Abstract The cracking of the active materials in a lithium-ion battery as an adverse consequence of lithiation-induced deformation can significantly cause the capacity loss and likely result in catastrophic failure of the lithium-ion battery. Following the work by Kishimoto et al. [1] , we introduce the Ĵ-integral for the elastoplastic deformation of an active material with a slit-type crack under chemomechanical loading in this work and prove that the Ĵ-integral is path-independent. We also demonstrate that the classical J-integral is path-dependent and is not appropriate for the fracture analysis of the lithiation-induced cracking of the active materials in lithium-ion batteries. Using the incremental constitutive model developed in this work, we numerically analyze the size dependence of the Ĵ-integral under a constant influx for a cylindrical Si-electrode with a central-slit crack. The numerical results reveal that the value of the Ĵ-integral increases with the increase of the crack size and the influx at the same lithiation time, and there exists a maximum value of the Ĵ-integral for a given physical-geometrical configuration. The lithiation-induced softening has a limited effect on the value of the Ĵ-integral. All of these results suggest that the Ĵ-integral can be used to analyze the lithiation-induced propagation of cracks in active materials.

中文翻译：

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分析具有预先存在裂纹的圆柱形硅电极：与路径无关的 Ĵ-积分

摘要 锂离子电池中活性材料的开裂是锂化变形的不利后果，会显着导致容量损失，并可能导致锂离子电池的灾难性故障。继岸本等人的工作之后。[1] ，我们在这项工作中引入了具有狭缝型裂纹的活性材料在化学机械载荷下弹塑性变形的 Ĵ 积分，并证明了该 Ĵ 积分是与路径无关的。我们还证明了经典的 J 积分是路径相关的，不适用于锂离子电池中活性材料的锂化诱导开裂的断裂分析。使用在这项工作中开发的增量本构模型，我们数值分析了具有中心狭缝裂纹的圆柱形 Si 电极在恒定流入下 Ĵ 积分的尺寸依赖性。数值结果表明，在相同的锂化时间，Ĵ-积分值随着裂纹尺寸和流入量的增加而增加，并且对于给定的物理几何构型，Ĵ-积分值存在最大值。锂化引起的软化对 Ĵ 积分值的影响有限。所有这些结果表明 Ĵ 积分可用于分析锂化引起的活性材料中裂纹的扩展。并且对于给定的物理几何配置存在 Ĵ-integral 的最大值。锂化引起的软化对 Ĵ 积分值的影响有限。所有这些结果表明 Ĵ 积分可用于分析锂化引起的活性材料中裂纹的扩展。并且对于给定的物理几何配置存在 Ĵ-integral 的最大值。锂化引起的软化对 Ĵ 积分值的影响有限。所有这些结果表明 Ĵ 积分可用于分析锂化引起的活性材料中裂纹的扩展。