Stresses and stress intensities at notches: ‘anomalous crack growth’ revisited

Abstract

In this paper, a new notch stress estimation scheme is presented within the context of conventional finite element solutions. The estimation method is based on a separation of an actual notch stress state into two parts. One part is a far-field stress in the form of membrane and bending components that satisfy far-field equilibrium conditions, and the other is a self-equilibrating part that provides an effective measure of the notch stress state. The self-equilibrating part can be directly related to notch geometry and captured using a rather coarse finite element model. The singular stress behavior at an arbitrary notch is then described by a closed form solution formulated using the self-equilibrating part of the stress state for a small crack emanating from a notch. The corresponding stress intensity factor solutions are then presented by considering both the far-field stress (also called structural stress) and self-equilibrating notch stress. The stress intensity solutions are formulated using existing solutions for typical simple crack geometry. One important feature of the notch stress and stress intensity solutions is that the current solutions not only capture the singular characteristics as the notch tip is asymptotically approached, but also recover the far-field (or nominal) stress state. Finally, the effectiveness of the present notch stress estimation scheme is demonstrated by using a series of well-known short crack growth data exhibiting ‘anomalous growth’. It has been found that, for instance, the anomalous growth discussed in, for example, Fat Eng Mat Struct 6 (1983) 315; Eng Fract Mech 29 (1988) 301; as well as Surface Crack Growth: Models, Experiments, and Structures (1990) 333, can be unified with long crack data as straight lines, without resorting crack closure considerations. As a result, a two-stage crack growth model is proposed within the context of K-dominant crack growth. The first stage is dominated by the notch-induced self-equilibrating part of the stress state and the second stage is dominated by the equivalent far-field stress state or structural stresses that satisfy equilibrium conditions and can be effectively computed in a mesh-insensitive manner. The implications of these findings on fatigue growth rate data generation and fatigue life predictions will also be discussed.