PSI - Issue 53

4

Camilla Ronchei et al. / Structural Integrity Procedia 00 (2023) 000 – 000

Camilla Ronchei et al. / Procedia Structural Integrity 53 (2024) 112–118

115

Note that, being the defects generally more than a single one, it can be expected that the defect with the maximum square root area becomes the fatigue fracture origin. Therefore, the above equation is expressed in terms of the maximum value of n area , that is, max n area . To the best knowledge of the present authors, an equation formally analogous to the previous one is not available for the case of cyclic shear loading. Therefore, w  is here evaluated by exploiting the following empirical relationship proposed by Beretta and Murakami (2000):

0 855 w w .   = 

(2)

In order to compute w  , a defect content analysis has to be performed by applying a statistical method deriving from the Extreme Value Theory (Murakami (1994)), since it is virtually impossible to directly measure the area of the largest defect existing in a component. However, for the sake of brevity, the steps of the defect content analysis are not here reported. At the end of such an analysis, by setting the so-called prediction volume equal to the volume of the specimen gauge region, the final value of max n area turns out to be equal to about 441  m. The fatigue limit under cyclic normal loading w  is, hence, computed according to the Kitagawa-Takahashi diagram at a number of loading cycles equal to 1·10 7 . However, the experimental fatigue limit was taken at a number of loading cycles 0 N slightly lower than 2·10 6 . Consequently, by considering the S-N parameters in Tab. 1, the fatigue limit w  at 0 N turns out to be equal to 96.48 MPa. Finally, also the fatigue limit under cyclic shear loading, w  , is computed (according to Eq. (2)), resulting equal to 82.49 MPa. Once w  and w  are determined, the fatigue criterion proposed by Carpinteri et al. (2015) is employed for the fatigue strength assessment and the lifetime estimation. The main steps can be summarised as follows: - step (i): definition of the critical plane orientation by means of an empirical relationship, which is a function of the ratio between w  and w  ; - step (ii): evaluation of the normal, N , and tangential, C , components of the stress vector w S related to the critical plane; - step (iii): computation of an equivalent uniaxial stress amplitude, eq,a  , defined through a quadratic combination of the amplitudes of an equivalent normal component, eq,a N , and the shear component, a C , that is:

2

m    = +     a w u N 

w    +    w 

2

2

, eq a N N

with

(3)

N

C



=

, eq a

, eq a

a

where a N and m N are, respectively, the amplitude and the mean value of N ; - step (iv): for both infinite and finite life fatigue tests, definition of a fatigue endurance condition:

, eq a w   =

(4)

f N , according to the following equation:

- step (v): for finite life fatigue tests, estimation of the fatigue lifetime,

2 * m

2

m

m

2

*                     0 0 f w w f N N N N    

0   N     N f

(5)

N

C



+

=

2

2

, eq a

a

w

where m , * m ,

0 N and

* 0 N are parameters of the S-N and T-N curves, as is reported in Tab. 1.

4. Results and discussion

The results in terms of stress components on the critical plane, i.e. eq,a N and a C , are plotted in Fig. 3 by considering the fatigue limits w  and w  in the present procedure, whereas the results obtained by employing the experimental fatigue limits , 1 af  − and