Size-dependent power laws for edge dislocations in Nickel superalloys: A molecular dynamics study

Abstract

We present in this work computational evidence, using molecular dynamics simulations, of a size effect in the relationship between the critical resolved shear stress for edge dislocation motion in nickel superalloys and the size of ${\gamma }^{\prime }$ precipitates, under certain conditions. We model the superalloy as periodically spaced cubic ${\gamma }^{\prime }$ precipitates inside a uniform $\gamma$ matrix. We then analyze the motion of paired edge dislocations in the $\gamma$ phase when subject to an external shear stress for various volume fractions of the ${\gamma }^{\prime }$ precipitate for a wide range of temperatures, from 300 K to 700 K. While the variation of dislocation velocity is not significant, the critical resolved shear stress is found to exhibit a power law dependence on the volume fraction of the ${\gamma }^{\prime }$ precipitate with two distinct regimes which have similar exponent but markedly different prefactors; we also observe that this two-regime behavior remains true across a wide range of temperatures. We present a detailed analysis of this behavior and reduce it to a linear dependence of the critical resolved shear stress on the length of the ${\gamma }^{\prime }$ precipitate along the direction of dislocation motion. We further identify the critical length scale underlying the transition between the two observed regimes as the total core width of the paired dislocations in a pure ${\gamma }^{\prime }$ system, which includes in addition to the complex stacking fault separating the partials of the paired dislocations the width of the anti-phase boundary that is formed between the super-dislocations. We present auxillary results using spherical precipitates that exhibit the same trend, but a full analysis of the interplay between size of the precipitate, volume fraction, and other related factors is not pursued in this work. Despite the special configurations considered in this work, the results presented here highlights non-trivial size-dependent effects, provides new details on the strengthening effect of ${\gamma }^{\prime }$ precipitates in nickel superalloys, and has important implications for larger scale dislocation dynamics studies for nickel superalloys.