Analytical model for effects of capsule shape on the healing efficiency in self-healing materials

The fundamental requirement for the autonomous capsule-based self-healing process to work is that cracks need to reach the capsules and break them such that the healing agent can be released. Ignoring all other aspects, the amount of healing agents released into the crack is essential to obtain a good healing. Meanwhile, from the perspective of the capsule shapes, spherical or elongated capsules (hollow tubes/fibres) are the main morphologies used in capsule-based self-healing materials. The focus of this contribution is the description of the effects of capsule shape on the efficiency of healing agent released in capsule-based self-healing material within the framework of the theory of geometrical probability and integral geometry. Analytical models are developed to characterize the amount of healing agent released per crack area from capsules for an arbitrary crack intersecting with capsules of various shapes in a virtual capsule-based self-healing material. The average crack opening distance is chosen to be a key parameter in defining the healing potential of individual cracks in the models. Furthermore, the accuracy of the developed models was verified by comparison to the data from a published numerical simulation study.