Predicting Shear Transmission Across Grain Boundaries with an Iterative Stress Relief Model

A new model is proposed to quantitatively describe the accommodation of shear from multiple deformation systems at a grain boundary. The model uses an iterative approach to sequentially determine the accommodating slip systems and their relative shear. The outcome of this iterative stress relief model is mainly controlled by the continuity of Burgers vector in the grain boundary and the evolution of the impinging stress tensor at the grain boundary. The model was tested by comparing predictions with observations of shear accommodation in  a -titanium quantified using orientation informed slip trace analysis and quantitative atomic force microscopy. Similar comparisons were conducted between tangential continuity model predictions and the experimental observations. These comparisons show that the iterative stress relief model agrees much better with the observations when used to predict the accommodating deformation system(s) compared to the tangential continuity model. Critical resolved shear stress ratios used in this iterative stress relief were optimized by maximizing the accuracy of the model predictions. The ranges of the optimized critical resolved shear stress ratios were determined to be basal 〈a〉: prism  〈a〉: pyramidal 〈a〉: pyramidal 〈c+a〉: T1 twin  =  1.0 : (0.8–1.0) : (1.0–1.3) : (1.6–9.5) : (3.0–9.5).