A probability characteristic of crack intersecting with embedded microcapsules in capsule-based self-healing materials

The micro-cracks in a material lead to a reduction in its overall strength and service life. The emerging capsule-based self-healing system provides a new strategy for repairing the cracks, effectively delaying the potential damage of the matrix, and prolonging the service life of composite materials. Determining the optimal size and dosage of microcapsules required to repair cracks in the matrix is essential for the development and design of capsule-based self-healing materials. This paper presents a novel two-dimensional capsule-based self-healing model composite material whose surface is paved by reproducible and random cells and some microcapsules are randomly dispersed in those cells to investigate the rupture behavior of microcapsules forced by growing cracks. An analytical model is proposed from the viewpoint of geometrical probability to express the probability characteristics of the embedded microcapsules stimulated by linear cracks in a two-dimensional capsule-based self-healing model composite. Additionally, the effect of the size and dosage of the embedded microcapsules on the intersection probability is analyzed, and the maximal probability is also found to improve the self-healing efficiency. Finally, the accuracies of these probability values and theoretical solutions are verified via computer simulation, and the results show that the developed model of the geometrical probability of the crack intersection with microcapsules randomly distributed in the cells of the matrix will help to provide a theoretical basis for the quantitative design of capsule-based self-healing materials.