Elastic-plastic fatigue crack growth under load cycling

Abstract

An analytical solution based on non-linear beam theory has been derived to compute the variation of total cyclic potential energy in fatigue crack growth under conditions of gross plasticity. It was assumed that the variation in total potential energy with crack length was equal to the cyclic value of J, written as Δ J = Jmax - Jmin where Jmax and Jmin are the maximum and minimum values of the contour integral J in the loading cycle. The solution is applicable to any geometry, providing fully tensile loading and cyclic creep occurs. It was applied to the contoured double-cantilever-beam (d.c.b.) geometry and Δ J was found to be dependent upon load P, crack length a, number of cycles N and the strain hardening and cyclic creep properties of the material. The results obtained may be applied in the study of crack propagation at relatively small deflections. Fatigue crack growth rates were investigated experimentally under tensile cyclic conditions, leading to generalized plasticity. Tests were performed on mild steel d.c.b. specimens at room temperature in laboratory air, 50 per cent r.h. at a loading frequency of 0.1 Hz. Load-deflection loops were monitored during the lifetime and it was found that the experimentally measured variations in potential energy were 5-10 per cent above the theoretical Δ J values. The difference is explained in terms of the shear force effect and also rotation at the crack tip not considered in the theoretical analysis. When the crack growth rate, d a/d N, was plotted against Δ J, a good correlation was obtained. These results offer supporting evidence to the thesis that crack growth rate at high strains is substantially controlled by Δ J.