PSI - Issue 52

Thi Ngoc Diep Tran et al. / Procedia Structural Integrity 52 (2024) 366–375 Thi Ngoc Diep Tran/ Structural Integrity Procedia 00 (2019) 000 – 000

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matrix contains elastic and plastic properties since most mechanical processes during the tensile load are caused in this region. The ductile damage can be described in ABAQUS by fracture strain and is determined by the stress-strain curve obtained from experiments. As a sub-option of ductile damage, the damage evolution through fracture energy is used to describe how the material degrades after this damage initiation criterion is met. Numerical modeling of the damage propagation and prediction of strength is provided by removing the finite elements in which the damage variable reached the value 1. Variation of friction coefficient on the matrix/particle interface between 0.3 and 0.6 does not yield noticeable difference in material behavior (Wang et al., 2020). Hence, the interface between the particles and the matrix has been modeled as zero friction. The Young's modulus of the homogenized material (see Fig. 2b) is calculated using Mori-Tanaka model (Klusemann and Svendsen (2010)). The following normalized material properties in Table 1 are used in the simulations: Table 1. Utilized material parameters ( -moduli were normalized by ) Material / Poisson’s ratios Homogenized material 10.1 0.24 Particle 14.4 0.18 Matrix 1 0.25 3.4. Mesh dependency A mesh dependency study is carried out to investigate the effect of mesh density on crack propagation. Coarse meshes can lead to inaccurate results in analyses (Qu et al. (2019)). As the mesh element density is increased, integration points are closer to stress concentration regions and the numerical solution converges to the exact solution. The computer resources required to run the simulation also increase as the mesh is refined. In this study, four specimens are meshed on a global seed interval of 0.01, 0.02, 0.04, and 0.08, respectively. The elements used are triangular and from the Plane stress 3-node linear CPS3 type. Crack propagation of four different numbers of the finite elements and the representations of FE meshing on the same particle and matrix are shown in Fig. 4a and Fig. 4b, respectively. It can be seen that different element sizes lead to different crack initiation and crack growth. The shape of the FE element can cause different damage localization, e.g., reinforcement particles with coarse mesh provide sharp-edged geometry and lead to crack initiation in the matrix. The corresponding stress results in Fig. 5 are normalized by the maximum tensile strength and show that models with finer mesh yield greater tensile strength since they have better stress distribution within the element, and the contact pressure between elements is calculated at different integration points (Liu and Glass (2013)). The mesh size 1 is chosen for further FE analyses.

Fig. 4. (a) Crack propagation of different numbers of the elements; (b) FE mesh in the same position for different mesh sizes.