Effects of lattice incompatibility-induced hardening on the fracture behavior of ductile single crystals. (English) Zbl 1115.74305
Summary: Plane-strain mode-I cracks in a ductile single crystal are studied under conditions of small scale yielding. The specific case of a (0 1 0) crack growing in the [1 0 1] direction for an FCC crystal is considered. Crack initiation and its subsequent growth are computed by specifying a traction-separation relation in the crack plane ahead of the crack tip. The crystal is characterized by a hardening model that incorporates physically motivated gradient effects. Significant traction elevation ahead of the crack tip is obtained by incorporating such effects, allowing a better basis for the explanation of experimentally observed cleavage in the presence of substantial plastic flow in slowly deforming ductile materials. Resistance curves based on parameters characterizing the fracture process and the continuum properties of the crystal are computed. Simulation results indicate that the length-scale of the lattice incompatibility-dominated region has to be comparable or larger than the length of the fracture process zone for gradient effects to have a significant effect on fracture resistance. Both the work of separation and the peak separation stress also play important roles in determining the fracture resistance of the crystal.
MSC:
| 74A45 | Theories of fracture and damage |
| 74E15 | Crystalline structure |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
lattice incompatibility; small scale yielding; hardening; traction elevation; resistance curvesReferences:
| [1] | Acharya, A.; Bassani, J. L., On non-local flow theories that preserve the classical structure of incremental boundary value problems, (Pineau, A.; Zaoui, A., IUTAM Symposium on Micromechanics and Damage of Multiphase Materials (1996), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht), 3-9 |
| [2] | Acharya, A.; Bassani, J. L., Lattice incompatibility and a gradient theory of crystal plasticity, J. Mech. Phys. Solids, 48, 1565-1595 (2000) · Zbl 0963.74010 |
| [3] | Acharya, A.; Beaudoin, A. J., Grain-size effect in viscoplastic polycrystals at moderate strains, J. Mech. Phys. Solids, 48, 2213-2230 (2000) · Zbl 0958.74013 |
| [4] | Bagchi, A.; Evans, A. G., The mechanics and physics of thin film decohesion and its measurement, Interface Sci, 3, 169-193 (1996) |
| [5] | Barenblatt, G.I., 1962. The mathematical theory of equilibrium cracks in brittle fracture. In: Dryden, H.L., Von Karman, Th., (Eds.), Advances in Applied Mechanics, Vol. 7. Academic Press, New York, pp. 55-129.; Barenblatt, G.I., 1962. The mathematical theory of equilibrium cracks in brittle fracture. In: Dryden, H.L., Von Karman, Th., (Eds.), Advances in Applied Mechanics, Vol. 7. Academic Press, New York, pp. 55-129. |
| [6] | Beaudoin, A. J.; Acharya, A.; Chen, S. R.; Korzekwa, D. A.; Stout, M. G., Consideration of grain-size effect and kinetics in the plastic deformation of metal polycrystals, Acta Mater, 48, 3409-3423 (2000) |
| [7] | Becker, R., Analysis of shear localization during bending of a polycrystalline sheet, J. Appl. Mech. Trans. ASME, 59, 491-496 (1992) |
| [8] | Beltz, G. E.; Rice, J. R.; Shih, C. F.; Xia, L., A self-consistent method for cleavage in the presence of plastic flow, Acta Mater, 44, 3943-3954 (1996) |
| [9] | Chen, J. Y.; Wei, Y.; Huang, Y.; Hutchinson, J. W.; Hwang, K. C., The crack tip fields in strain gradient plasticitythe asymptotic and numerical analyses, Eng. Fract. Mech, 64, 625-648 (1999) |
| [10] | Cuitiño, A. M.; Ortiz, M., Computational modeling of single crystals, Modelling Simulation Mater. Sci. Eng, 1, 225-263 (1992) |
| [11] | Cuitiño, A. M.; Ortiz, M., Three-dimensional crack tip fields in four-point-bending copper single-crystal specimens, J. Mech. Phys. Solids, 44, 863-904 (1996) |
| [12] | Crone, W. C.; Shield, T. W., An experimental study of the effect of hardening on plastic deformation at notch tips in metallic single crystals, J. Mech. Phys. Solids, 51, 1623-1647 (2003) |
| [13] | Crone, W. C.; Shield, T. W.; Creuziger, A.; Henneman, B., Orientation dependence of the slip near notches in ductile FCC single crystals, J. Mech. Phys. Solids, 52, 85-112 (2004) · Zbl 1045.74506 |
| [14] | Drugan, W. J.; Rice, J. R.; Sham, T.-L., Asymptotic analysis of growing plane strain tensile cracks in elastic-ideally plastic solids, J. Mech. Phys. Solids, 30, 447-473 (1982) · Zbl 0496.73086 |
| [15] | Elssner, G.; Korn, D.; Ruehle, M., The influence of interface impurities on fracture energy of UHV diffusion bonded metal-ceramic bicrystals, Scr. Metall. Mater, 31, 1037-1042 (1994) |
| [16] | Evans, A. G.; Hutchinson, J. W.; Wei, Y., Interface adhesioneffects of plasticity and segregation, Acta Mater, 47, 4093-4113 (1999) |
| [17] | Fleck, N. A.; Hutchinson, J. W., A phenomenological theory for strain gradient effects in plasticity, J. Mech. Phys. Solids, 41, 1825-1857 (1993) · Zbl 0791.73029 |
| [18] | Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (Eds.), Advances in Applied Mechanics, Vol. 33, Academic Press, New York, pp. 295-361.; Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (Eds.), Advances in Applied Mechanics, Vol. 33, Academic Press, New York, pp. 295-361. · Zbl 0894.73031 |
| [19] | Freund, L. B.; Hutchinson, J. W., High strain-rate crack growth in rate-dependent plastic solids, J. Mech. Phys. Solids, 33, 169-191 (1985) |
| [20] | Gurtin, M. E., On the plasticity of single crystalsfree energy, microforces, plastic-strain gradients, J. Mech. Phys. Solids, 48, 989-1036 (2000) · Zbl 0988.74021 |
| [21] | Huang, Y.; Gao, H.; Nix, W. D.; Hutchinson, J. W., Mechanism-based strain gradient plasticity—II. Analysis, J. Mech. Phys. Solids, 48, 99-128 (2000) · Zbl 0990.74016 |
| [22] | Hutchinson, J. W., Bounds and self-consistent estimates for creep of polycrystalline materials, Proc. R. Soc. London A, 348, 101-127 (1976) · Zbl 0319.73059 |
| [23] | Irwin, G.R., 1958. Fracture. In: Handbuch der Physik, Vol. 6, Springer, Berlin, p. 557.; Irwin, G.R., 1958. Fracture. In: Handbuch der Physik, Vol. 6, Springer, Berlin, p. 557. |
| [24] | Jiang, H.; Huang, Y.; Zhuang, Z.; Hwang, K. C., Fracture in mechanism-based strain gradient plasticity, J. Mech. Phys. Solids, 49, 979-993 (2001) · Zbl 1162.74446 |
| [25] | Jokl, M. L.; Vitek, V.; McMahon, C. J., A microscopic theory of brittle fracture in deformable solidsa relation between ideal work to fracture and plastic work, Acta Metall, 28, 1479-1488 (1980) |
| [26] | Kocks, U. F.; Tomé, C. N.; Wenk, H.-R., Texture and Anisotropy (1998), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0916.73001 |
| [27] | Kok, S.; Beaudoin, A. J.; Tortorelli, D. A., On the development of stage IV hardening using a model based on the mechanical threshold, Acta Mater, 50, 1653-1667 (2002) |
| [28] | Kysar, J. W., Directional dependence of fracture in copper/sapphire bicrystal, Acta Mater, 48, 3509-3524 (2000) |
| [29] | Kysar, J. W., Continuum simulations of directional dependence of crack growth along a copper/sapphire bicrystal interface. Part I: experiments and crystal plasticity background, J. Mech. Phys. Solids, 49, 1099-1128 (2001) · Zbl 1162.74447 |
| [30] | Lawn, B., Fracture of Brittle Solids. Cambridge Solid State Science Series (1993), Cambridge University Press: Cambridge University Press Cambridge |
| [31] | Niordson, C. F., Nonlocal plasticity effects on fracture toughness, (Khan, A. S.; Lopez-Pamies, O., Proceedings of Plasticity 2002 “Plasticity, Damage and Fracture at Macro, Micro, and Nano Scales” (2002), Neat Press), 591-593 |
| [32] | Pan, J.; Rice, J. R., Rate sensitivity of plastic flow and implications for yield-surface vertices, Int. J. Solids Struct, 19, 973-987 (1983) · Zbl 0543.73033 |
| [33] | Peirce, D.; Asaro, R. J.; Needleman, A., Material rate dependence and localized deformation in crystalline solids, Acta Metall, 31, 1087-1119 (1983) |
| [34] | Peirce, D.; Shih, C. F.; Needleman, A., A tangent modulus method for rate dependent solids, Comput. Struct, 18, 875-887 (1984) · Zbl 0531.73057 |
| [35] | Rahulkumar, P., 1999. Computational fracture mechanics using cohesive element formulations. Ph.D. Thesis, Carnegie Mellon University.; Rahulkumar, P., 1999. Computational fracture mechanics using cohesive element formulations. Ph.D. Thesis, Carnegie Mellon University. |
| [36] | Rahulkumar, P.; Jagota, A.; Bennison, S. J.; Saigal, S., Cohesive element modeling of viscoelastic fracture:application to peel testing of polymers, Int. J. Solids Struct, 37, 1873-1897 (2000) · Zbl 1090.74676 |
| [37] | Reimanis, I. E.; Dalgleish, B. J.; Evans, A. G., Fracture resistance of a model metal/ceramic interface, Acta Metall. Mater, 39, 3133-3141 (1991) |
| [38] | Rice, J. R., Tensile crack tip fields in elastic-ideally plastic crystals, Mech. Mater, 6, 317-335 (1987) |
| [39] | Rice, J. R.; Wang, J.-S., Embrittlement of interfaces by solute segregation, Mater. Sci. Eng. A, 107, 23-40 (1989) |
| [40] | Rice, J. R.; Hawk, D. E.; Asaro, R. J., Crack tip fields in ductile crystals, Int. J. Fract. Mech, 42, 301-321 (1990) |
| [41] | Rose, J. H.; Ferrante, J.; Smith, J. R., Universal binding energy curves for metals and bimetallic interfaces, Phys. Rev. Lett, 47, 675-678 (1981) |
| [42] | Rose, J. H.; Smith, J. R.; Ferrante, J., Universal features of bonding in metals, Phys. Rev. B, 28, 1835-1845 (1983) |
| [43] | Saeedvafa, M., Orientation dependence of fracture in copper bicrystals with symmetric tilt boundaries, Mech. Mater, 13, 295-311 (1992) |
| [44] | Saeedvafa, M.; Rice, J. R., Crack tip singular field in ductile crystals with Taylor power-law hardening II: plane strain, J. Mech. Phys. Solids, 37, 673-691 (1989) · Zbl 0713.73068 |
| [45] | Suo, Z.; Shih, C. F.; Varias, A. G., A theory for cleavage cracking in the presence of plastic flow, Acta Metall. Mater, 41, 1551-1557 (1993) |
| [46] | Tang, H., Acharya, A., Saigal, S., 2003. Directional dependence of crack growth along the interface of a bicrystal with symmetric tilt boundary in the presence of gradient effects, To appear in Mechanics of Materials.; Tang, H., Acharya, A., Saigal, S., 2003. Directional dependence of crack growth along the interface of a bicrystal with symmetric tilt boundary in the presence of gradient effects, To appear in Mechanics of Materials. |
| [47] | 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 |
| [48] | Tvergaard, V.; Hutchinson, J. W., The influence of plasticity on mixed mode interface toughness, J. Mech. Phys. Solids, 41, 1119-1135 (1993) · Zbl 0775.73219 |
| [49] | Wang, J.-S.; Anderson, P. M., Fracture behavior of embrittled F.C.C. metal bicrystals, Acta Metall. Mater, 39, 779-792 (1991) |
| [50] | Weertman, J., Dislocation Based Fracture Mechanics (1996), World Scientific: World Scientific Singapore · Zbl 0982.74004 |
| [51] | Wei, Y.; Hutchinson, J. W., Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity, J. Mech. Phys. Solids, 45, 1253-1273 (1997) · Zbl 0977.74574 |
| [52] | Wei, Y.; Hutchinson, J. W., Models of interface separation accompanied by plastic dissipation at multiple scales, Int. J. Fract, 95, 1-17 (1999) |
| [53] | Willam, K. J., Numerical solution of inelastic rate processes, Comput. Struct, 8, 511-531 (1978) · Zbl 0374.73038 |
| [54] | Xia, L.; Shih, C. F., Ductile crack growth-I. A numerical study using computational cells with microstructurally-based length scales, J. Mech. Phys. Solids, 43, 233-259 (1995) · Zbl 0879.73047 |
| [55] | Xia, Z. C.; Hutchinson, J. W., Crack tip fields in strain gradient plasticity, J. Mech. Phys. Solids, 44, 1621-1648 (1996) |
| [56] | Xu, X.-P.; Needleman, A., Void nucleation by inclusion debonding in crystal matrix, Modelling Simulations Mater. Sci. Eng, 1, 111-132 (1993) |
| [57] | Xu, X.-P.; Needleman, A., Numerical simulations of fast crack growth in brittle solids, J. Mech. Phys. Solids, 42, 1397-1434 (1994) · Zbl 0825.73579 |
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