PSI - Issue 42

Diego F. Mora et al. / Procedia Structural Integrity 42 (2022) 224–235

231

8

Diego F. Mora et. al./ Structural Integrity Procedia 00 (2019) 000 – 000

For stationary cracks, the crack tip can be located wherever within an element. For a propagating crack it is required that the crack itself, completely cut an element and, as consequence, the crack tip cannot be located everywhere in the element but only at the element edge as shown in Fig 6(b). Under these considerations, it may be inferred that, once a crack starts to propagate, it will keep cutting completely each of the elements that it will go through. In other words, in propagating cracks, the crack tip motion cannot arrest within an element. This is illustrated in Fig. 6(b).

Fig. 6. Crack types in ABAQUS. (a) Propagating crack; (b) Stationary crack.

For the static crack, full enrichment with additional degrees of freedom is associated with the nodes of the element affected by the crack (Moës, Dolbow, and Belytschko 1999) and it is given by:

 

  

4

(3)

( )   x u i i N +

i  

( )

( ) ( )

( ) N F  x

( )

XFEM u x

x x a

x b

N H

=

+ 

i

i

i



1

i C 

i D 

i S 

=



Clasical

Discontinuity

Singularity

Enriched

where C is the set of all nodes in the mesh, ( ) i N x are the nodal shape functions and i u stand for the physical nodal displacement for non-enriched nodes at node i . The sets D and S contain the nodes enriched with the Generalized Heaviside function ( ) H x and the crack tip functions ( ) F  x , respectively, with i a and i  b being the corresponding degrees of freedom. For the propagating crack, the near-tip asymptotic singularity is not considered and therefore the partial enrichment is used, which is given by: ( ) ( ) ( ) ( ) XFEM i i i i i C i D Clasical Enriched N N H   = +   u x x u x x a (4) The calculation of the crack propagation is carried out by applying the maximum principal stress criterion 0 max  . c  , it is assumed that the material behaves according to the linear elastic fracture c  at each temperature from the fracture toughness for initiation given in Eq. (1) for the steel under consideration. The embrittlement due to the neutron irradiation is simulated by considering a shift towards higher temperature in the reference temperature NDT RT . The value of c r stands for the critical radius from the crack tip to the maximum principal stress, which is assumed to have a value of 300 m  . In Ref. (Yang et al. 2018) was reported 100 m  for an RPV steel. However, this value has to be related with the experimental material parameters in the planned thermal-shock experiments. mechanics theory. Thus, the relationship in Eq. (6) is employed to derive 0 max c    (5) To estimate the critical stress