Probabilistic Modeling of Coating Delamination

Abstract

Studies of stressed state of solids made of homogeneous and functionally graded materials with internal or interfacial defects of different types causing stress concentration have been and continue to be one of the central fields of research in contact and mixed problems of elasticity. These studies reveal the stress behavior near stress concentrators and possible ways of stress reduction. Studies [1,2,3] belong to this research field and, also, are related to the topic of the current paper. On the other hand, nowadays practice imposes more and more stringent conditions on the fatigue performance of various joints. That brought to life usage of coatings. However, for the most part the knowledge about coating performance in the environment of cyclic loading is acquired empirically. It is a very long and expensive way. Therefore, it is natural that there is a demand for theoretical modeling of the fatigue performance of coated solids in various joints which may not only explain empirically observed effects but also predict possible ways of performance improvement.

The current paper presents a probabilistic model of coating delamination caused by fatigue crack propagation along the interface of a coating and substrate. The model is represented by two blocks. The first block consists of the formulation and analysis of a plane contact problem for a homogeneous elastic solid coated by a thin elastic layer made of another homogeneous elastic material. A small crack is located in the interface plane of the coating and substrate. The coated solid is indented by a smooth rigid punch with a certain normal force. The Coulomb friction is taken into account in the contact. Also, the solid is subjected to a residual stress at infinity. The problem is solved numerically and asymptotically and the dependence of the stress intensity factors at crack tips on the problem parameters is determined.

The second model block consists of the probabilistic model of coating delamination. It is assumed that the probability density of cracks in a thin interface layer versus crack semi-length is known and the crack propagation phase is much longer than the crack initiation phase, i.e. the crack propagation represents the main part of fatigue crack life. It is assumed that the punch is cyclically indented in the solid. The density of the crack distribution after N loading cycles is determined. Fatigue crack growth is considered based on the Paris equation. The probability of coating delamination is determined. The dependence of the probability of coating delamination and coating delamination life on various problem parameters is analyzed.