13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- ,max in O e e D (1) where in e is the equivalent inelastic strain range and ,max e is the maximum value of the von Mises equivalent stress over one cycle which occurs in tension for OP TMF. Since the loading is uniaxial, the loading in the vicinity of the notch is approximately proportional and hence using equivalent values is acceptable for this exercise for ease of computation. As a baseline, the maximum OD parameter for each geometry and applied load is shown in Fig. 6. As expected, this local approach gives high values for the OD parameter and is highly conservative [3, 10-14, 16]. The local approach incorrectly predicts increasing damage with increasing notch severity, which is totally inconsistent with the observed experimental lives. A regression analysis using a power law relationship was used to attempt to correlate the maximum OD parameter to lives, as shown in Fig. 7. This procedure does not collapse the life data. Figure 6. Maximum OD parameter for all specimen geometries 500 950 C C OP TMF. Figure 7. Correlation of maximum OD parameter with experimentally determined OP TMF lives. Rather than utilizing a local maximum quantity, nonlocal approaches utilize an averaged quantity over a domain or a point some distance away from the maximum. The simplest implementation is utilizing a point value some critical distance away from a key local quantity. Nonlocal quantities include averaging domains over a line, area or within a volume. The averaged generalized damage parameter can be defined as, 1 O O D D D dD D (2) where D is the averaging domain; line, area or volume. Nonlocal approaches on isotropic materials typically utilize a line or point method as the response is centered about the notch root [10-12, 14]. However, for the transversely isotropic response of directionally-solidified (DS) alloys when loaded longitudinally, cracks are observed to initiate away from the notch root. Additionally the maximum equivalent inelastic strain range and maximum von Mises stress occur away from the notch root and the response changes during loading, with temperature, applied load level and across specimen geometries. Directions of relevant spatial gradients change with applied conditions and do not coincide with surface normals or crystallographic directions. As such an area averaging approach was used on the response predicted by the axisymmetric finite element method. As the domain represents an axisymmetric volume, in this case this is also equivalent to a volume averaging scheme.
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