Crystal plasticity based constitutive model for uniaxial ratchetting of polycrystalline magnesium alloy

In the framework of crystal plasticity, a constitutive model is constructed to describe the uniaxial ratchetting of polycrystalline magnesium alloy at room temperature. At the scale of single crystal, three kinds of slip systems, i.e., basal 〈a〉, prismatic 〈a〉 and pyramidal 〈c + a〉 slip systems and one kind of twinning system, i.e., tension twinning system, are introduced into the model. New orientations of slip systems in the twinned region of single crystal are obtained by rotating the original ones, and then a rotation tensor is used in the proposed model. Evolution equations of dislocation slipping and twinning deformation are obtained in the form of power-law. Also, the residual twinning and its accumulation during the cyclic loading are considered in the proposed model. Finally, an explicit scale-transition rule is adopted to extend the proposed single crystal constitutive model to the polycrystalline version. The capability of the proposed model to describe the uniaxial ratchetting of the polycrystalline magnesium alloy is verified by comparing the predictions with corresponding experimental results. More predictions of the ratchetting of magnesium single crystal and polycrystalline alloys are also discussed by the proposed model.