Fractals in Fracture of Solids

Abstract

The revolution in geometry, which has recently led to the notion of the fractional dimension of real world bodies and the creation of fractal geometry, has substantially influenced fracture science. In the present chapter, the methods of the theory of fractals are applied to fracture phenomena. A brief overview of practical fractal geometry and some general work on fractals is given in the Introduction, Section 8.1. In Section 8.2, Fractal Analysis in Fracture Mechanics, a description of some experimental measurements of the fractality of fractures is provided for some metals and rocks. In Section 8.3, Fractal Cracks in Solids, the methods of fractal geometry are applied to brittle cracks with irregular and complicated structures. In Section 8.4, Nanofracture, some basic relations for nanoscale, which can serve as a reference scale in scaling laws, are given. An application of the methods of fractal geometry to fatigue and creep is treated in Section 8.5, Fatigue and Creep. Fractal geometry is treated in many books, some of which are indicated in the Introduction. However, for the mastering of the simplest methods, a reading of this chapter suffices; to feel so the reader is encouraged to solve the problems at the end of the chapter.