PSI - Issue 52

Chenxu Jiang et al. / Procedia Structural Integrity 52 (2024) 63–71 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 5 ensure comparable results, the crystallinity of 50% and strain rate ε̇ of 1×10 -5 s -1 were set for all cases. Fig. 3a illustrates the boundary conditions under tension, with load applied on the right side via displacement control, while the left and bottom surfaces were fixed on the X-axis and Y-axis, respectively, to prevent rigid body translation. Furthermore, simulations were conducted on single spherulites with 8, 36, 72, and 120 lamellae, and the results were displayed in Fig. 4a. As the number of lamellae increases from 8 to 120, the elastic modulus approaches a constant value. Consequently, the model with 120 lamellae is adopted for the subsequent multi-spherulite simulations. Analyzing mesh size is a critical aspect of finite element calculations, as it can impact convergence and calculation cost. The 4-node bilinear plane strain quadrilateral (CPE4) element and 3-node linear plane strain triangle (CPE3) element were utilized to examine mesh size. Fig. 4b shows the calculation results with different mesh size. It can be seen that as the mesh size decreases the calculation results of equivalent elastic modulus gradually converges. When the mesh size reaches 8×10 -5 mm, the relative error of three initial orientations 0°, 45°and 90° all less than 0.1%. Therefore, the mesh size of 8×10 -5 mm was used in the following research. 67

Fig. 3 (a) Single spherulite calculate model (b) Sheaves structure and the initial orientation of the principal axis

Fig. 4 (a) The change in equivalent elastic modulus of spherulite with different numbers of lamellae (b) The change in equivalent elastic modulus of spherulite with a different mesh size

3.2. Multi-spherulites model Based on the above analysis and experimental observation, the multi-spherulites model was established, which is illustrated in Fig. 5. The simulation domain consisted of a 2D rectangle with a size of 284×284 µm, and it contains 200 spherules with a fixed sheaf radius of 1 µm. The initial orientations of the principle axes were randomized, as illustrated in Fig. 6. The boundary conditions for tension were consistent with the single spherulite simulation shown in Fig. 5a. The crystallinity, strain rates, the number of lamellae, and mesh size were specified as 50%, 1×10-5 s -1 , 120, and 8×10 -5 mm, respectively.