Stress-function variational approach to the interfacial stresses and progressive cracking in surface coatings

• Formulate a semi-analytic method for determining interfacial stresses of hard coatings.
• Investigate the dependency of interfacial stresses upon structural and material parameters.
• Determine the spacing of progressive cracking in hard coatings based on an energy criterion with refined stress field.

Surface coatings are broadly used in cutting tools, protective surface, and recently developed flexible electronics. This paper provides a simple semi-analytic strain energy approach to analysis of the interfacial stresses and progressive cracking in hard coatings subjected to mechanical and thermomechanical loads. The problem is formulated within the framework of linear elastic fracture mechanics (LEFM). The free-edge stresses in cracked coating layers are determined by means of an efficient semi-analytic stress-function variational method formulated by the authors recently. Criterion for progressive cracking in the coating layers is established in the sense of energy conservation. The crack spacing is determined as a function with respect to the geometries, material properties, and external loads. Dependencies of the free-edge stresses and crack spacing upon the geometries and material parameters of the coating system as well as external loads are demonstrated. Numerical results show that given a coating system, the threshold load increases rapidly with the decrease of crack spacing; the thicker and stiffer the coating layer is, the easier the progressive cracking is. A universal scaling number on progressive cracking is obtained. The model is also validated by the results in the literature. The present phenomenological model is applicable for scaling analysis of cracking tolerance of surface coatings, data reduction of coating experiments, design of property-tailorable surface coating systems, etc.