Numerical Modelling of Short Fatigue Crack Growth

Abstract: Fatigue implies repeated loading and unloading of a structure, and components subjected to fatigue might experience nucleation of cracks, and subsequent crack propagation. This might lead to catastrophic consequences, such as complete failure of a structure. In order to accurately dimension against fatigue it is of uttermost importance to have a thorough understanding of the mechanisms behind the growth of fatigue cracks, and from this develop reliable methods for estimating the fatigue life. In this Thesis, the growth of short fatigue cracks is addressed. In this context, a short crack is defined as a crack shorter than a few grains of the material. It is well known that such short cracks can grow at lower applied loads and at higher growth rates than long cracks. Therefore, well established methods for predicting the growth of long cracks cannot be used for short cracks. The difference in growth behaviour is due to the sensitivity to the microstructure of the material and influence of the local conditions at the crack tip, for short cracks. Also short cracks are known to propagate through a different growth mechanism than long cracks. In order to formulate more accurate crack growth models, the mechanisms behind their crack growth and the impact on the growth behaviour must be known. This constitutes the scope of this Thesis. The first part of the Thesis deals with a microstructurally short edge crack, located within one grain of a semi-infinite body, loaded by a remote fatigue load under plane strain conditions. The crack is assumed to grow due to shearing and opening between the crack surfaces as a consequence of nucleation, glide and annihilation of discrete edge dislocations in the material. An edge dislocation can be seen as an error in a, otherwise, perfect crystal gitter, and gives rise to a singular stress field in its surroundings. Such dislocations, forming in front of the crack, represent the plastic zone in the material and have a strong effect on the stress field at the crack tip. The dislocations are free to move along specific slip planes in the material as long as the force exerted on them exceeds the lattice resistance, and as long as they do not collide with grain boundaries of the material. Also the external boundary, here defined as the free edge together with the crack itself, is modelled by dislocation dipole elements in a boundary element approach. The model have been used to evaluate the influence on the crack growth for a number of different situations such as variations in grain size, external load, overloads, crack length, initial crack angle, different descriptions of the grain boundary, and so on. In the second part of this Thesis, an experimental study was performed in cooperation with Volvo Aero Corporation (VAC). The aim of was to evaluate a computer program used for fatigue calculations, NASGRO, developed by Southwest Research Institute. Of special interest was to investigate if the program could be used for predicting the growth of short, semi-elliptical, surface cracks in thin titanium sheets. For the evaluation, ten titanium sheets of 2 mm thickness, each with a small starter notch, were used. From the initial notch a small fatigue crack was initiated. The growth of the crack was monitored until complete failure of the specimen. The crack length was continuously calculated by the use of the potential drop technique. The results from the experiments were compared to the results obtained from NASGRO, both regarding crack growth rate, crack shape and failure criteria. The results from the experiments and from NASGRO showed reasonable good agreement, up until just before final failure, were the correct crack path could not be simulated correctly.