Chapter 2. Literature review
2.5 Previous research on impulse loading on honeycomb protected structures
2.5.2 Impulse response of honeycomb composite
The above fundamental concepts are employed to understand the interaction of impacting body on elastic substrate. Based, on the impact dynamics, literature review of theoretical aspect of low-velocity and high-velocity impact on composite material is conducted.
indentation contact area and pressure distribution in the experiments is challenging as no measuring devices are available to overcome it. They presented an analytical model that provides the three-dimensional stress and displacement along with the contact area and pressure for a composite panel indented by a rigid sphere. For the accuracy verification, a series of quasi-static indentation tests were conducted on graphite/epoxy foam sandwich panels with a different combination of material properties, core, and facesheet. They confirmed the proposed analytical model by comparing the measured force-indentation and predicted values. The validated analytical predictions with experimental indentation results are found to be in remarkable agreement.
Hazizan and Cantwell (2003) conducted the indentation test and shear tests on two Aluminum honeycomb sandwich structures to study strain rate sensitivity. They observed that the flexural modulus of the facesheets and shear modulus of Aluminum honeycomb core failed to exhibit strain rate sensitivity at low-velocity impact. A series of static and dynamic three-point bending tests were conducted on Aluminum foam sandwich panels (Crupi and Montanini 2007). It was found that impact velocity under 1.2 m/s failed to exhibit strain rate sensitivity.
Olsson et al. (2006) derived the delamination threshold load criterion for the transversely isotropic plates subjected to small mass with high-velocity impact. They employed a closed-form approximation for the prediction of peak impact load and delamination threshold velocity. They focused on deriving the delamination threshold load for small mass with high-velocity impact for transversely isotropic plates that were regularly distributed laminates in at least three directions. The quasi-static impact experiments show that the delamination growth in the panel occurs with a rapid decrease in load. They found that the parameters like thickness, contact stiffness play a vital role in predicting the delamination threshold velocity. They considered a hemispherical impactor indenting on a thick isotropic elastic plate having thickness (h) with contact load (F).
A first-order approximation for the approach
between the impactor and the plate under small curvature was derived by Suemasu et al. (1994),23
* H
F
k
(2.22)
23
* H
F
k
(2.23)
where,
*
1 2 32
3 3
1 ln 2 0/
H H
H
k k
F k K h
They validated the theoretical model for a wide range of tests with 3D finite element model simulated using commercial package LS DYNA. They showed the anticipated
delamination threshold loads, and velocities are in excellent agreement with experimental and numerical results.
Zhou and Stronge (2006) proposed an analytical model for lightweight circular sandwich panels subjected to low-velocity impact. They studied the damage mechanism and impact response of Hybrid Stainless Steel Assembly (HSSA) lightweight sandwich panel with simply supported boundary conditions. A representative schematic of spherical ball striking at the center of the sandwich panel and its insight view of indentation is shown in Figure 2.20. They arrived a localized indentation law based on the assumption that the facesheets remain elastic and the core is rigid-perfectly plastic under quasi-static compression. It was evident that the low-velocity impact by a small mass exhibits residual dent without perforation of fibrous core sandwich panel which has thin facesheets. The dent of the facesheet mainly depends on the kinetic energy and the nose shape of the impactor as well as the mass density of the sandwich panel.
They conducted a series of impact experiments on fibrous core sandwich panels with varying sizes impacted by the spherical bodies at low velocities. Further, a detailed numerical investigation was conducted using finite element analysis to estimate the impact damage on HSSA lightweight sandwich panels. It was observed that the damage depends on both the structural parameters of the panel and impact variables. They developed a contact relation for the lightweight sandwich panel that incorporates the effect of local membrane stretching of top facesheets. For the cases where the indentation depth on the top facesheet is lesser than that of the core thickness, the force indentation relation varies linearly. Based on the contact relation, they proposed the analytical models for the quasi-static and dynamic behavior of the sandwich panels to evaluate the impact force when subjected to low-velocity impact on sandwich panels.
Figure 2.20 Representative schematic of spherical ball striking: a) center of the sandwich panel, and b) insight view of indentation (Zhou and Stronge 2006)
From the Figure 2.20, the profile of the local indentation of the upper facesheet can be characterized by,
0 1 r22 2r a
(2.24)
where,
‘0’ is the central transverse deflection
‘a’ is the radius of the local indentation region on the upper facesheet
a) b)
Thus, the total potential energy can be given as,
1 2 1 2
Π = V V U U (2.25)
where,
‘V1’ is flexible strain bending energy
‘V2’ is strain energy due to membrane stretching
‘U1’ is the work done by crushing force
‘U2’ is the work done by the contact force
In order to obtain the contact force, the total potential energy is minimized with respect to the central deflection, i.e., Π/ 0 0
2 2 2
0 0
2 2
64 (7505 4250 2791 )
3 1 17640 3
f
f
D v v qa
P a h
(2.26)
where,
‘Df’ is the diameter of the facesheet
‘hf ’ is the facesheet thickness
‘q’ is the yield stress of the core
‘P’ is the contact force
‘v’ is Poisson’s ratio
Jen and Chang (2008) conducted an experimental study on the four-point bending test of honeycomb sandwich beams with varying core densities. They evaluated the bending fatigue strengths of Aluminum honeycomb sandwich beams. The representative image of debonding failure mode of the specimen under four-point cyclic bending can be seen in Figure 2.21. They considered numerous local and global parameters for the evaluation of fatigue life of sandwich beams under cyclic four-point bending. The primary failure was identified as the debonding of the adhesive between the facesheet and the core. A finite element approach was employed by considering the geometry and dimensions of the adhesive to obtain the local stress and strain. They identified that the predicted locations of debonding initiations using circular-shaped combined interfacial stress parameters were identical with the observed fatigue experiments. Furthermore, there is a lack of systematic research on the fatigue strength of Aluminum honeycomb sandwich beams, and they conducted the experimental study on bending fatigue characteristics of Aluminum honeycomb sandwich beam. They observed that the failure mode of the honeycomb sandwich beam subjected to cyclic bending was debonded between the facesheet and the adhesive. The parameters such as global shear stress and bending stress failed to correlate with the fatigue strength of different types of test specimens due to the global parameter’s failure mechanism. They
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)