Multi-axial fatigue life assessment is important in power generation, aerospace, automotive, and many other industries. The newly developed path-dependent multi-axial cycle counting and fatigue life assessment method has been shown effective for some applications. For instance, when stress range is used as the only driving force for fatigue failure, the method correlates high cycle fatigue test data well. The method consists of two parts: (1) maximum-range (or maximum distance) based cycle counting method, so that the method can be applied to 2-D and 3-D stress or strain space, as compared to the conventional rainflow counting method, which is based on the peak-valley concept, therefore, can be applied only to uniaxial (1-D) loadings; and (2) a path-length based stress range is used as the fatigue damage parameter replacing the traditional concept of stress or strain range, which is the difference between the peak value and the valley value of a cycle. This method has been justified using the classical fracture mechanics in multidimensional stress space.

In this paper, we apply the method to analyze two additional classes of multi-axial fatigue test data reported in the literature: (1) low-cycle strain based tests, which has an important implications in high-temperature applications, such as piping/vessels in power industry, turbine, and automotive exhaust systems; (2) a series of test data that require an introduction of two parameters in either fatigue crack growth model or S-N curve based approach. For the latter, an incremental crack growth model reported earlier by the authors is recast to incorporate one additional stress based parameter to account either mean stress or maximum principle stress effects in multi-axial fatigue damage process, dependent upon material characteristics under consideration. The results show that strain-based low-cycle multi-axial fatigue data can be effectively correlated in the form of a single S-N curve using a path-dependent effective strain range definition. Furthermore, a two parameter based interpretation of the crack propagation model is capable of capturing effects of the maximum principle and mean stresses on multi-axial fatigue damage process associated with some of the test data. Finally, the physical basis of the method in these extended applications is discussed.

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