The Comparation of Arrhenius-Type and Modified Johnson–Cook Constitutive Models at Elevated Temperature for Annealed TA31 Titanium Alloy

Abstract

Constitutive models play a significant role in understanding the deformation behavior of materials and in optimizing the manufacturing process. In order to improve the reliability of calculation results, the high temperature flow behavior of TA31 titanium alloy obtained from an annealed hot-rolled plate has been investigated by a Gleeble-3500 thermo-mechanical simulator. The isothermal hot compression tests are conducted in the temperature range of 850 to 1050 °C and the strain rate range from 0.001 to 10 s-1 with a height reduction of 60%. The annealed TA31 shows a dynamic recovery characteristic during thermo-mechanical processing. The experimental data have been used to develop an Arrhenius-type constitutive model and a modified Johnson-Cook model under the consideration of coupling effect on strain, temperature, and strain rate, as well as the strain-softening phenomenon. The material parameters are determined by a global optimization method based on the initial values by means of a regression method. A comparation of the predicted results has been performed based on the modified Johnson-Cook model and those acquired from the Arrhenius-type model. The correlation coefficient and average absolute relative error of the modified Johnson-Cook model are 4.57% and 0.9945, respectively. However, when the optimization method has been applied, they are 15.77% and 0.9620 for the Arrhenius-type model, respectively. These results indicate that the modified Johnson-Cook model is more accurate and efficient in predicting the flow stress of annealed TA31 titanium alloy under a set of model material parameters. Furthermore, the simple mathematical expression of this model is helpful to incorporate it into the finite element software to obtain detailed and valuable information during the thermo-mechanical processing simulation for TA31 in further work.