Fatigue Crack Growth in Complex Stress Fields

Fatigue crack growth has been traditionally modelled using LEFM through the use of the Paris law. This requires an accurate method for stress intensity factor (K) calculation. Weight functions have been developed for one-dimensional cracks (e.g. edge and through cracks); these are functions that enable separation of the loading and geometry and considering the effect of each one of these two factors on the stress intensity factor (SIF) separately. They have been proven to be useful for arbitrary stress distributions where an accurate empirical formula for the stress intensity factor does not exist. Such cases include residual stress fields due to surface treatments or welds. However, in the case of surface cracks, or part-through cracks, the problem of modelling the growth of these cracks poses two main questions, namely, how should the Paris law be generalised to suit the two-dimensional scenario, and under arbitrary loadings, how can the SIFs be calculated for these cracks. Current solutions involve tedious mathematical calculations and are complicated functions. In this thesis, the concept of root mean square (RMS) SIF is examined and by drawing mathematical analogy with the one-dimensional case, a novel weight function is derived which enables calculation of RMS SIF values for a range of semi-elliptical surface cracks under arbitrary loadings. The accuracy of the weight function is verified through comparisons with finite elements results for a variety of loadings/geometries. The simplicity of the weight function construction method makes it a useful tool for fatigue life predictions where incremental recalculations of SIF is required as the crack grows. Surface treatments such as shot peening and laser peening are used for crack growth retardation. It is generally believed that it is through the introduction of what is termed ‘beneficiary compressive residual stresses’ that crack retardation occurs. The compressive residual stresses are superimposed on the ‘detrimental tensile stresses’ due to loading and hence lead to a lower SIF level. By having such a strong tool as weight functions, this general belief can be put to test. To this end, a set of experiments were carried out to study the behaviour of cracks in residual stress fields arising from laser peening. Edge cracks were grown in partially-peened specimens. Neutron diffraction stress measurements were taken and stress profiles were obtained for these specimens. Measurements of strain fields near the crack show the interaction between the crack and the stress field induced by the peening process. The effect of laser peening on crack growth is discussed and recommendations for future work are proposed. Overall the thesis proposes a weight function for surface cracks the uniqueness of which is in its simplicity, and develops an understanding of the nature of induced and transient stresses in laser-peened components. The concept of ‘effective fatigue stress’ is introduced and its calculation is described, and conclusions are drawn from the nature of this stress distribution.