Page 367 - Biaxial Multiaxial Fatigue and Fracture

Three-Dimensional Crack Growth: Numerical Evaluations and Experimental Tests 35 1

Stress Intensity Factors. Since Irwin [ 141 demonstrated the importance of the stress intensity
factor (SIF) in determining crack-tip stress fields in two dimensional problems, many different
methods have been devised for obtaining SIF's [15].
The stress intensity factors (SIF's) are computed using crack opening displacement method.
When one point formulae are employed, the Mode I, I1 and I11 SIF's are evaluated as:

where the displacement up is evaluated at point P as in Fig. 12; ubp, unP and ur are projections
of up on the coordinate directions of the local crack front coordinate system and 6=n and 6=-n
denote upper and lower crack surfaces respectively. Kp , KIP and KIIF' are approximations of
SIF's corresponding to the point P' along the crack front and on a normal line to the front as in
Fig. 12.

Fig. 12. Calculation of SIF using crack opening displacement.

During the crack growth, instabilities may cause peaks in the SIF values along the crack front.
It is advisable to enable the BEASY option that allows these peaks to be smoothed by either
smoothing the stress intensity factors or by smoothing the crack growth increment or by
performing both smoothing operations. This should also be used if the values computed at the
crack breakout points are not very accurate and give excessively high stress intensity factor
values, as it happens in the problem under study. As a matter of fact the asymptotic stress field
at the crack tip is usually obtained by performing analytical two-dimensional plane stress or
plain strain calculations. This yields the well known singularity which prevails along the
crack front within the body. However, at the intersection of the crack front with a free
boundary, the stress state is a genuine three-dimensional one for which two dimensional
P
approximations are not a plicable: the mode I stress singularity decreases at the free boundary
and takes the value r-0.45 ', whereas the mode I1 and mode I11 singularity increase in strength