Constitutive analysis to predict the hot deformation behavior of 34CrMo4 steel with an optimum solution method for stress multiplier

• Isothermal compression tests were conducted to study the flow behavior of 34CrMo4.
• The influence of strain is incorporated in constitutive model.
• An optimum solution method for stress multiplier α is proposed.

The hot deformation behaviors of steel 34CrMo4 is investigated by hot compression test with the temperature range of 1073–1373 K and the strain rate range of 0.01–10 s−1. The flow behaviors of 34CrMo4 steel were characterized based on the true stress–true strain curves. The hyperbolic sine law in Arrhenius type is adopted in the constitutive modeling for 34CrMo4. Solving algorithm of the stress multiplier α in hyperbolic sine law is a key factor to guarantee the constitutive model accuracy. How to solve the stress multiplier α is investigated and an optimum solution method for α is proposed. Meanwhile, the influence of strain is incorporated in constitutive analysis by considering the effect of strain on material constants α, n, Q and A. With the optimum solution method for stress multiplier α proposed, the stress prediction is satisfactory with the higher correlation coefficient, R = 0.988 and the lower average absolute relative error, AARE = 3.44% for the entire strain rate-temperature domain. The optimum solution method for stress multiplier α can also be applied for other materials to predict the flow behavior more accurately.