pj -= aipj + a12 a16/j
qj a= 12 +a22 a26 (3.8)
For Plane stress,
1 1 V12 1
all E ; a22 22- a21 a12 --; a66 1 -(3.9)
Ell E22 El1 G12
For Plane strain,
-7 ,"I.,
aj = aj (3.10)
a33
Equation (3.2) is used to calculate the SIF at the crack tip by displacement
method; one of the most used methods to get the value accurately. Finite Element
Method was used to calculate the displacements at the crack tip. The commercial
software, ANSYS, was used for FEA modeling. The crack tip nodal displacements
were then extracted from FEA model and fed to the analytical equations explained
above to calculate all the three modes of SIFs.
Single Crystal Specimen Geometries Used for Mixed-Mode Loading. Two
specimen geometries were used to investigate the effects of mode mixity at the
crack tip. One was a rectangular tension specimen (Fig. 3-4 on page 29) with
a center crack loaded such that the crack lied in the {111} plane. The crack
directions used were (101) and (121) family of directions.
The second specimen modeled is a round Brazilian disk (BD) specimen, loaded
in compression. This specimen with center crack has a mode mixity at the crack
tip, which varies as function of the crack angle '0', shown in Fig. 3-5 on page 29.
The crack lies on the {111} plane and crack directions used are (101) and (121)
family of directions. These specimen and crack orientations have been checked very
carefully, based on experimentally observed fatigue crack growth rates (FCGR)
[39]. At low temperature (< 4270C(), the dominant mode of FCG in FCC single
crystal superalloys is crystallographic crack propagation on octahedral planes