Residual Strength and Fatigue Lifetime of ... - Solid Mechanics
Residual Strength and Fatigue Lifetime of ... - Solid Mechanics Residual Strength and Fatigue Lifetime of ... - Solid Mechanics
B 2 1/ 2 ( S44 S55 S45) (4.17) where S44, S55 and S45 are compliance elements given by 1 S 44 G 23 1 S55 (4.18) G 13 S45 is zero for on-axis directions but appears for off-axis directions if G13G23. The total strain energy release rate is given by G G G (4.19) I II Mode II III x deflection at the crack tip Figure 4.13: Definition of x, y and z at the crack tip. The decomposition of the strain energy release rate to two components of GI+II and GIII is considered more useful for practical applications due to a present lack of experimental characterisation aimed at measuring the effect of GIII in terms of crack growth rate. In all recent studies the main focus has been on measuring the crack growth rate under pure mode I, II or mixed-mode loading at the crack tip. Due to difficulties associated with the mode III loading of the crack tip, this component has always been neglected. Thus, in the numerical routine presented, only the GI+II component of the energy release rate is used in the crack growth algorithm. This may introduce inaccuracy in the debond growth simulation if the mode III energy release rate contribution is large. These possible inaccuracies will be discussed later in this chapter. Debonded sandwich panels consisting of 2 mm thick plain-woven E-glass/polyester face sheets over 50 mm thick Divinycell H45 PVC foam are considered the simulation. Face sheet and core material properties are similar to those of the sandwich beam specimen analysed earlier, as listed 78 Mode I y deflection at the crack tip Mode III z deflection at the crack tip
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 79
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B <br />
2 1/<br />
2<br />
( S44<br />
S55<br />
S45)<br />
(4.17)<br />
where S44, S55 <strong>and</strong> S45 are compliance elements given by<br />
1<br />
S 44 <br />
G<br />
23<br />
1<br />
S55 (4.18)<br />
G<br />
13<br />
S45 is zero for on-axis directions but appears for <strong>of</strong>f-axis directions if G13G23. The total strain<br />
energy release rate is given by<br />
G G G<br />
(4.19)<br />
I<br />
II<br />
Mode II<br />
III<br />
x deflection at the crack tip<br />
Figure 4.13: Definition <strong>of</strong> x, y <strong>and</strong> z at the crack tip.<br />
The decomposition <strong>of</strong> the strain energy release rate to two components <strong>of</strong> GI+II <strong>and</strong> GIII is<br />
considered more useful for practical applications due to a present lack <strong>of</strong> experimental<br />
characterisation aimed at measuring the effect <strong>of</strong> GIII in terms <strong>of</strong> crack growth rate. In all recent<br />
studies the main focus has been on measuring the crack growth rate under pure mode I, II or<br />
mixed-mode loading at the crack tip. Due to difficulties associated with the mode III loading <strong>of</strong><br />
the crack tip, this component has always been neglected. Thus, in the numerical routine<br />
presented, only the GI+II component <strong>of</strong> the energy release rate is used in the crack growth<br />
algorithm. This may introduce inaccuracy in the debond growth simulation if the mode III<br />
energy release rate contribution is large. These possible inaccuracies will be discussed later in<br />
this chapter.<br />
Debonded s<strong>and</strong>wich panels consisting <strong>of</strong> 2 mm thick plain-woven E-glass/polyester face sheets<br />
over 50 mm thick Divinycell H45 PVC foam are considered the simulation. Face sheet <strong>and</strong> core<br />
material properties are similar to those <strong>of</strong> the s<strong>and</strong>wich beam specimen analysed earlier, as listed<br />
78<br />
Mode I<br />
y deflection at the crack tip<br />
Mode III<br />
z deflection at the crack tip
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