Coupled Spectral Based Crystal Plasticity And Phase Field Twinning Model And Its Application

Magnesium alloy is the lightest structural metallic material that can be widely used in the engineering.Due to the high strength-weight ratio and high rigidity-weight ratio,magnesium alloy is regarded as the ideal metallic material for reduce the weight of automotive structural parts.However,the plastic deformation behaviors of magnesium and its alloys are rather complex as magnesium alloy has hexagonal close packed structure which means that there are not enough slip modes.Thus,its application cost is high,and the application of magnesium alloy is seriously restricted.As a result,to improve the formability of magnesium alloy,the related plastic deformation mechanisms should be systematically investigated.Mesoscale crystal plasticity models,which can bridge the complex microstructure of the poly crystal and the mechanical properties,are very powerful in exploring the plastic deformation mechanisms of materials.However,in most of the well-developed crystal plasticity models,the twinning is treated as pseudo slip which is different from the real twinning,thus the morphology of the twinning cannot be spatially resolved.Although this approach can reflex the effect of twinning on the overall mechanical responses of the materials,the ability in exploring twinning related plastic deformation mechanisms is very limited.Thus,an efficient full-field crystal plasticity model that can accurately model dislocation and twinning simultaneously is required.To solve this problem and establish an efficient numerical approach to investigate the plastic deformation mechanisms of magnesium alloy,this work focuses on forming an efficient mesoscale full-field crystal plasticity model that can spatially resolve the dynamic process of twinning based on the physical property of the slip and twinning.The developed numerical models are then applied to investigate deformation twinning related plastic deformation mechanisms in Mg and its alloys.The details of the work include:(1)A phase field model for the coupled evolution of grain boundaries and deformation twinning is established.To model the block effect of grain boundaries on twinning 'propagation',a twin eigenstrain relaxation parameter has been introduced at the grain boundary regions to establish the phase field model for the coupled evolution of grain boundaries and deformation twinning within the elastic framework.Based on the present coupled model,the twin induced grain boundary migration,the preferred nucleation location and variants selection rule during the twinning 'propagation' has been captured successfully in magnesium and its alloy.(2)A coupled full-field crystal plasticity-phase field twinning model based on fast Fourier transform has been formulated.Based on the corresponding relation between the twinning order parameter and characteristic shear strain of the twinning,the twining order parameter which represent the twinning morphology has been directly incorporated into the crystal plasticity constitutive relation.Thus,the dislocation slip and twinning can be properly modeled simultaneously in the fast Fourier transform based crystal plasticity framework,and a robust and efficient full-field crystal plasticity model that can spatially resolve the dynamic process of twinning is established.This model is a robust and efficient numerical tool that can not only predict the morphology evolution during the twinning nucleation,growth and 'propagation' as well as the corresponded mechanical responses,but also gives deep insight into the complex interaction mechanisms among the dislocation slip,deformation twinning and grain boundaries in the polycrystal magnesium and its alloy.(3)The effects of the microstructure defects on the twinning nucleation,growth and overall mechanical properties of the magnesium alloy have been systematically investigated with the coupled full-field crystal plasticity-phase field twinning model.Through the systematical investigation,we have found that microstructure defects will promote the twinning nucleation and the nucleation and growth of the twinning can significantly relax the stress concentration induced by the microstructure defects.Thus,the twinning will suppression the further expansion of the structure defects in early stage of the deformation.(4)An efficient coupled full-field crystal plasticity-phase field twinning model based on fast Fourier transform in large deformation framework has been formulated,filled the gap that full-field crystal plasticity models with spatially resolved twinning processes cannot be used to predict the forming limit directly.Through the relation between the twinning order parameter and characteristic shear of the twinning,the twining order parameter has been directly incorporated into the crystal plasticity constitutive relation.Using the semiimplicit rate tangent modulus method to update the heterogeneous stress field directly and calculate the strain field with the fast Fourier transform based framework,the time consumed iterative processes can be avoided and a very efficient coupled full-field crystal plasticity-phase field twinning model for large deformation problems has been established.This model can not only predict the morphology evolution during the twinning processes and the corresponded mechanical responses,but also very computational efficiency can be used to predict the forming limit of magnesium alloys directly.