Despite significant advances in computational materials science, a quantitative, parameter-free prediction of the mechanical properties of alloys has been difficult to achieve from first principles. Here, we present a new analytic theory that, with input from first-principles calculations, is able to predict the strengthening of aluminium by substitutional solute atoms. Solute-dislocation interaction energies in and around the dislocation core are first calculated using density functional theory and a flexible-boundary-condition method. An analytic model for the strength, or stress to move a dislocation, owing to the random field of solutes, is then presented. The theory, which has no adjustable parameters and is extendable to other metallic alloys, predicts both the energy barriers to dislocation motion and the zero-temperature flow stress, allowing for predictions of finite-temperature flow stresses. Quantitative comparisons with experimental flow stresses at temperature T=78 K are made for Al-X alloys (X=Mg, Si, Cu, Cr) and good agreement is obtained.
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 precipitatestrengthening 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. The quantitative predictions of the model in the various materials above is then demonstrated.
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