Properties of dislocation lines in crystals with strong atomic-scale disorder

Abstract

We use a discrete dislocation dynamics (DDD) approach to study the motion of a dislocation under strong stochastic forces that may cause bending and roughening of the dislocation line on scales that are comparable to the dislocation core radius. In such situations, which may be relevant in high entropy alloys (HEA) exhibiting strong atomic scale disorder, standard scaling arguments based upon a line tension approximation may be no longer adequate and corrections to scaling need to be considered. We first study the wandering of the dislocation under thermal Langevin forces. This leads to a linear stochastic differential equation which can be exactly solved. From the Fourier modes of the thermalized dislocation line we can directly deduce the scale dependent effective line tension. We then use this information to investigate the wandering of a dislocation in a crystal with spatial, time-independent ('quenched') disorder. We establish the pinning length and show how this length can be used as a predictor of the flow stress. Implications for the determination of flow stresses in HEA from molecular dynamics simulations are discussed.

Microelasticity model of random alloys. Part I: mean square displacements and stresses

“…However, another viewpoint of the study of solute/dislocation interactions consists in considering the dislocation evolving in the internal stress field emerging from the solid solution. Using this viewpoint, one can rely on the large body of literature devoted to the depinning transition of elastic lines in random media [33,34,35,36]. In the case of a random uncorrelated stress environment, basic scaling arguments enable to estimate the critical resolved shear stress at 0 K as a function of the amplitude of the random stress field:…”

Microelasticity model of random alloys. Part II: displacement and stress correlations

“…It will allow to assess the influence of stress correlations on the dislocation roughness (i.e. the shape of the dislocation line) and to clarify recent results obtained with atomistic calculations [53] and continuous modeling [35]. More importantly, it will allow to investigate the solid solution strengthening in concentrated alloys by estimating the critical stress to unpin a dislocation from the underlying correlated stress.…”

“…A natural next step of this work is to combine the correlated stress environment discussed here with either a simple line tension model or a more advanced dislocation model accounting for long-range elasticity [35,51,52]. It will allow to assess the influence of stress correlations on the dislocation roughness (i.e.…”

“…In particular, this multi-scale approach will allow to relax some assumptions of average models [2,32,33] that rely on a unique dislocation length-scale to predict the critical resolved shear stress of the alloy. Some efforts have been pursued in this direction by investigating dislocation roughening in a random stress environment [35] or the strengthening associated to stacking fault inhomogeneities [54]. However, the stress environment considered in these studies was simplified and did not incorporate stress correlations evidenced in this study.…”

“…Assessing the stress correlations appears therefore crucial to better understand dislocation behavior in random alloys. However, we note that, so far, the effect of stress correlations has not been investigated in energy-based [2,32,33,34] or stress-based [26,35] dislocation models. The real space approach described in Part I [17] can be used to express spatial correlations.…”