Residual Strength and Fatigue Lifetime of ... - Solid Mechanics

Figure 4.12: Orthogonal mesh at the debond front.
The mode I+II strain energy release rate, GI+II, and the associated mode-mixity phase angle, I+II,
are determined from relative nodal pair displacements, obtained from the finite element analysis
using the CSDE method, as outlined in the introduction. The mode I+II energy release rate and
the related phase angle are given by
2 14 H11
2
G
I II
GI
GII
y x
8H11x
H 22
2
77
(4.14)
1
tan H 22 x x 1
I II
ln
tan 2 (4.15)
11
H y h
where y and x are the opening and sliding relative displacement of the crack flanks (see Figure
4.13), H11, H22 and the oscillatory index are bimaterial constants determined from the elastic
stiffnesses of the face and core, see the introduction chapter. h is the characteristic length of the
crack problem. h has no direct physical meaning. Thus, it is here arbitrarily chosen as the face
sheet thickness.
To investigate the effect of mode III loading at the debond front, the mode III strain energy
release rate, GIII, is evaluated. The mode III energy release rate is given by (Suo, 1990):
G
III
2
z
8x( B1
B2
)
(4.16)
where z is the out-of-plane (crack plane) relative displacement of the crack flanks as shown in
Figure 4.13, and x is the distance of the nodal pairs from the crack tip as shown in Figure 4.13.
Subscript 1 and 2 refer to two materials in a bimaterial interface, and B is the inverse of an
equivalent shear modulus given by (Suo, 1990):