Interactions between edge lattice dislocations and Σ11 symmetrical tilt grain boundaries in copper: A quasi-continuum method study

Abstract “Positive” and “negative” interactions between specified numbers of piled-up lattice dislocations and + Σ 11 ( 3 ¯ 1 1 ¯ ) and - Σ 11 ( 1 ¯ 3 1 ) symmetrical tilt grain boundaries in two bi-grain models of copper have been studied using the quasi-continuum method. The mechanisms of both interactions in representative loading stages are analyzed in terms of the evolution of grain boundary (GB) configurations and Burgers vector conservation. A unified geometrical criterion is proposed to predict “hard” and “easy” dislocation transmission without explicitly defining the “positive” and “negative” dislocation/GB interactions. The pile-up of incoming dislocations has a remarkable influence on both “positive” and “negative” interactions, and can activate dislocation transmission at smaller external loadings. Critical stress analysis for relatively easier dislocation transmission in “negative” interactions reveals that they depend on the ratio of total shear stresses on the incoming and outgoing slip planes and the ratio of total normal and shear stresses on the outgoing slip plane. An analysis of the Burgers vectors of residuals produced from dislocation/GB interactions shows that GBs impeding dislocation motion have larger residual values.