Issue 30

P. Livieri, Frattura ed Integrità Strutturale, 30 (2014) 558-568; DOI: 10.3221/IGF-ESIS.30.67 562 Finally, the effective Strain Energy Density shall be evaluated, by computing the average energy and by introducing an appropriate correction c w due to the load ratio. 1 3 2 2 3 1 1 3 2(1 λ ) 2(1 λ ) 1 3 K K 1 W e  + e E R R             (13)     2 2 2 2 1+        1 0 1-R 1          0 1-        0 1 1-R w R for R c for R R for R               (14) w SED c W   (15) Note that, since the integration fields are different under tensile and torsional loading and the two strengths shall be known for the SED evaluation, the proposed approach is actually a bi-parametric one. A mono-parametric version of such theory can be easily obtained by using only the parameters evaluated under tensile loading; i.e. using only R 1 and assuming, for a sake of simplicity, R 3 equal to R 1 . This choice is not suggested in [20], but it is here introduced just for this specific investigation. E XPERIMENTAL DATA FROM THE LITERATURE or a discussion on real data, experimental tests taken from literature are here considered. Data are taken from the recent paper [20] previously cited and such experimental data concern the fatigue tests on sharp notches, made of ductile cast iron, under multi-axial loading. Cylindrical specimens are made of EN-GJS400 cast iron with a circumferential V-notch. According to [20], the mechanical properties of the parent material are: YS = 267 MPa, UTS = 378 MPa and the Elongation to fracture equal to 11.5%. The reference fatigue strength of the parent material, under fully reversed, tensile and under torsional loading, are σ A = 150.4 MPa, τ A = 145.6 MPa. The notched specimens were tested under tensile, torsion, mixed in phase and out-of-phase fatigue loading. The main results are in Tab. 2. Tab. 2 shows the following parameters: R = Stress ratio; λ = nominal biaxiality ratio; φ= phase shift angle under combined loading. The Tab. 2 provides, as an index of the obtained results, the values σ A and τ A , i.e. the average strength at 2 millions of cycles to failure for the considered case. Figure 2 : Geometry of experimental specimens [20]. B [mm] D [mm] d[mm] α [°] r [mm] 200 20 6 90 0.1 Tab. 1 : Specimens size. F