Abstract Phase separation arises in many materials systems as a result of solute intercalation. It is in particular known that the mechanical stresses resulting from phase separation in lithium-ion batteries can be large enough to cause formation of a variety of defects and degradation of the host electrode upon cycling. Fracture mechanics models have been previously developed for identifying the critical conditions which lead to the growth of a pre-existing crack in two-phase electrode particles. Relying on a cohesive zone model in combination with the distributed dislocation technique, this work examines critical conditions corresponding to the onset of crack formation in an initially crack-free two-phase electrode. Considering a phase separating planar electrode, we utilize a Cahn-Hilliard type phase field model for capturing evolution of the concentration profiles during both intercalation and deintercalation half-cycles. Crack formation in the electrode subject to the diffusion-induced stresses is considered to result from strain localization at the place of pre-existing defects or weaknesses in the material whose behavior is modelled using a linearly softening traction-separation law. Numerical solution of the governing equations allows identification of a flaw-tolerant electrode thickness below which crack formation in the electrode becomes suppressed in the sense that the maximum opening along the cohesive zone cannot reach the critical separation required for crack formation, and hence, failure in the electrode is predicted to be dominated by the theoretical strength of the material rather than by crack formation. Since in the limit of small surface fluxes, uniform axial stresses develop in the individual phases, results of the analyses are also examined with reference to the results which follow from the analysis of the planar structure subject to uniform tension.

中文翻译：

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使用分布位错法对受扩散诱导应力影响的两相平面电极中裂纹形成的内聚建模

摘要 由于溶质嵌入，许多材料系统中都会出现相分离。众所周知，锂离子电池中的相分离导致的机械应力可能大到足以导致各种缺陷的形成和循环时主体电极的退化。之前已经开发了断裂力学模型，用于确定导致两相电极颗粒中预先存在的裂纹生长的临界条件。依靠结合分布位错技术的内聚区模型，这项工作检查了与初始无裂纹两相电极中裂纹形成开始相对应的临界条件。考虑相分离平面电极，我们利用 Cahn-Hilliard 型相场模型来捕捉嵌入和脱嵌半周期期间浓度分布的演变。受到扩散诱导应力的电极中的裂纹形成被认为是由于材料中预先存在的缺陷或弱点处的应变局部化所致，其行为使用线性软化牵引分离定律进行建模。控制方程的数值解允许识别可耐受缺陷的电极厚度，低于该厚度时，电极中的裂纹形成被抑制，因为沿着粘性区域的最大开口无法达到裂纹形成所需的临界间距，因此，预计电极的失效主要取决于材料的理论强度，而不是裂纹形成。由于在小表面通量的限制下，在各个相中会产生均匀的轴向应力，因此还参考对受均匀张力影响的平面结构的分析结果来检查分析结果。