Here u, v and w are the nodal displacements of nodes B, C, D, E and F at the
crack tip relative to B', C', D', E', and F' as shown in Fig. 4-3 on page 34.
TI is the natural co-ordinate system value defined as
2z
S- -( + 1)
L2
L2 is the length of the element along the crack front (Fig. 4-2 on page 33) and
[B]-1 is defined as
Re [-' (q2
Re[ '(piq2
qi)] Re [ P (p2
291)2]' Re[ / (1P2
12P)] I
0
0
/C44C55 C(5
(3.5)
As it is apparent from the [B]-1 matrix that K, and KI1 are only
(function of u and v) and KII, is function of w only.
D is the determinant of the equation
coupled SIFs
Re\[---- (pip2
D R[ /1-2 (/1P2
Re[ 12 (pijq2
1^1-92 ^'li
/2Pl)] Re[ P2 (P2
2qi)] Re[ 1 2 (q2
pi)]
qil)]
/i1 and P2 are the roots of the fourth order characteristic equation
all/4 2aI6/p3 + (2a12 + a66)2 2a26p + a22 = 0
and given by
pij aj + i30,and fj > 0
(as pij can be only a complex no.[6]2 )
2 The fourth order equation formulation was followed from the work of Lekhnit-
skii [6], refer to Appendix A.
(3.4)
[B]-1
(3.6)
(3.7)