Assessing the predictive capabilities of precipitation strengthening models for deformation twinning in Mg alloys using phase-field simulations

Precipitation strengthening is a key strategy for improving the overall mechanical properties of Mg alloys. In Mg-Al alloys, basal precipitates are known to strengthen against twinning, resulting in an increase in the critical resolved shear stress (CRSS) necessary for continued deformation. Although several models have been proposed to quantify the influence of precipitate shape, size, and distribution on the CRSS, the accuracy, scope, and applicability of these models has not been fully assessed. Accordingly, the objectives of this study are: (i) to analyze the accuracy of analytical models proposed in the literature for precipitation strengthening against twin thickening and propagation (in Mg-Al alloys) using phase-field (PF) simulations, (ii) to propose modifications to these model forms to better capture the observed trends in the PF data, and (iii) to subsequently test the predictiveness of the extended models in extrapolating to experimental strengthening data. First, using an atomistically-informed phase-field method, the interactions between migrating twin boundaries (during the propagation and thickening stages) and basal plates are simulated for different precipitate sizes and arrangements. In general, comparison of the increase in CRSS determined from the PF simulations and the predictions from four precipitation strengthening models reveals that modifications are necessary to the model forms to extend their applicability to precipitation strengthening against both twin thickening and propagation. A subsequent comparison between predictions from the extended models and experimental strengthening data for peak age-hardened samples reveals that the (extended) single dislocation and dislocation wall models provide reasonably accurate values of the increase in CRSS. Ultimately, the results presented here help elucidate the fidelity and applicability of the various hardening models in predicting precipitation strenghtening effects in technologically important alloys.