The temperature independent plateau stress of solid solution crystals

Abstract

A calculation of the plateau stress in solid solution crystals is presented assuming an arbitrarily oriented dislocation loop of lengthL, that moves under an applied stress. At high concentrations of solute atoms the dislocation segment does not interact with an individual solute atom but instead with all the solute atoms along the dislocation segment within a certain radius. The macroscopic flow stress is assumed to be determined by the maximum force that is encountered when a dislocation is moved over a distance equal to the distance between the position at zero stress and the critical position of an activated Frank-Read source. If the dislocation segment is assumed to be large compared to atomic distances, the interaction with groups of atoms will lead to an athermal process and therefore can explain the origin of the temperature independent flow stress in solid solution crystals. From this model the flow stress can be calculated with the help of statistical methods similar to those used in calculations of the movement of Bloch walls in magnetic materials. Besides the proper temperature dependence of the plateau stress the above model yields a dependence of the plateau stress upon the square root of the solute concentration, a result that is in good agreement with the measurements on silver, gold, and copperbased alloys. A linear relation between the solid solution hardening parameter dT/d√c and the strength of the solute atoms is obtained which is confirmed by the experimental results on copper-based alloys.