Resisting stress for constitutive analysis of hot deformation in modified 9Cr–1Mo (P91) steel Dipti Samantaray, C. Phaniraj n , A.K. Bhaduri, Sumantra Mandal, S.K. Albert Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamil Nadu, India article info Article history: Received 3 August 2012 Received in revised form 13 September 2012 Accepted 15 September 2012 Available online 23 September 2012 Keywords: Ferritic steel Hot working Constitutive analysis Flow behavior Resisting stress abstract Flow stress data from isothermal hot compression tests on modified 9Cr–1Mo steel over a wide range of strain rate (0.001–100 s 1 ) and temperature (1173–1373 K) were found to follow the universal Dorn power-law equation. Distinct stress regimes were observed with stress exponent values of 5 and 10 for low and high stress regimes, respectively. The flow behavior is rationalized by invoking resisting stress s R for dislocation motion and the modified stress exponent n 0 was close to 5 for the entire stress regime. At low stresses, s R /G ¼K(s/G) and approaches a constant threshold stress (s R /G ¼s H /G) in the high stress regime. This has been attributed to the transition in the mechanism from dislocation climb by–pass over particles at low stresses to Orowan bowing at high stresses. The stress dependence is found to obey rate equation of the form ð _ e kT =D L GbÞ¼ A 0 ½ðss R Þ=G n0 and the constitutive parameters A 0 , n 0 , K and s H /G evaluated at different strains were employed for predicting flow stress. The successful prediction of flow stress is reflected by a higher correlation coefficient (R ¼0.99) and a lower average absolute relative error (6.62%) for the entire investigated hot working domain. & 2012 Elsevier B.V. All rights reserved. 1. Introduction The flow behavior at high temperatures and strain rates is described in terms of suitable constitutive equations that ade- quately correlate flow stress, strain rate and temperature. Further, the accurate description of hot deformation behavior as influ- enced by the process parameters is useful in the simulation of metal forming processes by finite element analysis. Ever since it was pointed out by Sellars and Tegart [1], and Jonas et al. [2], the Garofalo sine-hyperbolic equation [3] with Arrhenius term has been adopted for hot deformation at high strain rates. The sine- hyperbolic description of the Zener–Hollomon parameter (i.e., temperature compensated strain rate) has been widely employed for predicting flow stress in the hot working domain. This is because the sine-hyperbolic equation correlates the stress depen- dence for the entire stress/strain rate regime as it suitably combines both the power-law valid at lower stresses and the exponential dependence applicable at higher stress limits. In the literature, there are excellent reviews on the topics which are of relevance to this paper. These are five power-law creep behavior dealt exhaustively by Kassner and Perez-Prado [4,5] and constitutive analysis in hot working comprehensively cov- ered by McQueen and Ryan [6], and recently by Lin and Chen [7]. Recent studies [8–16] show that the sine-hyperbolic expression can be employed for predicting flow stress at different strains with the purpose of developing a strain dependent constitutive equation, because in most of the forming processes, strain is a controlling parameter. For such a strain dependent constitutive analysis in P91 steel, a new relationship between the stress multipliers of Garofalo sine-hyperbolic equation has been pro- posed by Phaniraj et al. [15]. In our study on constitutive analysis in P91 steel [12], follow- ing the sine-hyperbolic equation, the constitutive parameters were evaluated at various strains. The value of apparent activa- tion energy Q was found to be in the range 369–391 kJ mol 1 which is higher than that of lattice diffusion (Q L ¼ 270 kJ mol 1 ) for g-Fe. Subsequently, it was pointed out in our previous work [13] that the observed Q can also be interpreted as Q ¼ 380 711 kJ mol 1 . Such apparent activation energy higher than Q L for high temperature deformation is generally rationa- lized by considering the correction for modulus variation with temperature and further by invoking the concept of resisting stress to dislocation motion that arises due to dislocation– dislocation and/or dislocation–precipitate interactions [17–19]. Therefore, in our previous study [13] on P91 steel, a strain dependent constitutive analysis was performed by considering the correction for shear modulus and diffusivity. It was observed that the plots of strain rate normalized by lattice diffusivity against flow stress normalized by shear modulus showed a distinct deviation from five power-law behavior at higher Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/msea Materials Science & Engineering A 0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.09.053 n Corresponding author. Tel.: þ91 44 27480118; fax: þ91 44 27480075. E-mail address: phani@igcar.gov.in (C. Phaniraj). Materials Science & Engineering A 560 (2013) 170–177