Chapter 3 - The theory of critical distances in detail: The history, background and precise definition of the TCD

Abstract

This chapter examines the theory of critical distances (TCD) with a brief history of the subject and describes a number of theories, which can all be described as critical distance theories. TCD is a group of methods, all of which use linear elastic analysis and a constant critical distance. Two of these methods, the point method (PM) and line method (LM), calculate a stress value and equate it to a characteristic strength for the material; the other two methods, imaginary crack method (ICM) and finite fracture mechanics (FFM), use energy concepts to consider the propagation of a crack of finite size, and thus, use the material parameters of Gc or Kc. Predictions obtained from the four methods are sufficiently similar that any one of them can be used in practice, depending on convenience. For e.g., if the results of finite element analysis (FEA) are available, as is generally the case for industrial components, then the PM or LM will be the most convenient; whereas the ICM and FFM can be expressed in the form of equations, at least for certain cases, allowing parametric studies to be conducted more easily. Combination of one of the stress-based methods with one of the energy-based methods is also possible. These combined methods are computationally more difficult, but may be appropriate in cases where the above methods break down, especially in the case of components whose size is small compared to L.