Rasmus ÿstergaard forside 100%.indd - Solid Mechanics

Interface crack in sandwich specimen 307
Table 1 Load-independent phase angle ω (in degrees) calculated for different values of the mismatch parameter and β for η = 0
β = 0.1 = 0.05 = 0.01 = 0.005 = 0.001
0 34 29 20 17 13
−0.1 31 28 23 21 19
−0.2 27 25 22 21 21
−0.3 21 20 18 17 18
−0.4 14 12 11 10 10
Fig. 5 The shift angle
ω ∗ = ω + γ − 90 ◦
determined for sandwich
specimens with thin core.
The dashed line shows the
extrapolation to η = 0
through the values found at
η = 0.1 andη = 0.15
ω ∗ [ ◦ ]
η = h/H
α = 0.8
α = 0.4
α = 0.0
Table 2 The phase angle ω (in degrees) computed with different values of the mismatch parameters and β for a specimen with
thickness ratio η = 0.2
β : 0.5 0.1 0.05 0.01 0.005 0.001
α: −1/3 −1/2
−0.4 27.1 26.1 24.4 23.9 23.0
−0.3 34.6 34.2 31.8 30.5 28.5 27.6 26.4
−0.2 39.7 38.9 35.7 33.9 30.8 29.9 28.4
−0.1 44.2 43.1 38.6 36.1 31.5 30.2 28.0
0.0 48.3 46.7 40.1 36.0 27.7 24.8 19.7
our method, is plotted as function of η for three values
of α and with β = 0. The dashed lines indicate linear
extrapolation to η = 0 using the values found at η =
0.15 and η = 0.1. The results from Suo and Hutchinson
(1989)areω ∗ (α = 0) = 0 ◦ , ω ∗ (α = 0.4) =−4.7 ◦
and ω ∗ (α = 0.8) = −14.3 ◦ . Our results agree with
them with an accuracy better than 0.5 ◦ .
4.3 The phase angle, ω, calculated for sandwich
specimens with finite core thickness
Tables 2–9 present ω for a wide range of material combinations
and face sheet/core thickness ratios relevant
for engineering purposes.
Some selected results are shown in Fig. 6; ω is shown
as function of and η. First, focus on the result for
β = 0 (solid lines). With β = 0 it follows from (4) and
(7) that the real and imaginary parts of the complex
stress intensity factor reduce to classical mode I and
mode II stress intensity factors. Then, ω can be understood
as the phase angle of classical stress intensity
factors for a specimen loaded with an axial force, so
that ω = 0 ◦ corresponds to pure mode I and ω = 90 ◦
is pure mode II. For close to unity, ω is not very
sensitive to η; indeed, for → 1 the results for all η
appear to converge towards the same value. This value,
ω = 49.1 ◦ , which is shown by an arrow in Fig. 6,isthe
value obtained for the symmetric, homogeneous DCB
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