Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples

Recent works show that the yield strength of metals increases steeply with decreasing sample size. In this work, it is shown that this sample size effect can be rationalized almost completely by considering the stochastics of dislocation source lengths in samples of finite size. The statistical first and second moments of the effective source length are derived as a function of sample size. The sample strength predicted from this effective length compares well with data.