Issue 51

A. S. Yankin et alii, Frattura ed Integrità Strutturale, 51 (2020) 151-163; DOI: 10.3221/IGF-ESIS.51.12 152 The main loading conditions referred to the literature when studying multiaxial fatigue are biaxial tension of cross-shaped specimens, tension with torsion and bending with torsion of cylindrical specimens. Meanwhile attention is paid not only to the proportional cyclic loading but also to more complex modes with phase shifting, different frequencies and other characteristics [16-20]. Apart from testing standard hourglass and tubular specimens, one can also test weld joint specimens [21, 22], specimens with grooves [23] and other stress raisers [24]. Cyclic effects may be associated with a cycle asymmetry due to static loadings caused, as an example, by gravity force or linear overloading. Apart from that, static loads may occur along an axis different from the cyclic ones, which results in bending cyclic loads with constant torsion and so on. Gerber [25], Goodman [26], Morrow [27], Smith [28], Oding [29], Birger [30] and many others [31-35] studied the influence of the asymmetry of the loading cycle on the fatigue behavior of various materials. As a rule, the experimental results are shown in the Haigh diagram (the stress amplitude versus the mean stress in the cycle), and different relations for their description are suggested. An increase of the mean stress leads to a decrease of fatigue strength. This effect is quite strong for brittle materials (e.g. cast iron) both in axial and in torsion [34]. However this effect is lower in torsion than in axial for ductile materials such as steels and aluminum alloys [31]. Thus, some authors [5, 36, 37] do not suggest taking into account the influence of the mean stress under torsion until the maximum values of shear stress do not exceed yield strength. Let us note that under cyclic loadings in the compression area there is an increase in fatigue strength which is more significant for brittle materials and less significant for ductile ones [5, 32]. In general, a similar behavior is demonstrated by the materials under constant static stresses under multiaxial loadings (e.g. an alternating bending with a constant torsion and so on) [5, 36-39]. However, there are much less studies in this area, compared to uniaxial effects, and there is no complex approach to studying this issue. Apart from that, works mostly pay attention to fatigue limit under more than 106 cycles, i.e. they consider such loadings that allow a material (conventionally) to endure an unlimited number of loading cycles. But if we design structures with a set (limited) service life in order to save resources, it is important to describe not only the fatigue limit but also S-N curves at different levels of additional static stresses. In the previous work [40] the authors researched the influence of the constant components of multiaxial loading (constant tension and alternating torsion, constant torsion and alternating tension-compression) on the fatigue life of 2024 aluminum alloy. It is shown that the influence of the constant static stresses results in a decrease of the number of cycles to failure. Moreover, the realized values of the constant static stresses obviously did not exceed the corresponding values of the conventional yield strength for the alloy. The purpose of this work is to check if it is reasonable to use various criteria for multiaxial fatigue using the experimental data presented in the article [40]. E XPERIMENTS Material and specimen he material used in the current experimental investigation is a common aeronautic material, 2024 aluminum alloy. The chemical composition of the alloy consists of Cu 4.28, Mg 1.48, Mn 0.75, Fe 0.28, Si 0.29, Zn 0.12, Ni 0.009, Ti 0.06, Cr 0.017, Pb 0.05. Mechanical properties for the material are listed in Tab. 1. Fatigue tests were performed on hourglass specimens. The specimen geometry is shown in Fig. 1. The specimens are designed in accordance with recommendations of national standard GOST 25.502. Stresses used in calculating were in accordance with the minimum cross-section of specimen. Property Symbol 2024 aluminum alloy Unit 0.2% Tensile yield strength σ y 336 MPa 0.3% Torsional yield strength τ y 153 MPa Ultimate tensile strength σ u 450 MPa Modulus of elasticity E 75.4 GPa Shear modulus G 30.0 GPa Table 1 : Mechanical properties of 2024 aluminum alloy. T