PSI - Issue 33

3

Pietro Foti et al. / Procedia Structural Integrity 33 (2021) 482–490 Foti et al./ Structural Int grity Procedia 00 (2019) 000–000

484

UTS 2

σ

(1)

C W =

2E

Being UTS  conventional ultimate tensile strength. As stated above the SED value considered by the method must be averaged in a so-called control volume. This control volume has a characteristic length 0 R that is assumed to be a material property evaluable under plane strain and plane stress conditions as reported by (Lazzarin and Berto, 2005a, 2005b) and by (Yosibash et al., 2004) dealing with cracks:

2

  

  

K

(1 )(5 8 ) 4     

(2)

R

plane strain

IC



0



UTS

2

K     

  

(5 3 ) 4 

(3)

R

plane stress

IC



0



UTS

0 R can be determined as shown by (Lazzarin and

While, in the case of a sharp V-notch the characteristic length

Zambardi, 2001).

1 

1 

   

   

2 2(1 )

1 

2

  

  

  

  

I K 

I

K

1  2(1 )

R

(4)

1 1

1





C

C

1

0

1 4 (

)    

1 2 (

)     

EW

C

UTS

On the other hand, the shape of the control volume depends on the local geometry having a sector-shaped cylinder for sharp notches and a crescent moon-like shape in the case of blunt notches. The position of the control volume, instead, has to be determined according to the loading conditions: dealing with sharp notches, the centre of the sector shaped cylinder control volume is on the notch tip; dealing with blunt notches the control volume axis of symmetry has to be oriented in a way that the center of curvature of the notch and the first principal stress maximum lie belongs to it. An overview of the control volume of all the conditions enlisted above are provided in Figure 1 while for more considerations about the analytic frame of this method and its application we remand to (Berto and Lazzarin, 2014; Radaj, 2015; Radaj and Vormwald, 2013).

Figure 1: Control volume for a) Sharp V-notch; b) blunt V-notch under mode I loading; c) blunt V-notch under mixed mode loading; d) Crack; e) U-notch under mode I loading; f) blunt U-notch under mixed mode loading (Foti et al., 2021)