Issue 38

M. de Freitas et alii, Frattura ed Integrità Strutturale, 38 (2016) 121-127; DOI: 10.3221/IGF-ESIS.38.16 122 playing a secondary role. However, other materials may initiate fatigue cracks on planes of maximum tensile strain or stress ranges, e.g. 304 stainless steel under certain load histories and cast irons [2]. In this case, even if the microcrack nucleates in shear, its so-called initiation life (which always includes some microcrack propagation) is controlled by its growth in a direction perpendicular to the maximum principal stress or strain. Moreover, a material can be shear-sensitive for short, but tensile-sensitive for long fatigue lives, a behavior that can depend as well on the loading type. The shear or tensile nature of the initiating microcrack can be evaluated from a stress scale factor (SSF), which usually multiplies the hydrostatic or the normal stress term from the adopted multiaxial fatigue damage parameter. Low values of the SSF indicate a shear-sensitive material, which should be described by shear-based multiaxial fatigue damage models such as Findley’s [3] or Fatemi-Socie’s [4]. On the other hand, large SSF values indicate that a tensile-based model like Smith-Watson-Topper’s [5] should be used instead to describe the crack initiation process. The approach proposed by Anes et al. [6] for tension-torsion histories combines the shear and normal stress amplitudes applied on the specimen cross section, using a SSF polynomial function that depends on the stress amplitude ratio (SAR) between the shear and normal components. Alternatively, models based on the critical-plane approach calculate multiaxial fatigue damage on the plane where it is maximized (not on the plane where the load is applied), while adopting a SSF value that is assumed constant for a given material, sometimes varying with the fatigue life (in cycles), but not with the SAR, stress amplitude level, or loading path shape. In this work, in-phase proportional tension-torsion tests are conducted in 42CrMo4 steel specimens for several values of the SAR. The SSF and two critical-plane approaches are then compared, based on their predicted fatigue lives and the experimentally measured ones. SSF E QUIVALENT S HEAR S TRESS A PPROACH he SSF equivalent shear stress approach proposed in [6] considers that both the SAR and the stress loading level significantly influence the material fatigue strength in tension-torsion tests. Such effects are accounted for through a polynomial SSF function, which is assumed to transform an axial damage into a shear one. With this equivalent stress, it is also possible to estimate fatigue lives N f , using the uniaxial shear stress SN curve represented as     b f block ssf A N max      (1)   a a a a ssf a b c d f g h i 2 3 2 3 4 5 ,                         (2) where σ a and τ a are respectively the amplitude of the axial and of the shear components of the tension-torsion loading, and λ  tan  1 ( τ a / σ a ) is the SAR. The constants a to i from the polynomial (2) should be fitted to a suitable data set, therefore the SSF function is assumed to be a material fatigue property that must be determined experimentally. C RITICAL P LANE A PPROACH he critical-plane approach assumes that fatigue lives can be calculated from the damage accumulated at the critical plane of the critical point according to some multiaxial fatigue damage model, which is supposed to properly account for the effect of the driving forces that initiate the fatigue crack in the given material. It also assumes that the damage accumulated on all other planes do not influence the initiation of the microcrack, based on the idea that although many intrusions and extrusions may be formed, usually only one fatigue crack usually initiates and grows from the critical point. The main calculation challenge when applying models based on this approach is to compute the accumulated damage in many candidate planes at the critical point, to find the direction of the critical one where it is maximized (and thus where the crack is expected to initiate). This search is very much simplified for in-phase proportional constant amplitude load histories, such as the ones studied in this work. Two pressure-insensitive stress-based critical damage models are briefly reviewed following, one in principle applicable to materials that are shear-sensitive (for which the main cyclic driving force for fatigue damage is  ) and the other to tensile sensitive materials. Findley's shear model Findley explicitly introduced the critical plane idea in 1959 [3], proposing a stress-based multiaxial fatigue damage model that can be applied to proportional or non-proportional loads (recall that the principal stress directions remain invariant T T