## 10 Fatigue crack propagation

10.1 Introduction

The determination of the fatigue crack propagation curve is an essential part of the fracture mechanics design approach. Residual strength calculation procedures have obvious shortcomings, but the prediction of fatigue crack propagation characteristics is even less accurate, despite the vast amount of research that has been done on this subject. Yet the developments achieved during the last decade justify a moderate optimism about the possibilities of prediction techniques.

This chapter deals with the problems of fatigue crack propagation. The use of fracture mechanics in fatigue, as expressed by the relation between the crack propagation rate and the stress intensity factor, is considered. However, the discussion is limited to an evaluation of the use and shortcomings of the relation. For a detailed analysis of its physical aspects reference is made to the pertinent literature [1-4]. The interaction effects of cycles of different amplitudes and the retardation effect [5] of overloads on crack growth during subsequent cycling, is considered, but the discussion is limited to its engineering implications. Methods to predict crack growth under service loading are dealt with separately in chapter 17.

### 10.2 Crack growth and the stress intensity factor

In the elastic case the stress intensity factor is a sufficient parameter to describe the whole stress field at the tip of a crack. When the size of the plastic zone at the crack tip is small compared to the crack length, the stress intensity factor may still give a good indication of the stress environment of the crack tip. If two different cracks have the same stress

10.J Crack growth and tlw stress intensity factor environment, i.e. the same stress intensity factor, they behave in the same manner and show equal rates of growth. The rate of fatigue crack propagation per cycle. da/dN. is governed by the stress intensity factor range AK:

= ./(AK)=f | (ima, - Smin)y/na\ =./ 1 IS. Jna\ (10.1)

where Smjx and ,Smin are the maximum and minimum stress in a cycle, and Sa is the stress amplitude. (The symbol S is used for cyclic stress.)

Figure 10.1. Relation between stress intensity factor and crack propagation rate [8] (courtesy

Chapman and Hall)

Figure 10.1. Relation between stress intensity factor and crack propagation rate [8] (courtesy

Chapman and Hall)

Paris [6] and Paris, Gomez and Anderson [7] were first to point this out. Data obtained from specimens tested at various stress levels should all be on a single curve (see chapter 1 for details). Figure 10.1 shows a plot of data [8] obtained at three different stress levels, but with the minimum stress in a cycle always virtually zero (the cycle ratio R = SmiJSmx = 0.05). The data in this figure indeed obey eq (10.1).

It was already mentioned in chapter 1 that eq (10.1) is sometimes assumed to be a simple power function:

in which C and n are supposed to be material constants. A double-logarithmic plot of da/dN versus AK would then be a straight line.

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