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Size effects on void growth in single crystals with distributed voids. (English) Zbl 1131.74009

Summary: The effect of void size on void growth in single crystals with uniformly distributed cylindrical voids is studied numerically using a finite deformation strain gradient crystal plasticity theory with an intrinsic length parameter. A plane strain cell model is analyzed for a single crystal with three in-plane slip systems. It is observed that small voids allow much larger overall stress levels than larger voids for all the stress triaxialities considered. The amount of void growth is found to be suppressed for smaller voids at low stress triaxialities. Significant differences are observed in the distribution of slips and in the shape of deformed voids for different void sizes. Furthermore, the orientation of the crystalline lattice is found to have a pronounced effect on the results, especially for smaller void sizes.

MSC:

74E15 Crystalline structure
74C20 Large-strain, rate-dependent theories of plasticity
Full Text: DOI

References:

[1] Borg, U.: Strain gradient crystal plasticity effects on flow localization, Int. J. Plast. 23, 1400-1416 (2007) · Zbl 1134.74326 · doi:10.1016/j.ijplas.2007.01.003
[2] Borg, U.; Kysar, J. W.: Strain gradient crystal plasticity analysis of a single crystal containing a cylindrical void, Int. J. Solids struct. 44, 6382-6397 (2007) · Zbl 1166.74324 · doi:10.1016/j.ijsolstr.2007.02.032
[3] Borg, U.; Niordson, C. F.; Fleck, N. A.; Tvergaard, V.: A viscoplastic strain gradient analysis of materials with voids or inclusions, Int. J. Solids struct. 43, 4906-4916 (2006) · Zbl 1120.74363 · doi:10.1016/j.ijsolstr.2005.05.022
[4] Dunne, F.; Petrinic, N.: Introduction to computational plasticity, (2005) · Zbl 1081.74002
[5] Evers, L.; Brekelmans, W.; Geers, M.: Scale dependent crystal plasticity framework with dislocation density and grain boundary effects, Int. J. Solids struct. 41, 5209-5230 (2004) · Zbl 1075.74020 · doi:10.1016/j.ijsolstr.2004.04.021
[6] Fleck, N. A.; Hutchinson, J. W.: A reformulation of strain gradient plasticity, J. mech. Phys. solids 49, 2245-2271 (2001) · Zbl 1033.74006 · doi:10.1016/S0022-5096(01)00049-7
[7] Fleck, N. A.; Muller, G. M.; Ashby, M. F.; Hutchinson, J. W.: Strain gradient plasticity: theory and experiment, Acta metall. Mater. 42, 475-487 (1994)
[8] Gan, Y. X.; Kysar, J. F.: Cylindrical void in a rigid-ideally plastic single crystal III: Hexagonal close-packed crystal, Int. J. Plast. 23, 592-619 (2007) · Zbl 1190.74004 · doi:10.1016/j.ijplas.2006.06.001
[9] Gan, Y. X.; Kysar, J. F.; Morse, T. L.: Cylindrical void in a rigid-ideally plastic single crystal II: Experiments and simulations, Int. J. Plast. 22, 39-72 (2006) · Zbl 1148.74311 · doi:10.1016/j.ijplas.2005.01.009
[10] Gao, H.; Huang, Y.; Nix, W. D.; Hutchinson, J. W.: Strain gradient plasticity – I: Theory, J. mech. Phys. solids 47, 1239-1263 (1999) · Zbl 0982.74013 · doi:10.1016/S0022-5096(98)00103-3
[11] Gudmundson, P.: A unified treatment of strain gradient plasticity, J. mech. Phys. solids 52, 1379-1406 (2004) · Zbl 1114.74366 · doi:10.1016/j.jmps.2003.11.002
[12] Gurson, A.: Continuum theory of ductile rupture by void nucleation and growth: part i. Yield criteria and flow rules for porous ductile media, J. eng. Mater. technol. 99, 2-15 (1977)
[13] Gurtin, M. E.: A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations, J. mech. Phys. solids 50, 5-32 (2002) · Zbl 1043.74007 · doi:10.1016/S0022-5096(01)00104-1
[14] Han, C. -S.; Gao, H.; Huang, Y.; Nix, W. D.: Mechanism-based strain gradient crystal plasticity – I. Theory, J. mech. Phys. solids 53, 1188-1203 (2005) · Zbl 1120.74356 · doi:10.1016/j.jmps.2004.08.008
[15] Haque, M. A.; Saif, M. T. A.: Strain gradient effect in nanoscale thin films, Acta mater. 51, 3053-3061 (2003)
[16] Hussein, M.I., Borg, U., Niordson, C.F., Deshpande, V.S., 2007. Plasticity size effects in voided crystals. J. Mech. Phys. Solids, in press, doi:10.1016/j.jmps.2007.05.004. · Zbl 1162.74338
[17] Koplik, J.; Needleman, A.: Void growth and coalescence in porous plastic solids, Int. J. Solids struct. 24, 835-853 (1988)
[18] Kysar, J. F.; Gan, Y. X.; Mendez-Arzuza, G.: Cylindrical void in a rigid-ideally plastic single crystal. Part I: Anisotropic slip line theory solution for face-centered cubic crystals, Int. J. Plast. 21, 1481-1520 (2005) · Zbl 1148.74318 · doi:10.1016/j.ijplas.2004.07.007
[19] Liu, B.; Huang, Y.; Li, M.; Hwang, K. C.; Liu, C.: A study of the void size effect based on the Taylor dislocation model, Int. J. Plast. 21, 2107-2122 (2005) · Zbl 1330.74033
[20] Liu, B.; Qiu, X.; Huang, Y.; Hwang, K. C.; Li, M.; Liu, C.: The size effect on void growth in ductile materials, J. mech. Phys. solids 51, 1171-1187 (2003) · Zbl 1077.74514 · doi:10.1016/S0022-5096(03)00037-1
[21] Ma, Q.; Clarke, D. R.: Size dependent hardness of silver single crystals, J. mater. Res. 10, 853-863 (1995)
[22] Mcelhaney, K. W.; Vlassak, J. J.; Nix, W. D.: Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments, J. mater. Res. 13, 1300-1306 (1998)
[23] Needleman, A.: Void growth in an elastic-plastic medium, J. appl. Mech. 39, 964-970 (1972)
[24] Nemat-Nasser, S.; Hori, M.: Void collapse and void growth in crystalline solids, J. appl. Phys. 62, 2746-2757 (1987)
[25] Niordson, C.F., 2007. Void growth to coalescence in a non-local material. Eur. J. Mech. A Solids, in press, doi:10.1016/j.euromechsol.2007.07.001. · Zbl 1133.74010
[26] Niordson, C. F.; Hutchinson, J. W.: Non-uniform plastic deformation of micron scale objects, Int. J. Numer. methods eng. 56, 961-975 (2003) · Zbl 1046.74013 · doi:10.1002/nme.593
[27] Niordson, C. F.; Tvergaard, V.: Size effects on cavitation instabilities, J. appl. Mech. 73, 246-253 (2006) · Zbl 1111.74576 · doi:10.1115/1.2074747
[28] O’reagan, T. L.; Quinn, D. F.; Howe, M. A.; Mchugh, P. E.: Void growth simulations in single crystals, Comp. mech. 20, 115-121 (1997) · Zbl 1031.74524 · doi:10.1007/s004660050226
[29] Peirce, D.; Asaro, R. J.; Needleman, A.: Material rate dependence and localized deformation in crystalline solids, Acta metall. 31, 1951-1976 (1983)
[30] Potirniche, G. P.; Hearndon, J. L.; Horstemeyer, M. F.; Ling, X. W.: Lattice orientation effects on void growth and coalescence in fcc single crystals, Int. J. Plast. 22, 921-942 (2006) · Zbl 1177.74108 · doi:10.1016/j.ijplas.2005.06.003
[31] Potirniche, G. P.; Horstemeyer, M. F.; Wagner, G. J.; Gullet, P. M.: A molecular dynamics study of void growth and coalescence in single crystal nickel, Int. J. Plast. 22, 257-278 (2006)
[32] Rice, J. R.; Tracey, D. M.: On the ductile enlargement of voids in triaxial stress fields, J. mech. Phys. solids 17, 201-217 (1969)
[33] Shu, J. Y.: Scale-dependent deformation of porous single crystals, Int. J. Plast. 14, 1085-1107 (1998) · Zbl 0977.74014 · doi:10.1016/S0749-6419(98)00048-5
[34] Stölken, J. S.; Evans, A. G.: Microbend test method for measuring the plasticity length scale, Acta mater. 46, 5109-5115 (1998)
[35] Tvergaard, V.: Effect of thickness inhomogeneities in internally pressurized elastic-plastic spherical shells, J. mech. Phys. solids 24, 291-304 (1976)
[36] Tvergaard, V.: Material failure by void growth to coalescence, Adv. appl. Mech. 27, 83-151 (1990) · Zbl 0728.73058 · doi:10.1016/S0065-2156(08)70195-9
[37] Tvergaard, V.; Niordson, C.: Nonlocal plasticity effects on interaction of different size voids, Int. J. Plast. 20, 107-120 (2004) · Zbl 1134.74339 · doi:10.1016/S0749-6419(03)00036-6
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