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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is formed. Then, the new geometry is re-meshed and boundary conditions are imposed. Afterwards, the code re-starts the analysis and continues until overall collapse conditions take place.

Figure 4. A schematic of the most relevant steps of the propagation procedure. (a) Input the geometry. (b) Creating stretching segment. (c) Crack tip motion 4. Numerical results In this section, numerical results devoted to assessing the accuracy and efficiency of the proposed modeling approach are reported. Specifically, two cases of study are analyzed, and the results are compared with the predictions of other numerical strategies. In both cases, computational meshes comprise 6-node triangular elements under plane strain conditions. Numerical simulations are developed using an incremental static analysis consistent with a displacement-based approach. Hence, the external loads are incremented in such a way as to produce a prescribed displacement variation of a selected control point. The fracture function introduced in Section 2.2 is defined using the maximum circumferential stress criterion proposed by Erdogan and Sih (Erdogan and Sih (1963)). 4.1. A cracked beam subjected to a three-point bending test Figure 5-a shows a FGM beam under a three-point bending test. The beam is 270 mm long and has a rectangular cross-section of width 18 mm and height 60 mm. Further, it has an initial vertical notch of 24 mm placed at mid-span. The gradation occurs vertically according to material properties reported in Table 1. Several Authors have investigated numerically this beam to assess the reliability of their numerical approaches aimed at reproducing crack propagation phenomena in FGMs. Among these, Kim and Paulino (Kim and Paulino (2004b)) have used a standard FE strategy enhanced by an automatic crack growth algorithm that operates remeshing actions for each increment of the crack advance. In addition, they have used singular elements arranged radially around the crack tip to better reproduce the singularity of stress fields. The results provided by Kim and Paulino have been assumed as a reference to assess the accuracy of the proposed strategy. In particular, a parametric investigation in terms of mesh configuration is conducted. Figure 5-b shows the mesh configurations adopted for the analysis of the beam by the proposed modeling approach. The first, denoted as M1, comprises 371 triangular elements arranged finally around the crack tip and coarser in the remaining region. The second ( i.e. , mesh M2) is a refined mesh with 1258 triangular elements. In particular, the domain is discretized with finite elements of almost the same size (no refinements in the crack tip region). Finally, the third mesh ( i.e. , mesh M3) is a raw configuration of 177 triangular elements.

Table 1. A cracked beam subjected to a three-point bending test: Material properties