A comparison of critical distance methods for fracture prediction

This paper is concerned with four methods which are used to predict the failure of bodies containing notches and other stress concentration features. Two of these methods, which we call the line method (LM) and point method (PM), use parameters taken from the elastic stress field ahead of the notch. The other two methods make use of linear elastic fracture mechanics (LEFM): we call these the imaginary crack method (ICM) and finite fracture mechanics (FFM). A common feature of all the methods is the use of a material constant with the units of length, which we call the critical distance.In this work we test the hypothesis that these four methods all give similar predictions. Firstly, we show analytically that, for the simple case of a straight, through-thickness crack in an infinite body, predictions using the LM are identical to those of the ICM and FFM and, in addition, there is a very simple relationship between the critical distances for the three methods. For notches no precise relationship exists; we used both closed-form solutions and finite element analyses (FEA) to compare predictions of failure from common types of notches, such as circular holes, edge notches and slots, in large (essentially infinite) bodies. We modelled both isotropic and anisotropic materials. In all cases, we found that predictions from the four different methods were of similar magnitude, always falling within an error band of ±10%. However, large differences emerge in the case of finite bodies when the remaining width is similar in size to the critical distance; then predictions become asymptotic in different ways. These findings have practical consequences for the use of these methods in engineering design. The results also promote some discussion about the theoretical basis of critical distance approaches.