PSI - Issue 21

Hakan Şahin et al. / Procedia Structural Integrity 21 (2019) 38–45 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

40

3

calculation, since no special element division or mesh is required around the crack front and no further post-processing after the solutions are needed; Ayhan and Nied (2002). Displacements of enriched elements are given in Eq.1-3. In these equations, unknown nodal K values are added to regular nodal unknown displacements in the isoparametric finite element formulation. N j (ξ,η,ρ) are the shape function. K I (Г), K II (Г) , K III (Г) are respectively mode-I, mode-II, mode-III stress intensity factor variations along element edge located on the crack front (Fig.1). Details of the formulation can be found in Ayhan and Nied (2002).

r



( , , )   

( , , )   

( , , ){ ( ) ( , , ) K F       

u

N

u Z 





0

1

j

j

ı

(1)

1

j



( ) ( , , )    

( ) ( , , )},   

K G

III K H

 

1

1

II

r



( , , )   

( , , )   

( , , ){ ( ) ( , , ) K F       

v

N

v Z 





0

2

j

j

ı

(2)

1

j



( ) ( , , )    

( ) ( , , )},   

K G

III K H

 

2

2

II

r



( , , )   

( , , )   

( , , ){ ( ) ( , , ) K F       

w

N

w Z 





0

3

j

j

ı

(3)

1

j



( ) ( , , )    

( ) ( , , )}.   

K G

III K H

 

3

3

II

Fig. 1. shows a 20-noded quadratic hexahedron element with three nodes along the crack front. According to the mesh sensitivity study, the effect of the crack tip element size on the solution was investigated and it was seen that a /400 gives converged results.

Figure 1: An arbitrarily oriented 20-node enriched crack tip element, Ayhan (2004).

The parameters affecting the SIFs at the crack front are the crack depth with respect to thickness of plate ( a/t), the crack aspect ratio ( a/c ) and the crack inclination angle, β . If the crack inclination angle with the horizontal axis is zero degree, the shear and tear components of the SIF are zero and the mode-I stress intensity factor, which is the mode of opening, is active. However in the other cases where the crack inclination is different from zero, the shear (mode-II) and tear (mode-III) modes of the SIF are also active and must be calculated. For this purpose β = 0, 15, 30, 45, 60, 75 degrees, which is the crack inclination angle with respect to the horizontal axis are considered. The angle θ is the positional angle on the crack front. As can be seen in Fig. 2 the crack inclination angle varies from 0 to 180 degrees.