Influence of stress correlations on dislocation glide in random alloys

Abstract

Solute strengthening is an important mechanism that contributes to improving the mechanical properties of alloys and particularly the recent generations of concentrated alloys. The stress field emerging from an elastic model of a random solid solution displays strongly anisotropic correlations that interact differently with dislocations of different characters. In the present work, we investigate the depinning transition of edge and screw dislocations evolving in such a correlated stress environment using a dislocation dynamics numerical model. We find that edge dislocations are only weakly affected by the correlations, while screw dislocations are strongly influenced, showing a smaller critical stress, which increases with the amplitude of the stress noise with a larger exponent than the edge dislocation. The numerical results are compared with existing statistical models of solute strengthening, allowing to discuss critically their assumptions.

Does the Larkin length exist?

“…To study a size effect on the dislocation yield stress and to approach a thermodynamic limit, we need to increase simultaneously the dislocation length and glide distance [15,25,26]. To this end, we will consider square cells in the (x, y) glide plane of side L x = L y = L, with periodic boundary conditions in both the x-and y-directions [28], see an illustration in the inset of figure 2. To implement equation ( 2) numerically, we discretize the L × L cell on a square lattice with a spacing a.…”

“…Following Larkin's pioneering work [29,30,39], we define here the Larkin length L c as the length above which Larkin's assumption ceases to hold valid. It is worth noting that this definition diverges from an alternative interpretation of the Larkin length, which is deeply entrenched in the plasticity community [28,[31][32][33]. In this alternate view, it is postulated that the restoring force due to the line tension acting on a bulge of width a (the correlation length of the noise) is counterbalanced by the random force when the bulge length is the Larkin length, L c .…”

“…• Region II: At intermediate ∆R, the critical force increases as A c ∝ ∆R 4/3 as seen from the fit in figure 2. At a given ∆R, the critical force seems independent of the system size, although studies have shown that subdominant size effects exist [25,26,28]. In Region II, there is a balance between line tension and noise, and the dislocation is flexible enough to wander across several valleys to find strongly pinned configurations.…”

“…The qEW equation has been extensively used to study the dynamics of surface roughening in a random noise [23][24][25] and other properties, such as size effects and distributions of critical forces [26]. However, the dependence of the critical force on the amplitude of the noise, which in the context of solid solution strengthening corresponds to the dependence of the yield stress on the concentration and solute mismatch [27], has been addressed in much less details [28] and is the subject of the present work.…”

“…In the plasticity community [31][32][33], L c is often defined from an equilibrium between line tension and random noise on a bulge of length L c . This definition has, however, been called into question [28,34,35] since close to the critical stress, the line is known to be rough on all length scales (a property recognized early on by Ladislas Kubin [36]) and thus should not be decomposable into a succession of bow-outs with a single length scale L c as some theoretical treatments imply [37,38]. Moreover, we have recently shown that this definition yields an incorrect scaling in the presence of a correlated noise [28].…”