Closed-form analysis of a thermally loaded on a foundation

A closed-form analytical model of a single layer with a linear elastic material behavior on a rigid foundation subjected to thermal loading is investigated. The closed-form analytical model is based on a higher-order displacement approach that takes the singularity exponent into account. Two applications are considered in this work. First, the interlaminar stresses are analyzed at the interface between the substrate and the material layer. These stresses are an indicator of the formation of interlaminar cracks, which cause the individual layer to peel off. Based on the interlaminar stresses, the closed-form analytical approach, which considers the singularity exponent in the displacement approach, is compared to a model with a second order displacement approach and a FEM model. In the second part, the development of transversal cracks is considered within the framework of Finite Fracture Mechanics, using a coupled stress and energy criterion. Transverse cracks often occur in thin brittle layers such as ceramic coatings and form in periodic patterns. In this work, a representative unit cell is considered - i.e. the material layer between two cracks. the resulting distance between two cracks can be determined when larger cooling temperatures are applied.