PSI - Issue 79

D. Marhabi et al. / Procedia Structural Integrity 79 (2026) 34–52

47

      

  

  



1

1 2



1













0 8        2



1





1

1



(1

)

(25.b)





and

 





1

1

0

2

   



1



1

max( ) RB n E E n   

The damage indicator of the Robert criterion is:

B - Global Criteria The global criteria are based on invariants of the stress tensors, which make it possible to reduce a tensor variable to a scalar quantity, and to establish equivalences with uniaxial loadings. In general, these criteria do not make it possible to predict the orientation of crack, however some of them, which use the first invariant of the stresses and the second invariant of the deviator tensor. Sines criterion [17] First established in 1955, this criterion was modified by its author in 1981 in order to express it as a function of the invariants of tensor and its deviator. It therefore only takes into account the alternating octahedral cission and the hydrostatic pressure 1 2 1 0 1 1 2 3 a m SI J I with A A E                  (26) The author is using the results of multiaxial tests by Cough et al [16] and his own biaxial tests. Kakuno K. -Kawada K. criterion [18] The Kakuno-Kawada criterion distinguishes the influences of the amplitude and the mean value of the hydrostatic pressure as well as the second invariant of the alternating parts J 2a by the deviating tensor.

Figure 7: Representation of Kakuna and Kawada criterion

  

  

  

2 1   

3   



1

P    P



J

a

Hm Ha

2



0

1



(27)

with

E

1      

KK





  

and

3

3



1

 





1





1 2

1

The validity of the criterion is imposed the conditions α > 0 and β > 0, is: 1 



1





and





3



0

1