · doi:10.1088/0965-0393/9/2/301
[5] Chawla N, Chawla KK (2006) Metal matrix composites. Springer, New York
[6] 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 · Zbl 1017.65533 · doi:10.1016/S0010-4655(97)00115-X
[7] 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 · doi:10.1016/j.commatsci.2005.12.032
[8] Frigo FM, Johnson SG (2005) The design and implementation of FFTW3. Proc IEEE 93: 216. doi: 10.1109/JPROC.2004.840301 · doi:10.1109/JPROC.2004.840301
[9] 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 · doi:10.1016/j.mechmat.2006.05.004
[10] Griffith AA (1921) Phenomena of rupture and flow in solids. Philos Trans R Soc A 221: 163. doi: 10.1098/rsta.1921.0006 · doi:10.1098/rsta.1921.0006
[11] Gungor MN, Liaw PK (eds) (1991) Fundamental relationship between microstructure and mechanical properties of metal matrix composites. TMS Warrendale, PA
[12] Guo XH, Shi SQ, Ma XQ (2005) Elastoplastic phase field model for microstructure evolution. Appl Phys Lett 87: 221910. doi: 10.1063/1.2138358 · doi:10.1063/1.2138358
[13] Gurson AL (1975) PhD thesis. Brown University
[14] Hu SY, Chen LQ (2001) A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta Mater 49: 1879 · doi:10.1016/S1359-6454(01)00118-5
[15] 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 · doi:10.1063/1.2709908
[16] 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 · doi:10.1063/1.1418260
[17] 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 · doi:10.1103/PhysRevLett.87.045501
[18] Khachaturyan AG, Semenovskaya S, Tsakalakos T (1995) Elastic strain energy of inhomogeneous solids. Phys Rev B 52: 15909. doi: 10.1103/PhysRevB.52.15909 · doi:10.1103/PhysRevB.52.15909
[19] 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 · doi:10.1016/0956-7151(91)90014-R
[20] 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 · Zbl 0942.74019 · doi:10.1016/S0022-5096(97)00038-0
[21] 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 · Zbl 0964.74054 · doi:10.1016/S0045-7825(98)00227-8
[22] 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 · Zbl 0954.74079 · doi:10.1016/S0045-7825(97)00218-1
[23] 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 · Zbl 0601.73106 · doi:10.1016/0022-5096(87)90034-2
[24] Needleman A (1990) An analysis of decohesion along an imperfect interface. Int J Fract 42: 21. doi: 10.1007/BF00018611 · doi:10.1007/BF00018611
[25] Salac D, Lu W (2006) Controlled nanocrack patterns for nanowires. J Comp Theor Nanoscience 3: 263
[26] 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 · doi:10.1016/j.mechmat.2005.06.026
[27] 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 · doi:10.1103/PhysRevLett.96.015502
[28] 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 · doi:10.1103/PhysRevE.75.066111
[29] Suresh S, Mortensen A, Needleman A (eds) (1993) Fundamentals of metal matrix composites. Butterworth, Stoneham, MA
[30] 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 · doi:10.1016/S0921-5093(03)00433-7
[31] 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 · Zbl 0866.73060 · doi:10.1016/0020-7683(94)00185-Y
[32] 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 · Zbl 1221.74079 · doi:10.1016/j.ijsolstr.2006.08.040
[33] 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 · doi:10.1063/1.1471389
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.