Chapter 2 - The theory of critical distances: Basics: An introduction to the basic methodology of the TCD

Abstract

This chapter introduces the basic methodology of the theory of critical distances (TCD) and its use in simplest forms. TCD is a group of methods which have certain features in common—that is, principally the use of a characteristic material length parameter and the critical distance L. This chapter describes the simplest method of analysis, the point method (PM), and some slightly more complex methods such as the line method (LM), area method (AM), and volume method (VM). It discusses easy ways to predict brittle fracture and fatigue, for e.g., where the elastic stress field around the stress concentration feature is known, as from finite element analysis (FEA). The implementation of TCD with a series of specific examples is also described. The first example is the prediction of brittle fracture in a test specimen, containing a notch, to introduce the point method (PM). The second example considers fatigue failure in an engineering component, again using the PM. The chapter illustrates a simple theory to make a link between the PM and linear elastic fracture mechanics (LEFM): and introduces the other related methods (the LM, AM and VM). It also provides an example, which looks at the prediction of size effects for notches.