PSI - Issue 72

Niki Tsivouraki et al. / Procedia Structural Integrity 72 (2025) 141–148

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3. Numerical The numerical methodology for assessing residual fatigue life and strength using random vibration responses closely mirrors the experimental approach (Fig. 3). The process consists of the following steps: 1. Initial Static Tensile Model: A static tensile model is implemented and validated against the results of the initial static tensile tests. 2. Progressive Fatigue Damage Model: A fatigue damage model, based on the Hashin failure criteria Soutis et al. (2023), Tsivouraki, Tserpes et al. (2024), is applied and validated using C-Scan images to track damage evolution. 3. Random Vibration Model: A random vibration model is executed and validated against experimental PSD Welch estimates. 4. Post-Fatigue Static Tensile Model: A second static tensile model is implemented following fatigue loading and validated against the second set of static tensile tests, Tsivouraki, Tserpes et al. (2024). Regarding the assumptions made in the numerical methodology, delamination is considered the sole damage mode in the progressive fatigue damage model, and linearity is assumed in the vibration response. The random vibration simulation process utilizes the modal superposition method to characterize the dynamic behavior of the coupon, Wijker et al. (2009).

Fig. 3. The numerical methodology for residual fatigue life and strength assessment through random vibration responses.

3.1. Numerical damage index From the second static tensile model, the numerical Damage Index is calculated using

t t n n n 

d

(4)

DI



nom

where n t is the

s um of initial and delaminated nodes and nd is the sum of initial nodes.

4. Residual frequency models Residual stiffness and strength are commonly used to evaluate fatigue damage accumulation in composite laminates, Tserpes et al. (2004). Residual stiffness degrades with the number of cycles, following an inverse trend to fatigue damage accumulation (Fig. 4(a)). A similar pattern is observed in residual frequency, as frequency is directly dependent on stiffness (Fig. 4(b)). In the literature, residual frequency models analogous to residual stiffness models have been proposed [9]. Table 1 presents the three empirical residual frequency models used in this study to assess fatigue damage and predict residual strength and fatigue life of thermoplastic coupons. 5. Results 5.1. Sensitivity of residual frequency to fatigue damage Fig. 5 presents the experimental and numerical variations of two eigenvalues: (a) f = 160.4 kHz and (b) f = 3.5 kHz, with respect to normalized number of cycles. The experimental eigenvalues f n correspond to the average values of 13 coupons, while f 0 is the eigenvalue of the referenced (undamaged) coupon. For the 160.4 kHz eigenvalue, the