Dislocation-precipitate interactions in crystals: from the BKS model to collective dislocation dynamics

The increase in the yield stress due to the presence of obstacles to dislocation motion such as precipitates is a multiscale phenomenon. The details on the nanoscale when an individual dislocation runs into a precipitate play an important role in determining plasticity on a macroscopic scale. The classical analysis of this phenomenon is due to Bacon, Kocks and Scattergood (BKS) from early 1970’s and has been followed by a large body of work both developing the theory and applying it to real experiments and their understanding. Beyond the microscopic details the next level of complexity is met in the micrometer scale when the physics of the yielding and the yield stress depend on two mechanisms: the dislocation-precipitate interaction, and the collective dynamics of the whole ensemble of dislocations in the volume. In this review we discuss the BKS relation and collective dislocation dynamics in precipitation-hardened crystals in the light of recent research, including large-scale discrete dislocation dynamics simulations, statistical physics ideas, and machine learning developments.