Issue 48

J. Christopher et alii, Frattura ed Integrità Strutturale, 48 (2019) 554-562; DOI: 10.3221/IGF-ESIS.48.53 556 where     0 0 0 1 exp r i m Q V C V t kT kT                    with t 0 is treated as a constant. Eqn. (6) is employed for the description of relaxation behaviour of different materials. In common, the simplified form of Eqn. (6) is represented as   0 ln 1 r r s t       (7) where s and  are constants and s = KT/  V;  =1/t 0 . S INE HYPERBOLIC RATE MODEL FOR STRESS - RELAXATION BEHAVIOUR (M ODEL -II) n addition to Feltham model (Model-I) [4], recently developed constitutive model for the description of stress- relaxation behavior of P91 steel has also been used to examine the stress-relaxation behaviour of the steel [8]. The model is based on the incorporation of stress dependent activation volume and average dislocation segment length into the kinetic rate theories [8,9]. The final relationship defining the inelastic strain rate in terms of internal stress (  i ) is represented by             1/3 2 2 3 2 1/3 2 exp sinh m D r i i r i r i in i r i b v Q b RT MkT M                                               (8) The rate equation for the evolution of internal stress with time is derived based on the power law relationship proposed by Argon and Takeuchi [10] and it is given as m r i i r r r r hm m                         (9) The coupled differential equations i.e. Eqn.(3), Eqn. (8) and (9) have been used to describe the stress-relaxation beahviour of the materials. There are three unknown constants such as initial relaxation stress (  r0 ), initial internal stress (  i0 ) and power law exponent (m) related to internal stress. The power law coefficient (h) given in Eqn. 9 can be obtained as 0 0 i m r h    . E XPERIMENAL DATA he relaxation stress vs. hold time data obtained for E911 steel in normalised and tempered condition has been used in the present investigation. The chemical composition (wt. %) of E911 ferritic-martensitic steel was as follow as: Fe-0.105C-9.16Cr-1.01Mo-1.0W-0.07Ni-0.20Si-0.35Mn-0.23V-0.068Nb-0.007P-0.003S-0.072N. Normalizing treatment involved austenitizing at 1323 K for 30 min followed by air cooling and tempering treatment was performed by soaking at 1023 K for 1 h followed by air cooling. TEM microstructure of E911 steel shows the tempered martensitic lath structure accompanied with dense dislocations as depicted in Fig. 1. Cylindrical specimens of 32.5 mm gauge length and 6.4 mm gauge diameter were machined from the normalised and tempered specimen blanks. Test specimen dimensions are shown in Fig. 2. Stress-relaxation tests were carried out in air environment (i.e. ambient condition without controlled atmosphere and possibility of air ingress into the furnace environment) at 873 K in a servo- hydraulic universal testing system equipped with three-zone-resistance heating furnace and proportional-integral-derivative temperature controller. Three-zone-resistance heating furnace provides much larger uniform temperature zone than the specimen dimension. Calibrated thermocouples were used in conjunction with the appropriate temperature indicating devices and the test temperature was controlled well within ± 2 K. Tests were performed by employing nominal loading strain rate of 1  10  4 s –1 to the desired total applied strain levels of 1.3 and 2.5%. After 24 hours of hold duration, the I T