IMPACT ENERGY ABSORPTION IN NOVEL, LIGHTWEIGHT SANDWICH
PANELS WITH METALLIC FIBRE CORES
J. Dean1, P. M. Brown2 & T. W. Clyne1
1. Department of Materials Science and Metallurgy, University of Cambridge, Pembroke
Street, Cambridge, CB2 3QZ, [email protected]
2. Dstl, Porton Down, Salisbury, [email protected]
ABSTRACT
The impact perforation of a novel type of sandwich panel has been studied experimentally and numerically. The sandwich
panels were composed of thin (0.4 mm) stainless steel faceplates sintered to a core of randomly oriented, slim metallic
fibres (type 304 stainless steel). The overall sandwich panel thickness can vary between 1.5 and 2 mm, which allows them
to be handled and processed in a similar way to monolithic metal sheet. The panels are known to exhibit high specific
bending stiffness [1], and are readily resistance weld-able [2]. Structures of this type are potentially attractive for industries
requiring lightweight, stiff panels with good vibration damping and energy absorbing characteristics. Their ability to absorb
energy when impacted is the subject of the present investigation. The results indicate that the presence of the fibre
network core material inhibits faceplate deformation such that the specific absorbed energy of the faceplates alone is
slightly higher than that of the sandwich panels. In order to inform their future design, numerical models are being
developed that serve to predict the energy absorbed during perforation. Using the finite element code ABAQUS/Explicit a
faceplate material model has been developed which accounts for both strain and strain rate hardening effects. The
fracture process is well captured using a critical strain failure model, providing reliable quantitative agreement and realistic
qualitative agreement. A simplified core material model that neglects the effects of anisotropy and cellular behaviour is
found to be too crude to reliably model the core behaviour. A more rigorous core modelling approach is required and one
such methodology, which utilises fibre network reconstructions obtained from X-ray micro-tomography, is discussed.
Introduction
There is a requirement, across many industries, for materials and/or structures that are suitable for impact and
crashworthiness applications. These materials must also satisfy the demands of manufacture (joining, forming etc.), as
well as those of cost. Sandwich panels, potentially, can fulfil these demands provided the correct core and face materials
are chosen.
An all-metal, lightweight sandwich panel, recently developed, incorporates an open network of sintered metallic fibres in
the core [3]. The sandwich panels are comparatively thin, being approximately 1.5 - 2 mm thick. The faceplates are
stainless steel (type 304) and are 0.4 mm thick. The fibres are melt spun stainless steel, approximately 5 mm in length
with a cross sectional diameter that varies between 60 and 100 microns. Some sandwich panel mechanical property data
have been reported elsewhere [1, 4], as have their resistance welding characteristics [2]. The core material has received
attention also, in particular the use of X-ray micro-tomography to characterise architectural features such as distributions
of fibre segment inclination angle [5]. Such characterisation is important, as the architecture of these sintered fibre
networks has been shown to influence their mechanical properties [6]. Novel uses for this core material, such as magnetomechanical bone growth stimulation have also been proposed [7]. However, it is suggested here that this material may
have characteristics that make it a suitable candidate for applications involving impact and crashworthiness. Attention here
is focussed on the energy absorbed during low velocity ballistic impact.
Previous studies have already highlighted the energy absorbing potential of sandwich panels [8-13]. Currently, however,
there is little available literature concerning the response of sandwich panels with metallic fibre cores to low velocity
impact. That of Zhou and Stronge [14] reports the results of low speed impact experiments on a Hybrid Stainless Steel
Assembly (HSSA), which incorporates vertically aligned metallic fibres sandwiched between thin steel faceplates (type
316), bonded using a structural adhesive. Their report is restricted to localised surface damage and does not include
penetration or perforation phenomena. They develop an analytical model that successfully predicts the contact force on
circular sandwich panels. They also modelled the residual indentation depth using ABAQUS, but noted that a suitable
material model for the core was unavailable.
In this paper, attention is focussed on the energy absorbed during full penetration by spherical projectiles and the
subsequent effects of increasing impact velocity on overall absorbed energy. Impact tests have been conducted on the
sandwich panel components, which allows for a quantitative evaluation of the respective contribution to energy absorption
afforded by the core and the face materials. Numerical simulations have then been conducted on a faceplate material
model and on a sandwich panel model.
Materials and Specimen Production
The sandwich panel faceplates are stainless steel (type 304) and are 0.4 mm thick. Experimentally determined mechanical
properties are shown in Table 1 and are used subsequently to calibrate the finite element faceplate material model. Tests
were conducted using a 10 kN ESH servo-hydraulic testing machine at a displacement rate of 0.01 mm/s. The fibres are
rapidly produced by direct solidification from the melt (type 304) onto large rotating drums with precisely machined surface
patterns that are used to tailor the fibre dimensions. In this case, the fibre length is ~5 mm. The fibres have a non-uniform
cross sectional area (approximately 60 - 100 µm in diameter) and are predominantly crescent shaped through their
section.
Table 1 – Measured Mechanical Properties for Type 304 Stainless Steel
Elastic Stiffness (GPa)
Yield Stress (MPa)
Ultimate Tensile Strength (MPa)
Fracture Strain
195
270
740
0.33
Sandwich panel manufacture involves sieving the fibres onto a single faceplate. This method of fibre distribution is known
to impart transverse isotropy to the core, with a plane of isotropy perpendicular to the faceplate normal [5]. The relative
density of the core is ~0.10 but can be increased to ~0.30 through the application of pressure during the manufacturing
process. A second faceplate is added once the desired core thickness has been achieved. The sandwich panel
components are then bonded by sintering in a vacuum furnace at 1195°C for 1.5 hours followed by gas quenching.
Impact Testing
Impact test specimens were cut using an Electric Discharge Machine (EDM). The impact specimens, 76.5 mm diameter,
were rigidly clamped (such that 60 mm of the 76.5 mm diameter was exposed). The specimens (faceplates, isolated core
material and sandwich panels) were impacted at normal incidence and sub-ordnance velocities by hardened, spherical
steel projectiles of 2 g mass and 8 mm diameter. Incident velocity was measured using a series of light gates comprising
three light emitting diodes and three light receiving photodiodes. The residual velocity was measured using an
electromagnetic induction technique whereby the moving (magnetic) projectile induced a current in two spaced copper
coils. The time between electrical pulses was recorded and the projectile velocity calculated. After penetration, the
impacted specimens were sectioned using the EDM.
Finite Element Modelling
Faceplate Material Modelling
Some well known plate perforation models are compared to data with varying degrees of success in [16]. Included is that
of Recht & Ipson [15], which is based on momentum conservation and frequently cited in the literature. Empirical
approaches to the problem are reviewed in [17]. Unfortunately, these models reveal little about the physical processes
occurring during penetration and are therefore somewhat limited in scope and usefulness. For this reason, investigations
of this type are predominantly experimental in nature although the increasing sophistication of explicit finite element codes
may prompt a change in this trend. However, modelling large deformations at high rates of strain is complex, and dynamic
material behaviour must be considered. Problems from excessive mesh distortion and evolving contact are common in
such analyses. Advanced numerical methods, i.e. adaptive re-meshing, can minimise or eliminate these problems,
although computation time is often compromised. It should also be emphasised that the accuracy of the material models,
the material data and the numerical simulations themselves, can significantly affect the results.
Most recently, Gupta et al [18] simulated a series of penetration experiments conducted on 1 mm thick aluminium sheets.
Their numerical analysis used a Johnson-Cook elasto-viscoplastic model available in ABAQUS/Explicit. Their model
successfully predicted the residual velocities of penetrating projectiles, as well as plate ballistic limits (minimum perforation
velocities). The qualitative agreement between the simulations and the experiments was also encouraging when the
Johnson-Cook failure model was employed. It appears, from the literature, that the Johnson-Cook plasticity and failure
models are well suited to capturing the major quantitative and qualitative features of the penetration process. This is
confirmed in a comprehensive series of numerical studies dealing with the ballistic penetration of steel and aluminium
sheets by Borvik et al [16, 19-22]. In all cases, Johnson-Cook constitutive equations, or modified versions of, were used to
analyse the response of steel and aluminium plates of varying thickness to localised ballistic impact. They report that the
simulations agree in most cases reasonably well with experimental data, particularly at high velocities, large mesh
densities and when using an adaptive re-meshing algorithm.
It is common in analyses of this type to assume axisymmetric behaviour. However, and unlike previous numerical studies
involving the penetration of monolithic metal plates, a 3-dimensional model is described herein. This was deemed
necessary since failure was observed to be non-axisymmetric during experiments. Mesh density was refined in the region
of most interest, i.e. directly beneath the projectile. Having a refined mesh in this region prevents the mesh from being
coarse relative to any impact induced strain gradients which had previously caused the simulations to prematurely abort.
No further distortion problems were encountered during the modelling process and no adaptive re-meshing algorithms
were initiated during the simulations.
The steel faceplates were modelled as elastic-plastic solids with isotropic hardening. Plate material data was obtained
from uniaxial tensile tests, Table 1. Two types of element formulation were considered. Firstly, 3-dimensional linear
hexahedral elements with reduced integration – type C3D8R, were used. Secondly, linear quadrilateral shell elements –
type S4R were used. It has been reported [18, 19] that the number of elements in the through-thickness plate direction is
important, yet here, where the 3-dimensional solid elements were employed, there was only a single element in the
through-thickness plate direction. It will later be shown that the results compare well to experimental data. This is no
doubt helped to some extent by the low plate thickness (0.4 mm), which is 2.5 times thinner than the plates described in
[18] and 30 times thinner than those in [20].
Despite the assertions of Borvik et al [19], that projectile plastic deformation is an important parameter during structural
impact problems, the projectile was modelled here as an analytical rigid body and simply assigned mass. Penalty contact
was defined between the projectile and the plate. The difficulties associated with evolving contact were overcome using
the ‘general contact’ algorithm in ABAQUS/Explicit. Friction effects were ignored throughout the analyses.
The rate dependence of the stainless steel faceplates was modelled using yield stress ratios, such as those described in
[24], based on data collected in [23]. The flow stress
to the quasi-static flow stress
σ0
σd
(at some plastic strain
at the quasi-static strain rate
ε0
ε p and plastic strain rate ε p )
through a yield stress ratio
R
is related
which is a function of
plastic strain rate. This prescription is given by:
σ d ( ε p , ε p ) = R ( ε p ) σ 0 ( ε p )
(1)
Adiabatic temperature rise has not been considered in order to reduce the model complexity. Gupta et al [18] suggest that
this assumption is valid based on finite element simulations that estimated the adiabatic temperature rise during thin-plate
projectile perforation. Their simulations showed a maximum temperature rise of 247°C for hemispherical tipped projectiles
perforating thin plates. They deemed this value to be too small to significantly affect the mechanical properties of the plate.
However, their investigation covered impact velocities in the range 70 < V < 120 m/s. At higher impact velocities the
temperature rises are likely to be much higher and thermo-physical phenomena should be considered.
Damage initiation in the faceplates was modelled using a ductile initiation criterion (critical failure strain). The ductile
criterion uses a phenomenological model to predict the onset of damage due to the nucleation, growth and coalescence of
voids. At the critical failure strain the material can no longer tolerate load and the elements are removed from the model.
Core Material Modelling
Since the core is an open network material, comprised of stochastic and tortuous fibre paths, a material model that fully
describes its constitutive behaviour is currently not available for numerical analysis and assumptions of isotropic
continuum behaviour are incorrect. Nevertheless, since the existing *CRUSHABLE FOAM material model in
ABAQUS/Explicit (which is perhaps the closest analogue to the network material) is incompatible with existing ABAQUS
failure models, an isotropic continuum approach was indeed adopted. As a preliminary exercise the core was modelled as
an arbitrarily soft material, using some limited material data obtained from tests on isolated core material (such as that
shown in Fig. 1). Type C3D8R solid elements were used and the same critical strain failure model employed to capture the
fracture process.
Figure 1: Isolated core material of the type employed for mechanical testing purposes
Impact Energy Absorption
Figure 2 plots the normalised absorbed energy for impact tests conducted on the sandwich panels. These data are
compared to results obtained from impact tests on isolated core and faceplate material. The results are normalised by
areal density to account for mass differences between the sandwich panel and its components. The data indicate that the
faceplates absorb the largest amount of specific energy, although without the core material the benefits of a sandwich
panel arrangement (i.e. high specific stiffness) are lost. This is because the faceplates absorb energy through a
combination of membrane stretching and dishing (i.e. global bending), which requires significant energy input. The
presence of the core material hinders these mechanical processes and a more localised failure response initiates.
However, the bending and dishing effects described for faceplate deformation are more prevalent at lower impact
velocities. At higher impact velocities, the faceplates (when isolated) naturally fail in a localised manner, such that the
inhibiting effects of the core on faceplate deformation are likely to be less significant when the sandwich panels are
impacted at high velocities.
10
8
2
Specific Absorbed Energy (Jm /kg)
Isolated Core Material
Two Faceplates (Separated)
Sandwich Panel
6
4
2
0
220
225
230
235
240
Incident Velocity (m/s)
Figure 2: Measured specific absorbed energy for the sandwich panel and its respective components.
Numerical Analysis
Faceplates
Figure 3 plots measured absorbed energies for single faceplates impacted by spherical projectiles. The data are
compared to the results obtained through simulations. The experimental results agree closest with predictions obtained
using shell elements since the shell element formulation is better suited to dynamic analyses that involve large bending
strains. Agreement is also better at the higher velocities, although it isn’t uncommon for agreement to be poorest at values
close to the ballistic limit. In contrast, the predictions obtained using solid elements show comparatively poor agreement
possibly due to the reduced integration element formulation which can lead to hourglassing (causing the elements to be
much stiffer than normal in bending). This would explain the larger predicted absorbed energies. The analytical model of
Recht and Ipson doesn’t agree well with the data, and does in fact predict a contrary trend to those obtained numerically.
Their model assumes a constant dynamic shear strength and neglects strain and strain rate hardening effects, which
would readily explain the disparity. The analytical model also requires an experimentally determined ballistic limit value,
which was in this case determined via simulation (175 m/s) since the ballistic limit velocity was below that obtainable with
the gas gun.
50
Analytical Prediction (Recht & Ipson ,1963)
Numerical Prediction (Solid Elements)
Numerical Prediction (Shell Elements)
Experimental Data
Absorbed Energy (J)
40
30
20
10
0
180
200
220
240
260
Incident Velocity (m/s)
Figure 3: Measured and predicted absorbed energies for single faceplates as a function of impact velocity
It can also be seen that faceplate energy absorption is largest at the lower impact velocities, where there is a more
pronounced bending response, Fig. 4(a). At these lower velocities, large amounts of energy are expended in global
faceplate deformation, and ductile failure. At the higher velocities the capacity of the plates to absorb energy through
bending diminishes, Fig. 4(b), and there is a corresponding drop in absorbed energy. With further increases in impact
velocity a transition point is reached above which no bending occurs and a plug of material is simply ‘punched’ from the
plate.
(a)
180 m/s
(b)
235 m/s
Figure 4: Equivalent plastic strain contours for two faceplates impacted at (a) 180 m/s and (b) 235 m/s, showing the
difference in the amount of global deformation that occurs with increasing impact velocity
The qualitative agreement between the simulations and experiment is seen to be excellent in Fig. 5. The plugging, inset
Fig. 5(a) and 5(b), and petalling phenomena observed experimentally are suitably captured in the model despite using
only a single element in the through-thickness plate direction. The penetration process as a function of time is presented in
Fig. 6, revealing a large build up of plastic strain at the periphery of the projectile prior to crack initiation. Once cracking
begins it propagates circumferentially removing a plug of smaller diameter which is then ejected. As the projectile
continues on its path a series of radial cracks develop, leading to petal formation. With time, the petals bend around their
respective plastic hinges followed by some elastic relaxation.
(a)
(b)
Figure 5: Comparison of (a) predicted and (b) experimentally obtained damage areas in faceplates impacted at 218 m/s
t = 7 µs
t = 21 µs
t = 28 µs
t = 42 µs
t = 91 µs
Figure 6: Cross section and plan view images of equivalent plastic strain contours as a function of time, for a single
perforated faceplate
Sandwich Panel
Currently, the sandwich panel model over-predicts the amount of energy absorbed by the sandwich panel due to the
simplified and unrealistic core material model. Encouragingly, however, the modes of deformation and fracture are very
well captured, as shown in Fig. 7.
(a)
(b)
Figure 7: Qualitative comparison between (a) predicted and (b) experimentally observed failure modes in the sandwich
panel when impacted at 235 m/s
More rigorous treatment of the core material is required in order to obtain reliable predictions. One method currently being
explored is the implementation of real fibre network geometry into ABAQUS/Explicit. Modelling attempts so far have been
limited to small plastic strains and small volumes of material (Fig. 8) due to the large computational burden.
(a)
(b)
Figure 8: (a) Reconstructed fibre network obtained using x-ray tomography data and (b) von Mises stress contours of the
same reconstruction when loaded in an FE analysis
Conclusions
Lightweight, all-metal sandwich panels with sintered, metallic fibre cores have been impacted by hardened, spherical steel
projectiles and the absorbed energy measured. Impact tests have also been conducted on isolated core and faceplate
material to ascertain their respective contribution to the overall absorbed energy. Numerical modelling procedures have
subsequently been developed to model energy absorption in the faceplates and the sandwich panel. The following
conclusions have been drawn:
•
The faceplates are the dominant contributors to sandwich panel energy absorption, having average specific
energy absorption more than double that of the core.
•
•
•
•
•
•
•
•
Faceplate energy absorption decreases with increasing impacting velocity over the velocity range studied as
global bending and ductile failure modes give way to localised failure and reduced bending.
Numerical simulations of faceplate energy absorption are in good agreement with experimental data, particularly
when using shell elements which are better suited to dynamic analyses involving large bending strains.
Qualitative agreement between the simulations and experiments for perforated faceplates are in excellent
agreement, with the main deformation features being reliably captured. Both plugging and petalling phenomena
were also successfully modelled.
The analytical model of Recht and Ipson is unsuitable for predicting energy absorption in faceplates, since it
assumes constant dynamic shear strength and therefore neglects strain and strain rate hardening effects.
The simulated perforation process shows that cracking originates in a circumferential region of high plastic strain
beneath the projectile, followed by circumferential crack propagation, plug formation and ejection, radial cracking
and petalling.
The core material hindered faceplate deformation during sandwich panel penetration leading to a reduction in
specific absorbed energy when compared to the faceplates alone. This is deemed less significant at impact
velocities where faceplate dishing does not occur (~>300 m/s).
The assumption of isotropic continuum core behaviour is too crude to reliably model energy absorption in
sandwich panels with sintered metallic cores, although the deformation features agree well with experiment.
More rigorous treatment of the core material is required if numerical modelling techniques are to be used to
inform the future design of sandwich panels with sintered, metallic fibre cores.
ACKNOWLEDGMENTS
Funding for this work was generously provided through a Dstl student CASE award. Acknowledgments are also due to Dr.
J. C. Tan for supplying figures 8(a) and 8(b).
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