×

A model for elastic-viscoplastic deformations of crystalline solids based on material symmetry: theory and plane-strain simulations. (English) Zbl 1423.74168

Summary: A model for the elastic-viscoplastic response of metallic single crystals is developed on the basis of the modern finite-deformation theory of plasticity combined with considerations of material symmetry. This is proposed as an alternative to conventional crystal plasticity theory, based on a decomposition of the plastic deformation rate into a superposition of slips on active slip systems. A simple special case of the general theory, modeling evolving geometrically necessary dislocations and their effect on hardening, is developed and used as the basis of numerical experiments.

MSC:

74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74A05 Kinematics of deformation
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74E15 Crystalline structure

Software:

CHIMP
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anand, L.; Balasubramanian, S.; Kothari, M., Constitutive modeling of polycrystalline metals at large strains, (Large plastic deformation of crystalline aggregates, (1997), Springer Berlin)
[2] Bell, J. F.; Green, R. E., An experimental study of the double-slip deformation hypothesis for face-centered cubic crystals, Philosophical Magazine, 15, 469-476, (1967)
[3] Cermelli, P.; Gurtin, M. E., On the characterization of geometrically necessary dislocations in finite plasticity, Journal of the Mechanics and Physics of Solids, 49, 1539-1568, (2001) · Zbl 0989.74013
[4] Cleja-Tigoiu, S.; Soos, E., Elastoviscoplastic models with relaxed configurations and internal variables, Applied Mechanics Reviews, 43, 131-151, (1990)
[5] Cullity, B., Elements of X-ray diffraction, (1978), Addison-Wesley · Zbl 0043.43903
[6] Del Piero, G.; Owen, D. R., Structured deformations of continua, Archive for Rational Mechanics and Analysis, 124, 99-155, (1993) · Zbl 0795.73005
[7] Deseri, L.; Owen, D. R., Invertible structured deformations and the geometry of multiple slip in single crystals, International Journal of Plasticity, 18, 833-849, (2002) · Zbl 1006.74022
[8] Edmiston, J. (2012). Continuum plasticity: Phenomenological modeling and X-ray diffraction experiments. Dissertation. UC Berkeley.; Edmiston, J. (2012). Continuum plasticity: Phenomenological modeling and X-ray diffraction experiments. Dissertation. UC Berkeley.
[9] Epstein, M.; Elzanowski, M., Material inhomogeneities and their evolution, (2007), Springer Berlin · Zbl 1130.74001
[10] Green, A. E.; Adkins, J. E., Large elastic deformations, (1970), Oxford University Press · Zbl 0227.73067
[11] Gupta, A.; Steigmann, D. J.; Stölken, J. S., On the evolution of plasticity and incompatibility, Mathematics and Mechanics of Solids, 12, 583-610, (2007) · Zbl 1133.74009
[12] Gupta, A.; Steigmann, D. J.; Stölken, J. S., Aspects of the phenomenological theory of elastic–plastic deformation, Journal of Elasticity, 104, 249-266, (2011) · Zbl 1320.74027
[13] Gurtin, M. E.; Fried, E.; Anand, L., Mechanics and thermodynamics of continua, (2010), Cambridge University Press
[14] Ha, S.; Kim, K. T., Heterogeneous deformation of al single crystal: experiments and finite element analysis, Mathematics and Mechanics of Solids, 16, 652-661, (2011) · Zbl 1269.74044
[15] Havner, K. S., Finite plastic deformation of crystalline solids, (1992), Cambridge University Press · Zbl 0774.73001
[16] Lubarda, V. A., Elastoplasticity theory, (2002), CRC Press Boca Raton, FL · Zbl 1014.74001
[17] Lucchesi, M.; Silhavy, M., Il’yushin’s conditions in non-isothermal plasticity, Archive for Rational Mechanics and Analysis, 113, 121-163, (1991) · Zbl 0717.73037
[18] Nagdhi, P. M., A critical review of the state of finite-strain plasticity, ZAMP, 41, 315-394, (1990) · Zbl 0712.73032
[19] Nagdhi, P. M.; Srinivasa, Characterization of dislocations and their influence on plastic deformation in single crystals, International Journal of Engineering Science, 32, 1157-1182, (1994) · Zbl 0899.73456
[20] Naghdi, P. M.; Srinivasa, A., Some general results in the theory of crystallographic slip, ZAMP, 45, 687-732, (1994) · Zbl 0812.73009
[21] Noll, W., Materially uniform simple bodies with inhomogeneities, Archive for Rational Mechanics and Analysis, 27, 1-32, (1967) · Zbl 0168.45701
[22] Owen, D. (2012). Private e-mail communication dated June 6.; Owen, D. (2012). Private e-mail communication dated June 6.
[23] Pipkin, A. C.; Rivlin, R. S., The formulation of constitutive equations in continuum physics (I), Archive for Rational Mechanics and Analysis, 2, 129-144, (1959), Reprinted In Collected works of R.S. Rivlin, Vol. 1 (G.I. Barenblatt and D.D. Joseph, eds.). Springer, NY, 1997. · Zbl 0092.40402
[24] Prager, W., Introduction to the mechanics of continua, (1961), Ginn & Co. Boston · Zbl 0094.18602
[25] Rajagopal, K.; Srinivasa, A., Inelastic behavious of materials. part 1: theoretical underpinnings, International Journal of Plasticity, 14, 945, (1998) · Zbl 0978.74013
[26] Rajagopal, K.; Srinivasa, A., On the role of the eshelby energy-momentum tensor in materials with multiple natural configurations, Mathematics and Mechanics of Solids, 10, 3, (2005) · Zbl 1104.74012
[27] Rengarajan, G.; Rajagopal, K., On the form for the plastic velocity gradient L_{p} in crystal plasticity, Mathematics and Mechanics of Solids, 6, 471-480, (2001) · Zbl 1077.74007
[28] Silling, S. A., Finite difference modelling of phase changes and localization in elasticity, Computer Methods in Applied Mechanics and Engineering, 70, 251-273, (1988) · Zbl 0635.73119
[29] Smith, G. F.; Smith, M. M.; Rivlin, R. S., Integrity bases for a symmetric tensor and a vector – the crystal classes, Archive for Rational Mechanics and Analysis, 12, 93-133, (1963), Reprinted In Collected works of R.S. Rivlin, Vol. 1 (G.I. Barenblatt and D.D. Joseph, Eds.), Springer, NY, 1997. · Zbl 0125.00802
[30] Steigmann, D. J.; Gupta, A., Mechanically equivalent elastic–plastic deformations and the problem of plastic spin, Theoretical and Applied Mechanics, 38, 397-417, (2011) · Zbl 1299.74030
[31] Steigmann, D. J.; Ogden, R. W., Note on residual stress, lattice orientation and dislocation density in crystalline solids, Journal of Elasticity, 109, 275-283, (2012) · Zbl 1253.74016
[32] Zangwill, W. I., Nonlinear programming, (1969), Prentice-Hall Englewood Cliffs, N.J · Zbl 0191.49101
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.