PSI - Issue 17

T. Martins et al. / Procedia Structural Integrity 17 (2019) 878–885 Martins, T., Infante, V., Sousa, L., Antunes, P.J., Moura, A.M., Serrano, B./ Structural Integrity Procedia 00 (2019) 000 – 000 5

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for the five contours at each node along the crack front. The average value for the several contours was taken and plotted along the crack front. In Fig. 3 the relevance of the mode I SIF in comparison to the rest is visible, which makes it an acceptable parameter to describe crack growth.

Fig. 4. vs and results from XFEM Fig. 5. plot along the crack angle for XFEM and FEM results Using XFEM allowed for faster computation of results, as well as preparation of the models involved, due to the independence between crack geometry and the element mesh. For FEM, not only this mesh required updates from one crack length to the next, the use of quarter point elements to model the crack tip singularity required the use of quadratic elements which made the solution much more time consuming. However, the results for variation in between contours, point to increased accuracy on the FEM side, where the percent variation between the first and last contour does not exceed 0.026%, whereas for XFEM the difference was 1000 times higher. Comparing both solutions for for the entire crack front, XFEM seems to consistently overestimate the result in regards to the FEM (Fig. 4). The finite element solution, in addition to showing a smoother variation of the SIF along the crack front, also displays a sudden decrease when approaching the surface of the component. The former behavior has been demonstrated to happen for this sort of semi-circular crack in analytical [5] and numerical [6] calculations. Functions of the geometric factor Y with crack length were retrieved for both the results of XFEM and FEM using adequate polynomial fittings (Fig. 5). 3.4. Fatigue Analysis: Crack Propagation Crack propagation modelling was performed to again compare the severity of the load spectra. For this analysis, the Paris, Walker, Forman and NASGRO equations were used. Material parameters for the propagation laws used were obtain through the fitting of experimental data collected by Serrano [7] and are listed on Table 3. For the special case of the Paris law which does not account for the effect of the stress ratio , 3 different regressions were performed: 2 for each set of data corresponding to both ratios tested ( = 0.1 , designated as data set S1, and = 0.3 , designated as S2), and one other fitted to all the data collected simultaneously. Table 3. AA 2024-T3 properties obtained for the several propagations laws. Reduced precision was used to be able to list the entire data. Paris S1 Paris S2 Paris S1+2. Forman Walker NASGRO 3.4 × 10 −11 8.4 × 10 −11 3.1 × 10 −11 3.3 × 10 −9 2.6 × 10 −11 2.7 × 10 −9 3.6 3.5 3.8 2.9 3.6 1.8 - - - - - - 0.21 1 - - - - - - - - 1