A new relationship between the stress multipliers of Garofalo equation for constitutive analysis of hot deformation in modified 9Cr–1Mo (P91) steel

Constitutive analysis is performed following the Garofalo sine–hyperbolic equation on the true stress–strain data obtained from isothermal hot compression tests on modified 9Cr–1Mo (P91) steel over a wide range of temperature (1123–1373 K) and strain rate (0.001–100 s−1). We propose a new relationship between the stress multipliers αg and αER for P91 steel as (αg/αER) = 0.27977+0.01531(np)2; where the adjustable stress multiplier αg is obtained by force fitting Garofalo equation (ε˙=constant[sinh(αgσ)]ng) and αER is obtained as αER = βe/np from the data fitted to power (ε˙∝σnp) and exponential (ε˙∝exp(βeσ)) laws for the entire stress/strain rate regime. αg was easily obtained knowing αER and following this, the other constitutive parameters ng, Q and ln Ag were determined and were found to be strain dependent except ng. The successful prediction of flow stress has been supported by a higher correlation coefficient (R = 0.994) and a lower average absolute relative error (5.03%) for the entire investigated hot working domain.

► Constitutive analysis is performed on compression flow stress data for P91 steel.
► A new relation between stress multipliers αg and αER is proposed as (αg/αER) = 0.27977 + 0.01531(np)2.
► The adjustable αg is obtained by force fitting the Garofalo equation ε˙=constant[sinh(αgσ)]ng.
► αER = βe/np is obtained from the plots of power (ε˙∝σnp) and exponential (ε˙∝exp(βeσ)) laws.
► Implications of the proposed relation to constitutive analysis are discussed.