Issue 48

J. Christopher et alii, Frattura ed Integrità Strutturale, 48 (2019) 554-562; DOI: 10.3221/IGF-ESIS.48.53 559 observed in log-log plot for both the strain holds. It can be seen that the predicted relaxation stress vs. hold time data obtained using Model-II follow the experimental data more closely compared to those derived from the Model-I. Figure 4: Variations in experimental relaxation stress (  r ) with hold time (t) for a) 1.3% and b) 2.5% strain holds. The predicted  r vs. t data using Model-I and Model-II have also been superimposed for both strain hold conditions. The variations in the deviation of stress values as  r =  r , exp   r , pred with time exhibit lower values for Model-II over Model-I. This further suggested statistical suitability of the Model-II for describing stress-relaxation behaviour of tempered martensitic 9% Cr steels (Fig. 5). Based on experimental observations in 9% Cr steels, it has been shown that the subgrain coarsening accompanied with decrease in dislocation density remains dominant during inelastic deformation under stress-relaxation conditions at elevated temperatures [12,13]. The reported increase in lath width or subgrain size indicated the increase in inter-barrier spacing (  ) for 9% Cr steels during stress-relaxation. It is known that inter-barrier spacing (  ) and activation volume (  V) is inversely related to internal stress. Therefore, the variations in internal stress as well as activation volume with the hold time are expected for 9% Cr steels. From the microstructural aspects, it is evident that Feltham relation [4] involving constancy in internal stress and activation volume is not applicable for describing the stress-relaxation behaviour of E911 steel. However, Model-II has been able to predict the evolution of internal stress, effective stress and relaxation stress with respect to hold time. This is shown in Fig. 6 for the strain hold of 1.3% as an example. Based on Freidel statistics [14], the internal stress and effective stress can be used to evaluate the inter-barrier spacing and activation volume. The relationships are given as 2 i M b     (10) and   3 1/3 2 (2 ) i e M V b                (11) where 'b' is the Burgers vector. Fig. 7 depicts the evolution of inter-barrier spacing and activation volume with the hold time. The observed increase in inter-barrier spacing and activation volume confirms that continual substructural coarsening of E911 steel during stress-relaxation. The comments related to the evolution of internal stress (  i ) and its dependence on relaxation stress (  r ) following Eqn. (9) is noteworthy. In several metals and alloys, based on stress change experiments during steady state creep, it has been observed that the relationship between internal stress and applied stress obeys power law. The exponent values in the range 0.7-1.0 were reported for Cd, Mg, Al-Li and Al-Mg alloys [15-18]. The observed power law exponent m = 0.81 for E911 steel is in agreement with those values observed for different materials [15-18]. Based on internal variable approach, it has also been found that the variations in  i /  a (where  a is the applied stress) with  a exhibited power law relation as  i /  a   a  0.21 or  i = 2.22  a 0.79 for P9 steel during secondary creep deformation [8,9]. The equivalence between the results obtained from stress relaxation tests and monotonic creep tests is