2D materials communicate with the environment through large area of surface. Recent experimental measurements have deepened our understanding of the friction between layers of 2D materials and suggested the interlayer properties, such as interlayer friction, can couple with intralayer properties and affect the overall behavior of multilayered 2D material systems. In this study, the effect of interlayer friction on asynchronous crack propogation and dissimilar crack paths is considered by integrating theoretical analysis and numerical simulation. It is found that the intact layer can postpone crack propogation in the neighbouring layer and cracks along dissimilar paths can communicate via interlayer sliding zone, resulting in a size-dependent fracture behavior.