Issue 57

M. Bentahar et alii, Frattura ed Integrità Strutturale, 57 (2021) 182-194; DOI: 10.3221/IGF-ESIS.57.15

 

K

K

1

1 4

 2 ) 8

I

I



(4)

tan( )

(

)

(

K

K

2 4

II

II

θ gives the direction of the maximum of the circumferential stress which determines the angle of bifurcation. Different parameters to characterize the singular zone The characterization of the singular zone subjected to several essential parameters, which makes it possible to study this zone such as, the stress intensity factor K and the integral of the contour J.

Figure 1: Singular zone meshing

Stress intensity factor Saverio [16] defined the stress intensity factor K, which is the only significant parameter, which allows to know the state of stress and strain at any crack point.

(5)

   I K F a

where, F is the geometric correction factor of the model used.

 3 4 1.12 0.23( / ) 10.6 / w 21.7 / w 30.4 / w F a w a a a           2

(6)

where the stress intensity factor K II is calculated by the relation.

 

  (3cos 1) 0

K

K

sin

(7)

I

II

Contour Integral J Several authors in fracture mechanics have allowed to model the problem of the presence of a crack in an in- depth way and have developed the calculation methods. Among these authors Rice [17] and Bui [18] with contour integrals (J), Nguyen [19] and Destuynder [20] by introducing an arbitrary field in the formulation of the integral they have approached. Indeed, work has been developed on the basis of elasticity in small displacements and mainly addresses the first phase of the cracking process. Relation betweenK and Jparameters In the fracture mechanics, we have two Eqns. (8) and (9) which allow to assemble the two parameters one obtains according to Tran [21]:

 

   dP J

1

2

(8)

K

I

I

da

E

 

   2 dP J

1

2 II

(9)

K

II

da

E

184