Development of Coupled Crystal Plasticity Finite Element-Phase Field (CPFE-PF) Model for Studying Microstructure Evolution and Designing High Performance Hexagonal Metals and Alloys

Deformation behavior of light weight and high strength hexagonal metals such as Mg and Ti alloys is determined by the coupled dislocation and twinning plasticity. Establishing the quantitative relations between the mechanical properties and plasticity as well as microstructure evolution can promote developing high performance hexagonal materials.<br/>We develop a coupled crystal plasticity finite element-phase field (CPFE-PF) model to predict the mechanical properties of these materials under complex loading conditions. In this coupled CPFE-PF model [Guisen Liu, Hanxuan Mo et al, Acta Materialia 202 (2021) 399–416], the CPFE solves the elastic fields and plastic deformation, and passes the elastic fields to PF for calculating elastic driving force for twinning. PF method spatially distinguishes twin domains from parent and passes the evolution rate of twins to CPFE for calculating twinning rate. In this way, the coupled CPFE-PF model can predict evolution of 3D twins and influence of coupled dislocation-twinning activities on deformation behavior of magnesium alloy that agree well with experimental observation.<br/>To model the evolution of physically sharp twin/parent interface during twinning deformation (instead of artificial diffuse interface due to long-range stress field) and remove the results dependence on mesh orientation, we further improve this CPFE-PF model from two aspects: 1) adopt a coarse mesh in CPFE calculation of stress and strain, and a local refined mesh in PF computation of interface evolution with numerical smoothing and fitting; 2) the twin/parent interface can only propagate when the neighboring partially twinned coarse element has fully transformed to twin phase. This improved model can obtain a relatively sharp interface (about one-element in thickness) during twinning deformation, and meanwhile retain high computation efficiency in solving elastic field. Furthermore, this local refinement-smoothing method solves the originally mesh orientation dependent interface normal and stress distribution, and can predict same twin morphology irrespective of mesh orientation.<br/>The improved CPFE-PF model can model the evolution of physically sharp interface and meanwhile obtain numerically mesh-insensitive twin morphology as well as stress response. Thus, it has promising application in modeling twin-twin interaction to prevent the diffuse mixture of multiple domains (multi-variant and parent), and can be further generalized to model martensitic transformation which requires both physically sharp interface and numerically mesh-insensitive interface orientations. This model can be further developed by incorporating more atomistic twinning mechanisms such as automatic nucleation to quantitatively predict the effects of complex processing or loading conditions on the mechanical behavior of Mg and Ti alloys, where coupled dislocation-twinning plasticity is involved, providing reference for designing high performance hexagonal alloys.