PSI - Issue 5

Kulbir Singh et al. / Procedia Structural Integrity 5 (2017) 294–301 Kulbir Singh/ StructuralIntegrity Procedia 00 (2017) 000 – 000

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helium embrittlement and void swelling (Lechtenberg 1985) (Dubuisson et al. 1993). These materials are nonetheless affected by dose dependent lose of impact strength and fracture toughness, along with rise in ductile to brittle transition temperature (DBTT). It is believed that dislocation mobility evolution is the major reason for such different characteristics. Dislocations are linear crystallographic defects present within the crystals and their mobility is fundamental property to determine the plastic deformation in crystals (Taylor 1934a) (Taylor 1934b) (Hull et al. 2001). Crystal plasticity material models are mainly developed for FCC materials as they have well known slip system and their dislocation mobility is mostly temperature independent as compared to BCC materials, in which dislocations mobility have strong temperature dependence (Balasubramanian 1969) (Voyiadjis et al. 2005) (Cereceda et al. 2016) (Kubin et al. 1998) due to high value of Peierls’s barrier (1 GPa). This leads to dependence of plasticity behavior on thermally activated phenomenon (Kink pair nucleation) especially at low temperature. Constitutive model is proposed to address this temperature dependence plastic behavior for non-irradiated and irradiated BCC materials. Nomenclature Interaction coefficient of system A with obstacle system F Average obstacle strength based on quadratic average rule Average obstacle spacing Burger’s vector Phonon/viscous drag coefficient Obstacle diameter ∆ 0 Pair activation enthalpy at 0K Boltzmann constant Average length of screw dislocation segment on slip system s Dislocation curvature radius near obstacle on slip system s Critical radius of curvature of dislocation to bypass the obstacle 0 Peirels shear stress at 0K Dislocation loop annihilation parameter 2. Constitutive model for non-irradiated case Dislocation mobility in BCC crystals is defined for two regimes 1) thermally activated regime and 2) athermal regime. This description accounts for the strong temperature or strain rate dependence on the flow stress in BCC materials. In thermally activated regime , thermally activated kink pair nucleation governs the mobility of dislocation and hence, the dislocation velocity is dependent upon the effective stress and temperature. In current work following expression is adapted for the strain rate (Kocks et al. 1975) (Tang et al. 1998) (Naamane et al. 2010) (Monnet et al. 2013) (Gururaj et al. 2015) in thermal regime based on Orowan’s relation which relates mobile dislocation density ( ), velocity (v) with strain rate ( ̇ ) as ̇ = : ̇ = 8 2 [− Δ 0 (1 − [ 0 ] ) ] In Athermal regime velocity of double kink pair is close to the edge dislocation velocity ( v k ~v edge =τ eff b/B ), hence the mobility of dislocation is only dependent upon the effective resolved shear stress ( ). Strain rate in this regime is expressed as ̇ = ̇ 0 ( / ) , here ̇ 0 is reference shear strain rate and n is constant. The general expression for strain rate with combined effect of two regimes assuring smooth transition between two regimes is given by expression. 1 ̇ ⁄ = 1 ̇ ⁄ + 1 ̇ ⁄ . Distance between forest obstacles encountered by the screw dislocation govern the average length of screw dislocation segment, especially at low temperature which in turn effects the velocity. The relation = max[ − 2 ; ] is used to calculate screw segment average length which is based on average obstacle spacing ( ) and dislocation curved shape radius R s (Monnet et al. 2013) (Tang et al. 1999). Here + = 1/min(√ ; (2 +