An investigation into Arrhenius type constitutive models to predict complex hot deformation behavior of TC4 alloy having bimodal microstructure

The purpose of this study was to determine the plastic deformation behavior of TC4 alloy having bimodal microstructure at hot forming conditions and establish a suitable constitutive model. The bimodal microstructure was obtained by plate die forging at 985 °C to a deformation of 40% and then annealing at 720 °C for 1 h followed by air cooling. Quasi-static tensile tests were performed at temperatures ranging from 750 to 900 °C and strain rates of 0.0001–0.1 s−1. The experimental stress-strain curves revealed that the alloy exhibited complex deformation behavior with considerable strain hardening, dynamic recovery, and continuous dynamic recrystallization. The processing map is established to delineate the safe and unsafe thermomechanical conditions for material hot forming that revealed the existence of superplasticity at 0.0001 s−1 and 750–900 °C, DRX at 0.001 s−1 and 800–900 °C, and flow instabilities at 0.1–0.01 s−1 and 800–850 °C. Modified Arrhenius type constitutive models with strain compensated using polynomial equation (PSCAM) and exponential equation (ESCAM) were established to predict the complex deformation behavior of the alloy. Also, a novel optimization method utilizing an evolutionary algorithm (EA) and generalized reduced gradient (GRG) was employed to establish an optimized polynomial strain compensated Arrhenius type constitutive model (OPSCAM). The predictability of the three established models is evaluated and compared during strain hardening and dynamic softening of the material. The correlation coefficients of ESCAM, PSCAM, and OPSCAM were 0.98, 0.99, and 0.99, respectively, showing a good correlation for the three models. Percentage average absolute relative error for the three models is 13.76%, 9.66%, and 9.14%, respectively, during strain hardening and 12.40%, 8.41%, and 6.78%, respectively, during dynamic softening. The study showed that OPSCAM could adequately predict the deformation behavior of TC4 alloy with bimodal microstructure during both hardening and softening regions and could be used to simulate the hot forming process.