PSI - Issue 39

Daniela Scorza et al. / Procedia Structural Integrity 39 (2022) 503–508 Author name / Structural Integrity Procedia 00 (2019) 000–000

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work, two values of V are considered, as is listed in Table 1, that is:

3 1 2400 V mm = (specimen gauge region volume),

and 7 9 09 cr V . E mm = + (crankshaft volume). It is worth noting that, by increasing V , the probability to find bigger inclusions also increases, reducing, as a consequence, the values of the fatigue strengths computed in correspondence of ( ) 6 2 10 ⋅ loading cycles. Further, the experimental fatigue strengths are considered and reported in Table 1. 3

Table 1. Fatigue strength under normal and shear loadings by varying the control volume. Volume, V wl σ ( MPa ) wl τ ( MPa ) Exp. tests 375 282 V 1 =2400m 3 309 260 V cr =7.9E+09mm 3 274 231

4. The Carpinteri et al. criterion in conjunction with the area -parameter model The criterion proposed by Carpinteri et al. (Carpinteri et al., 2015; Vantadori et al., 2022) has been developed to estimate the high-cycle fatigue strength (either endurance limit or fatigue lifetime) of smooth structural metallic components submitted to any periodic proportional or non-proportional multiaxial loading. The main steps of the criterion are hereafter summarised. Firstly, the averaged directions of the principal stress axes, 1 ˆ , 2 ˆ , 3 ˆ , are determined on the basis of their instantaneous directions at the critical material point, P. More precisely, such axes coincide with the instantaneous principal directions corresponding to the time instant at which the maximum principal stress 1 σ achieves its maximum value during the loading cycle. Then, the normal w to the critical plane is linked to the direction 1 ˆ through an off-angle δ , defined as follows: ( ) 2 1 1 3 1 8 af , af , π δ τ σ − −   =  −    (3) to ( ) 6 2 10 ⋅ ) for fully reversed normal stress and for fully reversed shear stress, respectively. The multiaxial fatigue limit condition is expressed by the following non-linear combination of the equivalent normal stress amplitude, eq ,a N , and the shear stress amplitude, a C , acting on the critical plane: ( ) ( ) 2 2 1 1 1 eq ,a af , a af , N C σ τ − − + = with ( ) 1 eq ,a a af , m u N N N σ σ − = + (4) m N and a N are the mean value and the amplitude of the normal stress, respectively, and u σ is the material ultimate tensile strength. From Eq. (4), an equivalent uniaxial normal stress amplitude, eq ,a σ , is defined as follows: ( ) 2 2 2 1 1 1 eq ,a eq,a af , af , a af , N C σ σ τ σ − − − = + = (5) The finite life fatigue strength is computed by using Basquin-like relationships for both fully reversed normal stress, ( ) 1 0 m a af , f N N σ σ − = , and fully reversed shear stress, ( ) 1 0 m* a af , f N N τ τ − = . a σ is the amplitude of normal stress at fatigue life f N ; m is the slope of the S-N curve under fully reversed normal stress, a τ is the amplitude of shear stress at fatigue life f N and m* is the slope of the S-N curve under fully reversed shear stress. where 1 af , σ − and 1 af , τ − are the fatigue strengths (at a given number of loading cycles, 0 N , generally assumed equal where