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Fatigue crack propagation behaviour under variable amplitude loading is significantly influenced by load history induced sequence effects. Because the understanding of the causes of such sequence effects is still rather limited, crack propagation predictions become difficult. In the present investigation an exploratory test program with simple variable amplitude load sequences was performed, which was designed to improve the general understanding of sequence effects and to offer a basis both for an evaluation of existing crack propagation prediction models and for the development of improved methods.The investigations were performed on center cracked 8 mm thick A1 7475-T7351 specimens. In the first part of the study constant amplitude tests were performed over a wide range of R-ratios. The test results and the transition of the fracture mode during tests could be represented on the basis of the effective AK-value.In the second part of the paper tests with simple systematically varied sequences of high loads, low loads and underloads were performed and the crack propagation behaviour was measured. In order to obtain detailed information on the crack propagation increments per cycle, fractographic analyses were also performed. It was found that also under variable amplitude loading the crack propagation approximately followed the effective AK-values, except in one case.A linear (non-interaction) prediction model could not describe the observed crack propagation behaviour. The results of the application of a model assuming a constant crack opening level are also given. Finally, some general viewpoints regarding further developments of models are outlined. NOMENCLATURE a = crack length, mm a, = crack length before fracture mode transition a2 = crack length after fracture mode transition C = constant in crack propagation equations CA = constant amplitude loading history d a / d N = crack propagation rate, mm/cycle dK/da = variation of the stress intensity factor due to an increase in crack length K = stress intensity factor, MNm-3'2 AK = range in stress intensity factor between the maximum load and the minimum load in a cycle, MNm-3'2 K, , = maximum stress intensity in a cycle, MNm-3'2 Kmi, = minimum stress intensity in a cycle, MNm-3'2 Kop = stress intensity factor at opening of a fatigue crack, MNrn-"' AK8 = K,, -KO9 = stress intensity range between the maximum load in a cycle and crack opening, MNm-3'2 n = exponent in crack propagation equations N = cycle number N,= cycle number to failure N4 = cycle number up to a crack length of a = 4 mm R = stress ratio (= Smin/Smax) N,in,,,c = prediction after a linear calculation *Visiting scientist from the Institute of Aeronautical Materials, Beijing, China. 315 316 S. ZHANC et al. S = stress, N/mmz S,,, = maximum stress in a cycle, N/mm2 S,,, = minimum stress in a cycle, N/mmz Sap = crack opening stress, N/mm2 So,, = 0.2% offset yield strength, N/mm2 S, = ultimate tensile strength, N/mm2 6 =strain, % t = time U = AK,,/AK w = specimen width, mm a = geometry factor

For the evaluation of the local elastoplastic strains and stresses at the notch root suitable approximation formulas of sufficient accuracy are often used. In the present study the “equivalent strain energy density” concept for elastic-plastic notch strain-stress analysis has been developed. It was found that the evaluation of the strain energy density in the notch tip plastic zones does not require any input data other than the material stress-strain relation and the elastic stress concentration factor. The concept was verified on the basis of the results obtained from plane strain elastic-plastic finite element analysis using the material model after Mro´z. Comparison of the two sets of results revealed satisfactory accuracy of the equivalent strain energy concept. It was also shown that all stress and strain components in the notch tip can be calculated by complementing the method with Hencky’s equations. Neuber-based calculations were also included in the study. It was found that the energy concept was superior to Neuber’s rule, especially in the presence of high inelastic strains in the notch tip.

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