Issue 48

J. Christopher et alii, Frattura ed Integrità Strutturale, 48 (2019) 554-562; DOI: 10.3221/IGF-ESIS.48.53 555 0 t e in          (1) Further, the elastic strain rate ( e   ) given in Eqn. (1) is written as r e C      (2) The interrelationship between stress-relaxation rate and inelastic strain rate can be obtained from Eqn. (1) and Eqn. (2) as r in e C          (3) Eqn. (3) indicates that the decrease in elastic strain is exactly balanced by an increase in inelastic strain during relaxation. This leads to the decrease in stress values with hold time. Eqn. (3) represents a generalised relationship for the description of stress-relaxation behaviour for any materials. In common, developed models for stress-relaxation mainly focus on the interrelationship between inelastic strain rate and relaxation stress. The inelastic strain rate given in Eqn. (3) captures only the creep strain developed during stress relaxation. Time independent part of inelastic strain (i.e. plastic strain) has been assumed to be insignificant in the present investigation. Between the existing models [3], the model proposed by Feltham [4] is widely used to describe the stress-relaxation behaviour of different metals and alloys [4-7]. In this study, in addition to the Feltham model, the relationship recently proposed by Christopher and Choudhary [8] based on the sine hyperbolic kinetic rate formulation coupled with the evolution of internal stress has been employed to describe the stress-relaxation behaviour of materials. The physical constants associated with these models have been determined by the minimization of errors between experimental and predicted relaxation stress vs. hold time data for two different strain hold levels of 1.3 and 2.5% at 873 K for E911 steel. Among these two models, the appropriate relationship applicable for the E911 steel has also been identified in this study. M ODELLING FRAMEWORK Feltham Relationship for stress-relaxation behaviour (Model-I) ased on kinetic theory of dislocation-local obstacle interaction, Feltham [4] proposed the inelastic strain rate relationship to describe the stress-relaxation behaviour and it is given as     0 exp r i in m Q V kT                     (4) where 0   is the characteristic strain rate that includes a frequency factor, the area swept out by an activated dislocation and the Burgers vector (b) and  r   i is equal to the effective stress (  e ). According to Feltham [4], the parameters such as characteristic strain rate ( 0   ), mobile dislocation density (  m ) and activation volume (  V) are unaltered during deformation under stress-relaxation and the internal stress  i is assumed as a constant. Eqn. (4) is substituted in Eqn. (3) and integration of Eqn. (3) with appropriate boundary conditions is represented as     0 0 0 exp r r t r i r m Q V d C dt kT                        (5) where  r0 is the relaxation stress at t = 0. Eqn. (5) yields 0 0 ln 1 r r kT t V t            (6) B