Rasmus ÿstergaard forside 100%.indd - Solid Mechanics

Interface crack in sandwich specimen 311
Fig. 8 The curves show normalized lengths of the intact part of the sandwich specimen that gives 5% error in the energy release rate
calculated by (16)
Tvergaard and Hutchinson 1993). A detailed fracture
mechanical characterization of the interface would thus
include measuring interfaces under various mode mixities.
Inspired by Sørensen et al. (2006), we propose a test
set-up for measuring the interfacial fracture toughness
for face sheet/core debonding under mixed mode loading
conditions. The test is based on a double cantilever
beam sandwich specimen loaded with uneven bending
moments (DCB-UBM). The moments are applied by a
wire/roller system at the cracked ends of the specimen.
The uncracked end is supported by rollers maintaining
static equilibrium. Figure 9 shows a sketch of the test
set-up. The force in the wire is assumed to be the same
everywhere and the applied moments are then determined
solely from the wire force, F, and the moment
arms, ℓ1 and ℓ2. The ratio between the applied moments
are ℓ1 and this ratio is altered by changing the distance
ℓ2
between the rollers on each arm.
The imposed loading consists of the moments M1,
M2 and M3 = M1 − M2 and is a special case of the
load situation analyzed above (P1 = P2 = P3 = 0).
For this load combination the energy release rate is
G = c2
16h3
M2 1
− (M1 − M2) 2
.
I1
+ M2 2
I2
I3
The mode mixity is obtained from (17) where now λ
becomes
M1
V M2
λ =
U
C2 − C2
M1
M2 (C3
. (18)
− 1) − C3
As an example, consider an adhesive joint consisting
of aluminum adherents having the elastic constants
E2 = 70GPa, ν2 = 0.3 and epoxy adhesive with the the
elastic constants E1 = 7 GPa and ν1 = 0.3. Assume that
η = h/H = 0.1. Assuming plane strain conditions,
(2) and (1) give≈ 0.1 and β = −0.28 ≈ −0.3,
respectively. From Table 1 we find ω( = 0.1, β =
−0.3, η = 0) = 21◦ and from Table 2 we obtain
ω(0.1, −0.3, 0.2) = 32◦ . By linear interpolation between
these two values we find an estimate of the phase
angle ω(0.1, −0.3, 0.1) ≈ 26.5◦ .
Having determined ω, we obtain the load ratio parameter
λ from (18). Then, we can determine ψ for any
combination using (17). The mode mixity is shown as
function of the ratio between the moments in Fig. 10.
As a second example, consider a sandwich specimen
with a polymer foam core (E1 = 200 MPa, ν1 = 0.3)
and glass fiber face sheets (E2 = 40 GPa, ν2 = 0.3).
Assuming plane strain conditions, (2) and (1)gives≈
0.005 and β =−0.28 ≈−0.3. Here we assume η = 5.
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