Issue 50

K. Singh et alii, Frattura ed Integrità Strutturale, 50 (2019) 319-330; DOI: 10.3221/IGF-ESIS.50.27 321 M ATERIAL MODEL he dislocation based material model is developed for BCC materials accounting for 12 slips systems ({110} 1/2<111>). This material model accounts for temperature dependent plasticity along with the influence of irradiation-induced defects in the form of interstitials loops. The following subsections discuss the various constitutive equations used in the material model. Temperature dependent plasticity The temperature dependence of plasticity in BCC materials is accounted by two independent formulations meant for thermal and athermal regimes. Dislocation velocity in thermal regime is governed by kink pair nucleation [7-9] and is taken as a function of effective shear stress and temperature value. Subsequently, using Orowan’s relation  = m bv  to relate mobile dislocation density ( m  ) and dislocation velocity ( v ) with strain rate (  ), the thermal regime strain rate is expressed as 2 0 0 8 Δ 1 q p eff eff Thermal m s B H b exp l B k T                 = − −               (1) where p & q are material constants. Eqn. 1 gives the dependence of strain rate on temperature, effective resolved shear stress and, an average length of screw dislocation segment. Athermal regime’s dislocation mobility is controlled by the velocity of edge dislocations, which leads to effective resolved shear stress dependence. However, a minor thermal component is observed due to the presence of thermally activated jog drag. For the athermal regime, the following expression is adapted for strain rate to ensure the accurate coupling between strain rate sensitive macroscopic response and rate sensitive microscopic evolution of critical shear stress [9]. 2 0 0 8 Δ 1 q p eff eff Athermal m B H b exp X B k T                  = − −               (2) X  represents the distance swept by a kink pair before its annihilation with another kink pair along with an infinitely long screw dislocation. Various terms in Eqn. (2) are defined as: 2 k v X J  = , / k eff v b B  = and 2 0 0 8 Δ 1 q p eff eff B H J exp Bh k T               = − −               Based on time spent in each regime, the harmonic mean is calculated from individual strain rates representing each regime to obtain the generalized expression for the strain rate [9, 11]. 1 1 1 Total Thermal Athermal    = + or s Total s l X l X    = + (3) This expression represents the flow rule for the material model. At lower temperature range (thermal regime), the value of s l is smaller than X  which makes total strain rate dependent upon the s l , whereas in athermal regime X  reduces as compared to s l , making total strain rate as X  dependent. Hardening and obstacles strengthening Hardening in the material is considered, which arises due to resistance to dislocation motion provided by the obstacles cutting the slip planes. These obstacles in the form of forest dislocation can multiply during plastic deformation and increase T