13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- the driving force for early stage fatigue needs to be characterized with fatigue indicator parameters (FIPs) describing the local fields (rather than far field basis of the stress intensity factor in LEFM). The present approach quantifies the driving force with a crystallographic version of the Fatemi-Socie parameter adapted to evaluate the FIP on each octahedral slip system, i.e., FIP 1 2 p n y k (4) where p is the cyclic plastic shear strain range on slip system , n is the peak stress normal to this slip system, y is the cyclic uniaxial yield strength of the polycrystal, and k=0.5, as proposed by Fatemi and Socie [5]. Several investigators have successfully employed approaches akin to the Fatemi-Socie parameter along with crystal plasticity formulations for studying the effects of microstructure on fatigue life [6][7]. The value of such a parameter was further explored by Reddy and Fatemi [8], who postulated that the Fatemi-Socie parameter represents the fatigue driving force and plays a role similar to that of the ∆K or the ∆J in predicting fatigue crack formation and early growth. Recently, Castelluccio and McDowell [9] correlated the Fatemi-Socie parameter with the cyclic crack tip displacement using crystal plasticity simulations. To numerically regularize the FEM discretization and also to represent the finite physical scale of the fatigue damage process zone, the α FIP values are calculated at each integration point and then averaged along bands (i.e., nonlocal FIPs), parallel to slip planes across entire grains, as depicted in Figure 1. 2.2.1 Life estimation This approach focuses on the interaction between small fatigue cracks and the microstructure at a mesoscale level; therefore, crack growth on a grain-by-grain basis. In other words, the number of cycles to crack the first grain (nucleation) is first computed, and then the cycles required to extend the microstructurally small crack within each of the neighboring grains is computed. Each nonlocal FIP is employed in fatigue life correlations using a hierarchical approach to estimate the life to completely crack a grain along a band. The nucleation relation is assumed to follow the semi-empirical empirical law [6] 2 = ( ) , g nuc gr N FIP d (5) Table 1. Parameters of the constitutive model at 650°C for octahedral and cube slip systems. F 0 kJ/mol p Q 0 s -1 τ 0 GPa S 0 MPa f c h B GPa h S GPa d D MPa 0 GPa Oct. 295 0.31 1.8 120 810 350 0.42 400 10 6024 72.3 Cube 295 0.99 1.6 4 630 48 0.18 100 4.5 24 28.6 Other: λ=0.85, 0 = 192GPa. Elastic constants: C11 = 166.2GPa, C12 = 66.3GPa, C44 = 138.2GPa.
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