PSI - Issue 25

Pietro Foti et al. / Procedia Structural Integrity 25 (2020) 201–208 Pietro Foti, Filippo Berto / Structural Integrity Procedia 00 (2019) 000–000

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4

2.2. Strain energy density method: basic concepts The strain energy density (SED) method, an energetic local approach, can be applied to investigate both fracture in static condition and fatigue failure by making the assumption that the brittle fracture occurs when the local SED W, evaluated in a given control volume, reaches a critical value C W W  that results to be independent of the notch opening angle and of the loading type as demonstrated by Lazzarin et al. (2001; 2002 and 2008). Dealing with an ideally brittle material, it is possible to evaluate the mean SED critical value through the conventional ultimate tensile strength t  :

2 t

σ

(1)

C W =

2E

The method can be also linked to other local approaches such as the NSIF approach. For more considerations about the analytic frame of this method we remand to Berto et al. (2014) and to Radaj et al. (2013). Regarding the control volume mentioned above, in plane problems, both in mode I and mixed mode (I+II) loading, it is a circle or a circular sector with radius 0 R respectively in the case of cracks and pointed V-notches, as shown in Fig. 2.

Figure 2: Control volume (area) for: a) sharp V-notch; b) crack.

0 R can be estimated both under plane strain and plane stress conditions as reported by Lazzarin et al.

The radius

(2005a and 2005b) and by Yosibash et al. (2004) dealing with cracks:

2

IC        t K

(1 )(5 8 ) 4     

(2)

R

plane strain



0

2

t     K  

(5 3 ) 4 

C   

(3)

R

plane stress



0

In the case of a sharp V-notch the critical radius can be assessed as shown by Lazzarin et al. (2001):

1 

1 

2 2(1 )

   

  

1 

2

  

  

1 K     C t   

I K 

I

1  2(1 )

(4)

R





1 1

1

C

0

1 4 (

)    

1 2 (

)     

EW

C