An analysis of nonuniform and localized deformation in ductile single crystals

Publisher Summary This chapter focuses on micromechanics of crystals and polycrystals. In Section II of the chapter, a brief outline of only some of the important features of the micromechanics of crystalline plasticity is given. The discussion is confined to plastic flow caused by dislocation slip, and face-centered-cubic crystals are used in the examples of dislocation mechanisms. Particular attention is paid to kinematics and to the phenomenology of strain hardening, because these are shown to play dominant roles in macroscopic response. In Section III, constitutive laws for elastic-plastic crystals are developed. The framework draws heavily on Hill's analysis of the mechanics of elasticplastic crystals, but the theory is extended by incorporating the possibility of deviations from the Schmid rule of a critical resolved shear stress for slip. Deviations from the Schmid rule are motivated by micromechanical models for dislocation motion and are shown to lead to deviations from the “normality flow rule” of continuum plasticity. The implications of these “non-Schmid effects” regarding the stability of plastic flow are brought out via some examples of models for kinks bands and shear bands in Section IV. In Section IV some examples of analyses of elastic-plastic deformation in crystals are discussed. The chapter concludes with some suggestions for fruitful research. These involve extensions of the theory to finite-strain rate-dependent polycrystalline models.

Micromechanics of Crystals and Polycrystals

A phenomenological description of crystallographic slip and pencil glide in single crystals is outlined, with emphasis on the behavior under prescribed strains Theoretical relations are established between these single-crystal properties and the behavior of quasi-homogeneous, quasi-isotropic polycrystals deforming uniformly on a macroscopic scale, at subdiffusive temperatures Experimental comparisons between single crystals and polycrystals are reviewed, considering flow stress, work hardening, temperature and strain rate effects, and various effects of grain size

T. J. Brown

Papers

Latent hardening in aluminum