PSI - Issue 53

Andrea Zanichelli et al. / Procedia Structural Integrity 53 (2024) 3–11 Author name / Structural Integrity Procedia 00 (2019) 000–000

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4

After that, the critical plane orientation is determined and, finally, the fatigue assessment of the structural component analysed is performed according to the Carpinteri et al. criterion by employing the stress components acting on the critical plane at the verification point, P cr . 2.1. Methodology application to plain specimens In case of plain specimens without notches, the critical plane orientation is determined according to the original formulation of the Carpinteri et al. criterion (interested readers may refer to Carpinteri et al. (2015), Vantadori et al. (2020), and Vantadori et al. (2021a)). Moreover, the verification point P cr , where the fatigue assessment of the structural component analysed is performed, coincides with the hot-spot on the material surface. Then, the fatigue life, N cal , is computed according to the Carpinteri et al. criterion, by iteratively solving the following equation:

2

2

2 * m

2

m

m

   

     

σ

N

N

N

 

  

  

  

, 1 , 1 − −

af

0

cal

cal

2

2

(1)

N

C

σ

+

=

0 N N    

, eq a

, 1 −

a af

N

τ



0

af

cal

where , 1 af τ − are the fully-reversed normal and shear stress fatigue strength referred to N 0 loading cycles, respectively, m and m* are the slopes of the S-N curves under fully-reversed normal and shear loading, respectively, C a is the amplitude of the shear stress component lying on the critical plane, and , eq a N is given by: , 1 af σ − and

m N   u     σ

, eq a N N

a = +

σ

(2)

, 1 −

af

where a N and m N are the values of the amplitude and the mean value of the normal stress component acting on the critical plane, respectively.

2.2. Methodology application to notched specimens

In case of specimens containing notches, the critical plane orientation is determined according to a procedure based on the Critical Direction Method (Araújo et al. (2017), Araújo et al. (2020)). According to such a procedure, different material planes passing through the hot-spot itself and characterised by different orientations α (measured with respect to the notch bisector) are considered. Note that a suitable angular increment, α ∆ , between two different material planes needs to be set. An initial critical plane candidate is assumed, corresponding to an initial orientation 0 α = ° . The amplitude, ( ) a N α , and the mean value, ( ) m N α , of the normal stress component related to the critical plane candidate are computed in different equally spaced points, belonging to the segment starting from the hotspot and moving inside the component, up to a length equal to twice the average grain size of the material, 2d . Such values are then averaged along the critical plane candidate, thus obtaining ( ) a N α and ( ) m N α . Finally, the fatigue parameter, ( ) , eq a N α , related to the considered orientation is computed, in accordance with the Carpinteri et al. criterion, by means of the following equation:

  

  

N

( ) α

m

N

( ) α = + a N

σ

(3)

( ) α

, eq a

, 1 −

af

σ

u

Subsequently, a new orientation is taken into account (that is, another critical plane candidate is considered), and the procedure is iterated for all material planes inward the structural component analysed. The orientation, cr α , producing the maximum value of the above fatigue parameter is assumed as the critical plane.