If a crack surface is a slip plane, it is logical that the crack growth rate on that
slip plane will correlate with its RSSI.
Chen and Liu [57] proposed a crack driving force parameter for correlating
FCG data, which is based on the resolved shear stresses on the active slip planess.
This parameter may be better than AK for the correlation of FCG data since it
takes into consideration of the deformation mechanisms, grain orientation and the
actual crack path.
The resolved shear stress field of a slip system is defined by its intensity
coefficient, which can be calculated once the Mode I, II and III crack tip fields are
obtained.
The resolved shear stress is given by [58]
Tss = bibjjj (6.7)
where bi and b are the Burgers vector and its magnitude; nj is the unit normal
vector of the slip plane; and ryj is the crack tip stress tensor field given by [57]
[1yi] [Kf1 (0) + K1fi' (0) + Ki f i' (0)] (6.8)
where r and 0 are the local polar coordinates at the crack tip as shown in
the Fig. (6-4 on page 64); fij(0) are the angular component of the stress field.
Substituting equation (6.8) into equation (6.7), the resolved shear stress is
1
s ] [KIf' (0) + Ki f i (0) + Ki if"(0)][n ] (6.9)
where b' and nj are the unit Burgers vectors and unit normal vectors of the
slip planes respectively.
The above equation indicates that Trss preserves the 1//r singularity, and the
intensity of T,ss, is dependent on the (i i-I 1 orientation relative to the crack surface.
For a given crystal orientation and crack geometry, the angle 0 is equal to the angle