Issue 38

S. Suman et alii, Frattura ed Integrità Strutturale, 38 (2016) 224-230; DOI: 10.3221/IGF-ESIS.38.30 226 loading is considered proportional. In contrast, under non-proportional loading, the axial and shear stresses (strains) do not maintain a constant ratio during the load cycle. This causes the principle stress planes to rotate during the cycle, which has been observed to cause additional cyclic hardening or softening in some metals [16]. Such load paths also make the prediction of fatigue life more challenging. The non-proportional load paths shown in Fig. 1 were designed to provide discriminating test conditions for evaluating the critical plane parameters. Specifically, the “check” path and “box” path simulated actual loading scenarios experienced in aircraft engine components, whereas the “triangle” path, “s” path, and “double check” path were designed to produce varying combinations of normal-stress “subcycles” on the shear-based critical plane. The critical-plane stresses are discussed in more detail in the following sections. Figure 1 : Multiaxial load paths considered in this study. D AMAGE PARAMETER DEVELOPMENT FOR LIFE ESTIMATION Critical Plane Analysis s previously mentioned, the critical plane method allows designers to compute the fatigue damage on the crack plane; however, the identification of the critical plane is dictated by several factors including load level, load type, load path, and the behavior of the material. Similarly, the definition of the critical plane itself may vary among different researchers, and various proposals can be found throughout the literature. Many researchers define the critical plane as the plane possessing the maximum value of the damage parameter, whereas others have used the plane on which a particular stress or strain component (such as the normal or shear stress range) is maximized. In this work, the latter definition was adopted, with the maximum shear stress range used to identify the orientation of the critical plane. This definition was established after thorough analysis of a large amount of uniaxial and multiaxial fatigue data from high strength steel and titanium alloys. In comparing the correlation of the data sets from different parameters (described below) calculated on the maximum shear plane and the plane of maximum damage parameter, the differences were found to be very small. Additionally, using the maximum shear plane as the critical plane significantly reduces the mathematical computation (as it is easier to identify), and also makes optimization of the material constants needed by each parameter much simpler. It should also be noted that the critical plane definition proposed in this paper is for constant amplitude fatigue cycles, and may not be appropriate for variable amplitude loading cases because the orientation of the critical plane may change from cycle to cycle. Critical Plane Damage Computations Several well-accepted damage parameters were initially used to model the fatigue damage in the data sets mentioned above; however, the Findley parameter [10], Fatemi & Socie parameter [16], and Erickson et al. parameter [17] were found to provide better correlations between experimental and predicted fatigue lives for all the data sets, and thus are presented in detail in this paper. These damage parameters are expressed in the equations below: Findley (Eq. 1), Fatemi & Socie (Eq. 2), and Erickson et al. (Eq. 3). a max DP τ kσ   (1) max max n y γ σ DP 1 k 2 σ           (2) A