A novel constitutive model for stress relaxation of Ti-6Al-4V alloy sheet

In this paper, the stress relaxation tests were performed on Ti-6Al-4V alloy sheet with different initial total strains and different temperatures. Based on the experimental data, a novel empirical equation for predicting the stress versus time curves was proposed, and then an explicit constitutive model for describing the stress relaxation behaviours was further developed. The average prediction error was less than 8.27%, proving the proposed prediction curves were valid. In addition, two material constants which depend on initial stresses and total strains were introduced to accurately describe the stress relaxation curves. Then the methods for solving these two material constants under different initial conditions were presented. Finally, a simple method for dividing the stress relaxation stages was proposed. There are three stages in the stress relaxation curve studied in this paper, including the loading stage, stress relaxation-I and stress relaxation-II. A symbol called η_i which represents the normalized ratio of instantaneous stress to initial stress was used. When time τ is equal to α, the ratio of instantaneous normalized stress to normalized initial stress is reduced to η₁ = 1/e, and the instantaneous plastic strain at this moment is (1 − η₁) of the total plastic strain.