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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3.1. Specimen geometry The geometry of the tensile specimen is shown in Fig. 2a. A numerical model of this experimental sample size is computationally unattainable due to the huge number of particles, so this study only considers a representative part of size 2.2 × 1.6 2 in the region of the gauge length. This representative part is shown in Fig. 2b. Actual microstructure is modeled in the central region while the neighboring top and bottom regions are homogenized. The volume fraction of particles in the composite is approximately 20%. In the following sections, only the central layer of the actual microstructure (matrix and particles) is shown in the simulation results.

Fig. 2. (a) Geometric illustration of the tensile specimen; (b) Material layers in the modeled part.

3.2. Modeling of the particles

Microscopic particle geometry and its distribution from the original micrograph are obtained by using image processing methods in MATLAB (The MathWorks Inc (2022)) (Fig. 3a). The pixel-shaped particle frames are refined by applying a Savitzky-Golay finite impulse response (FIR) smoothing filter of the 3 rd -degree polynomial and the frame length of 15. However, this smooth curve requires too many connection points, which is problematic to sketch a spline in ABAQUS (Simulia (2018)). Therefore, the connection point numbers of each particle must be reduced by keeping the first point and then every 5th point after the first. To obtain a closed boundary, the last point is replaced by the first point of the curve (Fig. 3b). Finally, the coordinates of the particles must be converted from pixel to mm and saved in text files. The particles with the coordinates from text files are automatically generated as two dimensional parts in ABAQUS using Python (Van Rossum and Drake Jr (1995)). The number of particles in the simulation is 99. To simulate the tensile test, two boundary conditions are set as follows: (1) The upper edge is pulled with 0.03 mm along the vertical and (2) movements in the x- and y-direction of the bottom edge are fixed. The boundary conditions of the left and right sample edges are traction-free (Fig. 3c).

Fig. 3. (a) Microscopic particle geometry from the original; (b) Approximation of particle’s shape; (c) Geometry of the FE model with boundary conditions in ABAQUS.

3.3. Material properties

The material behavior of the homogenized layers is modeled as elastic since the study intends to observe the crack initiation and the damage process of the composite only in the middle layer. The particles are stiff, and the surrounding