13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- A critical area approach [11, 13] was first evaluated for determining the integration domain. This method identifies the domain within which the damage quantity is a percentile of the maximum value, max crit O O A A D P D (3) where A is the total area of the section of interest, crit A is the critical area and P is a value between 0 and 1 that represents the percentile quantity used to define the critical domain. The critical area for all notch geometries based on 95-percentile (P = 0.95) under a 500 MPa applied net section stress is shown in Fig. 8. The size of the critical area decreases with increasing notch severity due to increases in the spatial gradients in the damage parameter. The area averaged damage parameter using a 95-percentile area domain is shown in Fig. 9 for each notch geometry and three applied net section stresses. This method exhibits similar trends as using the local damage approach; increases in notch severity always produce additional damage in conflict with experimental observations. Figure 8. OP TMF 500 950 C C 95-percentile critical areas based on OD parameter. Figure 9. Nonlocal 95-percentile critical area OD as a function of applied load and stress concentration. Invariant averaging domains have been used successfully in notch and component analysis [11, 12, 16]. For evaluating this approach, two methods are implemented: (1) a surface-sweep of the notch surface into the component as seen in Fig. 10(a) and (2) a circular-sweep within the component centered about the location of the maximum damage parameter shown in Fig. 10(b). An iterative method was utilized to achieve the desired critical area domain for each component as the axisymmetric component areas are irregular. A bisection zero finding method was implemented to reduce the residual i crit i R A A L to a satisfactory tolerance by iterating on the critical length L. The area scale was parametrically varied to achieve an optimum domain for the largest net section stress amplitude case as shown in Fig. 11. Increasing the averaging area decreases the area average damage parameter as one might expect. As the averaging area increases, the difference in the driver between 2 tk and 3 tk lives becomes indistinguishable which is consistent with
RkJQdWJsaXNoZXIy MjM0NDE=