Issue 32

N. Bisht et alii, Frattura ed Integrità Strutturale, 32 (2015) 1-12; DOI: 10.3221/IGF-ESIS.32.01 4 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)     θ 3 3 2 1 sin sin  2 3 cos cos 4 2 2 2 4 2 2 2 I II K K r r v k k G G                        (2) 2  sin  2 2 III K r w G    (3) 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