Bimaterial problems with an interfacial cavity for some boundary conditions subjected to uniform heat flux normal to the interface

Abstract

Stress analysis is carried out for a bimaterial infinite plane with an interfacial cavity. Uniform heat flux applies to the normal to the interface. Four combinations of boundary conditions are considered, that is, isothermal and adiabatic boundary conditions for heat flux analysis, and external force and displacement boundary conditions for stress analyses. The infinite plane consists of two bonded dissimilar materials of a half plane with a single notch. To achieve analytical solutions, a rational mapping function and a complex variable method are used. By changing the mapping function, other geometries for the notch can be analyzed. Complex stress functions for isothermal and external boundary conditions can be only achieved for stress calculation. The stress intensities of debonding are investigated for various debonding lengths for some elliptical holes, and for the debonding extensions. Complex stress functions for isothermal and displacement boundary conditions can be expressed by an infinite series and stress components et al. cannot be calculated. However, a solution of interfacial rigid inclusion can be solved. Complex stress functions for the adiabatic boundary are achieved by the integral forms for external force and displacement boundary conditions, and the integral cannot be carried out, and therefore, stress components cannot be achieved.

Keywords:

• Dissimilar plane
• bimaterial problem
• heat flux
• interfacial cavity
• isothermal boundary
• adiabatic condition
• complex stress function
• mapping function
• external stress function
• mapping function