13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- grain size distributions on fatigue resistance [2]. This work employs similar fatigue and crystal plasticity models to assess the effect of multiaxial straining and stress concentration on early fatigue life. The finite element simulations are calibrated to represent RR1000 Ni-base superalloy and render the microstructure explicitly. The fatigue lives are correlated to a variant of the Fatemi-Socie FIP that is averaged over nonlocal volumes that are oriented as bands aligned with the crystallographic slip planes. The model considers the influence of grain size effects for fatigue cracks that nucleate and extend into neighboring grains. 2 Modeling and simulation 2.1 Constitutive model At the scale of individual grains we employ a physically-based crystal plasticity constitutive model for RR1000 superalloy adapted from the work of Lin et al. [3]. The crystallographic shearing rate is given by ( ) ( ) ( ) 0 ( ) ( ) ( ) 0 0 0 0 / = exp 1 , / q p b B S F sgn B k T (1) in which ( ) is the shearing rate of slip system , ( ) is the resolved shear stress, T is the absolute temperature, Fo, p, q, 0 , τ0, µ, and µ0 are material parameters that may differ for octahedral and cube slip systems, as listed in Table 1 for 650°C, and kb is Boltzmann‟s constant. The evolution laws for slip resistance ( ( ) S ) and back stress ( ( ) B ) are written as ( ) ( ) ( ) ( ) 0 = S D S h d S S , (2) ( ) ( ) ( ) ( ) ( ) = B D B h r B , (3) in which 1 ( ) 0 0 ( ) = B D c h r S f and S 0 , h B , h S , d D , 0 , f c , λ, are constants that differ for octahedral and cube slip planes (see Table 1). The initial values are specified as 0S for the slip resistance and zero for the back stress. This formulation considers 12 octahedral and 6 cube slip systems and was implemented as a user-material subroutine (UMAT) in ABAQUS 6.9 [4] using an implicit integration scheme. Discussion of model parameters and their estimation can be found in Ref. [1]. 2.2 Fatigue driving force During crack nucleation and early growth, the local fatigue driving force is affected by the microstructure, which has particular implications for microstructurally small cracks (MSCs). Hence,
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