Solute strengthening in random alloys

Abstract Random solid solution alloys are a broad class of materials that are used across the entire spectrum of engineering metals, whether as stand-alone materials (e.g. Al-5xxx alloys) or as the matrix in precipitate-strengthening materials (e.g. Ni-based superalloys). As a result, the mechanisms of, and prediction of, strengthening in solid solutions has a long history. Many concepts have been developed and important trends identified but predictive capability has remained elusive. In recent years, a new theory has been developed that builds on one historical model, the Labusch model, in important ways that lead to a well-defined model valid for random solutions with arbitrary numbers of components and compositions. The new theory uses first-principles-computed solute/dislocation interaction energies as input, from which specific predictions emerge for the yield strength and activation volume as a function of alloy composition, temperature, and strain-rate. Being a general model for materials that otherwise have a low Peierls stress, it has broad application and has been successfully applied to Al-X alloys, Mg-Al, twinning in Mg alloys, and recently fcc High-Entropy Alloys. Here, the new theory is presented in a general and systematic manner. Approximations and limiting cases that reduce the complexity and facilitate understanding are introduced, and help relate the new model to various physical features present among the historical array of models, other recent models, and simulation studies. The quantitative predictions of the model in the various materials above is then demonstrated.