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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observed to result in more significant damage, mainly due to elevated concentration gradients and stresses, as demonstrated by Klinsmann et al. (2016). As mentioned in the preceding chapter, the graph illustrating the highest values of radial and circumferential stresses over time is closely connected to the changing pattern of the maximum concentration difference, ∆ . Both stress components exhibit peaks at the exact moment in time. When the Li diffusion rate takes precedence, we anticipate elevated mechanical stresses. Additionally, this analysis helps identify the two critical regions within the geometry. Due to the concentration gradient, the outer section of the fiber experiences more significant free swelling strains compared to the inner region (Varna et al., 2014). Positive radial stresses occur at the center of a structure because the outer portion tries to expand further, resulting in radial tractions on the inner part. On the other hand, negative hoop stresses are present in the outer region and positive in the inner region. This happens because the outer region's attempt to expand in the circumferential direction is constrained by the inner region, which does not expand as much due to a lower concentration of ions. Two potential types of damage can occur: the development of arc cracks near the fiber's surface and central cracks positioned at the fiber's symmetry plane (Fig. 2(b) and (c)), which are influenced by the radial strength of the fiber. Initially, we can simplify matters by assuming that radial cracks have no impact on ion diffusion because these cracks are entirely within the particle's interior and are not exposed to the Li ions. Conversely, surface cracks do affect diffusion by obstructing ion movement with their exposed surfaces. To demonstrate this fact, we can compare graphs that display the concentration discrepancies over time (as shown in Fig. 5). Notably, the surface cracks result in a more significant concentration difference within the particle.

Fig. 5 The maximum concentration difference compared to arc crack and center crack.

To show this observation, concentration distributions are compared for the central crack and arc crack in Fig. 6. When the crack is situated at the center, the distribution of Li diffusion closely resembles that of a particle lacking any cracks, as depicted in Fig. 6(a). Conversely, when a surface crack is present, it hinders the ionic transformation process and generates a substantial concentration gradient, leading to elevated radial stresses concentrated at the tips of the crack (Fig. 6(b)). Furthermore, the presence of increased radial stresses in proximity to the crack tips can exert an influence on the behavior of ionic diffusion. The electrochemical processes drive concentration gradients, and these gradients can undergo modification due to the deformations induced by the stress in the material. This alteration in diffusion can impact the rate of chemical reactions and the movement of substances within the material.