Issue 50

K. Singh et alii, Frattura ed Integrità Strutturale, 50 (2019) 319-330; DOI: 10.3221/IGF-ESIS.50.27 327 The stress field (for equivalent stress) in the unit cell is transformed into probability density for the non-irradiated and irradiated case. The probability density of the local stress field in the unit cell and the corresponding Weibull distribution of the stress field in the unit cell are plotted against the equivalent stress for various irradiation conditions in Fig. 3. It shows the results for different irradiation conditions (irradiation flux and temperature). The irradiation temperature defines the size of the dislocation loop ( ) irr d , whereas the flux controls the irradiation defect number density ( irr N ) of irradiation defects. Similar defect size (say 15 nm in Fig. 3a and 3b) with different irradiation defect number density ( irr N ) represents the material exposed to different flux levels but at the same temperature during irradiation. In the case of Fig. 3a and 3c, the irradiation defect density is same but differ in defect size; this depicts the material irradiated at different temperature values but same flux. Presence of irradiation defects shifts the mean stress value towards higher magnitude relative to the non- irradiated case representing the irradiation hardening. It is observed that there is a significant shift in equivalent stress towards higher magnitude for all cases of irradiated material. The direct dose dependence of the local stress field (represented by the change in Weibull distribution) due to irradiation defects is evident from the reported results. Based on the FEA results, it is found that the influence of inclusion (with or without crack) is negligible in estimating the relative change in the stress field due to the presence of irradiation defects. Moreover, the stress raising effect of the local defects like inclusion is explicitly handled by MIBF model by having the probabilistic distribution of the carbides with a crack like defects. The Weibull parameters (  shape and  scale) estimated for each irradiation conditions are presented in the form of the relative change in their value with respect to the non-irradiation case. This relative change in Weibull parameter is plotted as a function of irradiation defect number density for each defect size (shown in Fig. 4). Through this curve, it is possible to estimate the relative change in the stress field at the microstructure level for the material exposed to irradiation conditions at a specific temperature and flux level. Knowing the value of the Weibull parameters for the non-irradiated case, the parameters for irradiated material can be estimated. Through these parameters, it is viable to determine the change in local stress distribution at microstructure level for desired irradiation conditions (flux and irradiation temperature) and finally lead to predicting the fracture response under irradiated condition using MIBF model. Figure 4: Relative change in Weibull distribution parameters for different irradiation defect size and number density. Subscript ‘RL’ represents the relative value of the corresponding parameter. For example, the relative change in the shape parameter is defined as (β irr – β non-irr ) / β non-irr . C ONCLUSIONS he material model developed for BCC materials to define the temperature dependent plasticity along with irradiation modeling is discussed. The two different constitutive equations representing thermal and athermal regime can describe the plasticity behavior satisfactorily, which is confirmed with experimental validation. The irradiation defects are treated as barriers to the motion of the dislocation, and the evolution of various irradiation related parameters is incorporated. Presence of irradiation defects in the form of interstitial loops affects the local stress field for different irradiation conditions is presented for the unit cell model (with and without inclusion). Shifting of equivalent stress towards higher magnitude for irradiated material signifies the irradiation hardening in the material. Different irradiation conditions T