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

in Table (4.1). The debonded panels are square with a side length of 310 mm. An elliptical
face/core debond with a short radius (b) of 45 mm and a large radius (a) of 76.5 is created at the
centre of the panel. 8-node isoparametric brick elements (SOLID45) are used in the finite
element model. Due to the current lack of suitable experimental fatigue crack growth rate data,
the crack growth rate vs. strain energy release rate is simply assumed to be constant for modemixity
phase angles larger and smaller than -10 degrees and chosen arbitrarily as
da
dN
da
dN
2
0. 000005GI
II
for >-10 (4.20)
2
0. 000002GI
II
for -10 (4.21)
where GI+II is the difference between maximum and minimum strain energy release rate in each
cycle and da/dN is the crack growth rate. The simulation is conducted in load control with a
maximum amplitude of 0.35 kN and loading ratio of R=Fmin/Fmax=0.1.
To investigate the distribution of mode I, II and III components of strain energy release rate and
mode-mixity phase angle along the debond front, radar diagrams from the analysis of the
debonded panels exposed to maximum amplitude of the fatigue load are shown in the following
figures. Debonded panels with a short radius of 45 mm and a ratio of large radius/short radius
(a/b) of 1.7, 1.4 and 1.1 are analysed. In the diagrams 0 and 90 degrees correspond to the points
on the debond front on the short and large radiuses of the ellipse. Figures 4.14 (a) and 4.14 (b)
illustrate the distribution of mode I+II energy release rate (GI+II) and the related phase angle in
the first cycle along the debond front. Maximum GI+II and mode-mixity phase angle occur at the
short ellipse radius because of smaller crack length and decrease towards the larger radius. This
can be attributed to the development of membrane forces in the face sheet at larger radiuses. As
the radius of the ellipse increases the membrane forces become larger, and a subsequently larger
part of the strain energy in the specimen should be used to stretch the debonded face sheet rather
than create new crack surfaces, decreasing the energy release rate at the crack tip. As the ratio
a/b decreases to one (circle) distribution of both GI+II and mode-mixity, the phase angle becomes
more even as expected. The mode-mixity phase angle for all a/b ratios is between -5 and -10
degrees along the debond front, which indicates a mode I dominated loading at the crack tip.
The mode III strain energy release rate along the debond front is shown in Figure 4.15. In the
symmetry plane (0 and 90 degrees) - due to the symmetry effect and the boundary conditions -
the out-of-plane deformation (crack plane) at the crack flanks is zero and consequently the mode
III strain energy release rate is zero. The maximum GIII on the panels with an a/b ratio of 1.7 is
almost 9% of the maximum GI+II , implying the importance of mode III loading at the crack tip in
the elliptical debond case with a large a/b ratio. The mode III strain energy release rate is very
small for the a/b ratio of 1.1 and is not shown in the diagrams. For debonds with a small a/b ratio
the debond is close to a circle and the mode III effects are insignificant. Figure 4.15 reveals that
the maximum mode III crack tip loading occurs close to the longer radius of the ellipse (around
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