Jafari Reza, Farzin Mahmoud, Mashayekhi Mohammad, “A Microstructure-Based Constitutive Model for Superplastic Forming”, Metallurgical and Materials Transactions A, Vol. 43, No. 11, pp. 4266-4280, 2012.
A constitutive model is proposed for simulations of hot metal forming processes. This model is constructed based on dominant mechanisms that take part in hot forming and includes intergranular deformation, grain boundary sliding, and grain boundary diffusion. A Taylor type polycrystalline model is used to predict intergranular deformation. Previous works on grain boundary sliding and grain boundary diffusion are extended to drive three-dimensional macro stress–strain rate relationships for each mechanism. In these relationships, the effect of grain size is also taken into account. The proposed model is first used to simulate step strain-rate tests and the results are compared with experimental data. It is shown that the model can be used to predict flow stresses for various grain sizes and strain rates. The yield locus is then predicted for multiaxial stress states, and it is observed that it is very close to the von Mises yield criterion. It is also shown that the proposed model can be directly used to simulate hot forming processes. Bulge forming process and gas pressure tray forming are simulated, and the results are compared with experimental data.