PSI - Issue 61

İmren Uyar et al. / Procedia Structural Integrity 61 (2024) 195 – 205 İ. Uyar, E. Gürses / Structural Integrity Procedia 00 ( 2019) 000 – 000

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Fig. 9. Crack tip speeds of (a) central crack, (b) surface crack ( /∆ =1 corresponds to beginning of crack growth) During crack growth, crack tip speeds are calculated for three distinct initial crack lengths ( = 0.2 , 0.3 , 0.4 ) in a center crack scenario and three different initial crack arc angles ( 40 ° ,45 ° ,50 ° ) in curved crack scenarios, all under identical ionic concentration loading rates ( ̇ = 0.0001 mol/s), see Fig 9. The crack tip speeds are calculated when crack propagates and the calculation is finished when crack reaches outer boundary (i.e. ≅ 0.9 ). The results unequivocally demonstrate that crack tip speeds are inversely proportional to the initial crack lengths, indicating that smaller cracks propagate at significantly higher speeds. The crack tip speeds observed for the center crack agree with the findings reported by Klinsmann et al. (2016) qualitatively. Also, crack tip speeds in Klinsmann et al. (2016) during lithium insertion demonstrate a comparable relationship between the initial crack size and crack tip speed. Specifically, smaller initial crack lengths lead to delayed crack growth compared to larger ones due to the increased load necessary for initiation. This delay causes a greater accumulation of elastic energy, resulting in faster crack propagation once the crack is initiated. In our study, this delay is also observed in smaller crack lengths. For instance, the actual starting time of the crack for = 0.2 is = 0.13 , while for = 0.4 is = 0.08 . Furthermore, the propagation of cracks commences at relatively low speeds during the initial time steps, subsequently peaking as the cracks approach the material boundaries. This phenomenon highlights the critical influence of crack size and geometry on the dynamics of crack propagation under specific loading conditions. 5. Conclusion This study proposes a coupled electrochemical-mechanical model to investigate ionic diffusion-driven stress development and crack propagation in a fiber. The analyses demonstrated a direct correlation between the concentration difference ( ∆ ) and the maximum radial and circumferential stresses, with both peaking simultaneously. When the concentration difference is significant, tensile radial stress develops within the fiber, while compressive circumferential stress occurs in its outer region. Additionally, two types of initial cracks were studied: arc cracks near the fiber's surface and central cracks at the symmetry plane, influenced by the fiber's radial strength. Surface cracks were shown to hinder ion diffusion, resulting in a larger concentration difference within the fiber compared to central cracks. The initial cracks are found to propagate at the maximum concentration difference. In cases where the crack does not start propagating from the point of maximum concentration difference and remains inactive, subsequent exposure of the fiber to a constant maximum outer concentration initiates the relaxation process. In general, this study emphasizes the complex relationship between mechanical stresses and ion diffusion in fiber materials, revealing their susceptibility to damage and offering valuable insights for engineering

applications. References

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