Abstract
Imposed shape change of metals increases the load carrying capacity per unit area of cross-section. In tensile tests, the stress, σ, increases with strain, ε, which is work-hardening characterized by monotonic decrease of slope, (∂σ/∂ε). The uniform elongation, εunif, terminates whenever the increase in load carrying capacity due to increase in slope for an incremental strain becomes less than that of the decrease in cross-sectional area, the Considere criterion. Hence microstructure evolution to extend εunif defines the ductility of the material. The imposed strain cause slip to occur on parallel lattice planes, the spacing, hγ, which decrease with strain. The resulting dislocation structure must satisfy two criteria, one the passage stress of parallel dislocation separated by spacing, hτ, of one slip system and the intersection of dislocations on interpenetrating slip systems. Due to dislocation annihilation, hτ > hγ, and the resulting flow stress is a function of ∂σ/∂ε and strain. From this relation, the operative strength of obstacle, α, is derived and plotted versus strain, the comparison of which with change of thermomechanical processing can inform how to increase ductility. The new approach is implemented into the Crystal Plasticity Finite Element Method (CPFEM) to predict the onset of both diffuse and localized necking during various strain paths. Finally, CPFEM is employed to demonstrate the effect of α on the onset of localized deformation.