The central objective of the research performed in this study was to be able to better understand and predict fatigue crack initiation and growth from stress concentrations subjected to complex service loading histories. As such, major areas of focus were related to the understanding and modeling of material deformation behavior, fatigue damage quantification, notch effects, cycle counting, damage accumulation, and crack growth behavior under multiaxial nominal loading conditions. To support the analytical work, a wide variety of deformation and fatigue tests were also performed using tubular and plate specimens made from 2024-T3 aluminum alloy, with and without the inclusion of a circular through-thickness hole. However, the analysis procedures implemented were meant to be general in nature, and applicable to a wide variety of materials and component geometries. As a result, experimental data from literature were also used, when appropriate, to supplement the findings of various analyses.
Popular approaches currently used for multiaxial fatigue life analysis are based on the idea of computing an equivalent stress/strain quantity through the extension of static yield criteria. This equivalent stress/strain is then considered to be equal, in terms of fatigue damage, to a uniaxial loading of the same magnitude. However, it has often been shown, and was shown again in this study, that although equivalent stress- and strain-based analysis approaches may work well in certain situations, they lack a general robustness and offer little room for improvement. More advanced analysis techniques, on the other hand, provide an opportunity to more accurately account for various aspects of the fatigue failure process under both constant and variable amplitude loading conditions. As a result, such techniques were of primary interest in the investigations performed.
By implementing more advanced life prediction methodologies, both the overall accuracy and the correlation of fatigue life predictions were found to improve for all loading conditions considered in this study. The quantification of multiaxial fatigue damage was identified as being a key area of improvement, where the shear-based Fatemi-Socie (FS) critical plane damage parameter was shown to correlate all fully-reversed constant amplitude fatigue data relatively well. Additionally, a proposed modification to the FS parameter was found to result in improved life predictions in the presence of high tensile mean stress and for different ratios of nominal shear to axial stress. For notched specimens, improvements were also gained through the use of more robust notch deformation and stress gradient models. Theory of Critical Distances (TCD) approaches, together with pseudo stress-based plasticity modeling techniques for local stress-strain estimation, resulted in better correlation of multiaxial fatigue data when compared to traditional approaches such as Neuber’s rule with fatigue notch factor.
Since damage parameters containing both stress and strain terms, such as the FS parameter, are able to reflect changes in fatigue damage due to transient material hardening behavior, this issue was also investigated with respect to its impact on variable amplitude life predictions. In order to ensure that material deformation behavior was properly accounted for, stress-strain predictions based on an Armstrong-Frederick-Chaboche style cyclic plasticity model were first compared to results from deformation tests performed under a variety of complex multiaxial loading conditions. The model was simplified based on the assumption of Masing material behavior, and a new transient hardening formulation was proposed so that all modeling parameters could be determined from a relatively limited amount of experimental data. Overall, model predictions were found to agree fairly well with experimental results for all loading histories considered.
Finally, in order to evaluate life prediction procedures under realistic loading conditions, variable amplitude fatigue tests were performed using axial, torsion, and combined axial-torsion loading histories derived from recorded flight test data on the lower wing skin area of a military patrol aircraft (tension-dominated). While negligible improvements in life predictions were obtained through the consideration of transient material deformation behavior for these histories, crack initiation definition was found to have a slightly larger impact on prediction accuracy. As a result, when performing analyses using the modified FS damage parameter, transient stress-strain response, and a 0.2 mm crack initiation definition, nearly all variable amplitude fatigue lives, for un-notched and notched specimens, were predicted within a factor of 3 of experimental results. However, variable amplitude life predictions were still more non-conservative than those observed for constant amplitude loading conditions. Although there are numerous factors which could have contributed to this non-conservative tendency, it was determined that some of the error may have resulted from inaccuracies in life prediction curves, the modeling of material deformation behavior, the consideration of normal-shear stress/strain interaction effects, and/or linear versus nonlinear damage accumulation.
In addition to crack initiation, fatigue crack growth behavior was also of interest for all tests performed in this study. Constant amplitude crack growth in notched specimens was observed to be a primarily mode I process, while cracks in un-notched specimens were observed to propagate on maximum shear planes, maximum tensile planes, or a combination of both. Specialized tests performed using precracked tubular specimens indicated that the preferred growth mode was dependent on friction and roughness induced closure effects at the crack interface. As a result, a simple model was proposed to account for frictional attenuation based on the idea that crack face interaction reduces the effective stress intensity factor (SIF) by allowing a portion of the nominally applied loading to be transferred through the crack interface. Crack path/branching, growth life, and growth rate predictions based on the proposed model were all shown to agree relatively well with the experimentally observed trends for all loading conditions considered.
For notched specimen fatigue tests, although crack growth was observed to be mode I-dominated, constant amplitude crack growth rates under multiaxial nominal stress states were observed to be higher than those for uniaxial loading at the same SIF range. While T-stress corrections were able to account for this difference in some cases, growth rates for pure torsion loading still had the tendency to be higher than those for uniaxial loading. Additionally, using short crack models to account for stress concentration and initial crack geometry effects was found to improve growth rate correlations in the notch affected zone. For 90° out-of-phase loading conditions, small crack growth appeared to have been dominated by the mode I loading from the axial component of the applied stress, but as cracks grew, they turned, and mode I SIF range alone was unable to successfully correlate crack growth rate data.
Finally, for variable amplitude crack growth, two state-of-the-art analysis models, UniGrow and FASTRAN, were used to predict crack growth behavior for the notched specimens tested in this study. UniGrow is based on the idea that residual stress distributions surrounding the crack tip are responsible for causing load sequence effects, while FASTRAN attributes these effects to varying degrees of plasticity induced closure in the crack wake. While both models were able to predict nearly all uniaxial constant amplitude crack growth lives within a factor of 3 of experimental results, they both produced conservative predictions under uniaxial variable amplitude loading conditions. For variable amplitude torsion and combined axial-torsion crack growth, however, the degree of conservatism in these predictions was found to reduce. This was attributed to an increase in experimental growth rates due to multiaxial stress states effects, which are not accounted for in either UniGrow or FASTRAN. By comparing differences in crack growth life between tests performed using full and edited versions of the same loading history, it was found that FASTRAN was generally better able to account for the effects of small cycles and/or changes in loading history profile. Additionally, initial crack geometry assumptions were found to have a fairly significant impact on analysis results for the specimen geometry considered in this study.