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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3. Boundary conditions and study parameters To simplify the study and obtain general results, we model a single fiber with a radius = 1.1 in a 2D plane strain setting (Fig.2(a)). We also incorporate two different possible initial crack configurations, which are the center crack and surface crack (Fig.2(b) and (c)). Three different crack lengths are used for the center crack during the comparison of crack tip speeds, which are = 0.2,0.3,and 0.4 mm, respectively. For the surface crack, the arc angles are chosen as 40°,45°,and 50°, and the radius of the arc ( ) is 0.7 . The ionic concentration is applied linearly to the outer boundary up to 1 / , with a concentration of zero at the initial state and reference ionic concentration 0 = 0.0001 / . In other words, when solving the diffusion problem, we present the effect of the electrolyte during the charging state. The simulations continue with the maximum concentration, denoted as = , and stop when the maximum concentration difference ( ∆ ) , i.e., the difference between the highest and lowest concentration in the fiber, decreases to 20% of its maximum value (( ∆ ). In other words, the average Li concentration in the fiber reaches a level exceeding 80% of the applied concentration. The material parameters are selected for Li and the fiber, as shown in Table 2 with the references. The temperature is set to room temperature, and for the critical energy release rate, the value falls within the range of experimental results for this material (Amanieu, 2014).

(a)

(b)

(c)

Fig. 2. Geometry and boundary conditions for the Li intercalation (a) uncracked fiber; (b) fiber with a central crack, (c) fiber with a surface crack

Table 2. The material parameters used in numerical examples. Material parameters Values Ref

Material parameters

Values

Ref

9.3 Amanieu et al. (2014) 0 Amanieu et al. (2014)

7.8×10 −15 2 / Newman et al. (2006) Klinsmann et al. (2016) 3.497×10 −6 3 / Zhang et al. (2007) 10 / 2

0.3 530 /

3 -

4. Coupled system results 4.1. Uncracked Specimen Results

The fiber model shown in Fig. 2 (a) does not contain any internal damage mechanisms and is utilized for calculating ion concentration and stress distributions. The ionic concentration (applied to the outer surface) is linearly increased up to 0.5 . Once it reaches the maximum value ( ̅ ), a constant concentration is maintained up to (total time) (as indicated by the red curve in Fig. 3 (a)). Additionally, we calculate the concentration difference within the fiber ( ∆ ) during the loading process, as shown by the blue curve in Fig. 3 (a). In Fig. 4, we present the ionic concentration distributions at three different time steps relative to the loading curve. At the onset of