A new approach to the mechanics of fatigue crack growth in metals: Correlation of mean stress (stress ratio) effects using the change in net-section strain energy

Abstract

An unsolved problem in the mechanics of fatigue crack growth is why mean stress or stress ratio in a fatigue cycle has a profound effect on growth rate when compared in terms of stress intensity factor range (ΔK). Specifically, there has not been any fracture-mechanically-consistent theory to explain the effects of mean stress on fatigue crack growth. In this work, a new and generalized driving force parameter for fatigue crack growth, which effectively incorporates the mean stress or stress ratio effect, is developed from energy principles of solid mechanics. A successful explanation of the effect of mean stress on the growth rate is provided. The driving force is the accumulated change in net-section strain energy, which develops as a function of increasing crack length and decreasing net-section size in fatigue. A generalized mechanics analysis, showing how to account for the stress amplitude and the maximum stress of a fatigue cycle in the change in net-section strain energy, is presented. Equivalently, the new crack growth parameter can also be interpreted as the cumulative work done by cyclic loading at the crack length at which the crack growth data is determined. Several experimental data, including some historically significant fatigue crack growth data, generated on aluminum, steel and titanium alloys, are used to demonstrate the success of the correlation. As a further validation of the proposed concept, it is shown that the empirical Walker parameter (ΔK0.5Kmax0.5), which had some success in correlating stress ratio effect, is in fact related to the change in net-section strain energy.