Fiber-reinforced composites have good material properties, but defects around inclusions may exist during molding process and many micro-cracks around inclusions may occur because of thermal differences between an inclusion and a matrix. It is necessary to analyze the mechanical interaction between an inclusion and a crack fracture-mechanically for the reliable use of the composites.
In this study, the plane interaction problem between a circular elastic inclusion and a finite straight crack, located in the infinite body matrix under mechanical loading at infinity and remote uniform heat flow, is considered. By using the complex variable theory, the existing solution for the edge dislocation interacting with a circular inclusion and the obtained solution for the temperature dislocation interacting with a circular inclusion, the thermoelastic problem of a straight crack in the vicinity of the interface is formulated. By numerical analysis dislocation distribution functions can be obtained easily. The stress intensity factors of the crack-tip close to the interface are expressed in terms of the values of the distribution functions of the dislocations. Several numerical examples are given to demonstrate the effects of geometrical parameters and material properties on the stress intensity factor of the crack-tip close to the interface. The present solutions are identical with the existing solutions and FEM results. Some mistakes of previous researchers are corrected.
