Modelling Combined Hardening Mechanisms in Alloys through the Analysis of Dislocation Percolation

The critical resolved shear strength of pure metals is given by the Peierls-Nabarro equation; impurities or alloying elements will significantly increase . Additional strength is introduced by strain hardening (SH), the grain size effect (GSE), precipitates and particle dispersion. The combination of these mechanisms is generally described in an additive manner, which can be justified by the Taylor expansion of a multivariate function. This approach is highly empirical and involves extensive parameter fitting. The Kocks-Mecking model (KM) and discrete dislocation dynamics show that SH is mainly due to forest effects (latent hardening). Consequently, the main explanation for alloy strength must be sought in the resistance against dislocation percolation through a field of obstacles with different strengths, with the slip length limited by the grain diameter. This hypothesis is explored by reviving early graphical simulations to the percolation problem by introducing a grain boundary and variable obstacle strength in an efficient computer program. Such simulations and theoretical considerations demonstrate the limitations of the additive description of combined hardening. An alternative approximation is proposed, based on the statistical analysis of dislocation percolation, dislocation junctions and dislocation-grain boundary interaction.