Modeling effects of initial dislocation microstructure on the yield strength in FCC single crystal Cu with dislocation dynamics

Three dimensional dislocation dynamics (3D-DD) method was used to study how initial dislocation microstructure, with varying dislocation density, length and distribution, affects the yield strength in face-centered cubic (FCC) single crystal Cu. Initial dislocations are generated for three average lengths for each one of the seven dislocation densities ranging from 0.1-5 × 1012 m/m3.They are randomly distributed on slip planes. The uniaxial tension simulation results for two crystallographic loading orientations, [1 0 0] and [1 1 1], all show that the yield strength has a well-defined linear relationship with the average length of these dislocations, except for very low dislocation densities where small number of dislocations lead to a stochastic behavior. This indicates that dislocation-density based crystal plasticity formulations, including the square-root relationship between flow stress and dislocation density, only work when dislocation densities/numbers are sufficiently large so that a statistically accurate description of the microstructure can be obtainable.