Issue 50

K. Singh et alii, Frattura ed Integrità Strutturale, 50 (2019) 319-330; DOI: 10.3221/IGF-ESIS.50.27 325 Application of the material model In the present work, a relative change in local stress at the microstructure level is predicted, and the same will be used as input to the MIBF model. Predicted stress field would assist in estimating the rupture probability based on a local approach. MIBF model relies on crystal plasticity results in terms of heterogeneity of the stress field at the microstructure scale [10]. The concept, theory, and application of MIBF model are discussed in detail elsewhere [10, 24-27]. Generally, a compact tension (CT) specimen is modeled in the FEA framework to apply the MIBF. An elementary volume (zone near the crack tip) consists of cleavage triggering sites like carbides having specific size distribution depending upon materials composition. Each carbide is a potential site for the cleavage and taken as the point of nucleation. The rupture (propagation) will be triggered at such sites according to the Griffith criterion (local stress and critical stress). Finally, the MIBF model provides the failure/rupture probability based on the carbide size distribution and local stress distribution obtained from crystal plasticity. MIBF model is capable of reproducing the variation in toughness with temperature and irradiation without arbitrarily introducing a change in cleavage critical stress. To assess the effect of various irradiation conditions at the microstructure level, a unit cell model is analyzed at 300 K for non-irradiated and irradiated material cases. In the unit cell, the small inclusion of radius 2µm (with and without crack) present at the center of the unit cell is envisaged (unit cell with inclusion case, shown in the Fig. 2). This is to account for fracture behavior dependency upon the defects present at the microscale. Mostly, inclusions (sulphides, oxides, nitrides, etc.) which act as a crack initiator are harder than the surrounding material. In the present study, the inclusion is assumed to be elastic and have E value ~ 300 GPa. The direction of loading is oriented such that it inclines with [-149] direction of the crystallographic axis. The displacement controlled loading in the form of 10 % global strain is applied at one face of the unit cell, while the opposite face is restricted. Figure 2: Unit cell model with inclusion, the meshed model with a highlighted area of consideration for Weibull distribution’s parameter estimation R ESULTS AND DISCUSSION he various irradiation conditions are analyzed corresponding to different defect size and number density. Each set of defect size (2 nm , 5 nm , 10 nm , 15 nm , 25 nm , 50 nm ) and their number density ( 12 3 1 10 mm −  , 12 3 2 10 mm −  , 12 3 4 10 mm −  12 3 6 10 mm −  , 12 3 8 10 mm −  , 12 3 10 10 mm −  , 12 3 12 10 mm −  , 12 3 14 10 mm −  ) represents the particular irradiation condition in terms of irradiation temperature and dose. The simulation results obtained are further post-processed to get the frequency distribution of the equivalent stress value in the unit cell. This is used in the MIBF model in the form of Weibull distribution to calculate the failure probability of toughness specimen. Further, an effect of irradiation on local stress distribution is estimated in terms of relative change in parameters of Weibull distribution with respect to the non-irradiated case. This relative change in parameters as a function of irradiation defect size and number density assist in estimating the fracture toughness of irradiated materials. The rate of change of parameters of Weibull distribution due to irradiation corresponds to the rate of change of the local stress distribution in the elementary volume due to the respective irradiation condition. The purpose of the current work is to solely provide an effect of T