PSI - Issue 54

Xingling Luo et al. / Procedia Structural Integrity 54 (2024) 75–82 Xingling Luo et al. / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 2. Schematic of cohesive model (Naghdinasab et al., 2018).

3. Results In this section, a comparison between the models with and without cohesive elements was performed to assess the effect of cohesive-zone elements under tensile loading. The stress distribution for a single nodular inclusion under tensile loading is depicted in Fig. 3. To enhance the visibility of the crack, the deformation was magnified by a factor of 5. The von Mises stresses ranged from – 50 MPa to 650 MPa. It should be highlighted that the highest stress was always developed around the left and right edges of the inclusion – the places with the largest stress on concentration. Debonding of graphite from the matrix observed in Fig. 3 (II) happened due to the complete degradation of cohesive elements, caused by deformation under tension. As in Paggi and Wriggers (2011), the average stress was determined as the sum of the horizontal reactions divided by the length of the unit cell side. The globally assigned cohesive-zone elements reduced the stiffness of the model (Fig. 4). Furthermore, the engineering stress in all the models increased with the increase of the applied displacement. It is also notable that there were drops around the global strain of 0.51% and 0.58% in the cohesive model (points b and c). This is because crack propagation sharply reduced the resisting cross-sectional area, thereby limiting the load bearing capacity of the material. In the presence of cracks, the fracture energy was released, leading to a decrease in the reaction force. However, this does not affect the microscopic mechanical properties of the specimen. Further, the effect of PBCs in models both with a cohesive modelling approach and without it, is discussed in this section. Two boundary conditions were considered in this model: (i) constrained bottom edge (“pinned”) (Fig. 1b); (ii) PBCs. The implementation of the latter can significantly increase the accuracy of microstructural RVE modelling, especially in a relatively small system of less than 100 particles (Collini and Pirondi, 2019). The stress concentration only appeared on the left and right sides of the nodular graphite in the CZM model. It is noted that the crack first started in the PBC models (Figs. 3(II) and 3(III)). Moreover, the crack initiated between the interface of the graphite particle and the matrix and then propagated into the latter. This observation corresponds to a ductile response, since the inelastic deformation appeared in the matrix, causing the specimen to crack at the macroscale. The use of PBCs decreased the stiffness degradation and delayed the onset of cracks (Fig. 4) since these BCs laterally constrained the unit cell. Considering the cohesive elements increased stiffness degradation while the PBCs decreased it, the model combining PBCs and CZE was in good agreement with the experimental data.