Finite element modelling of fatigue crack growth of surface cracked plates

Abstract

A multiple degree of freedom numerical procedure applicable to the prediction of the fatigue crack growth of surface cracks in plates under a combined tension and bending load is described. This procedure performs a three-dimensional finite element analysis to estimate the stress intensity factors at a set of points along the crack front, and then calculates the crack growth increments at these points invoking a fatigue crack growth relationship. A new crack front is established using a cubic spline approximation. A remeshing technique developed enables the procedure to be implemented automatically, and then fatigue crack growth can, therefore, be predicted in a step-by-step way. Following the descriptions of some theoretical background and technical details, several important problems in the evaluation of stress intensity factors by the finite element method are discussed. They include the sensitivity of stress intensity factor results to crack shape, the effect of mesh orthogonality and the J-integral path independence. It is shown that the stress intensity factor results are sensitive to the crack front shape, that the cubic spline approximation to a crack front can eliminate the oscillation of stress intensity factors around the crack front defined by the polygonal line and consequently increase the stress intensity factor accuracy, and that the J-integral path independence is usually maintained but is lost at the free surface if a slightly non-orthogonal intersection exists between the free surface and the crack front.

Introduction

Surface cracks, which are most likely to be found in many structures in service, such as pressure vessels, pipeline systems, off-shore structures and aircraft components, have been recognised as a major origin of potential failure for such components. The study of fatigue crack propagation from such defects has been an important subject during recent decades. The surface crack in a finite thickness plate subjected to remote tension, bending or combined loading, as shown in Fig. 1, is a well-studied configuration, to which most effort for surface crack problems has so far been devoted, and is commonly considered to be representative of the surface crack family.

Based on the experimental fact that the crack shape of propagating surface cracks in a plate under cyclic tension, bending or combined loading is approximately semi-elliptical, a theoretical model with two degree of freedom, as shown in Fig. 2(a), has been proposed [1] for predicting the fatigue crack growth of surface cracks. The model assumes the growing crack to be of semi-elliptical shape, but allows for change in crack aspect ratio. Fatigue crack growth is then calculated along both the depth and surface directions through two coupled Paris fatigue crack growth equations. This method has been widely used in practical assessments of fatigue crack propagation for surface cracks.

Obviously, the theoretical model contains a crack shape assumption, which may lead to an uncertain error in the prediction of fatigue crack growth, especially when a complex stress distribution across the plate thickness is involved. In this case the crack may significantly deviate from the assumed semi-elliptical shape. On the basis of the initial work by Smith and Cooper [2], a sophisticated predictive method has recently been developed by the authors. The method integrates an appropriate fatigue crack growth law at a set of points along the surface crack front instead of its two extremes, which enables the crack front of growing cracks to be directly traced so that the crack shape assumption mentioned above can be avoided. The stress intensity factors (SIFs) along the crack front are calculated by the finite element (FE) method, and an automatic technique has been developed in order to automatically recreate finite element models as the crack propagates.

This paper describes some theoretical background and technical details associated with the numerical simulation method developed by the authors. Three important problems in the estimate of stress intensity factors along the front of planar cracks by finite element analyses, i.e. the SIF sensitivity to crack front shape, the influence of a non-orthogonal mesh on the SIF accuracy, and the J-integral path independence, are also discussed. The fatigue crack growth characteristics of surface cracks in plates, such as crack shape development and deviation from semi-elliptical shape, aspect ratio change and stress intensity factor variation, will be examined, and their differences from those obtained through the method with a semi-elliptical shape assumption will be revealed in the following papers [18], [19].