Issue 38

S. Suman et alii, Frattura ed Integrità Strutturale, 38 (2016) 224-230; DOI: 10.3221/IGF-ESIS.38.30 228 Proportional, N f = 36,078 S-Path, N f = 34,816 Triangle Path, N f = 176,559 Check Path, N f = 168,803 Double Check, N f = 141,421 Figure 3 : Critical plane stresses for the tests conducted on DA 718. The critical-plane shear and normal stresses from these specialized tests are shown in Fig. 3, along with the resulting fatigue lives. Note that for all the tests, the shear stress cycles and normal stress cycles were nearly identical in magnitude; consequently, the differences in fatigue lives can be attributed to the number and positioning of the normal stress subcycles on the critical plane. Of particular interest is the fact that the proportional and S-path tests had similar lives, despite the fact the S-path contained three subcycles in comparison to one in the proportional test. This would indicate that the number of subcycles is of less importance than the magnitude. In comparing the triangle, check, and double-check tests, it is evident these tests also had similar lives (within expected scatter), but the lives were over four times longer than the proportional and S-path tests even though the normal stress cycles were similar in magnitude. The difference in the three latter tests was that the peak normal stress did not occur at the same time as the peak shear stress; i.e., the normal and shear cycles were offset. This again indicates a negligible effect from the number of subcycles, but a very large influence from the timing of a subcycle. In other words, when the normal stress cycle peaks simultaneously with the shear cycle, significantly more damage occurs, resulting in a shorter life. Based on these observations, it was concluded that the Erickson parameter does not accurately model the fatigue damage in complex, multiaxial load paths. Specifically, the subcycle summation term is unnecessary. However, a different term is needed to model the interaction between the shear and normal stresses on the critical plane. A new critical-plane parameter that eliminates many of the shortcomings of the previous models is shown in Eq. 5. This parameter makes use of the shear strain range (   ) multiplied by the maximum shear stress in order to capture the effects of strain hardening in the LCF regime and mean shear stresses in the HCF regime. The effect of the interaction between normal and shear stresses on the critical plane is accounted for by the product of these stresses in the secondary multiplicative term. The value of σ o in this equation is arbitrary, and simply used to maintain unit consistency. Note also that the parameter contains only two material-dependent constants (k and w), relative to the six required by the Erickson model. Thus, this parameter requires substantially less computational effort to fully implement in comparison to the Erickson model.       w 1 w max max 2 o σ τ DP = G γ τ 1 k σ              (5) The application of this new parameter to the Ti-6Al-4V data set referenced in Fig. 2 is shown below in Fig. 4(a). In comparing this plot with the one shown in Fig. 2(c), it is evident the new parameter provides a similarly excellent correlation of both the uniaxial and multiaxial fatigue data throughout the full LCF/HCF spectrum. A second set of fatigue data, taken