PSI - Issue 77

Muhammad Jahanzeb Zia et al. / Procedia Structural Integrity 77 (2026) 111–118 Muhammad Jahanzeb Zia et al. / Structural Integrity Procedia 00 (2026) 000–000

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models can simulate the gradual stiffness degradation of plies under multiaxial loading, enabling a more realistic representation of crack propagation in both the matrix and fibres. 2.3. Boundary conditions and meshing The specimen was fully constrained at the bottom part by restricting all degrees of freedom for linear 2D dynamic plane strain analysis, while a linear displacement profile was applied at the top part, under constant strain rates of 0.08 mm s – 1 and 0.1 mm s – 1 (Fig. 2a). Mesh refinement was a critical factor in the simulation of stress waves: excessively fine meshes were computationally prohibitive, whereas overly coarse meshes violated the Courant condition required for accurate wave propagation. Consequently, quadrilateral shell elements (S4R in Abaqus notation) with reduced integration were employed for the analysis (Fig. 2b). In total, ~2600 elements of 0.3 mm size were generated. A linear geometrical order was adopted for the explicit formulation to ensure numerical stability and to avoid unnecessary computational complexity. Following model optimization, each simulation required approximately 58 hours of computation on a Core i5 processor with 32 GB RAM. Element deletion was not employed; instead, failed elements were retained to analyse the failure evolution based on the BK law.

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Fig. 2. Boundary conditions (a) and mesh of the studied geometry comprising S4R quad elements (b).

3. Results and discussion 3.1. Failure analysis and AE generation

During tensile loading, stress was concentrated at the notch, which was intentionally introduced as a weak point to facilitate the monitoring of different damage modes. Selected nodes, indicated in Fig. 3a, were designated as virtual sensor pickup points for AE signals. These nodes were positioned at varying distances within the damage zone, enabling the extraction of output signals at multiple locations. Based on the Courant condition, the wave propagation velocity in E-glass composite material is approximately 10,307 m/s. Consequently, resonance effects and wave reflections at the specimen boundaries were considered, and data were collected at all nodes indicated in Fig. 3a. It is evident that matrix cracking occurred at different time instances; for example, at point P5, it was observed at 0.38 s, whereas at point P6 it occurred at 0.22 s (Fig. 3b). Fiber breakage was detected at 0.22 s at both locations, as illustrated in Fig. 3c. Next, the waveform at point P3 is shown in Fig. 4. At approximately 0.22 s, a significant AE activity was recorded, corresponding to the simultaneous occurrence of matrix cracking and fibre breakage. Subsequent events at 0.38 s and 0.45 s were attributed to AE waves generated primarily by matrix cracking. These damage modes were further validated through the frequency distributions observed in the spectrograms for the respective instances, as illustrated in Fig. 5.