To address the problem of whether microcapsules can crack in time and release healing agents to repair the microcracks generated in the matrix to ensure excellent self- healing performance, the study combined with a cohesion model to establish a three- dimensional numerical model containing prefabricated cracks and microcapsules through XFEM, and analyzed the process of matrix cracking and microcapsule cracking besides its intrinsic mechanism from a microscopic point of view. The research focused on the ratios of elastic properties, fracture properties, core-shell ratios, and interfacial strength between microcapsules and the epoxy resin matrix, to elucidate their impact on crack propagation paths and the crackability of microcapsules. The results show that: (1) the cracking of microcapsules primarily depends on their ratios of elastic and fracture properties with the matrix, particularly the latter having a more significant effect on the microcapsule cracking; (2) at the same elastic property ratios, a larger core-shell ratio facilitates easier cracking of microcapsules; (3) the high interface strength between microcapsules and matrix facilitates the cracking of microcapsules. These findings offer crucial insights for the design of crackability in microcapsules and provide theoretical guidance for the application of self-repairing composite materials.