Quantitative analysis of hetero-deformation induced strengthening in heterogeneous grain structure

A single-phase bimodal grain structure is considered to develop a physical model to quantify hetero-deformation induced (HDI) strengthening at the yield point, which cannot be simply predicted by the conventional rule-of-mixtures using the Hall-Petch equation. Based on the classic theory of single-ended continuum dislocation pileup, the modified model parameterizes the effective width of hetero-boundary affected region (Hbar) as well as the contribution of HDI stress to 0.2% proof stress. To further verify the model equations, the equimolar CoCrNi medium entropy alloy was selected as a model material. The heterogeneous grain structure (HGS) was introduced via thermal-mechanical treatment, and statistical analysis of microstructure was performed by means of electron backscattered diffraction. By substituting derived parameters, our model can predict theoretical values of the yield stress and the width of Hbar, both comparable to the experimental value from tensile testing, as well as previous experimental observations. The reasonable agreements can not only prove the validity of the current modified model, but also bring out physical explanations for the extra strengthening in heterostructured materials.