The stress statistics of the first pop-in or discrete plastic event in crystal plasticity

The stress at which the first discrete plastic event occurs is investigated using extreme value statistics. It is found that the average of this critical stress is inversely related to the deforming volume, via an exponentially truncated power-law. This is demonstrated for the first pop-in event observed in experimental nano-indentation data as a function of the indenter volume, and for the first discrete plastic event seen in a dislocation dynamics simulation. When the underlying master distribution of critical stresses is assumed to be a power-law, it becomes possible to extract the density of discrete plastic events available to the crystal, and to understand the exponential truncation as a break-down of the asymptotic Weibull limit.