CHAPTER 3
SIF EQUATION FORMULATION FOR MIXED MODE LOADING
The stress intensity solution, for all the three modes for isotropic materials,
using crack tip nodal displacements method is given by [38]:
K, -= P 2 [4(vB _D) +vE V]
Kil P /2 [4(UB_ UD) + -E UC] (3.1)
K +1 L
Here u, v and w are the displacements of the nodes B, C, D and E at the crack tip
along x, y and z directions respectively. L is the length of the element at the crack
tip normal to the crack front (Fig. 3-1 on page 24).
These equations show that all three stress intensity factors KI, K1 and K111
are decoupled. For anisotropic materials it is not possible to use the same equation,
as their material properties are direction dependent. Because of this directional
dependence the stress intensity factor for the same material changes according to
the orientation of the crack plane with material orientation.
As has been discussed earlier, an orthotropic material has three independent
elastic constants, E, v and G. The elastic constants in material coordinate system
get transformed to specimen coordinate system by equation (1.7). The interde-
pendence of displacements in anisotropic materials due to shear coupling results in
coupled stress intensity factors.
Anisotropy was incorporated in the 3-D model to calculate SIF for mixed-
mode loading. It can be shown that mixed mode stress intensity factors can be