Phase Field Simulation On AZ31 Mg Alloy Grain Growth During Recrystallization In Real Spatio-time Scale

Phase-field approach based on Ginzburg-Landau phenomenological theory, classical thermodynamics and dynamics theory has shown the most promising potential to accomplish the prediction of microstructure evolution during heat treatment in the industrial application scale of micrometers and minutes.However,the physical meaning of most model parameters in the approach is not very clear and the real value of the parameters cannot be found accurately so that the majority of simulations published by this method were phenomenological and qualitative.In this research a model has been established to simulate the realistic spatio-temporal microstructure evolution by deriving out all the physical values of the parameters in the model.A set of rules has been established in first time to be referred for other simulations.AZ31 magnesium alloy,one of the most widely used commercial deforming magnesium alloys,has good strength and ductility as well.However,the property of this alloy cannot be improved effectively by ageing strengthening and solution strengthening and recrystallization becomes the main method to optimize its microstructure and properties.A wrought AZ31 magnesium alloy plate was selected to study microstructure evolution during recrystallization by present simulation work.Comparing simulation results with some experimental data will identify the correctness of the present model.A special local free energy density expression was suggested for simulation of recrystallization because stored strain energy has to be considered in grains before recrystallization.Meanwhile,the composition variable is taken into account in the expression because it is believed that diffusion plays an important role in the recrystallization of the alloy.The model can be easily adapted to other alloys system as long as the necessary kinetic and thermodynamic data such as the segregation activity energy,the free energy-concentration curves are available.The values of parameters B₁ and B₂ in the expression were then derived with choosing a reasonable value of restored energy from a reference according to deformation strain.The value A,A₁ and A₂ were decided by fitting the local free energy density function with the curve of free energy as a function of composition obtained by the soft ware THERMOCALC.The grain boundary profile is studied in to ascertain coupling coefficient K₁ and gradient coefficient K₂ whose realistic value is the key to accomplish simulation in realistic spatio-temporal space.A concept called grain boundary range is proposed.The range here represents a scale within that the grain boundary energy is spread,and its value is far larger than the width of lattice distortion caused by irregular atom arrangement at grain boundary.The boundary range of the AZ31 alloy was discussed as between 1-2μm according to its physical concept and the experimental microstructure observation.Finally,the parameter related to grain boundary mobility was expressed in the form of Arrhenius formula and the activity energy has been found out as the the value of the boundary segregation activity energy of Zn atoms whose difference with matrix atoms in size is the largest among all foreign atoms in the alloy.In order to obtain the value of constant L₀,the grain size at different time during recrystallization at 400℃by simulation was found in different artificial mobility to meet that by experimental.The parameters in the present model are taken from physical analysis or experimental described as above so that the microstructure evolution can be simulated in real length and time space between 250℃to 400℃to do a comparison with actually measured grain morphology and size by experimental.The correctness and effectiveness of present model has been proved by the comparison in microstructure characteristics,single grain evolution,and average grain size and variation degree of grain size.It is shown that the simulated results have a good agreement with the experimental results between temperatures 300℃to 400℃for up to 100 minutes but not the temperature 250℃which implies a mechanism variation in the activity energy. The segregation of Zn around the grain boundary takes an important role during the grain boundary migration though the content of Al is larger in the alloy system than Zn. The degree of grain size fluctuation increases with increasing recrystallization temperature and annealing time and the grain size fluctuation becomes particularly severe when the recrystallization temperature is over a critical value of 350℃,which agrees well with the existing experimental data in the AZ31Mg alloy. The influence of restored energy and grain boundary energy on recrystallization is systemically studied during annealing of AZ31Mg alloy by simulation.The simulation results show that grain size,grain growth velocity and the degree of grain size fluctuation decrease with increasing restored energy.The grain size,grain growth velocity and the degree of grain size fluctuation increase with increasing grain boundary energy when the energy is larger than a critical value which is 0.33J/m² in this alloy system,and the effect of grain boundary energy on recrystallization behaviors can be neglect when grain boundary energy is less than the critical value.