A Model of the Yielding of Single Crystals Due to Inhomogeneous Deformation

Johnston-Gilman's theory of yielding was extended to the inhomogeneous deformation where the yielding takes place by the increase of the plastic zone or slip bands. The plastic strain rate \(\dot{\gamma}^{*}\) and the mobile dislocation density N _m in slip bands at an applied stress were assumed to be determined by the condition that \(\dot{\gamma}^{*}\) should take a maximum value or (\(\partial\dot{\gamma}^{*}/\partial N_{m})_\tau{=}0\). The differential equation representing the yielding curve was formulated for the case where the velocity-stress relation of an isolated dislocation is expressed by υ=(τ/τ ₀ ) ^m and the fractional area of the plastic zone is a given function of strain. This model correlates the velocity-stress relation directly with the lower yield stress. Calculated results for specific cases were in satisfactory agreement with experiments.