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Molecular-dynamics simulation-based cohesive zone representation of intergranular fracture processes in aluminum. (English) Zbl 1120.74782
Summary: A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics (MD) simulations. An MD model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat \(\Sigma 99\) \([1\, 1\, 0]\) symmetric tilt grain boundary in aluminum. Under hydrostatic tensile load, the simulation reveals asymmetric crack propagation in the two opposite directions along the grain boundary. In one direction, the crack propagates in a brittle manner by cleavage with very little or no dislocation emission, and in the other direction, the propagation is ductile through the mechanism of deformation twinning. This behavior is consistent with the Rice criterion for cleavage vs. dislocation blunting transition at the crack tip. The preference for twinning to dislocation slip is in agreement with the predictions of the Tadmor and Hai criterion. A comparison with finite element calculations shows that while the stress field around the brittle crack tip follows the expected elastic solution for the given boundary conditions of the model, the stress field around the twinning crack tip has a strong plastic contribution. Through the definition of a Cohesive-Zone-Volume-Element-an atomistic analog to a continuum cohesive zone model element-the results from the MD simulation are recast to obtain an average continuum traction-displacement relationship to represent cohesive zone interaction along a characteristic length of the grain boundary interface for the cases of ductile and brittle decohesion.

74R20 Anelastic fracture and damage
74E20 Granularity
74S30 Other numerical methods in solid mechanics (MSC2010)
74S05 Finite element methods applied to problems in solid mechanics
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[1] ABAQUS/Standard User’s Manual, 2004. Hibbitt, Karlsson, and Sorensen, Inc.
[2] Abraham, F.F., The atomic dynamics of fracture, J. mech. phys. solids, 49, 2095-2111, (2001) · Zbl 1012.74007
[3] Abraham, F.F.; Brodbeck, D.; Rafey, R.A.; Rudge, W.E., Instability dynamics of fracture: a computer simulation investigation, Phys. rev. lett., 73, 272-275, (1994)
[4] Barber, M.; Donley, J.; Langer, J.S., Steady-state propagation of a crack in a viscoelastic strip, Phys. rev. A, 40, 366-376, (1989)
[5] Camacho, G.T.; Ortiz, M., Computational modeling of impact damage in brittle materials, Int. J. solids struct., 33, 2899-2938, (1996) · Zbl 0929.74101
[6] Chen, Q.; Huamg, Y.; Quiao, L.; Chu, W., Failure modes after exhaustion of dislocation glide ability in thin crystals, Sci. China (series E), 42, 1-9, (1999)
[7] Ching, E.S.C., Dynamic stresses at a moving crack tip in a model of fracture propagation, Phys. rev. E, 49, 3382-3388, (1994)
[8] Clarke, A.S.; Jonsson, H., Structural changes accompanying densification of random hard-sphere packings, Phys. rev. E, 47, 3975-3984, (1993)
[9] Cleri, F.; Phillpot, S.R.; Wolf, D., Atomistic simulations of intergranular fracture in symmetric-tilt grain boundaries, Interf. sci., 7, 45-55, (1999)
[10] Cormier, J.; Rickman, J.M.; Delph, T.J., Stress calculation in atomistic simulations of perfect and imperfect solids, J. appl. phys., 89, 99-104, (2001)
[11] Costanzo, F.; Allen, D.H., A continuum thermodynamic analysis of cohesive zone models, Int. J. sci. eng., 33, 2197-2219, (1995) · Zbl 0899.73029
[12] Dahmen, U.; Hetherington, J.D.; O’Keefe, M.A.; Westmacott, K.H.; Mills, M.J.; Daw, M.S.; Vitek, V., Atomic structure of a σ99 grain boundary in al: a comparison between atomic-resolution observation and pair-potential and embedded-atom simulations, Philos. mag. lett., 62, 327-335, (1990)
[13] Dávila, C.G., 2001. Mixed-mode decohesion elements for analysis of progressive delamination. 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Seattle, WA 16-19 April 2001, article: AIAA-01-1486.
[14] Farkas, D., Bulk and intergranular fracture behavior of nial, Philos. mag. A, 80, 1425-1444, (2000)
[15] Farkas, D., Fracture mechanisms of symmetrical tilt grain boundaries, Philos. mag. lett., 80, 229-237, (2000)
[16] Farkas, D.; Duranduru, M.; Curtin, W.A.; Ribens, C., Multiple-dislocation emission from the crack tip in the ductile fracture of al, Philos. mag. A, 81, 1241-1255, (2001)
[17] Gall, K.; Horstemeyer, M.F.; Van Schilfgaarde, M.; Baskes, M.I., Atomistic simulations on the tensile debonding of an aluminum – silicon interface, J. mech. phys. solids, 48, 2183-2212, (2000) · Zbl 1052.74502
[18] Gao, H., A theory of local limiting speed in dynamic fracture, J. mech. phys. solids, 44, 1453-1474, (1996)
[19] Gumbsch, P.; Zhou, S.J.; Holian, B.L., Molecular dynamics investigation of dynamic crack stability, Phys. rev. B, 55, 3445-3455, (1997)
[20] Hai, S.; Tadmor, E.B., Deformation twinning at aluminum crack tips, Acta mater., 51, 117-131, (2003)
[21] Honeycutt, J.D.; Andersen, H.C., Molecular dynamics study of melting and freezing of small lennard – jones clusters, J. phys. chem., 91, 4950-4963, (1987)
[22] Iesulauro, E.; Ingraffea, A.R.; Arwade, S.; Wawrzynek, P.A., Simulation of grain boundary decohesion and crack initiation in aluminum microstructure models, ()
[23] Klein, P.; Gao, H., Crack nucleation and growth as strain localization in a virtual-bond continuum, Eng. fract. mech., 61, 21-48, (1998)
[24] Komanduri, R.; Chandrasekaran, N.; Raff, L.M., Molecular dynamics (MD) simulation of uniaxial tension of some single-crystal cubic metals at nanolevel, Int. J. mech. sci., 43, 2237-2260, (2001) · Zbl 0993.74522
[25] Langer, J.S., Models of crack propagation, Phys. rev. A, 46, 3123-3131, (1992)
[26] Langer, J.S., Dynamic model of onset and propagation of fracture, Phys. rev. lett., 70, 3592-3594, (1993)
[27] Langer, J.S.; Nakanishi, H., Models of crack propagation. II. two-dimensional model with dissipation on the fracture surface, Phys. rev. E, 48, 439-448, (1993)
[28] Lutsko, J.F., Stress and elastic constants in anisotropic solids: molecular dynamics techniques, J. appl. phys., 64, 1152-1154, (1988)
[29] Mishin, Y.; Farkas, D.; Mehl, M.J.; Papaconstantopoulos, D.A., Interatomic potentials for monoatomic metals from experimental data and ab initio calculations, Phys. rev. B, 59, 3393-3407, (1999)
[30] Nguyen, O.; Ortiz, M., Coarse-graining and renormalization of atomistic binding relations and universal macroscopic cohesive behavior, J. mech. phys. solids, 50, 1727-1741, (2002) · Zbl 1004.74009
[31] Nose, S., A unified formulation of the constant temperature molecular dynamics method, J. chem. phys., 81, 511-519, (1984)
[32] Parrinello, M.; Rahman, A., Polymorphic transitions in single crystals: a new molecular dynamics method, J. appl. phys., 52, 7182-7190, (1981)
[33] Pond, R.C.; Garcia-Garcia, L.M.F., Deformation twinning in al, Inst. phys. conf. ser., 61, 495-498, (1982)
[34] Raynolds, J.E.; Smith, J.R.; Zhao, G.-L.; Srolovitz, D.J., Adhesion in nial – cr from first principles, Phys. rev. B, 53, 13883-13890, (1996)
[35] Rice, J.R., Dislocation nucleation from a crack tip: an analysis based on the Peierls concept, J. mech. phys. solids, 40, 239-271, (1992)
[36] Schiotz, J.; Vegge, T.; Di Tolla, F.D.; Jacobsen, K.W., Atomic-scale simulations of the mechanical deformation of nanocrystalline metals, Phys. rev. B, 60, 11971-11983, (1999)
[37] Spearot, D.; Jacob, K.I.; McDowell, D.L., Non-local separation constitutive laws for interfaces and their relation to nanoscale simulations, Mech. mater., 36, 825-847, (2004)
[38] Tadmor, E.B.; Hai, S., A Peierls criterion for the onset of deformation twinning at a crack tip, J. mech. phys. solids, 51, 765-793, (2003) · Zbl 1145.74311
[39] Tvergaard, V.; Hutchinson, J.W., The relation between crack growth resistance and fracture process parameters in elastic – plastic solids, J. mech. phys. solids, 40, 1377-1397, (1992) · Zbl 0775.73218
[40] Tvergaard, V.; Hutchinson, J.W., Effectt of strain-dependent cohesive zone model on predictions of crack growth resistance, Int. J. solids struct., 33, 3297-3308, (1996) · Zbl 0905.73056
[41] Van der Ven, A.; Ceder, G., The thermodynamics of decohesion, Acta mater., 52, 1223-1235, (2004)
[42] Weertman, J.; Weertman, J.R., Elemantary dislocation theory, (1992), Oxford University Press New York · Zbl 0734.73065
[43] Wei, Y.J.; Anand, L., Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals, J. mech. phys. solids, 52, 2587-2616, (2004) · Zbl 1084.74014
[44] Wolf, D., Correlation between structure, energy, and ideal cleavage fracture for symmetrical grain boundaries in fcc metals, J. mater. res., 5, 1708-1730, (1990)
[45] Wolf, D.; Jaszczak, J.A., Tailored elastic behavior of multilayers through controlled interface structure, J. comp. aided mater. design, 1, 111-148, (1993)
[46] Wortman, J.J.; Evans, R.A., Young’s modulus, and Poisson’s ratio in silicon and germanium, J. appl. phys., 36, 153-156, (1965)
[47] Yamakov, V.; Wolf, D.; Salazar, M.; Phillpot, S.R.; Gleiter, H., Length-scale effects in the nucleation of extended lattice dislocations in nanocrystalline al by molecular-dynamics simulation, Acta mater., 49, 2713-2722, (2001)
[48] Yamakov, V.; Wolf, D.; Phillpot, S.R.; Mukherjee, A.K.; Gleiter, H., Dislocation processes in the deformation of nanocrystalline al by molecular-dynamics simulation, Nature mater., 1, 45-48, (2002)
[49] Yamakov, V.; Wolf, D.; Phillpot, S.R.; Gleiter, H., Dislocation – dislocation and dislocation-twin reactions in nanocrystalline al by molecular-dynamics simulation, Acta mater., 51, 4135-4147, (2003)
[50] Yamakov, V.; Wolf, D.; Phillpot, S.R.; Mukherjee, A.K.; Gleiter, H., Deformation mechanism crossover and mechanical behavior in nanocrystalline materials, Philos. mag. lett., 83, 385-393, (2003)
[51] Yamakov, V.; Saether, E.; Phillips, D.R.; Glaessgen, E.H., Dynamic instability in intergranular fracture, Phys. rev. lett., 95, 015502-015514, (2005)
[52] Zavattieri, P.D.; Espinosa, H.D., An examination of the competition between bulk behavior and interfacial behavior of ceramics subjected to dynamic pressure-shear loading, J. mech. phys. solids, 51, 607-635, (2003) · Zbl 1018.74519
[53] Zavattieri, P.D.; Raghuram, P.V.; Espinosa, H.D., A computational model of ceramic microstructures subjected to multi-axial dynamic loading, J. mech. phys. solids, 49, 27-68, (2001) · Zbl 1013.74055
[54] Zimmerman, J.A., Jones, R.E., Klein, P.A., Bammann, D.J., Webb III, E.B., Hoyt, J.J., 2002. Continuum definitions for stress in atomistic simulation, SAND Report, Sandia National Laboratory, SAND2002-8608.
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