锂离子电池充放电过程电极裂纹扩展分析

Analysis of electrode crack propagation in Lithium battery during charge process

采用基于有限变形理论和扩散诱导应力假设的本构方程,建立了三维直角坐标下张量形式的锂离子扩散—应力耦合模型。利用有限元法,结合断裂理论中的K准则,判定裂纹的开裂。将该模型应用到柱形电极和球形电极上,在其中添加三维裂纹,研究应力强度因子与裂纹尺寸的关系;并结合材料的断裂韧性,得到了裂纹开裂的临界尺寸amin。研究发现:电极中长度超过临界尺寸的裂纹将扩展,柱形电极中沿轴向发展的裂纹将持续扩展直至贯穿,沿径向发展的裂纹将逐渐稳定不会贯穿;球形电极中的裂纹也将逐渐稳定,贯穿与否取决于电极尺寸。且该三维模型不仅仅限于轴对称情况,还适用于包含任意缺陷形式的颗粒电极,具有普遍意义。研究成果可对颗粒电极内部缺陷筛查提出优化建议。

A lithium-ion diffusion-stress coupling model in the form of a tensor in three-dimensional rectangular coordinates was established using the constitutive equation constructed by the finite defor‐mation theory and the diffusion-induced stress hypothesis.Combined with the K criterion in fracture theory,the expansion of crack is determined by using the finite element method.The model is applied to the column electrodes and spherical electrodes,where three-dimensional cracks are added to study the relationship between stress strength factors and crack size.Combined with the fracture toughness of the material,the critical size of crack propagation is obtained.Cracks in the electrode that are lon‐ger than the critical size will expand,cracks in the column electrode developing in axial direction will continue to expand until they run through,cracks along radial development will gradually stabilize and will not run through,and cracks in the spherical electrode will gradually stabilize,depending on the size of the electrode.The 3D model is not limited to axis symmetry,but is suitable for particle elec‐trodes containing any form of defect,which is of general significance,and the results can make optimi‐zation recommendations for the screening of particle electrode internal defects.