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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ionic diffusion, lithium ions penetrate the region very close to the fiber’s surface. At this moment, the fiber exhibits a gradient with high concentration at the surface, while the ionic concentration at the fiber’s center remains nearly zero. The concentration difference rises as the outer surface concentration increases. The maximum value of ( ∆ ) is observed at 0.5 when the surface concentration reaches its peak. After this point, i.e., > , Li ions migrate to the inner part of the fiber. At the end of the diffusion process, the concentration gradient and ∆ decline, see Fig. 4 (c). The role of concentration difference in the generation of mechanical stress becomes evident when comparing the concentration difference values in Fig. 3 (a) with the maximum values of radial and circumferential stresses at corresponding time steps in Fig. 3 (b). The graph depicting the highest magnitude of maximum stresses over time is directly correlated with the time history of the maximum concentration difference ∆ . Both variables exhibit peaks at the same time point. When the concentration difference is substantial, the outer region of the fiber undergoes greater expansion than the elastic stretching in the interior. Consequently, tensile radial stress develops within the fiber, while compressive circumferential stress occurs in its outer region. As the diffusion process concludes, the concentration gradient and all associated mechanical stresses gradually decay.

(a) (b) Fig. 3 (a) Loading condition and concentration difference ∆ (b) The highest value of the radial stress and the highest values of circumferential stress with respect to time

(a) (c) Fig. 4 Normalized ionic concentration distribution at three different time steps (a) A ( 0.25 ), (b) B ( 0.5 ) (c) C ( ) 4.2. Crack Formation and Growth In a phase field fracture framework, multiphysics coupling allows for simulating fiber failure due to diffusion induced stresses while examining their susceptibility to cracking. For instance, higher discharge rates have been (b)