Open Access

ARTICLE

A Multi-Scale Theoretical Scheme for Metal Deformation

by Robb Thomson, Retired,¹, D. E. Kramer¹

1 Metallurgy Division, NIST, Gaithersburg, MD 20877
2 Center for Simulational Physics, University of Georgia, Athens, GA 30602

Computer Modeling in Engineering & Sciences 2002, 3(2), 245-254. https://doi.org/10.3970/cmes.2002.003.245

Abstract

A conceptual theoretical scheme for single crystal metal deformation is presented consisting of multi-scale models from dislocation dynamics to the continuum constitutive relations. The scheme rests on the fundamental observations that deformation is characterized by partially ordered internal dislocation wall structures, discontinuous strain bursts in time, and strain localization in a surface slip band structure. A percolation strain model corresponds to elementary slip line burst events, with percolation parameters to be supplied from experiments and dislocation dynamics studies of wall structures. A model for localization of the slip lines into bands is proposed (for suitable loadings) which envisions channels for slip formed from the dense planar walls (otherwise called GNB's). A rudimentary continuum model is constructed from the outputs of these models which consists of two principal internal variables, and exhibits the desired hardening behavior with strain. The continuum model is based on two different material properties in the slip bands, and in the matrix between the bands. The scheme does not yet include mechanisms for the underlying dislocation ordering or patterning, but addresses the transport of dislocations through these (presumably known) structures.

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