# Crystalline Plasticity and Structured Deformations

## Abstract

The connection between the geometrical changes at small length scales in single crystals and their macroscopic response has been the subject of extensive experimental studies. In (Deseri and Owen (2000)), experimental evidence that points to a connection between hardening behavior of single crystals undergoing single slip and changes in the separation of active slip-bands has been collected. Although the relation between the structure and separation of both slip-bands and of slip-lines, on the one hand, and the strain hardening of crystals, on the other hand, is still not well understood (Kubin (1993), pp. 145–146), the existence of such a relation was already established by the year 1950 (Hill (1950), p. 6). Experimental evidence is cited in (Barrett (1952)), p. 349 for two basic phenomena: (i) in crystals that deform without appreciable hardening, such as lead, further deformation due to slip continues on existing slip-lines, and (ii) in crystals that deform with appreciable hardening, such as aluminum, further deformation due to slip entails the formation of new slip-lines (Crussard (1945), p. 291; Brown (1952) p. 468). Moreover, in aluminum crystals, a significant number of active slip-lines become inactive as deformation progresses (Yamaguchi (1993), pp. 301–305; Crussard (1945), p. 290). In spite of the fact that the average separation of *all* slip-lines, i.e., active and inactive together, decreases with deformation in aluminum crystals (Crussard (1945), p. 291), there is evidence that the separation of *active* slip-bands increases with deformation in the f.c.c. alloy Cu_{3}Au (Salama et al. (1971), *et al*,1971, p. 402).

## Keywords

Structure Deformation Helmholtz Free Energy Free Energy Density Small Length Scale Threshold Point## Preview

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