Issue 50

K. Singh et alii, Frattura ed Integrità Strutturale, 50 (2019) 319-330; DOI: 10.3221/IGF-ESIS.50.27 324 r d is the reference diameter (taken as 2 nm), ( ) irr irr lim N d is the material parameter defining its saturated value for increasing dose. The factor size f is multiplied with Eqn. 14, this incorporates the defect size dependence of the dislocation velocity. The various material parameters [7-9, 11] used in the material model are listed in Tab. I. Parameter Value Parameter Value b 0.2481 nm B k 8.6173×10 -5 eV/K E 236.4-0.0459T GPa c f 6  0.35 . AF coll  0.7 p 0.593 . AF non coll  − 0.1 q 1.223 self K 100 0 Δ H 0.76 eV forest K 2 3, 1 300 self K min T   +     0  360 MPa c 1 D 10 nm irr  0.3 B 10.5×10 -11 MPa.s -1  4 prop y 2 nm  4 initial  4×10 12 m -2 r d 2 nm initial m  = initial  ( ) irr irr lim N d 150×10 6 m -2 Table I: Various material parameters considered in material model. Figure 1: Validation of a material model with experimental results: resolved shear stress variation as a function of temperature. Finite element formulation The constitutive equations discussed in previous sections encompass the behavior of BCC materials under both non- irradiated and irradiated conditions. Flow rule is defined by Eqn. 1, 2 & 3, Eqn. 4 to 10 define the hardening behavior, Eqn. 12 defines the evolution of dislocation density and Eqn. 13 and Eqn. 14 defines the evolution of irradiation defects and mobile dislocation density, respectively. These equations are solved at each increment for 12 slip systems to estimate the plasticity behavior. The constitutive equations are formulated with finite strain formulation using the MFRONT interface [20] and subsequently solved with finite element solver. The results are validated with available experimental data in terms of resolved shear stress [21-23]. The material model predicts satisfactorily the temperature dependence of plasticity in BCC materials (shown in Fig. 1). For irradiated material, it is also capable of predicting the effect of irradiation defects for different size and number densities, highlighting the influence on hardening and strain localization [9].