Chapter 2. Literature review
2.5 Previous research on impulse loading on honeycomb protected structures
2.5.3 Low-velocity impact studies on sandwich structures
focused on finding a suitable parameter to correlate with the fatigue strength data of the sandwich beams. The obtained local parameters from the interfacial stress demonstrated a better correlation with the fatigue strength data than the global parameters. They found that the local parameters based on the exhibited failure mechanism predicted the fatigue strength more accurately.
Figure 2.21 Representative image of debonding failure mode of the specimen under four-point cyclic bending (Jen and Chang 2008)
Tan and Sun (1985) employed an empirical Meyer’s power contact law to model localized contact stiffness of plastically deformable core. A semi-analytical technique was formulated by idealizing the composite structure with lumped spring and mass model (Choi 2006). Such approaches are material and geometric specific and require detailed material characterisation. For plastically deformable cores, the theoretical models tend to deviate from experimental observations (Bao et al. 2004; Fatt and Park 2001; Koissin et al. 2004; Koissin et al. 2004).
Figure 2.22 Representative schematic of response types during impact on plates: a) very short impact times, b) short impact times, and c) long impact times (Olsson et al. 2006)
Fatt and Park (2001) developed the analytical model for the prediction of transient deformation response of composite sandwich panels subjected to low-velocity impact.
To predict the low-velocity impact response, they employed equivalent single and multi-degree of freedom systems. They predicted the impact response for different boundary conditions of sandwich panels, i.e., four-sided clamped, simply supported, two-sided clamped, and rigidly supported. They considered the facesheets as orthotropic and symmetric. The equivalent masses were derived by assuming velocity distributions and computing the kinetic energies in terms of global deflection of sandwich panel and top facesheet indentation. Most of the available literature states that the indentation load at failure and damage characteristic features were acquired from the static indentation tests. However, the recent studies on the impact show that the peak impact force at damage instigation is slightly higher than that of static indentation due to the strain rate sensitivity in the core and facesheet along with the inertia of projectile and sandwich. The key point of their analytical studies is to consider the projectile and sandwich panel inertia along with the strain rate sensitivity of core and facesheet materials in the low-velocity impact response.
The load-indentation behavior can be obtained by using principle of minimum potential energy. Therefore, the total potential energy
Π isΠ U D V- (2.27)
where,
‘Π’ is the strain energy due to bending,
‘D’ is the work due to the crushing of core
‘U’ is the total strain energy Very short impact times
a)
Response dominated by dilatationalwaves
short impact times Long impact times
b)
Response dominated by flexuralwaves
c)
Quasi-static response‘V’ is the work done by the indentation force
Furthermore, the local indentation was assumed due to the bending as follows
2 2 2
2 2
2 2
2 2 2 2
for 0 +
( , ) 1 1
for + , 0, 0,
x y R
x R y R
w x y
R R
R x y x y
(2.28)
where,
‘ ’ is the deflection under the indenter,
‘ ’ is the lateral extent of the deformation zone,
‘R’ is the radius of the indenter,
The strain energy due to bending of the orthotropic facesheet is
2 2 2
2 2 2 2 2
11 2 22 2 12 2 2 66
s
1 2 4
2
w w w w w
U D D D D dA
x y x y x y
(2.29) where,‘Dij’ is the laminate bending stiffness matrix,
‘dAdxdy’, A is the surface area of the deformed facesheet,
Meo et al. (2005) presented the honeycomb sandwich panel behavior under low- velocity impact loading. They conducted the studies on both the experimental and numerical investigation of sandwich panels subjected to impact damage. They employed the test panels from the engine nacelle fan cowl doors of a large commercial aircraft and conducted the low-velocity impact study at five energy levels, ranges from 5 J to 20 J. They studied various parameters such as failure mechanism, damage initiation, and damage propagation of the sandwich panels. They noticed that the conducted energy levels cause barely visible impact damage (BVID) in the top facesheet of the test specimen. They performed numerical simulation using LS-DYNA3D transient finite element analysis for the computation of the contact forces, load distribution, failure analysis, and the impact damage initiation, and delamination. They successfully predicted the impact energy absorption of the sandwich panel and the extent of impact damage. They achieved a good agreement in the validation of numerical results with experimental results. From the experimental results, they suggested that a perfect numerical model can give substantial information for the designer to understand the mechanism of low-velocity impact which help to design a proficient impact resistant aircraft structure.
Yu et al. (2008) performed quasi-static and impact experiments on the Aluminum- foam core. Bending deformation and modes of the impact velocity under 5 m/s follows the similar pattern subjected to quasi-static loading. The representative image showing the impact damage areas after impact and the samples sectioned at impact location for the floor sandwich specimens can be seen in Figure 2.23. A theoretical model was
developed using Gibson’s model for the prediction of failure modes and had good
Figure 2.23 Representative image: a) impact damage areas after impact, and b) samples sectioned at impact location for the floor sandwich specimens (Shin et al. 2008)
agreement with the experimental results. Several other researchers also worked on conducted low-velocity impact studies on different sandwich structures which were used in the Korean low floor bus (Shin et al. 2008). Sandwich structures are made of Aluminum and balsa core with woven glass fabric facesheets and Aluminum and balsa core with Aluminum facesheets. Using a three-dimension scanner, the damage location and depth of indentation was quantified. Impact test results show the woven glass fabric sandwich panels have less impact damage compared to Aluminum facesheet panel with Aluminum core. Series of experiments were conducted to evaluate the damage resistance of sandwich panels for the combination of carbon and glass facesheets with Nomex core (Park et al. 2008). The damage was investigated using scanning acoustic microscope (SAM).
Castanié et al. (2008) developed a discrete mass approach for the evaluation of static indentation on core and sandwich panels. It can predict the contact force subjected to low-velocity impact on metal skinned sandwich structures. They considered the interface effect between facesheet and honeycomb core in their model.
They suggested that the direct application of their model enabled the contact law when skinned sandwiches were subjected to quasi-statistic load. They found that the model demonstrated highly accurate correlation during indentation tests and three-point bending tests.