t-x
Crack Surface
Figure 6-4: Details of crack tip displacements and stresses at a distance r and 0
from the crack tip in the crack coordinate system
between the trace of a particular slip plane on the plane normal to the slip plane
and the horizontal axis. The intensity of Trs, is linearly proportional to the quantity
resolved shear stress intensity coefficient, K.s which for a given slip system can be
defined as the limiting value of the resolved shear stress, T.rs, multiplied by 27r,
as r approaches zero [56, 57]
Krs, = limia 8.v2r (6.10)
r--O
where r is the distance of the crack tip and Tr~, is defined as the projection
of the stress tensor [oa] on a plane whose outward normal is S in the direction of
slip b (Fig. 6-5 on page 65). The two distinct advantages in using K.rs are: (1)
the dependency of Tr-, on r is eliminated; (2) the angle 0 has a definite physical
ri ii. which is directly related to the orientation of the slip system.
Telesman and Ghosn [56] used the above model to calculate AKrs for 2-D
model and checked the validity of this parameter by plotting it against da/dN data
(Fig. 6-6 on page 65). Also AK for mode I has been plotted against da/dN to