The same strain-rate sensitivity coefficient of 1/6 demonstrated from DRX critical and steady state during hot deformation for metallic materials

•The constitutive models on DRX critical and steady state have been constructed.•The linear relationship of DRX critical and steady state stress has been verified.•The same strain-rate sensitivity coefficient of 1/6 could be obtained on two states. Metal forming and shaping is becoming advanced and their processing is becoming modelled gradually. Arrhenius constitutive models for critical and steady state when dynamic recrystallization (DRX) for metallic materials have been constructed from internal variables. Isothermal compression on two typical metallic materials were conducted for verification. Stress of DRX critical and steady state was identified through flow curves according to Poliak-Jonas and their microstructure. The linear relationship between critical and steady stress during hot deformation has been validated.