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A computational procedure for rate-independent crystal plasticity. (English) Zbl 1054.74549
Summary: In the rate-independent theory of crystal elasto-plasticity there have been three long-standing problems. The first is to determine which slip systems are active, and the second is to determine the increments of shear on the active slip systems. Third, because of the typical multiplicity of slip systems in ductile crystals, the selection of slip systems required to produce an arbitrary deformation increment is not necessarily unique. The purpose of this paper is to present a robust calculation scheme which determines a unique set of active slip systems and the corresponding shear increments in a rate-independent theory. We show by comparing the predictions from our computational procedure for the rate-independent theory against corresponding predictions from a procedure for a similar but rate-dependent theory (with a low value of the rate sensitivity parameter) that the results from the two procedures are essentially indistinguishable.

MSC:
74E15 Crystalline structure
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74S99 Numerical and other methods in solid mechanics
Software:
ABAQUS
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[1] ABAQUS, ()
[2] Anand, L.; Kalidindi, S.R., The process of shear band formation in plane strain compression of fcc metals: effects of crystallographic texture, Mech. mater., 17, 223-243, (1994)
[3] Asaro, R.J., Micromechanics of crystals and polycrystals, Adv. appl. mech., 23, 1-115, (1983)
[4] Asaro, R.J., Crystal plasticity, ASME J. appl. mech., 50, 921-934, (1983) · Zbl 0557.73033
[5] Asaro, R.J.; Needleman, A., Texture development and strain hardening in rate dependent polycrystals, Acta metall., 33, 923-953, (1985)
[6] Asaro, R.J.; Rice, J.R., Strain localization in ductile single crystals, J. mech. phys. solids, 25, 309-338, (1977) · Zbl 0375.73097
[7] Bassani, J.L., Plastic flow of crystals, Adv. appl. mech., 30, 191-258, (1993) · Zbl 0803.73009
[8] Bassani, J.L.; Wu, T.-Y., Latent hardening in single crystals II. analytical characterisation and predictions, (), 21-41 · Zbl 0731.73021
[9] Bronkhorst, C.A.; Kalidindi, S.R.; Anand, L., Polycrystal plasticity and the evolution of crystallographic texture in face-centered cubic metals, Phil. trans. royal soc. London A, 341, 443-477, (1992)
[10] Chin, G.Y.; Mammel, Generalization and equivalence of the minimum work (Taylor) and maximum work (Bishop-Hill) principles for crystal plasticity, Trans. metall. soc. AIME, 245, 1211-1214, (1969)
[11] Golub, G.H.; Van Loan, C.F., Matrix computations, (1983), The Johns Hopkins University Press Balitmore, MA · Zbl 0559.65011
[12] Gurtin, M.E., An introduction to continuum mechanics, (1981), Academic Press New York · Zbl 0559.73001
[13] Havner, K.S., Finite plastic deformation of crystalline solids, (1992), Cambridge University Press · Zbl 0774.73001
[14] Hill, R., Generalized constitutive relations for incremental deformation of metal crystals by mutislip, J. mech. phys. solids, 14, 95-102, (1966)
[15] Hill, R.; Rice, J.R., Constitutive analysis of elastic-plastic crystals at arbitrary strain, J. mech. phys. solids, 20, 401-413, (1972) · Zbl 0254.73031
[16] Kalidindi, S.R., Polycrystal plasticity: constitutive modeling and deformation processing, ()
[17] Kalidindi, S.R.; Bronkhorst, C.A.; Anand, L., Crystallographic texture evolution during bulk deformation processing of fcc metals, J. mech. phys. solids, 40, 537-569, (1992)
[18] Mandel, J., Generalisation de la theorie de la plasticite de W. T. Koiter, Int. J. solids struct., 1, 273-295, (1965)
[19] Mandel, J., Thermodynamics and plasticity, (), 283-311
[20] Peirce, D.; Asaro, R.J.; Needleman, A., An analysis of nonuniform and localized deformation in ductile single crystals, Acta metall., 30, 1087-1119, (1982)
[21] Press, W.H.; Flannery, B.P.; Teukolsky; Vetterling, W.T., Numerical recipes. the art of scientific computing, (1986), Cambridge University Press Cambridge · Zbl 0587.65003
[22] Rice, J.R., Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity, J. mech. phys. solids, 19, 433-455, (1971) · Zbl 0235.73002
[23] Schmidt, E.; Boas, W., Plasticity of crystals, (1935), Chapman and Hall London
[24] Simmons, G.; Wang, H., Single crystal elastic constants and calculated aggregate properties, (1971), The MIT Press Cambridge, MA
[25] Strang, G., Linear algebra and its applications, (1988), Harcourt Brace Jovanovich College Publishers Forth Worth
[26] Taylor, G.I., Plastic strain in metals, J. institute of metals, 62, 307-324, (1938)
[27] Taylor, G.I., Analysis of plastic strain in a cubic crystal, (), 218-224 · Zbl 0098.40202
[28] Taylor, G.I.; Elam, C.F., The distortion of an aluminum crystal during a tensile test, (), 643-667
[29] Taylor, G.I.; Elam, C.F., The plastic extension and fracture of aluminum single crystals, (), 28-51
[30] Weber, G.; Lush, A.M.; Zavaliangos, A.; Anand, L., An objective time-integration procedure for isotropic rate-independent and rate-dependent elastic-plastic constitutive equations, Int. J. plast., 6, 701-744, (1990) · Zbl 0714.73023
[31] Wu, T.-Y.; Bassani, J.L.; Laird, C., Latent hardening in single crystals I. theory and experiments, (), 1-19 · Zbl 0731.73020
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