PSI - Issue 75

Laurent Gornet et al. / Procedia Structural Integrity 75 (2025) 129–139 Author name / Structural Integrity Procedia (2025)

130

2

Fatigue experiments were conducted under fully tensile, cyclic loading (tension – tension) at ambient temperature across several laminate layups. In parallel, self-heating tests were performed to rapidly assess the intrinsic dissipation mechanisms and estimate the fatigue limit based on thermal stabilization criteria. A strong correlation was observed between the fatigue limits obtained via classical testing and those derived from the self-heating method, thereby validating the reliability and efficiency of the latter approach. To model the S – N (Wöhler) curves, a PINN-based framework was developed, leveraging the underlying physics of fatigue behavior as soft constraints within the training process. The implementation was carried out in Python using the Keras and TensorFlow libraries. The proposed model demonstrates accurate prediction capabilities for the fatigue response of composite materials. A commented Python script is provided in the appendix to illustrate the numerical implementation of the method . 2. Characterization of a unidirectional carbon/epoxy composite material The material studied is a high-strength unidirectional carbon fiber fabric with epoxy resin. All static, fatigue and self-heating tests are conducted on symmetric carbon/epoxy laminates with dimensions of 250 × 20 × 2.5 millimeters (ASTM D3039, ISO 527). The plates are polymerized in a vacuum bag in an oven, under conditions identical to those of the industrial manufacturing cycle. The entire experimental campaign is presented in the reference Westphal 2014. The quasi-static and fatigue mechanical properties of the material were determined from a canonical identification database. To characterize the elementary material, quasi-static tensile tests to failure were performed on the stacking sequences [0] 8 , [+45/-45] 4S , and [+67.5/-67.5] 4S . The complete identification of the elastic mechanical properties under plan stress assumption of the elementary ply was carried out based on these three tests. Mechanical properties are presented in Tab 1.

Table 1: Mechanical characteristics of the carbon / epoxy TR50/R367-2

 12 0

1 ( ) E MPa

2 ( ) E MPa

12 ( ) G MPa

7400

0.31

3200

110780

11 ( R MPa 

)

11 (%) R 

22 ( R MPa 

)

12 (%) R 

12 ( R MPa 

)

22 (%) R 

2270

74

13

1.6

64

0.8

3. Fatigue Limits by Self-Heating Method Conventional fatigue tests enabled the construction of S-N curves (Wöhler curves), illustrating the relationship between the number of cycles to failure and the applied load amplitude. These curves provide a comprehensive overview of the performance of laminated composite materials under different loading regimes. For a S-N curve the ratios R = / = is fixed. In parallel, fatigue limits determined from self-heating tests were compared to those obtained through conventional fatigue testing. The results demonstrated a strong correlation between the two methods, validating the self-heating approach as a fast and efficient alternative for assessing the durability of Metals (Doudar et al. 2004, Doudard et al. 2010, La Rosa et al. 2000, Risitano et al. 2011, Naderi et al. 2012) and composite materials (Naderi 2102, Gornet et al. 2013, Muller et al. 2018, Demilly et al. 2024). Fatigue tests were conducted under controlled conditions at room temperature, using cyclic tension-tension loading at a frequency of 5 Hz. Various stacking sequences were tested to better understand the influence of laminate architecture on fatigue behavior (Westphal 2014). The analysis method for self-heating curves proposed here allows us to determine an endurance limit value that is consistent with the results obtained from classical fatigue curves (Westphal 2014, Gornet et al. 2013). This self heating curve analysis method is based on plotting asymptotes and identifying their intersection. If the laminate exhibits a single damage mechanism responsible for its failure, the endurance limit is experimentally determined by plotting the asymptote at infinity on the self- heating curve and locating its intersection with the curve’s horizontal