Issue 32

N. Bisht et alii, Frattura ed Integrità Strutturale, 32 (2015) 1-12; DOI: 10.3221/IGF-ESIS.32.01

Figure 4 : Crack tip meshing and different parameters.

Figure 5 : Nodes used for defining crack path.

The analysis uses a fit of the nodal displacements in the vicinity of the crack. The actual displacements at and near a crack for linear elastic materials are given by Paris [31] as:     3 3 2 1 cos cos  2 3 sin sin 4 2 2 2 4 2 2 2 I II K K r r u k k G G                         (1)







K

K

r

r

θ 2

3

3

  

 

  

  











2 1 sin sin k  



 2 3 cos cos k  

v

(2)

I

II





4 2 G

2 4 2 G 

2

2



III K r

2



w

(3)

 sin 



G

2

2

where: u, v, w = displacements in a local Cartesian coordinate system, shown in Fig.6. r, θ = coordinates in a local cylindrical coordinate system, shown in Fig.6. G = shear modulus K I , K II , K III = stress intensity factors relating to deformation shapes, shown in Fig.6. ν = Poisson’s ratio

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