PSI - Issue 39

Arturo Pascuzzo et al. / Procedia Structural Integrity 39 (2022) 649–662 Author name / Structural Integrity Procedia 00 (2019) 000–000

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4.2. A beam with three holes under a three-point loading This case serves as an effective test to check the ability of the proposed modeling approach to predict crack propagation phenomena in FGMs structures with articulate geometries under mixed-mode conditions. Figure 7-a shows an FGMs beam with three holes subjected to three-point bending. The beam has a total length of 508 mm and it has a rectangular cross-section with a width of 25.4 mm and a height of 203.2 mm. The gradation develops horizontally over a region of length 101.6 mm that departs from 76.2 mm from the left side of the beam. In the graded region, there is a vertical notch of 38.1 mm. Table 2 summarizes the material properties.

Table 2. A beam with three holes under a three-point loading: Material properties X 1 (mm) Young’s modulus (MPa) Poisson’s ratio

Fracture Toughness (MPa m 1/2 )

-127 -50.8 50.8 330.2

1 1 3 3

0.3 0.3

1 1

0.25 0.25

1.5 1.5

Figure 7. (a) A FGM beam with three holes subjected to three-point bending. (b) Mesh configuration adopted in the numeric simulation

Figure 7-b depicts the mesh configuration used for the analysis. It comprises 1857 triangular elements arranged finely around the crack tip and quite raw in the remaining part of the computational domain. The short segment that stretches during the simulation comprises 3 elements of variable length (see the zoomed view in Figure 7-b). The predictions of the proposed model are compared with the results reported in the literature and achieved by other numerical methodologies. In particular, the results reported by Kim and Paulino in (Kim and Paulino (2004b)) (achieved by the same modeling approach used to analyze the graded beam discussed in Section 4.2) and that predicted by Ooi et al. (Ooi et al. (2015)) have used as reference. Note that, Ooi et al. have utilized a Scaled Boundary Finite Element Method (SB-FEM) approach, which presents an efficient remeshing procedure that refines polygons around the crack tip without changing the remaining elements. Figures 8-a and b compare the crack trajectories and the values of Stress Intensity Factors (K I , K II ) extracted during the crack advance, respectively.