Models for the Critical Resolved Shear Stress

Taylor model for the critical resolved shear stressCritical resolved shear stress which is proportional to the square root of the accumulated dislocation density is reviewed from one-dimensional perspective and extended to three-dimensional space. Interactions between slip systems, as well as slip and twin systems are formally summarized into the interaction matrixInteraction matrix between deformation modes. Interaction matrices for FCC, BCC, and HCP crystals are considered. Interaction between twin and slip systems in HCP crystals is reviewed with reference to the existing literature. The effect of length scale of metal microstructureLength scale of metal microstructure on strength and strain hardening is first introduced from the scale dependent nature of geometrically necessary dislocationsScale dependent nature of geometrically necessary dislocations and then detailed process of dislocation motion inside grains of finite size is examined by dislocation dynamics simulation. The results are incorporated into the model of critical resolved shear stress. Effect of grain boundaries which impede movement of dislocations is introduced also to the model of dislocation mean free path.