An analytical solution for stress relaxation in cracked coatings

An analytical form of the local stress responsible for cracking of coatings under tensile stress is given, taking into account the stress relaxation induced by the existing cracks. The solution obtained under the assumption of an elastic behavior of materials is a function of the stress in the absence of cracks, elastic constants and geometry (coating thickness and distance between neighboring cracks). A parameter unattainable through the model is determined by comparison with finite element calculations. The solution is in excellent agreement with the finite element results, but it is inconsistent with other existing models.