Generalized model of incipient plasticity with parametric variations

Incipient plasticity ubiquitously signifies the onset of elastic to plastic deformation in a variety of solids under the influence of mechanical load. For instance, the process is mediated by events like dislocation nucleation in crystals and shear transformation zone activation in glassy solids. While the exact mechanism may vary depending on the type of material, there is a universal characteristic on account of which the process is modeled in terms of thermally activated events with rates depending non-linearly on the temperature and activation parameters. This model has led to a widely employed method of estimating the activation parameters of the governing mechanisms by analyzing the statistical distribution of critical loads obtained through a series of repeated measurements. However, the conventional statistical formulation assumes the activation parameters to remain fixed during the sequence of measurements. The present study critically examines this premise and presents a generalized mathematical 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 activated events 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, our findings can offer a fresh perspective on this longstanding issue with a simple and universal explanation without invoking the possibility of various non-trivial mechanisms of incipient plasticity. • Generalized model allows activation parameter fluctuations. • Small variations cause significant distortion in critical load statistics. • Rigid-parameter model severely underestimates activation volumes. • Explains anomalously small activation volumes observed in experiments.