Mechanical Response Of Crystal Plasticity For Hexagonal Close Packed Magnesium

The crystal plasticity finite element model is an integaration between the finite element method and the crystal plasticity theory to predict the plastic deformation of materials from micro lattice scale.Compared with the traditional isotropic constitutive theory,the plastic deformation of metals is attributed to the slip of dislocation and deformation twins.So the crystal plasticity theory is more close to the real physical essence of plastic deformation of metals.Based on the slip and twinning mechanisms of physical essence of material deformation,the crystal plasticity finite element can be used to simulate the anisotropic mechanical behavior of metal deformation which can not be considered in the traditional finite element method.The orientations and textures of materials after deformation can be predicted and it will provide a strong support for studying the microstructure of material.Relative to the face centered cubic and body centered cubic metals,a more complex plastic deformation mechanism is exhibited in the hexagonal close packed structure metals.Furthermore,the generation and evolution of twins play an important role in the whole plastic deformation.Based on this phenomenon,the twinning deformation is incorporated into the crystal plasticity theory in this paper.The constitutive relation and hardening mode containing twinning deformation are deduced and the different hardening mechanisms are adopted for different deformation twins.The main research works are as follows:(1)The hexagonal close packed structure metal magnesium is chosen for the research object.Considering the relations among the slip(twinning)plane and direction,shear deformation and gradient tensor,the transformation between the micro plastic deformation mechanism and the macro mechanical response is established.Based on the Taylor model,the deformation twins are taken into account in the crystal plasticity theory.The constitutive relation of crystal plasticity which is composed of the slip,twinning and their interactions is derived.(2)Due to the differences of deformation modes and hardening characteristics between tensile twinning and compressive twinning,the different appropriate hardening models are adopted to describe their deformation and the interactions between them.The FORTRAN language is used to compile the user defined material subroutine(UMAT)based on the abovementioned crystal plasticity model.The simulations of crystal plasticity finite element are implemented by embedding this program into the finite element software ABAQUS.(3)The model of plane deformation of single crystal magnesium is established by considering seven orientations with different loading directions.Six kinds of deformation mechanisms,i.e.the basal,prismatic,pyramidal <a> and pyramidal <c+a> slips,tensile twinning and compressive twinning,are used to accommodate the plastic deformation of magnesium.The plastic deformation of magnesium is predicted from microscopic view point by using the uniform calibrated material parameters.The deformation characteristics,stress-strain curves,relative activities of different slip(twinning)systems and orientation evolution for seven kinds of orientations are also obtained.The predictions are in good agreement with the experimental results and it shows that it is reasonable to use the crystal plasticity theory for predicting the mechanical responses and texture evolutions of materials.(4)Based on the knowledge of the viscoplastic self-consistent model,the differences between the viscoplastic self-consistent model and the elastic viscoplastic crystal plasticity model are analyzed in their constitutive relations,transitions from microscopic to macroscopic,hardening mechanisms and simulation costs.The viscoplastic self-consistent model is also modified.The same Pierce hardening with the elastic viscoplastic crystal plasticity model and the different Voce hardening are considered.With the same loading boundary conditions and orientations of magnesium single crystal,the corresponding stress-strain curves and relative activities are predicted.The comparison between different hardening models is carried out.The results show that the simulations obtained by Pierce hardening model is more consistent with the experimental data.(5)The plastic deformation of polycrystalline magnesium is predicted by using the modified viscoplastic self consistent model.The stress-strain curves at different strain rates and the yield surfaces at different strain are calculated and compared with the experiments.It reflects the yield characteristcis and strain rate effect of polycrystalline magnesium.Several different modulus assumptions are adopted and their corresponding stress-strain curves,relative activities,yield surfaces and pole figures after deformation are calculated respectively.A hardening trend from intense to weak is exhibited in these hypotheses.In addition,the same trend is found in all the above responses.