The effect of crack length and maximum stress on the fatigue crack growth rates of engineering alloys

Abstract

The fatigue crack growth rate (FCGR) curve of metallic alloys is usually divided into three regions. Region II is often referred to as the Paris regime and is usually modelled with a power law relationship with a single exponent. Regions I and III are located at the beginning and end of the FCGR curve, respectively, and are frequently modelled with asymptotic relationships. In this paper we hypothesize that fatigue crack growth is governed by power law behaviour at all crack lengths and all stress intensity factor ranges (ΔK). To accommodate for the changes in the FCGR slope at regions I - III mathematical pivot points are introduced in the Paris equation. Power law behaviour with the presence of pivot points enables direct fitting of the crack length vs. cycles (a-N) curve to obtain the FCGR as a function of ΔK. This novel approach is applicable to small and long crack growth curves and results in accurate multilinear FCGR curves that are suitable for reconstruction of the measured a-N curves. The method is subsequently applied to i) different alloys to show local changes in the FCGR curve for changes in alloy composition and heat treatments, ii) naturally increasing ΔK testing of microstructurally small cracks to obtain accurate small crack FCGR data. The comparison with accurate long crack data shows that small cracks are faster, but the transition from region I to region II occurs at a specific fatigue crack growth rate which results in an apparent shift in ΔK at the transition. iii) Long cracks, which show that the FCGR increases with maximum stress for a given ΔK and stress ratio when the maximum stress approaches the yield stress. The maximum stress phenomenon becomes important in the case of fatigue testing, where the initial crack lengths are usually small and maximum stresses are high. It is concluded that for long cracks the phenomenon explains why the Paris equation is applicable rather at low maximum stress, while the Frost-Dugdale equation is more applicable at high maximum stress.