Generalized model of incipient plasticity with parametric variations

Incipient plasticity is typically associated with thermally activated events like the nucleation of dislocations in crystalline solids and the activation of shear transformation zones in metallic glasses. A widely employed method of estimating the activation parameters of such mechanisms involves analyzing the statistical distribution of critical loads obtained through a series of repeated measurements. However, the conventional mathematical approach assumes the activation parameters to remain fixed during the sequence of measurements. The present study critically examines this premise and presents a generalized statistical model that allows the statistical variations of activation parameters. Using a simple Monte Carlo scheme, it is demonstrated that even small fluctuations of activation parameters can significantly affect the statistical distribution of measured critical loads. The Monte Carlo calculations, along with atomistic simulations, further show that imposing the assumption of rigidly fixed parameters on an activated process with parametric fluctuations can lead to severe underestimation of the activation parameters. As many experimental studies have consistently reported perplexingly small activation volumes estimated using the conventional statistical approach, we propose that our findings can offer a fresh perspective on this longstanding issue.