Issue 37

N.R. Gates et alii, Frattura ed Integrità Strutturale, 37 (2016) 160-165; DOI: 10.3221/IGF-ESIS.37.22 161 crack plane also affects the nucleation and growth of small cracks by influencing the amount of friction and interlocking between opposing crack faces. Therefore, the inclusion of a maximum normal stress term is able to account for the effects of mean stress in a manner that holds physical significance. The FS parameter predicts fatigue life in terms of shear fatigue properties based on the following equation:                      ' ,max ' max 1 2 2 2 b c f o o n f f f y k N N G (1) where Δ γ max is the maximum range of shear strain experienced on any plane, σ n,max is the maximum normal stress occurring on the same plane for the cycle of interest, σ y is the material yield strength, and k is a material dependent parameter reflecting the influence of normal stress on fatigue damage. The maximum normal stress is normalized by yield strength as a means of preserving the unitless feature of strain. The right hand side of Eq. 1 represents the shear strain-life curve for the material under consideration. In the event that shear fatigue properties are not available for damage calculation, the right side of Eq. 1 may alternatively be expressed in terms of uniaxial fatigue properties as follows:                                                   ' ' ,max ' max 1 1 2 1 2 1 2 2 2 b c b f f n e f p f f f y y k N N k N E (2) where ν e is elastic Poisson’s ratio, ν p is Poisson’s ratio for fully plastic conditions, usually taken to be 0.5, and all other fatigue properties correspond to the fully-reversed uniaxial strain-life equation. Since the normal stress term is multiplied by a strain term, the FS parameter is also able to account for changes in fatigue damage brought about by cyclic and/or non-proportional hardening. Damage parameters based on only stress or only strain terms, on the other hand, cannot reflect these changes in material constitutive behavior. Additionally, because the normal stress term is multiplied by the shear strain range, the FS parameter assumes that cyclic shear strain must be present in order for fatigue damage to occur. This is important because it prevents the prediction of fatigue damage in situations where only a static axial stress may exist on a plane. Overall, the FS parameter, based on either shear or uniaxial fatigue properties, has been shown to correlate experimental and predicted fatigue lives well for a variety of materials and loading conditions. Despite this fact, when analyzing some recent literature data, e.g. [4,5], it was found that the parameter can result in non-conservative life predictions when significant tensile mean stress is present. Although increasing the k value in the FS parameter can improve mean stress correlation by increasing the influence of the maximum normal stress term, this has a detrimental effect on the correlation of fatigue data generated under other multiaxial loading paths. As a result, in the first part of this study, modifications to the FS parameter are investigated in an attempt to improve fatigue life predictions. In addition to mean stress effects, Shamsaei [6] performed fatigue tests on 1050 steel for different multiaxial loading paths which produced the same fatigue damage predictions based on the FS parameter. From the results of these tests, however, it was found that the average experimental fatigue life for cyclic torsion with static tension loading was around half of the life predicted for in-phase axial-torsion loading at the same damage value. Conversely, the average life for cyclic torsion with pulsating tension loading was around a factor of 2.5 longer than for in-phase loading. Although a factor of ±2.5 error is still very reasonable for multiaxial fatigue life predictions, these results suggest that there is room for some improvement in fatigue damage calculation with respect to the quantification of normal-shear stress/strain interaction. Considering the load path dependence of fatigue damage, the second part of this study focuses on a limited number of fatigue tests designed to differentiate between the original FS parameter and the modified parameter developed in the first part of the study. These tests were performed using tubular specimens of 2024-T3 aluminum alloy under loading conditions which result in the same damage value based on the original FS parameter, but different damage values for the modified parameter. Differences in experimental lives were then compared to predictions to determine which parameter more closely reflects the fatigue damage variation between loading paths. M ATERIAL AND TESTING PROCEDURES he material chosen for the fatigue tests performed in this study was aluminum alloy 2024-T3. Mechanical properties for the material include a yield strength (0.2% offset) of 330 MPa, ultimate tensile strength of 495 MPa, and modulus of elasticity of 73.7 GPa. Additional deformation and fatigue properties can be found in [7]. All tests T