Solid-Solution Hardening due to the Size Effect

Abstract

Based on a model developed in an earlier paper, the stress required to move a dislocation through a solid-solution fcc crystal at 0°K is determined. It is assumed in this paper that the solute interacts with a dislocation due to the elastic distortion caused by a size difference between solute and solvent. The results of this analysis are combined with the previous one to consider combined modulus and size interactions. The critical resolved shear stress predicted by this analysis is compared to a number of systems for which experimental data is available, and the agreement is found to be quite satisfactory. The analysis predicts that for dilute solutions the critical resolved shear stress should be proportional to the solute concentration to the ⅔ power, that in almost all cases the stress is determined by the size interaction, and that widely separated partial dislocations require a stress several times greater than perfect dislocations for motion.