Issue 41

A. Carpinteri et alii, Frattura ed Integrità Strutturale, 41 (2017) 66-70; DOI: 10.3221/IGF-ESIS.41.10 68 Then, the fatigue strength is assessed by means of an equivalent strain amplitude together with a unique material reference curve (i.e. the tensile Manson-Coffin curve). More precisely, the above equivalent strain amplitude is expressed by a combination of the amplitudes of both the normal,  , N a , and tangential,  , C a , displacement vectors acting on the critical plane:                  2 2 2 , , , a eq a N a C a a (3) By equating Eq. (3) with the tensile Manson-Coffin equation, the number f N of loading cycles to failure can be worked out through an iterative procedure. F ATIGUE EXPERIMENTAL CAMPAIGN he strain-based multiaxial fatigue criterion formulated in conjunction with the control volume concept is here applied to a set of data recently published [10]. In particular, uniaxial and multiaxial fatigue tests have been carried out on circumferentially V-notched round bars made of Ti-6Al-4V titanium alloy. Each specimen presented a V-notch depth equal to 6 mm, an opening angle equal to  90 and a notch root radius equal to about 0.1 mm. The experimental fatigue tests have been performed by means of an MTS 809 servo-hydraulic biaxial machine. All tests have been conducted under load control at a frequency from 5 to 10 Hz, depending on the applied load. Details of the loading conditions being examined are reported in Ref. [10]. According to the notch geometry and the material properties (that is, the values of NSIFs ranges and HCF strengths), the control volume radius 1 R is equal to 0.051 mm, whereas the control volume radius 3 R is equal to 0.837 mm. The above difference in the values of control volume radii is not only due to the different behaviour in the crack propagation under tension or torsion loading, but also to the higher plasticity around the notch tip experienced under torsion loading with respect to tension loading. C RITERION VALIDATION ll experimental data being examined (see the previous Section) are characterised by fatigue life between 3 10 and  5 6 10 loading cycles and nominal load ratio equal to  1 . In particular, we consider six different fatigue test series on V-notched specimens: (1) one series of tests under pure tension fatigue loading and one series under pure torsion fatigue loading; (2) two series of tests under combined in- (    0 ) and out-of-phase (    90 ) tension and torsion loading, with a constant biaxiality ratio,  , equal to 0.6 ; (3) two series of tests under combined in- (    0 ) and out-of-phase (    90 ) tension and torsion loading, with a constant biaxiality ratio,  , equal to 2.0 . Different values of the distance r to determine the verification point position are computed according to Eq. (1): (a) for pure tension loading, i.e.   0 , r is equal to  1.9 m R ; (b) for pure torsion loading, i.e.    , r is equal to  11.3 m R ; (c) for combined in- and out-of-phase tension and torsion loading characterised by   0.6 , r is equal to  7.5 m R ; (d) for combined in- and out-of-phase tension and torsion loading characterised by   2.0 , r is equal to  10.8 m R . Note that Eq. (1) has been obtained through a best-fit procedure by taking into account some values of  related to the experimental data reported in Refs [5,10]. The values of the material parameters related to the Manson-Coffin curves, required for the application of the criterion, are reported in Ref. [11]. The effective Poisson ratio,  eff , is assumed to be equal to the elastic Poisson ratio (that is,   0.3 ). T A