3. Antiplane Shear loading
Txz Re
v2r cos 0 + [3 sin 0
T k- =k3 f Re n (B.5)
U 0
2r /VcoS 0 + [13 sil 0
w = k3 Re (B.6)
L C45 + /-3C44 J
where,
pj = all 2 + a12 a16/j
a22
qj = al2/j +- -a 26
'II
p/ and p2 are the two roots with positive imaginary parts as defined by the
equation
all 4 2aI6/_3 + (2a12 + a66)/2 2a26/ + a22 = 0
and p3 is the root of the characteristic equation [26]
a55/2 2a45p + a44 = 0
or [28]
C44 2 + 2c45/p + C55 = 0
The relative crack face displacement field equation (top face relative to the
bottom face, i.e. prime with respect to unprime as shown in Fig. 4-3 on page 34)
for the crack tip element is given by Manu and Ingraffea as [29],
Inplane crack opening displacement for Mode I loading
v = [2VB vc + 2VE -VF+VD+ -4VB+Vc+ 4VE VF) + 2(VF
+vc 2vD)] ) + [(T 1)(2B vc) (1 + T)(2VE VF)
(B.7)