Strain localization in ductile single crystals

Strain localization in ductile crystals deforming by single slip was analyzed. The plastic flow is modeled as rate-in-sensitive; and localization, viewed as a bifurcation from a homogeneous deformation mode to one which is concentrated in a narrow ''shear band'', is found to be possible only when the plastic hardening modulus for the slip system has fallen to a certain critical value, h/sub cr/, where h/sub cr/ is sensitive to the precise form of the constitutive law governing incremental shear. The general form of this constitutive law is developed. Incorporated within it is the possibility of deviations from the Schmid rule of a critical resolved shear stress. It is shown that h/sub cr/ may in fact be positive when there are deviations from the Schmid rule. It is suggested that micromechanical processes such as ''cross-slip'' in crystals provide specific cases for which stresses other than the Schmid stress may influence plastic response and, further, there is an experimental association of localization with the onset of large amounts of cross-slip. The specific form of h/sub cr/ is given for a constitutive model that corresponds to the non-Schmid effects in cross-slip, and a dislocation model of the process is developed from which an estimate of the magnitude of the parameters involved is made. The work supports the notion that localization can occur with positive strainhardening, h/sub cr/ greater than 0, and the often-invoked notions of the attainment of an ideally plastic or strain softening state for localization may be unnecessary. 6 figures.