Determining the hot forming limits of titanium alloy sheet under different strain paths by constant equivalent strain rate hot gas bulging tests

Abstract

This study aims to determine the hot forming limit diagram (FLD) of titanium alloy sheet using constant equivalent strain rate hot gas bulging tests. A novel method was proposed to calculate pressure-time curves under different strain paths, ensuring that the equivalent strain rate during hot deformation remains constant. The key of this method is the development of a VUMAT material subroutine that accurately reflects anisotropic hardening and r-value evolution, and the pressure loading curves under different strain paths were determined by coupling with the VUAMP amplitude subroutine embedded with a PID control algorithm. Based on dies with different cavity structures and unbonded double-layer samples, the FLDs of TA32 titanium alloy sheet under linear and nonlinear strain paths were obtained by carrying out hot gas bulging tests at 800 ℃ with a strain rate of 0.001 s-1. The results demonstrate that the proposed approach is applicable for determining the pressure-time curves under various complex strain paths, and it is experimentally verified that the equivalent strain rate of the sample apex is maintained near the target value during the bulging process. Furthermore, the significant effects of anisotropy and strain path change on the forming limits were quantitatively analyzed. The developed method is not only beneficial for testing the hot biaxial mechanical properties of materials, but also useful for controlling the strain rate during the hot forming of complex thin-walled components to improve the formability of materials.