Fracture of Solids With Microdefects

The book covers some problems of fracture of solids with linear or penny-shaped cracks or rigid inclusions. The analysis of the interaction of a macrocrack with small defects or microcracks in the frame of linear fracture mechanics is the main topic of the book.

The problem of the interaction of the macrocrack with microcracks has been intensively studied for almost two decades. One of the pioneering papers was published in 1984 by the authors of the present book. In the frame of linear elasticity a problem of interaction of the cracks, holes, or inclusions most often has been reduced to a system of singular integral equations. Although exact solutions to the system of singular integral equations exist in a few special cases, the problem, in general, is solved by various asymptotic methods. The series solution over a small parameter representing the ratio of the linear sizes of the microcrack to the macrocrack was first obtained by Tamuzs and Romalis in 1984. It was shown that the two dominant terms in the Stress Intensity Factor (SIF) at the tip of the macrocrack do not depend on mutual interaction of the microcracks and only depend on the interaction of the macrocrack with each microcrack. Therefore, one can use the principle of superposition to solve a problem of interaction of a macrocrack with arrays of small defects.

This method is applied to various macrocrack-microdefect interaction problems of 2-D and 3-D elasticity and thermoelasticity. A review of other approaches to the problem is given at the end of the book.