Stress concentrations and bonding strength in encapsulation-based self-healing materials

In encapsulation-based self-healing materials, filled capsules with the healing agent are embedded in a matrix. But between the capsule and the matrix an interface always exists. The strength of the interface between both components is proved to play a crucial role in the correct working of the self-healing. This paper analyzes numerically the role of the interface bonding strength and the stress concentration around a cylindrical capsule embedded in a homogeneous, isotropic and elastic matrix, which undergoes a uniform and uniaxial far-field stress. Geometry and load condition make it to use a two-dimensional plane strain model. This model is based on a combination of the classical Finite Element Method and cohesive surface techniques implemented in the commercial code Abaqus. Two types of interfaces have been studied: perfect and imperfect bonding. A detailed validation of the model against analytical expressions has been conducted in order to guarantee a correct behavior of the interface elements. The influence of the elastic mismatch between the capsule and the matrix on the stress concentrations has been assessed, as well as the possibility of using capsules with different thicknesses. In order to prevent debonding, a study to provide the optimum combination of material elasticities, capsule thicknesses and bonding strength has been performed. The initiation and propagation of the interfacial crack have been also fully addressed. In that direction, once a crack is initiated, the role of the elastic mismatch and the capsule thickness is also assessed. This model can predict the suitability of the mechanical performance of the interface and whose role is typically underestimated during the preparation process of encapsulated self-healing materials.