PSI - Issue 57

Kimmo Kärkkäinen et al. / Procedia Structural Integrity 57 (2024) 271–279 K. Ka¨rkka¨inen et al. / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 3: Crack profiles for every other crack tip position (a) constant amplitude, (b) overload and (c) underload. Increasing crack length is indicated by increasing line opacity.

Fig. 4: Opening level contour plot for the entire crack surface at R = 0, (a) constant amplitude, (b) overload and (c) underload.

maximum load. It was also noted that the kinematic hardening model was sensitive to the number of load cycles between crack tip node releases, as also reported by Antunes et al. (2015). This was especially true if less than four load cycles were applied per growth increment, which was the number chosen for present results. Furthermore, it is worth noting that when analyzing closure level by node contact criterion, the result is intrinsically dependent on element size; according to a sensitivity analysis conducted by the authors, finer mesh generally yielded higher closure levels, as well as faster closure level saturation. To obtain reliable results, the state-of-the-art numerical analysis has well-defined recommendations for crack growth scheme and element sizes, which were discussed in Section 2. Usually only the displacement of the first node behind the crack tip is monitored, as it should have the largest influence on the crack tip damage accumulation. It is clear that far-field contact also a ff ects crack propagation to a degree, and total closure influence should be an integral quantity, a weighted sum of the contact over the entire crack surface, but this is not yet incorporated in crack closure models. In present work however, levels of plasticity-induced closure for the entire crack surface are presented in Fig. 4; the opening level for every node behind each crack tip position forms a contour figure in the shape of a triangle, as x / r < a / r , i.e., closure cannot be observed in front of the crack tip. Line x / r ≈ a / r (technically ( x + l e ) / r = a / r ) corresponds to the opening level of the first node behind the crack tip (presented more conventionally in Fig. 5a), and line x / r = 0 to opening level at the defect edge. From Fig. 4 the e ff ect of the applied loading irregularity can be clearly observed; in both cases, overload and un derload, all built-up closure disappears from behind the crack tip position where the loading irregularity was applied, e ff ectively forming a closure-free crack (Maierhofer et al., 2014). This can be attributed to crack tip blunting, which