Grain Growth And Texture Formation Of AZ31 Mg Alloy With Second Phase Particles Under Applied Stress By Phase Field Simulation

Magnesium alloys as the lightest structural materials with many excellent properties have been widely used in automotive,aerospace,3C and other industries.However,Mg alloys have low strength and poor plasticity in room temperature,which limit their application.To improve their mechanical properties,controlling and designing the microstructure(e.g.,grain size,grain distribution,and texture)have been commonly used.Although the grain refinement and texture formation can be greatly influenced by means of the addition of the second-phase particles,it is unclear about the effects of applied stress on texture evolution and grain growth.As the rapid growing in the field of computational materials,it will be very effective to optimize mechanical properties in Mg alloys by controlling microstructure evolution through computer simulations.In this work,a phase-field model is established to simulate the effects of the second-phase particles on grain growth and texture evolution in AZ31 alloy under applied stress.In this phasefield model,the elastic energy item is introduced to describe the work from the applied stress.Also,the contribution of the second-phase particles to the free energy is considered by adding an extra term to the free energy expression.The order parameters are defined to represent a physical variable of grain orientation in terms of three angles in spatial coordinates so that the grain volume of different order parameters can be used to indicate the texture of the alloy.The eigenstrain tensors for different grains are different because of elastic anisotropy of the Mg lattice.The tensor is defined by transforming standard eigenstrain tensor according to the angle between(0001)plane of a grain and direction of applied stress.Therefore,different grains contribute to different amounts of work under applied stress.All physical parameters in the model are determined by physical or experimental analysis so that the microstructure evolution can be simulated for real AZ31 Mg alloy in real length and time scales.Then using this model,the effects of the content,size,shape and distribution of the secondphase particles on the grain growth for the AZ31 alloy are investigated.It is shown that the addition of second-phase particles results in a strong refinement effect,reducing the grain size compared to that of the alloy without the particles.Nevertheless,when the volume fraction of the particles is greater than a specific value,further more particles have little effect.In AZ31 alloy,it is found that when volume fraction of particles is 3%and 10%,the second-phase particles should have a critical size of 300 nm and 500 nm for the grain refinement effect to occur.If the size is smaller than the critical size,the large particles will more strongly hinder grain growth;in contrast,when the size is larger than the critical size,the large particles will exhibit a weaker hindering effect than small particles.Moreover,the results show that the spherical second-phase particles hinder grain growth better than ellipsoid particles and much better than rod-shaped particles when the volume fraction of reinforcing particles is 2%.However,when the volume fraction is greater than 4%,the effect of three types of particles are almost the same.Furthermore,the refinement effect of the second-phase particles increases with the temperature.Both 2D and 3D phase field models are performed to investigate the effect of applied stress on the grain growth.It reveals that the 2D and cross-sectional 3D morphologies are similar and the grain-growth rate increases with applied stress in a same manner in both simulations.The simulation results show that the applied stress strongly influences grain growth in AZ31 alloy at elevated temperature,and the grain-growth rate increases with applied stress.When the applied stress is higher than 800 MPa,the stress can lead to abnormal grain growth.The grain growth under applied stress is not consistent with the von Neumann-Mullins grain-growth law.Meanwhile,the texture deformation in AZ31 alloy under applied stress at elevated temperatures is also investigated.The simulation results show that the texture remain random during grain growth without stress.The uniaxial compressive stress would result in an intensive texture of the<0001>axis parallel to the direction of compressive stress in AZ31 alloy after grown at elevated temperatures,when the applied stress is 400 MPa.Comparing texture simulation results with limited experimental EBSD data,it will identify the correctness of the model.The mechanism of texture formation is discussed by analyzing the distribution of elastic energy density for polycrystalline.As the grains of<1010>and<2110>crystal orientations have higher elastic energy density and the grain of<0001>crystal orientation has lower one,the<0001>grain will be grown preferably resulting to a lower total energy of the polycrystalline system,which indicates that elastic energy density plays a more critical role in determining the type of the texture.The simulation also finds that the applied stress would result in an intensive<0001>basal texture only when it is greater than 400 MPa.Finally,the effect of the second-phase particles on the texture formation in AZ31 alloy under applied stress is studied.The simulation results show that the more second-phase particles,the weaker texture formation is.It exists a critical size of the second-phase particles,which can hinder the texture formation utmost.When the volume fraction of the particles fixes 4%constantly,the critical size of the particles is 1.7?m.When the volume fraction of the particles is 4%,the applied stress above 600 MPa results in a more intensive texture of<0001>,while the fraction is higher than 12%,the applied stress causes a weakly texture and the texture strength has a tiny effect with the increase of the applied stress.