A statistical model for predicting size effects on the yield strength in dislocation-mediated crystal plasticity

Abstract

A unified statistical dislocation-mediated crystal plasticity model is proposed to understand how the sample size affects the yield strength of metals in different crystal systems, namely, single crystals, columnar-grain structured thin films, and polycrystals. The model takes into account the randomness of the pre-existing dislocation network, grain orientation, and grain size to predict the crystal strength as a function of the extrinsic (i.e. sample dimensions) and intrinsic (i.e. microstructural dimensions) length scales. The model is shown to rigorously capture the effect of size across all three crystal systems, i.e. convergence, scatter and overall trend of the strength, and the results are in good agreement with published experimental and simulation results. The developed model provides an accurate and efficient approach to predict the yield strength in metals.