Issue 53

A. Chatzigeorgiou et alii, Frattura ed Integrità Strutturale, 53 (2020) 306-324; DOI: 10.3221/IGF-ESIS.53.24





E' 2 π 8 L

E' 2 π 8 L



 











B C C 4u 4u u u B

B

C



   



(2)

K

4 Δ u

Δ u

II

1

1

1

1

1

1



     E' 2 π 8 1 v L 

E'

2 π



 







C C 4u 4u u u

B 3

B 3

B 3

C 3



   



(3)

K

4 Δ u

Δ u





III

3

3

8 1 v L 

where

 E E plane strain v  2

  E E plane stress 







1

B i i u u   

C C i i u u  

B

΄

C

΄

i Δ u

i Δ u

In the case of mixed-mode loading condition K I and K II , and in order to evaluate the crack propagation, an equivalent SIF ( eq K ), should be calculated, and compare it with the critical SIF (KIc, fracture toughness). This equivalent SIF can be evaluated from a number of criteria. In this paper, Tanaka’s (Eqn. (4)) [19] and Richard’s (Eqn. (5)) [20] criteria are presented and evaluated:

4

4

4 I II K = K +8K eq

Tanaka’s criteria

(4)

1 K K K 2 2



 2

(5)

2

  



1 K 

Richard’s criteria

4

eq

I

II

where a 1 =1.155 It is obvious that if K II =0, then K eq is equal to K I . The comparison of the two criteria, with fixed



I K to  

I K

MPa m

MPa m

100

0 160

and varying

, is presented in

I K K    , then the criterion of Richard gives higher results. For the calculation of eq K ,

Fig.2. It is obvious that when

inside the code, Richard’s criterion is taking into account.

Figure 2: Comparison of Tanaka's and Richard's criteria for the Keq [19,20].

The K III SIF has already been considered in various studies (for example Diaz et al. [21]). Since the verification models in our study are in mixed-mode I and II (see section ‘Verification of the code’), we have considered only K I and K II SIFs. The K III SIF may be also included in our code for out of plane sliding mode III (Fig. 12).

308