On Labusch’s solid solution depinning and strength estimate

Abstract

Labusch’s simplified, analytical, mathematical solution of the dislocation-glide model provides an estimate of the strength contribution from atoms in solid solution and plays a fundamental role as part of multi-scale models that scale up local binding estimates from atomistic simulations. Precise numerical solutions of the model show that the stress is proportional to the solute concentration to the power of ¾ and disagrees with the power of ⅔ in Labusch’s analytical solution, where the strength is assumed to be controlled by Larkin-scale bulges forming initially on a straight dislocation. Instead, subsequent bulge coarsening during loading is found to be the mechanism that controls the depinning strength.