Influence of slip system hardening assumptions on modeling stress dependence of work hardening

Abstract

Due to the discrete directional nature of processes such as crystallographic slip, the orientation of slip planes relative to a fixed set of loading axes has a direct effect on the magnitude of the external load necessary to induce dislocation motion (yielding). The effect such geometric or textural hardening has on the macroscopic flow stress can be quantified in a polycrystal by the average Taylor factor M ̄ . Sources of resistance to dislocation motion such as interaction with dislocation structures, precipitates, and grain boundaries, contribute to the elevation of the critically resolved shear strength τ crss. In continuum slip polycrystal formulations, material hardening phenomena are reflected in the slip system hardness equations. Depending on the model, the hardening equations and the mean field assumption can both affect geometric hardening through texture evolution. In this paper, we examine continuum slip models and focus on how the slip system hardening model and the mean field assumption affect the stress-strain response. Texture results are also presented within the context of how the texture affects geometric hardening. We explore the effect of employing slip system hardnesses averaged over different size scales. We first compare a polycrystal simulation employing a single hardness per crystal to one using a latent hardening formulation producing distinct slip system hardnesses. We find little difference between the amplitude of the single hardness and a crystal-average of the latent hardening values. The geometric hardening is different due to the differences in the textures predicted by each model. We also find that due to the high degree of symmetry in an fcc crystal, macroscopic stress-strain predictions using simulations employing crystal- and aggregateaveraged hardnesses are nearly identical. We find this to be true for several different mean field assumptions. An aggregate-averaged hardness may be preferred in light of the difficulty encountered in experimentally verifying slip system strength in a polycrystal. We also examine model performance under different stress states. We find that, due to a higher degree of geometric softening in torsion, the latent hardening model more closely correlates oxygen free high conductivity copper compression and torsion data than the aggregate-averaged model. Both models predicted similar material hardening rates in torsion and compression, however. Finally, we propose an aggregate-averaged hardening equation with a heightened dependence on the Taylor factor as defined by the average crystal shearing rate that predicts a higher material hardening rate in compression as compared to torsion to correlate the data. We then use the model to predict compression followed by torsion results.