8.13 Impact and Mechanical Evaluation of Composite Sandwich Structures

8.13 Impact and Mechanical Evaluation of Composite Sandwich Structures I Mohagheghian, L Yu, C Kaboglu, and JP Dear, Imperial College London, London, United Kingdom r 2018 Elsevier Ltd. All rights reserved.

8.13.1 Introduction 8.13.1.1 Quasi-Static Failure Modes 8.13.1.2 Low Velocity Impact Failure Modes 8.13.1.3 High Velocity Impact Failure Modes 8.13.1.4 Grading the Core 8.13.1.5 Outlines of Current Investigation 8.13.2 Material 8.13.3 Quasi-Static Deformation 8.13.3.1 Experimental Set Up 8.13.3.2 Three-Point Bending 8.13.3.3 Four-Point bending 8.13.3.4 Summary 8.13.4 Low Velocity Impact Response 8.13.4.1 Results 8.13.5 High Velocity Impact Response 8.13.5.1 Experimental Set Up 8.13.5.2 Results 8.13.5.2.1 Semi-rigid impact 8.13.5.2.2 Rigid impact 8.13.6 Conclusions Acknowledgments References

8.13.1

239 240 241 241 242 243 243 244 244 244 247 249 249 250 251 252 252 252 255 260 260 260

Introduction

Sandwich structures have been found very attractive in many engineering areas including aviation, marine, automotive and energy applications1–4 because of their high strength and stiffness to mass ratio. In addition, their noise reduction, thermal insulation, and impact energy absorption characteristics make them very favourable for engineering applications. Sandwich structures essentially consist of two thin layers of material with strong in-plane mechanical properties and a thick and light core to separate these two layers and to resist compression and shear forces. A schematic of a sandwich beam is shown in Fig. 1. The flexural rigidity (D) of a sandwich beam (shown in Fig. 1) can be calculated by the following equation:5 D¼

Es bh3 Es bhd2 Ec bc3 þ þ 6 2 12

ð1Þ

where b is the width of the beam, h and c are the thickness of skin and core and d is the distance between the mid-plane of the two skins, as illustrated in Fig. 1. Eq. (1) is valid for an isotropic beam, but it can also be applied for a composite sandwich beam where Es is the Young’s modulus of the composite skin in the x direction (Fig. 1) and Ec is the Young’s modulus of the core. For most composite sandwich structures, normally EscEc and c, dch. Therefore, these sandwich structures have a very high flexural rigidity,

Fig. 1 Schematic of a sandwich beam.

Comprehensive Composite Materials II, Volume 8

doi:10.1016/B978-0-12-803581-8.10055-4

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compared to thin composite laminates. This is the result of the high magnitude of the term Es d2 in Eq. (1). For sandwich structures to be efficient, low cost and low density cores are required. Various core materials have been used for construction of sandwich panels including polymeric and metallic foams, natural materials such as balsa wood, honeycomb and lattice structures. In this article, we will mainly focus on sandwich panels with fibre reinforced composite skins and polymeric foam cores.

8.13.1.1

Quasi-Static Failure Modes

Various attempts have been made through the last three decades to understand better the effect of design parameters on the failure modes of sandwich structures which ultimately determine their strength. Triantafillou and Gibson6 identified various quasi-static failure modes of sandwich beams including face yielding, face wrinkling, core yield in shear, core yield in compression or tension, interface debonding and core indentation. Triantafillou and Gibson6 derived analytical expressions for each failure mode and then generated failure mode maps for different sandwich constructions. The critical failure mode was found to depend on core and face material as well as geometrical parameters. Many of the failure modes mentioned above are relevant for face and core materials which deforms plastically and have not been observed in composite sandwich structures with foam core. Mines et al.7 investigated different composites sandwich constructions in a three-point bending configuration. They observed two main failure mechanisms including upper skin compressive failure and core shear failure. The failure modes for composite sandwich beams with carbon/ epoxy skins and (polyvinyl chloride) PVC closed-cell foams was investigated by Daniel et al.8 They identified failure modes including face sheet compressive failure, adhesive bond failure, indentation failure, core failure and face wrinkling. The necessary condition to activate each failure mode was discussed. Lim et al.9 investigated the failure modes of composite sandwich beams with E-glass/epoxy skins and PVC foam cores. Through a systematic study, the influence of various parameters including foam density (54–117 kg m3), span of the beam (100–250 mm) and the thickness of the skins (0.45–1.9 mm) on the failure modes was investigated. Three main static failure modes were reported for three-point bending configuration including core shear, core compression and skin fracture. They proposed theoretical expression for these three failure modes. A failure mode map was then generated based on five non-dimensional parameters: compressive strength ratio (face/core), modulus ratio (face/core), normalised thickness (face/core), normalised span (span/thickness of the core) and compressive to shear strength ratio of the core. Steeves and Fleck10,11 studied the static collapse mechanisms of sandwich composite beams with glass/epoxy skins and PVC foam cores using experimental, theoretical and numerical methods. Similarly, Steeves and Fleck10 derived analytical expression for four competing failure mechanisms which ultimately determine the strength of a composite sandwich beam. These mechanisms include face micro-buckling, face wrinkling, core shear failure and indentation or core crush failure. A schematic of these failure modes are shown in Fig. 2. Micro-buckling and face wrinkling failure both occur at the upper skin where the stresses are compressive. Face wrinkling involves short wavelength elastic buckling of upper face skin11 and occurs when the core has a low stiffness.8 In this case, the core does not provide sufficient resistance against transverse movement of the skin. In contrast, for micro-buckling to occur, a high

Fig. 2 Four competing failure modes reported by Steeves and Fleck.10,11

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density core (i.e., a stiff core) is necessary.10 A sudden drop in load was observed associated with this failure mechanism.10 For the other two failure modes, deformation of the core by shear (core shear cracking) or by compression (indentation) is responsible for the failure of the structure. As mentioned before, the transition between failure modes depend on the mechanical properties of both skins and core as well as geometrical and loading parameters. Mines et al.7 suggested that the transition between core shear and skin compressive failure depend on the beam span. For longer beams, skin compressive failure is more favourable while shorter beams are more susceptible to core shear failure. It was reported that if upper skin failure occurs, the sandwich beam shows a more stable post-failure behaviour which results in a good energy absorption capability.7 In contrast, the core shear failure is very unstable and has a lower energy absorption capacity. Konsta-Gdoutos and Gdoutos12 investigated the effect of load and geometry on the failure modes of sandwiches with carbon/epoxy skins and PVC closed-cell foams of two densities (100 and 250 kg m3). Simply supported and cantilever beams were studied under concentrated, uniform and triangular loading. Similarly, a critical beam span was observed for which a transition from core shear to compressive failure of upper skin occurs. The critical length was found to increase by increasing the core density or by changing the loading from concentrated to uniform or to triangular.

8.13.1.2

Low Velocity Impact Failure Modes

In many applications, composite sandwich structures may be exposed to low velocity impact. The vulnerability of these structures to transverse impact has been acknowledged and has been the subject of many investigations.13–21 In this section, we review some of these studies. Hazizan and Cantwell13 investigated the low velocity impact response of composite sandwich beams made of woven glass fibre phenolic resin and 11 different foam cores including linear PVC, PEI (Polyetherimide) and PVC/PUR (Polyurethane). The tests were performed using a drop tower with a hemispherical indenter and impact energy ranging from 0.1 to 1.94 J. They found that the dynamic response of the studied sandwiches is a clear function of elastic properties of the foam core. For a given impact energy, the peak force increases with increasing the shear modulus of the core. The failure mode was also dependent on the elastic stiffness of the foam core. For a sandwich structure with a PVC/PUR foam core, shear cracking observed as a dominant mode of failure for low density/low modulus cores (shear modulus, 13–22 MPa). For cores with intermediate modulus (shear modulus, 30–38 MPa), compressive failure of upper skins and for cores with high modulus (shear modulus, 50–75 MPa) delamination between the core and the top layer was observed. For PVC and PEI cores, which their shear modulus ranging from 11 to 37 MPa, compressive failure of upper skins was found more common. In order to determine the contribution of various energy absorption mechanisms including shear, bending and indentation, Hazizan and Cantwell13 proposed a simple energy-balance model. They found that for a low modulus/density core the majority of energy was absorbed by shear followed by indentation and bending. In contrast, for a high modulus/density core the majority of energy was absorbed by indentation followed by bending and shear. Lim et al.9 compared failure modes under quasi-static bending and low velocity impact. Under low velocity impact, two main failure modes were observed including upper skin failure and shear cracking in the core. In case of shear failure, the cracks propagated either along the interface or through the core itself. Increasing the skin thickness or decreasing the core density promote the core shear cracking. Lim et al.9 also compared the energy absorption capability of sandwiches with different core density (ranging from 54 to 117 kg m3). For core densities below 97 kg m3, shear failure in core was dominant. For this failure mode, increasing the core density only caused a moderate increase in energy absorption. However, sufficient increase of the core density resulted in a change in the failure mode to compressive skin failure and a significant increase in the energy absorption. Zhou et al.22 studied the effect of core material on the low velocity impact perforation of composite sandwich structures. Linear and cross-linked PVC as well as PET (Polyethylene terephthalate) foam cores with different densities were considered. The tests were performed on the plates using a hemispherical indenter. Their results suggest that the perforation resistance is strongly influenced by the properties of the foam core such as density and fracture characteristics. Increasing the density of cross-linked PVC core from 60 to 200 kg m3 enhanced the perforation resistance by eight times.

8.13.1.3

High Velocity Impact Failure Modes

Composite sandwich structures are also being used in aviation and marine applications for which the structure might face threats from high velocity impacts (e.g., bird strike, engine debris or ballistic threats). As a result, the ability of composite sandwich structures to resist high velocity impact perforation need to be considered in the design. Unlike quasi-static and low velocity impact studies, fewer researches are available in the literature regarding high velocity impact failure modes. Reddy et al.23 investigated the perforation response of composite sandwich panels (made of GFRP skins and PVC foam cores) under quasi-static, low and high velocity (up to velocities of 305 m s1) impacts. Sandwich with various composite skin thicknesses and core densities were impacted using projectiles with two nose shapes: hemispherical and conical. It was observed that under dynamic loading, increasing the thickness of skins causes less debonding between the core and skin but more delamination in the composite skin itself. Reddy et al.23 argued that while the core controlling the failure mechanisms and consequently energy absorption under quasi-static and low velocity impact loading, at higher impact velocities it only makes a little contribution in the energy absorption of the panel. Under ballistic impact, indentation, fracture, fragmentation and delamination of the laminate were suggested as the primary energy absorption mechanisms.23 The ballistic limit and residual velocity were reported to be identical for the two projectile nose shapes.

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Fig. 3 Two main failure modes observed for composite sandwich structures under high velocity impact.24

Kepler24 investigated the perforation response of composite sandwich panels (GFRP skins and PVC foam core) at velocities of 70 and 93 m s1. Projectiles with three nose shapes: hemispherical and conical (with different cone angles) were used. Various failure mechanisms were observed including delamination in composite skins, debonding in the interface between core and the skins and core cracking.24 Similar to Reddy et al.,23 delamination was observed to increase by increasing the impact velocity. Debonding was reported to be smaller for projectiles with conical nose shape. The core cracking can occur in two different modes: cross cracking and punching/plugging as depicted in Fig. 3.24 While punching/plugging occurs as a result of localised deformation, when there is more contribution from global deformation of the plate, cross cracking is observed.24 The cracks imitate from the centre, where the shear stresses are maximum, and propagate with an angle of 451. Kepler24 reported a tendency from punching/ plugging to cross cracking when the impact velocity is increased. Kepler24 also observed that increasing the impact velocity causes a transition from petalling in the back skin to full delamination. In a separate study, Kepler25 analytically investigated the contribution of different damage mechanisms in penetration of composite sandwiches. Analytical expressions were given for fibre stretching, matrix fracture, core compression, core fracture, debonding and friction. The contribution of cone cracking, debonding and delamination was found to be small compared to fibre stretching, core compression and core shear for a range of projectile nose shapes. However, the total estimate of absorbed energy by Kepler25 was significantly lower than experimentally measured values. Skvortsov et al.26 proposed an analytical model aiming to determine the energy absorption contribution by elastic response as well as various damage mechanisms in a composite sandwich panel subjected to high velocity impact. Different load histories and distributions were considered. Their results indicate that the ratio of energy restored by elastic deformation to the energy dissipated by various damage mechanisms varies not more than 20% for the range of loading considered. At higher velocities, the contribution of energy associated with irreversible damage becomes dominant.26 This is because of decrease in the contribution from global deformation (i.e., more localised deformation at higher impact velocities). The contribution of the core in the perforation resistance was studied by Buitrago et al.27 They compared two configurations: (i) a composite sandwich plate and (ii) two spaced composite plates (no foam in between) separated by a distance equal to thickness of the foam core. Negligible difference in the perforation resistance was observed between the two configurations indicating no significant contribution from the core in the energy absorption. The same question on the contribution of the core was addressed by Ivañez et al.28 numerically again by comparing a sandwich plate with a spaced-composite plates (no foam core between the skins). Ivañez et al.28 observed slight increase in the ballistic limit for composite sandwich panel (4.2%) despite increasing the weight of structure by 20%. When compared based on residual velocity, composite sandwich performs better at impact velocities close to ballistic limit (36% reduction in residual velocity). At the velocities well above the ballistic limit, most of the energy is absorbed by fracture in the composite skins with a negligible contribution from the foam core. This makes the residual velocity of the two configurations converge as the impact velocity increases. Nasirzadeh and Sabet29 studied the effect of core density on the perforation response of composite sandwich plates for impact velocities up to 150 m s1. The composite skins were made of glass fibre and core made of polyurethane foam with a density ranging from 37 to 240 kg m3. The highest ballistic limit was found for a core density of 49 kg m3. Nasirzadeh and Sabet29 argued that for foams with medium range density (49 and 70 kg m3) the compression of the core causes yawing of the projectile during perforation and increases the contact area between the projectile and the back skin. For foam with low and high densities no yawning was observed.

8.13.1.4

Grading the Core

It can clearly be seen from the last sections that the property of the foam has a significant influence on the performance of composite sandwich structure. Various attempts have been made to optimise the core properties for achieving the best performance. Grading the core, changing the density and consequently the elastic properties of the core either continuously or step-wise, has been proposed in the literature as an approach to tailor the properties of the core and consequently the properties of sandwich structures. Apetre et al.19 explored the possibility of reducing the interfacial shear stresses and maximum strains in the core by grading the through thickness properties. Using an analytical approach, Apetre et al.19 suggested that functionally graded core can efficiently be

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used to mitigate or completely prevent impact damage in composite sandwich structures. A functionally graded syntactic foam was fabricated by Gupta.30 A continuous grading in the core was achieved by using hollow micro-balloons with different wall thickness. The structure showed significant improvement in energy absorption (300–500% increase) under compression compared to plain syntactic foams which could withstand 60–75% compression without any significant loss in strength. Cui et al.31 investigated the energy absorption capability of a functionally graded foam core under low velocity impact. Finite element simulations were used with density of the core changed according to different gradient functions. It was suggested that grading the core can result in a superior energy absorption capability. The performance enhancement was greatest for the core with highest density gradient. Zhou et al.32 investigated the perforation resistance of composite sandwich plates under low velocity impact using a hemispherical indenter. For composite skins, thin layers of carbon fibre skins (0.35 mm) were used. For core, various combinations of linear PVC, cross linked PVC and PEI foam layers with different densities were bonded together in a three layers arrangement. Plugging was found to be the dominant failure mode. Sandwiches with graded core showed superior perforation resistance. When the core layer with the highest density placed against the impacted skin, the perforation resistance was greater than when it was placed against the distal skin. Grading the core has also been used for protection against blast and shock loadings. Wang et al.33 performed shock tube tests on composite sandwich panels using E-Glass Vinyl Ester (EVE) composite skin and step-wise graded styrene foam cores. Two stepwise graded cores were compared against the uniform core with the same average density. When a core layer with lower density was located first in contact with the blast loading, significant compression was observed. As a result, the amount of damage in the distal composite skin was reduced. Gardner et al.34 argued that under shock loading, increasing the number of monolithically graded foam core layers reduces the acoustic wave impedance between successive layers and helps maintaining the structural integrity of composite sandwiches. The wave propagation through the graded core was studied by Kiernan et al.35 using Split Hopkinson Pressure Bar (SHPB) tests. They suggested that the amplitude of the pressure wave can be amplified or diminished through the core depending on the choice of grading. The plastic dissipation energy was also influenced by gradient function.35 Kelly et al.36 performed full-scale air blast experiments on GFRP sandwich panels with various core materials. By grading the core, they observed mitigation of throughthickness crack propagation as well as reduction of damage in the higher density layers. This ultimately resulted in a smoother plate profile of the distal composite skin and lower out-of-plane displacement compared to sandwich with uniform core.

8.13.1.5

Outlines of Current Investigation

The aim of this study is to investigate the effect grading the core on the mechanical and impact performance of composite sandwich panels. For this purpose, sandwich panels are made using GFRP skins and PVC foam core. Quasi-static bending tests in three-point and four-point configurations are performed on sandwich beams. 2D digital image correlation is employed to monitor the deformation of the core throughout the bending. Low velocity impact tests are performed using a drop tower facility. Two types of impactor are used: rigid (made of steel) and semi-rigid (made of high density polyethylene, HDPE). The perforation resistance of composite sandwich plates are then assessed under high velocity impacts. The tests are performed using a gas gun at impact velocities ranging from 178 to 230 m s1. Similar to low velocity impact tests, projectiles with different levels of deformability are used.

8.13.2

Material

Composite sandwich panels in this study were manufactured using Resin Infusion under Flexible Tool (RIFT). Composite skins were made of unidirectional E-glass fabric (Gurit XE603, þ 451 Double Bias Stitched Fabric). The biaxial E-glass fibres were placed in [0/90/45/  45/90/0]s lay-up. Stacking sequence of laminates has a direct influence on the impact performance of composite structures. For low velocity impact, stacking sequence affects the amount of delamination and consequently the post-impact performance of the composites.37 Guidelines were proposed by Fuoss et al.38 for laminate stacking sequence to achieve better impact damage resistance. For high velocity impact, stacking sequence was also found to affect the ballistic limit.39 The layup in this study is chosen to provide maximum bending resistance with 01 fibres oriented along the x axis (Fig. 1) in the top and bottom surfaces of the composite skin. To minimise the experimental variables, the same composite layup is chosen for the impact experiments considering that this layup might not offer the best impact performance. Epoxy, Prime 20LV from Gurit with slow hardener was employed for the matrix. For sandwich core, PVC foams from AIREX in three densities were used. The skin and core materials used in this study, is a common material combination employed for marine applications and wind turbine blades. The mechanical properties of these three products are listed in Table 1. Three core configurations were made of these foam cores including one uniform and two graded cores. The details of three core arrangements are listed in Table 2. All three configurations consist of three layers of 5 mm thick foam. To ensure strong adhesion between these layers, their surface were covered with epoxy resin before infusion process. In the configuration with uniform core, MMM, only foam with medium density (AIREX C70.75) was used. For graded core LHL, a layer of high density foam (AIREX C70.90) was sandwiched between two layers of foam with low density (AIREX C70.55). For HLH configuration, low density core layer was placed between two layers with the highest density.

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Table 1

Impact and Mechanical Evaluation of Composite Sandwich Structures

Mechanical properties of PVC foams used in this study Compressive strength (MPa)

Tensile strength (MPa)

Shear strength (MPa)

Tensile modulus (MPa)

60

0.9

1.3

0.85

45

PVC

80

1.45

2.0

1.2

PVC

100

2.0

2.7

1.7

Product

Material

AIREX C70.55 AIREX C70.75 AIREX C70.90

PVC

Table 2

Density (kg m3)

MMM

Skin Core

Skin Average core density (kg m3)

8.13.3

Shear modulus (MPa)

Shear elongation at break (%)

69

22

16

66

104

30

18

84

130

40

23

Various configurations of sandwich composite samples used in this study

Configuration Symbol

Layup

Compressive modulus (MPa)

LHL

HLH

6 Layers of glass fibre (in 0/90/  45/ þ 45/90/0 lay-up, total 1800 gsm) with epoxy matrix (1.5 mm) 100 kg m3 foam (5 mm) 60 kg m3 foam (5 mm) 80 kg m3 foam (5 mm) 80 kg m3 foam (5 mm) 100 kg m3 foam (5 mm) 60 kg m3 foam (5 mm) 60 kg m3 foam (5 mm) 100 kg m3 foam (5 mm) 80 kg m3 foam (5 mm) 6 Layers of glass fibre (in 0/90/  45/ þ 45/90/0 lay-up, total 1800 gsm) with epoxy matrix (1.5 mm) 80

73

87

Quasi-Static Deformation

In this section, the quasi-static flexural strength of sandwich beams is evaluated with three- and four-point bend loading. 2D digital image correlation is employed to monitor strain development in the foam core during different stages of deformation.

8.13.3.1

Experimental Set Up

Quasi-static bending tests were performed using three- and four-point bending configurations according to ASTM C393. Sandwich beams with dimensions of l (300)  W (75)  t (18) mm3 were cut down from larger panels manufactured using RIFT. The schematic of the composite sandwich beam and the specifications of the three- and four-point bending tests are shown in Fig. 4. The width of the sandwich beam (W) is chosen to be 75 mm. This gives the ratios of W/tD4.2 and W/l¼ 0.25, which satisfy the specification by ASTM C393 (i.e., 3oW/to6 and W/lo0.5) for non-standard configurations. As explained by theoretical calculations of Lim et al.,9 the geometry of the beam (i.e., the non-dimensional parameters such as h/c and l/c (Fig. 1)), has a great influence on the failure mode of the sandwich beam. In this study, the main focus is on the change in the failure mode of a composite sandwich beam (a single beam geometry) by altering the properties of the core. The tests were conducted using a screw driven machine (Instron 5800 series) with cross head speed of 6 mm min1. To reduce the effect of contact stresses below the rollers, rubber pads with the thickness of 3 mm were employed. For monitoring the deformation of the core during the experiment, 2D DIC (GOM Aramis 5M) was employed. A camera captured images with the resolution of 2448  2050 pixels every 2 s during the test. The image recording was synchronised with Instron measurements so as to correlate the strain map in the core with the global deformation of the beam.

8.13.3.2

Three-Point Bending

Firstly, the result of three-point bending tests are presented. Fig. 5 shows force against cross head displacement, measured using Instron, for three core configurations: MMM, LHL and HLH. The details of each configuration can be found in Table 2. At the early stage of deformation, the response is linear and very similar for all three configurations. The distinction between the three configurations becomes apparent for cross head displacement greater than 3 mm, when the core starts going through extensive deformation. The peak load is different and is highest for MMM followed by HLH and LHL. For MMM, a sudden drop in the force is observed after experiencing a peak force of about 2800 N. A photograph of the beam cross section at this time is shown in Fig. 5. No sign of shear cracking or delamination can be seen. The failure in the upper composite skin however, is apparent in the photograph taken from top of the beam in Fig. 5 and is the main reason for the load drop.

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Fig. 4 Schematic of a composite sandwich beam: (a) three-point and (b) four-point bending test configurations.

Fig. 5 Comparison between the response of composite sandwich beams with uniform (MMM) and graded (LHL and HLH) cores under three-point bending.

To better understand the state of deformation in the core, full-field compressive and shear strain contours, calculated by DIC, are plotted in Fig. 6. The values in Fig. 6 are normalised by the uniaxial shear and compressive strains at the point of yield. The normalised compressive and shear strains ^ey and ^exy are defined as ^ey ¼ ey =eyðYÞ ^exy ¼ exy =exyðYÞ ;

ð2Þ

where ey and exy are compressive and shear strains respectively. The uniaxial compressive yield strain ey(Y) and uniaxial shear yield strain exy(Y) are calculated by dividing the value of compressive and shear strength in Table 1 by compressive and shear modulus respectively. For the uniform core, MMM, the strain values are normalised by yield strain values calculated for AIREX C70.75, ey (Y) ¼0.014 and exy(Y) ¼ 0.040. For LHL and HLH which consists of two layers of the foam with different densities, the values are normalised by yield strain values calculated for AIREX C70.55, ey(Y) ¼ 0.013 and exy(Y) ¼ 0.039, which is the layer with a lower density. Normalising the shear and compressive strains helps to better observe the competition between the two dominant failure modes: core compression and shear cracking throughout the deformation. However, it should be noted that as the core material is

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Fig. 6 Three-point bending test results for a composite sandwich beam with a uniform (MMM) core: (a) force against cross head displacement and (b) full field strain contours calculated by DIC.

under multi-axial loading, and not uniaxial loading, the critical normalised strain values (defined as ^ey and ^exy ¼ 71) do not exactly reflect yielding of the core due to shear or compression. The full-field normalised strains are plotted for MMM configuration at four cross head displacements in Fig. 6. At Point 1, the beam is in elastic range and the shear and compressive strains are below their critical values. At Point 2, deviation from the linear trend starts in Fig. 6(a). At this point, localised core compression starts appearing under both upper and lower rollers. At Point 3, the compressive strain under the rollers, particularly under the upper roller, exceeds the critical value (ie, ^ey ¼  1). Point 3 represents the point of maximum bending force in Fig. 6(a). The contour plots at Point 3 shows that the shear strains in the core are still in the elastic range and uniformly distributed along the beam. The extent of core compression under the upper roller increases after Point 3 and results in reduction in the bending force (Point 4). At Point 4, shear strains are still uniformly disturbed and, except for a very small area, are still below their critical value. This indicates that core compression is the dominant failure mode for this configuration. It is believed that the significant core compression under the upper roller causes local deformation of the upper composite skin which later on leads to failure in this skin. Next, the response of two configurations with graded core will be considered. As indicated in Fig. 5, for both cases the peak force is significantly lower than MMM configuration. This is despite the fact that average core density of HLH is even higher than MMM. For HLH configuration, after deviation from the linear part, the force remains relatively constant until a sudden drop in the force is observed. The photograph of the specimen at this time is shown in Fig. 5. A shear crack with 451 is initiated in the middle layer and propagates through the adjacent foam layer (foam layer with high density). The crack propagation extends further through the interface between the core and the composite skin. Similarly, the full-field contours for shear and compressive strains are plotted at four different points for HLH configuration in Fig. 7. At Point 1, where the response of beam is still linear, some localised core compression is already developed under the rollers. The compressive strain values passed their critical value at this point in Fig. 7. Shear strains are developing in the middle layer (low density layer) at Point 2 while the extent of core compression remains limited to a small area under the rollers. At Point 3, both shear and compressive strains reach their critical values in the foam middle layer. After this point the load remains almost constant while the deformation in the middle layer is distributed relatively uniformly along the beam. This is in contrast to MMM configuration in Fig. 6 where the deformation in the core is highly localised at the centre of the plate. The uniform deformation of the core in this case enables the beam to sustain larger deformation without any significant loss in its load carrying capacity.

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Fig. 7 Three-point bending test results for a composite sandwich beam with a graded (HLH) core: (a) force against cross head displacement and (b) full field strain contours calculated by DIC.

The extensive deformation in the core remains limited to the middle layer at Point 4 and ultimately results in formation of a shear crack in this layer (Fig. 5). Next, the response of a sandwich beam with LHL configuration will be assessed. Compared to other configurations, LHL has the lowest peak force (Fig. 5). Similar to HLH configuration, the force after reaching its peak value remains relatively constant (the force slightly decreases as the deformation proceeds). The load drop is postponed to a much larger cross head displacement which is very useful for energy absorption purposes. No sign of shear cracking in the core exist in this case. Similar to MMM configuration, the main reason for the load drop is the failure of the upper composite skin. The deformation of this configuration is assessed in more details in Fig. 8. As the low density foam layers are now located in contact with skins, closer to the rollers, the core compression under rollers occurs at cross head displacements as low as 2.5 mm (Point 1). At Points 2 and 3, shear deformation also starts developing in both low density layers, but their values remains below the critical value. The core crushing of the top foam layer under the upper roller is still dominant with limited crushing around the lower rollers. By compressing core under the roller, small area on the upper foam layer outside the contact area goes under tension (^ey 41). At Point 4, deformation in the core develops predominantly in the low density core layers and remains mainly in the centre of the beam.

8.13.3.3

Four-Point bending

In this section, the tests performed by three-point bending are repeated using four-point bending configuration. The results are shown in Fig. 9. Similar to three-point bending tests in Fig. 5, the peak force of both graded cores: LHL and HLH is lower than that of the uniform core, MMM. The load for two graded cores, however, remains at a nearly constant level for a longer period of time without any significant loss in load carrying capacity. The photograph of the beams at specific cross head displacements are shown in Fig. 9. No sign of cracking in the core exists for MMM at the point of load drop. Examination of test samples at this cross head displacement indicates that the upper skin failure, as shown in Fig. 9, causes this load drop. For HLH configuration, shear cracks are originated from both upper and lower rollers at the cross head displacement of about 16 mm (as highlighted in Fig. 9). However, only a small load drop occurs as a result. It should be noted that in the absence of core crushing, the difference in the strength between LHL and HLH configurations observed for three-point bending in Fig. 5 is reduced for four-point bending (Fig. 9).

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Fig. 8 Three-point bending test results for a composite sandwich beam with a graded (LHL) core: (a) force against cross head displacement and (b) full field strain contours calculated by DIC.

Fig. 9 Comparison between the response of composite sandwich beams with uniform (MMM) and graded (LHL and HLH) core under four-point bending.

The response of MMM configuration is assessed in more details in Fig. 10 where the deformation of the core is monitored using DIC. In the linear part of the response (Point 1), compressive and shear strains are still small and are in the elastic range. The level of shear and compressive strains both increase at the deformation proceeds to Point 2. Whilst the compressive strains reach their critical limit under both upper and lower rollers, the value of shear strains remains below their critical value. As a result, core crushing under the rollers are believed to be responsible for deviation from linear trend at

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Fig. 10 Four-point bending test results for a composite sandwich beam with a uniform (MMM) core: (a) force against cross head displacement and (b) full-field strain contours calculated by DIC.

Point 2 and reduction in the rate of increase in the load. At Points 3 and 4, both compressive and shear strains reach their critical values (value of 71 for shear and  1 for compression). The deformation of the core in the middle section of the beam remains small. The deformation of HLH configuration under four-point bending is shown in Fig. 11. Similar to three-point bending, the deformation is mainly developed in the low density layer in the middle of the beam. Shear and compressive strains reach their critical values nearly at the same time (Point 3). In the absence of localised deformation, the load remains relatively constant without any significant load drop up to the cross head displacement of 20 mm. The deformation of LHL configuration is shown in Fig. 12. For LHL configuration, core crushing starts simultaneously under all 4 rollers and soon extends to a larger area in the low density core layers (Point 3 in Fig. 12). The shear strains also increases at Point 3 but remains below the critical value. Similarly, the deformation is distributed uniformly in the core area between the upper and lower rollers.

8.13.3.4

Summary

In this section, the effect of grading the core on the flexural bending response of composite sandwich structures is investigated. The effect of grading the core is found to be influenced by the type of loading. In the case of three-point bending, localised deformation occurs underneath the loading pin which its extent can be increased or decreased depending of the choice of the grading. In the next section, the influence of grading the core will be investigated predominately for scenarios where the deformation is highly localised (similar to that of three-point bending). For this purpose, impact tests on composite sandwich plates with a high ratio of projectile diameter over the plate length will be considered. Both low and high velocity impact tests will be used.

8.13.4

Low Velocity Impact Response

In this section, the performance of composite sandwich panels will be assessed under low velocity impact. The sandwich panels were tested in the plate configuration. The specimens were clamped to a metallic support with a clamping plate using 12 M8 bolts. The clamping plate made of steel and had an opening of 75  75 mm2. Special care was taken to prevent crushing of the foam core when tightening the bolts. The geometry of test plate and the clamp are shown in Fig. 13(a).

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Fig. 11 Four-point bending test results for a composite sandwich beam with a graded (HLH) core: (a) force against cross head displacement and (b) full-field strain contours calculated by DIC.

The impact tests were performed using a drop tower facility. A schematic of the test set up is shown in Fig. 13(b). To achieve different impact energies, a mass of 30 kg was dropped from various heights up to 0.7 m. This resulted in impacts with velocities of up to 3.7 m s1 and energies of up to about 205 J. A flat-faced cylindrical impactor with diameter of 24.8 mm was used. The impactor were made from two materials: (i) mild steel which only undergoes small elastic deformation (rigid impact) and (ii) High Density Polyethylene (HDPE) which undergoes larger deformation (semi-rigid impact). It should be noted however that despite large deformation, no permanent plastic deformation was observed in HDPE after impact. The impactors were connected to a PCB load cell (model 224C) through which the force trace was measured during impact. The deformation of the plate was monitored by a high speed camera (Phantom Miro M/R/LC310), as shown in Fig. 13(b).

8.13.4.1

Results

The impact force traces using two types of impactors (rigid and semi-rigid) are compared in Fig. 14(a) for uniform core (MMM). The impact conditions were exactly the same for both cases: impact velocity of 3.7 m s1 and impact energy of 205 J. Since the impact conditions and the size of the impactor are the same, the initial part of the response is identical (ie, similar slope of force-time curve). The distinction between the two responses becomes apparent at the time of about 3 ms. At this time, a sharp drop in force is observed for the test using a rigid impactor. This load drop is associated with the failure of the front composite skin. A series of high speed images is shown for both impactors in Fig. 14(b) and (c). The damage in the front skin can be observed in Fig. 14(b) at t¼ 3.1 ms. After the first drop, the force increase again as the foam core starts being compressed and densified. The load increases up to value of about 16 kN before ultimately drops to zero at the time of about 9 ms. The second load drop is associated with the failure of lower composite skin. In contrast, for a semi-rigid impactor (HDPE) no such sharp drop in load is observed. There are some oscillations in the force starting from t ¼ 4 ms which is believed to be the result of crack formation in the upper skin, as can be seen high speed images in Fig. 14(c). The cracks, which are normally originated from the clamp, propagates inward but does not cause total failure of the upper skin. The main difference between the two cases here can be related to the extent of deformability of impactor. While development of concentrated shear strains at the sharp edge of the rigid impactor causes the failure of the upper skin, larger deformation in HDPE impactor especially around the edges reduces the shear strain and suppresses the failure mode observed for rigid impactor.

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Fig. 12 Four-point bending test results for a composite sandwich beam with a graded (LHL) core: (a) force against cross head displacement and (b) full-field strain contours calculated by DIC.

Next, the response of the two graded cores (LHL and HLH) are compared against the uniform core (MMM) in Fig. 15. Similar to the previous section, the impact conditions remain the same (impact velocity of 3.7 m s1 and impact energy of 205 J) and the response is compared for both rigid and semi-rigid impactors. The impacted samples are sectioned and compared in Fig. 15. For semi-rigid impact, the slope of force trace is slightly lower for LHL (Fig. 15(a)). The value of peak force however is independent of core arrangement and is approximately similar for all configurations. For MMM and LHL, considerable amount of core compression is apparent with limited bulging in the back composite skin. The amount of permanent deformation is also the same (as evident in the force-displacement curve in Fig. 15(a)). No failure in the front-facing composite skin is observed for any of these configurations. For HLH configuration, for which the stiffer core layer (layer with the highest density) is located just underneath the impacted skin, a load drop occurs at impactor displacement of about 19 mm (Fig. 15(a)). This load drop is associated with the failure of the impacted composite skin. Positioning higher density layer beneath the impacted skin therefore seems to promote failure in composite skin. The further support provided by this stiffer foam layer increases shear strains at the composite skin in areas adjacent to impactor edges which increases the chance of shear failure in the composite skin. For rigid impact, Fig. 15(b), same amount of impact energy (205 J) causes full perforation in all composite sandwich structures. Two load drops exist in Fig. 15(b) associated with failure of first the impacted and then the distal composite skins. Similar to semirigid impact, the slope of force trace is slightly lower for LHL and the level of peak force is almost identical despite the difference in the core arrangement.

8.13.5

High Velocity Impact Response

In this section, the performance of sandwich panels investigated in the previous section will be assessed under high velocity impacts, ranging from 178 to 203 m s1. The plate dimensions and the boundary conditions are identical to what described in Section 8.13.4. In the absence of force measurement, high speed 3D digital image correlation (DIC) will be employed to obtain full-field strain and out-of-plane displacement contours during the impact event.

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Fig. 13 Schematic of (a) test specimen and boundary condition, and (b) drop weight test set up.

8.13.5.1

Experimental Set Up

High velocity impact tests were conducted using a gas gun apparatus with 3-m-long barrel. A schematic of test set up is shown in Fig. 16. Two pairs of IR sensor were located at the end of the barrel and used to measure the projectile velocity. The end of barrel as well as target area were confined in a transparent safety chamber. The chamber, made of thick polycarbonate panels, helps illuminating the target, observing the impact event and protecting the surrounding from the flying fragments caused by the impact. In order to measure the deformation of the target, high-speed 3D digital image correlation (DIC) was employed. The test set up here is similar to what described by Mohagheghian et al.40 Two synchronised high-speed cameras (Phantom Miro M/R/LC310) were located at the back of the target chamber. They were separated by 410 mm and had a distance of 925 mm from the centre point of the target. This gives an angle of approximately 251 between the two cameras which is the best recommended angle to do stereo vision measurements.41 The cameras were recording at the rate of 40,000 frames per second. A pair of identical Nikon lenses with a fixed focal length of 50 mm was used for both cameras. High speed cameras were triggered simultaneously using the signal generated by IR sensors. Halogen lamps were used to illuminate the target. To prevent any effect of heating from the halogen lamps, the lights were turned on just a few seconds before the test. Similar to low velocity impact tests, two types of projectile were employed to achieve rigid and semi-rigid impacts. For semi-rigid impact, HDPE projectiles with mass and diameter of 18.2 g and 24.8 mm were used. For rigid impact, aluminium alloy 6082 T6 was employed. To reduce the experimental variables, two projectiles were made with the same diameter and mass. Since the density of aluminium (2700 kg m3) is about three times bigger than that of HDPE (930 kg m3), a hollowshaped cylindrical projectile with flat nose was manufactured. The dimensions of the cylinder is shown in Fig. 17. To track the centre mass of the cylinder a narrow groove was machined with a distance of 15.5 mm from the impacting face (as shown in Fig. 17).

8.13.5.2 8.13.5.2.1

Results Semi-rigid impact

An example of 3D DIC results is shown in Fig. 18. The test was performed on LHL configuration at the impact velocity of 204 m s1. No perforation occurred at this impact velocity. The impact duration was about 0.6 ms and maximum out-of-plane

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Fig. 14 Deformation of a composite sandwich plate with uniform core (MMM) subjected to low velocity rigid and semi-rigid impacts. (a) The comparison between force traces. (b) and (c) High speed image sequences for rigid and semi-rigid impacts respectively.

displacement (8.25 mm) and maximum major strain (1.6%) occurred at the centre of the specimen at time of about 0.2 ms (Fig. 18). The out-of-plane displacement profile along the defined section of the distal composite skin is divided in two parts in Fig. 18: during loading and unloading. The interval between each profile is 25 ms. The duration of loading phase is longer in comparison with unloading phase and the deformation is more localised at the centre of the plate. Cross section of impacted specimens are shown in Fig. 19 for four impact velocities. At the velocity of 178 m s1, no failure in composite skins was observed in any of the three configurations. At this impact velocity, the central out-of-plane displacement and major principal strain, measured using 3D DIC, are plotted in Fig. 20 for uniform as well as graded cores. Similar to the results of low velocity impact (Fig. 15), the slope of the force trace is slightly lower for LHL compared to the other two configurations. The central major principal strain of LHL reaches the maximum value of 1.2% compared to 1.52% for MMM and 1.6% for HLH configurations. At the impact velocity of 204 m s1, the front-facing composite skin is perforated with a crack propagating through the foam cores (Fig. 19). In contrast, despite considerable amount of core compression in the low density foam layer for LHL configuration,

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Fig. 15 The effect of grading the core on the impact performance and failure mode of a composite sandwich structure using (a) a semi-rigid and (b) a rigid impactor. In this figure (L), (M) and (H) represent low (AIREX C70.55), medium (AIREX C70.75) and high (AIREX C70.90) density PVC foam layers.

Fig. 16 Schematic of test set up used for high velocity impact tests.

no perforation occurs for LHL and MMM cases. The displacement profile during the loading phase and the central major strain history of graded cores (LHL and HLH) are plotted against that of uniform core (MMM) in Fig. 21 for this impact velocity. The response of HLH is very different from the other two cases from the early stages of deformation (t ¼ 0.05 ms in Fig. 21(c)). The higher out-of-plane displacement of HLH configuration indicates that the front-facing composite layer was perforated at the very early stages of deformation. The central major strain of HLH reaches the peak value of 2.9% compared to 1.75% for MMM and 1.55% for LHL configurations. The response of MMM and LHL is very similar throughout the deformation. This is reflected both in terms of history of central out-of-plane displacement and major strain. At to0.15 ms however, the deformation profile for MMM is more uniform across the plate compared to LHL configuration. The more localised deformation in LHL can be the result of core crushing in the first foam layer.

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Fig. 17 Dimensions of the hollow cylindrical projectile, made of aluminium 6082 T6, used for high velocity rigid impact.

The extent of damage in the composite sandwich plates increases further by increasing the projectile initial velocity (Fig. 19). Impact velocity of 215 m s1 (impact energy of about 420 J) is sufficient to cause fracture in the distal composite skin layer for sandwich with uniform core (MMM). For both graded cores, no sign of damage exist in the distal composite layer at this impact velocity which indicates a better perforation resistance for the graded cores. All composite sandwich plates are fully perforated as the impact velocity reaches 230 m s1 in Fig. 19.

8.13.5.2.2

Rigid impact

In order to assess the influence of projectile deformability on the perforation resistance of composite sandwich structures, a series of impact tests was carried out using hollow cylindrical projectiles made of aluminium, as described in Section 8.13.5.1. Similar to the previous section, tests were performed at four different velocities including 178, 204, 215 and 230 m s1. For lower velocities, 178 and 204 m s1, for which the full perforation was less likely, 3D DIC image correlation was employed. The performance of different cores were then assessed based on the maximum out-of-plane displacement and major principal strain at the nonimpacted surface (distal composite skin). An example of the test results is shown in Fig. 22 for LHL configuration impacted at the velocity of 204 m s1. This is the same velocity as the test performed for semi-rigid impact in Fig. 18. Out-of-plane displacement and major principal strain contours are plotted in Fig. 22(a). The plate reaches approximately the same level of maximum out-of-plane displacement as the semi-rigid impact (8.25 mm) at t ¼ 0.125 ms before fibres in the distal composite skin starts fracturing. The damage in the both impacted and distal composite skins are shown in Fig. 22(b). A disc with the same diameter as that of projectile is detached by shear failure from the impacted skin. Considerable amount of delamination is also apparent in the impacted face. In the distal skin, a limited amount of fibre breakage is observed at the centre of the specimen. Major strain at the centre of the plate reaches a value of 4.5% before losing DIC data at the centre of the plate, as a result of fibre breakage. Similar to semi-rigid impact, for post-mortem examination, the impacted samples were cut in half. The cross section of the samples are compared for three different cores at four impact velocities in Fig. 23. In general, the extent of damage in specimens is greater than in those impacted exactly at the same impact velocity and energy but using a semi-rigid impactor in Fig. 19. At the impact velocity of 178 m s1, the impacted composite skin of all sandwiches are perforated. Despite considerable damage in the core, especially for the two graded cores, no damage in the distal composite skin is observed. The maximum out-of-plane displacement and major principal strain of these three configurations are compared in Fig. 24. Similar to the semi-rigid impact results in Fig. 19, the maximum strain is lowest for LHL configuration. Both out-of-plane displacement and major principal strain are highest for HLH configuration. The extent of damage increases by increasing impact initial velocity. Punching/plugging as defined in Fig. 3 is the dominant failure mode. For MMM configuration, at impact velocity of 204 m s1, the cracks kink out at 451 leaving a conical fracture surface toward the distal skin. This cone-cracked fracture zone is associated with a mixed tensile and shear failure mode.22 By increasing the impact initial velocity, the angle is gradually decreased until it nearly becomes straight (circular hole) at the impact velocity of 230 m s1. This reduction in the angle is attributed to the increase in the contribution of the shear forces as the deformation becomes more localised at higher impact velocities. At the impact velocity of 215 m s1, sandwich plate with uniform core (MMM) is perforated through both skins. For graded cores (LHL and HLH) however, full perforation is postponed to higher velocities which again shows a better impact performance of graded cores.

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Fig. 18 3D Digital Image Correlation (DIC) results for composite sandwich plate (LHL configuration) impacted at the velocity of 204 m s1 using a semi-rigid (HDPE) impactor.

Fig. 19 Cross section of impacted composite sandwich structures by a semi-rigid (HDPE) impactor at four impact velocities. In this figure (L), (M) and (H) represent low (AIREX C70.55), medium (AIREX C70.75) and high (AIREX C70.90) density PVC foam layers.

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Fig. 20 Comparison between responses of composite sandwich structures with three core configurations impacted at the velocity of 178 m s1 by a semi-rigid (HDPE) impactor. (a) and (b) The central out-of-plane displacement and major principal strain measured using 3D DIC.

Fig. 21 Comparison between responses of composite sandwich structures with three core configurations impacted at the velocity of 204 m s1 by a semi-rigid (HDPE) impactor. (a)–(c) The out-of-plane displacement profile and (d) the comparison between central major strain measured using 3D DIC.

As observed in Fig. 23, the impact initial velocity of 230 m s1 is sufficiently high to cause full perforation for all core configurations. At this impact velocity, the absorbed energy is used as a criterion to compare different core configurations. The absorbed energy is calculated by subtracting the residual energy of the projectile, after it exits the distal composite skin, from its initial kinetic energy. For this purpose, two high speed cameras were employed to track the location of the projectile before and after it impacted the sandwich plate. In some cases, the projectile had a rotational as well as a translational velocity when it exited the plate. The translational velocity was measurement by tracking the centre of the mass, which its location was previously marked by a groove in the projectile (as explained in Section 8.13.5.1). For calculating the rotational velocity, two points of the projectile were tracked. An example of the initial and residual velocity measurement is shown in Fig. 25. The absorbed energy of three core configurations at impact velocity of 230 m s1 is compared in Fig. 26. The absorbed energy is lowest for HLH configuration. It should be noted however that the difference between all three configurations is very small (about 4%).

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Fig. 22 Impact response of a composite sandwich plate (LHL configuration) impacted at the velocity of 204 m s1 using a rigid (aluminium) impactor. (a) The out-of-plane displacement (Uz) and major principal strain (emax) contours measured using 3D DIC. (b) The photograph of the impacted sample.

Fig. 23 Cross section of impacted composite sandwich structures using a rigid (aluminium) impactor at four impact velocities. In this figure (L), (M) and (H) represent low (AIREX C70.55), medium (AIREX C70.75) and high (AIREX C70.90) density PVC foam layers.

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Fig. 24 Comparison of maximum out-of-plane displacement and major principal strain, measured using 3D DIC, between three core configurations at impact velocity of 178 m s1 using a rigid (aluminium) impactor. In this figure (L), (M) and (H) represent low (AIREX C70.55), medium (AIREX C70.75) and high (AIREX C70.90) density PVC foam layers.

Fig. 25 Velocity measurement for rigid impact. The measuring of translational initial velocity (top row) and the measuring of rotational residual velocity of the projectile (bottom row).

Fig. 26 Comparison between absorbed energy by composite sandwich structures with different core configurations at impact velocity of 230 m s1 using a rigid impactor. In this figure (L), (M) and (H) represent low (AIREX C70.55), medium (AIREX C70.75) and high (AIREX C70.90) density PVC foam layers.

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Conclusions

In this article, the effect of grading the core on the deformation as well as perforation resistance of composite sandwich panels was investigated. Quasi-static bending tests in three-point and four-point configurations were performed on sandwich beams. 2D digital image correlation was employed to monitor the deformation of the core during bending. Grading the core was found to lower the strength of the beam but it caused a more stable failure process which can be especially useful in design when catastrophic failure of the structure should be prevented. Low velocity impact tests were performed on sandwich plates using cylindrical flat-nosed impactors made of steel (rigid impact) and made of high density polyethylene, HDPE (semi-rigid). The tests were conducted using a drop tower facility with impact velocities up to 3.7 m s1 with impact energies up to 205 J. The deformability of the impactor has a significant influence on damage and failure of the composite sandwich structure. The damage is more severe for rigid impactor. Density of the core layer beneath the impacted composite skin plays an important role in damage and failure initiation. Additional support provided by a denser (i.e., stiffer) layer increases shear strains at impacted composite skin in areas adjacent to impactor edges which increases the chance of shear failure in this skin. The performance of the sandwich plate were also assessed under high velocity impacts ranging from 178 to 230 m s1. Similarly, the tests were performed using both rigid and semi-rigid projectiles. High speed 3D digital image correlation was employed to extract full-field displacement and strain contours during impact. Grading the core has a notable effect on the perforation resistance. If a foam layer with a lower density is located immediately before the impacted skin, the perforation is less likely than for the uniform core. Benefit from grading the core can be increased if the failure of the impacted composite skin can be postponed for example by using a more deformable projectile. Similar to the case of intense distributed loading (e.g., sandwich plates tested by Wang et al.33 under shock loading), the results in this article show that grading the core can also provide better performance when deformation is highly localised (e.g., under low and high velocity impact loading). In this article, two graded configurations were examined over a wide range of loading conditions (from quasi-static to high velocity impact loading). The findings from this study are of much value in the application of sandwich structures to aerospace, marine, automotive and wind turbine energy sectors. In a separate study, we investigated the effect of various sandwich configurations including step-wise graded cores with the same average density as that of uniform core and core with different densities under high velocity impact loading.42 Generating failure maps of composite sandwich structures for different graded core configurations under various loading conditions can significantly benefit designers to achieve the best solutions in the minimum weight basis. Analytical as well as numerical models can be efficiently employed for this purpose. However, few attempts have been made by researchers in the literature to model perforation in foam-based composite sandwich structures.22,28,32,43 It is clearly an important aspect of the research to be tackled in the future. Accurate prediction of perforation in composite sandwich plates requires an advanced failure model for foam materials capable of prediction fracture under multiaxial loading conditions and over a wide range of strain rates.

Acknowledgments Much appreciated is the strong support received from Beijing Institute of Aeronautical Materials (BIAM) through AVIC Centre for Materials Characterisation, Processing and Modelling, for supporting Dr. Iman Mohagheghian as a postdoctoral researcher; the First Aircraft Institute (FAI) through the AVIC Centre for Structural Design and Manufacture, for supporting Dr. Long Yu during his PhD; and the Turkish Government in the form of a graduate scholarship, Professor Andy Morris, Chief Engineer, EDF Energy and AVIC for supporting Mr. Cihan Kaboglu during his PhD.

See also: 8.11 Foreign Object Impact on Composite Materials and the Modeling Challenges. 8.12 Multiscale FE Modelling and Design of Composite Laminates Under Impact. 8.14 Composites Under Dynamic Loads at High Velocities

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