Stress transfer through fully bonded interface of layered materials

• Decoupled governing equations are obtained by the plane assumption.
• General solution to the governing equations is derived for the BVP.
• The closed-form solution for a coating system is provided using stationary potential energy.
• The present approximate solution well agrees with the finite element results.
• The formulation interprets the elastic modulus reduction and interfacial compliance.

Plane strain elastic theory of stress transfer in multi-layered materials is formulated and is used to investigate the stress distribution of a coating system under a tensile load. When the substrate layer is subjected to a uniaxial load, the load is transferred to the coating through interfacial shearing stress. With the aid of a plane assumption, decoupled governing equations are obtained, and the general solution of the displacement field can be derived for both the coating and the substrate layers. Using the boundary conditions and the interfacial continuities, we obtain a closed-form solution for the elastic fields in both the overlay and the substrate layers, which takes the first-term of a series-form solution. Although the singularity effect of stress at the ends of the interface and loading points cannot be exactly illustrated due to the simplification and assumptions, the proposed formulation provides excellent agreement with the finite element results of the transferred stress in the thickness direction of the coating system. Comparisons with the existing models demonstrate the capability and limitation of the proposed formulation. This theory can serve as a baseline for future fracture analysis, inelastic analysis, and thermomechanical analysis of multi-layered materials.