Constitutive equations for high temperature flow stress of TC4-DT alloy incorporating strain, strain rate and temperature

• Isothermal hot compression tests were conducted to study the flow behavior of TC4-DT titanium alloy.
• Constitutive equation incorporating the compensation of strain was developed.
• Deviation appeared between predicted data and experimental data above the strain rate of 0.1 s−1.
• A modified constitutive equation considering the compensation of strain rate and temperature increment was carried out.
• The new modified constitutive equation showed the high prediction capabilities of the modified constitutive equation.

In order to get a reliable constitutive equation for the precise simulation, high temperature flow behavior of TC4-DT titanium alloy was investigated by conducting isothermal hot compression tests in temperature range of 1203–1293 K at an interval of 15 K and strain rate range from 0.001 to 10 s−1 on Gleeble-1500 simulator. The results revealed that all the true stress–strain curves showed the characteristics of strain hardening (at the true strain lower than 0.14) followed by flow softening and it was particularly significant at higher strain rates and lower temperatures. The effect of strain rate and temperature incorporating strain on the flow behavior was considered by establishing a constitutive equation with the material constants expressed by a polynomial fitting of strain. The stress values predicted by the constitutive equation demonstrated a well agreement with the experimental results at the strain rates under 1 s−1. A modified constitutive equation considering the compensation of strain, strain rate and temperature increment was developed and could predict the flow stress over the entire range of strain rates and temperatures except at the conditions of 1293 K at 1 s−1 and 10 s−1 and 1278 K at 10 s−1. The correlation coefficient (R) and average absolute relative error (AARE) were 99.3% and 5.07% respectively, which confirmed that the modified constitutive equation could give an accurate and precise estimate of the flow stress of TC4-DT titanium alloy.