The response of polymeric composite structures to air-blast loading: a state-of-the-art

Abstract

Composite materials are finding use in an increasing number of structural applications as a result of their high specific strength, high specific stiffness, thermal resistance and the potential for tailoring of properties to suit specific applications. Fibre-reinforced composites, foam core sandwich panels and fibre-metal laminates (FMLs) are examples of composite materials that are employed in high-performance engineering applications, for example in yachts, passenger aircraft, racing cars and sports equipment. Explosive loading is a potential threat to many of these structures, and therefore an improved understanding of the response of such systems to air-blast loading is important.

This paper reviews recent experimental and numerical work on the response of composite materials, sandwich structures and hybrid materials to air-blast loading. Commonly employed experimental techniques used to simulate air-blast loading conditions are described, along with the results from recent experiments on plain composite laminates, polymeric sandwich panels and FMLs. The influence of loading distribution, materials and test geometry on the failure of composites is discussed. The latter part of paper discusses numerical modelling considerations and reports methods and results from recent numerical modelling work on the blast loading of composites.

Introduction

Explosions have many causes, such as the ignition of a gas in a processing plant (vapour cloud explosions), the rapid depressurisation of a pressure vessel^1,2 in an aircraft that has suffered a breach in its structural integrity,³ as well as the detonation of explosives.^1,4 Vapour cloud explosions and mechanical failure of pressurised structures are usually accidental events and can be prevented through careful design and vigilant maintenance/inspection protocols. Explosive detonations are generally the result of military action or deliberate terrorist activity.

The requirement to protect people, plant and structures from explosions has greatly increased in recent years, because of an alarming increase in global terrorist activity. Indeed, the US State Department figures indicate that terrorist attacks caused the death of more than 87 000 people during the 5-year period from 2006 to 2010.⁵ While there were very few explosions associated with these attacks, explosions caused a disproportionately high number of deaths and injuries.⁵ Damage is accentuated when the explosion occurs in a confined space, such as in a subway tunnel or a transport vehicle.

Composite materials are finding increasing use in a wide range of structural applications. Such trends are associated with advantages, such as high specific strength and stiffness properties, a superior thermal resistance and the ability to tailor their properties to a required application. Examples of the use of composite materials in load-bearing structures include bicycle frames, racing car bodies, marine vessels, the latest generation of fuselages and aircraft wings. Fibre-reinforced polymer composites are also widely used in hybrid structures, such as foam core sandwich panels and fibre-metal laminates (FMLs). Polymer composite sandwich panels are being deployed in the marine and aerospace industries, exhibiting excellent specific stiffness properties because of the increased second moment of area. Fibre-metal laminates, such as Glass Laminate Aluminium Reinforced Epoxy (GLARE), are being used in large passenger aircraft as a result of their excellent fatigue performance.

Given the possibility of explosive loading on such structures,⁶ there is a clear need to understand the response of polymer composite materials to conditions associated with air-blast loading. This article reviews recent work on the response of polymer composite materials to air-blast loading. Fundamental blast loading theory is initially presented, followed by descriptions of the common experimental techniques used to simulate air-blast loading conditions for research purposes. The findings of recent experimental investigations concerning the response of plain composite laminates, polymeric sandwich panels and FMLs are then reported. The final part of this review focuses on numerical modelling considerations, with particularly emphasis on recent numerical modelling work on the blast loading of composites.

Air-blast loading

Basic theory

An explosive detonation in air is followed by a shock wave that rapidly compresses the surrounding air, creating a high pressure, short duration blast wave, which can, in turn, have destructive effects on objects in its path. During the process of an explosion, the blast travels as an incident wave until it strikes an object. Upon striking the object, a reflected wave is generated which travels back towards the point of explosion. At a point, some distance from the centre of the explosion, the reflected wave meets the incident wave, producing a single vertical wave front. The structure below the point of intersection of the reflected wave and the incident wave experiences a single shock, whereas the surface above this point experiences a shock history, which is a resultant of the incident and reflected waves. During the blast process, the pressure builds up to a peak value, then decays to a local ambient value, dropping further to a partial vacuum with very small amplitude and eventually returns to ambient pressure. The portion of the pressure–time history below zero is referred to as the ‘negative or suction phase’, which has little effect on the response of structures, and the portion above zero is called the ‘positive phase’.⁷ Figure 1 shows a typical pressure–time history for a blast wave.⁸ The characteristics of the blast wave initially depend upon the source of the explosion, but are also influenced by the propagation media, distance travelled, degree of confinement (creating reflections, causing quasi-static pressure accumulation and preventing dissipation of the explosive energy) and proximity to the ground. In most blast studies, the negative phase of the blast wave is ignored, and only the parameters associated with the positive phase are considered, because it is generally accepted that damage is caused by the positive phase.^9,10

Typical pressure–time history from a far-field explosion

The distance between the source of the explosion and the object of interest is known as the stand-off distance. Increasing the stand-off distance causes the pressure magnitude to decrease and the blast duration to increase. Near-field explosions occur in very close proximity to a structure (short stand-off distances), and the resultant loading is difficult to approximate using closed-form solutions. As the stand-off distance increases, the explosion is termed as a far-field explosion. If the explosion is unconfined, these are lower pressure, longer duration blasts with the characteristic shape shown in Fig. 1.^1,4 It is evident from this figure that an unconfined far-field explosion is characterised by a rapid rise in pressure to the peak overpressure followed a gradually decaying slope. The properties of the far-field pressure profile can be determined by the Hopkinson–Cranz scaling laws, where pressure and duration are expressed as variables of the Hopkinson-scaled distance Z given in equation (1). 1 where R is the stand-off distance (m) and w is the Trinitrotoluene (TNT) equivalent charge mass (in kg).

Experimental techniques

The complexity of the explosive loading regime, as well as the multiplicity of variables that influence it, leads to many possible explosion scenarios that could potentially be applied to a composite structure. As mentioned above, one of the advantages of composite materials is that their properties can be tailored to suit specified operating and overload conditions. However, the structural designer must identify the most likely threats, since there is no universal ‘ideal’ material (composite or otherwise) for every potential scenario. Whereas the response of composite materials to static and low velocity impact loading has received much attention, less is known about their behaviour under explosive loading conditions.

While it would be ideal to use scaled explosive detonations for research purposes, experimentation involving explosives is hazardous to perform and carries significant legal responsibilities. As a result, it is often difficult for research institutions to conduct meaningful blast tests. Measuring the loading conditions and resulting structural response is challenging, since explosive loading produces high-intensity pressure waves, light flashes as well as a fireball. Owing to the multiplicity of possible explosion loading conditions, and the difficulties associated with explosive detonation testing, some researchers have developed techniques for simulating what are considered to be the salient features of a blast load for different threats.^3,11–36 The usefulness of these different devices depends on the blast loading characteristics under consideration. Experimental approaches for replicating air-blast loading include:

•

pressure blow down apparatus

•

impact testing with ‘soft’ projectiles

•

shock tube facilities

•

in field, medium scale, explosive detonations at large distances from the test specimens

•

small laboratory-scale explosive detonations in close proximity to the test specimen.

The pulse pressure loading works by Schleyer et al. ^3,11,12 are good examples of the use of pressure blow down apparatus to generate explosion loading. Pulse pressure loading rigs simulate relatively long duration events, such as hydrocarbon gas explosions arising from industrial accidents and rapid depressurisation of aircraft following fuselage rupture. Typical pressure–time histories reported in Refs. 3, 11 and 12 are triangular with peak pressures 100–400 kPa, typical load durations in the range 25–200 ms (longer durations correspond to higher pressures), and rise times between 15 and 100 ms. Fibre-metal laminates have been subjected to pulse pressure loading by Simmons et al. ¹³ However, the test facility was not capable of generating sufficiently high pressures to cause significant damage. The blast pressure loading resulting from a hydrocarbon gas explosion is, in general, adequately simulated using a pulse pressure loading device, but is unsuitable for investigating damage resulting from the detonation of close-range plastic explosives. In particular, the rise times are too long to represent the loads associated with an explosive detonation.

Soft projectile impact involves launching deformable projectiles at test specimen in an attempt to produce shock-type loading on the specimen. The loading characteristics are highly repeatable and are easy to idealise for the purposes of modelling.¹⁴ The properties can be varied by altering the projectile material, density, projectile length and impact velocity. Cellular materials have been used to simulate blast loading; for example, Radford et al. ¹⁴ developed a technique in which small cylinders of aluminium foam were fired from a gas gun at impact velocities of 500 m s⁻¹. In addition, foam projectile impact has been used to simulate blast loading in other works on metallic sandwich structures^15,16 and, more recently, by Russell et al. ¹⁷ to study the blast loading response of square section honeycomb cores sandwich panels manufactured from carbon fibre epoxy laminates. The initial specific impulse, obtained from the initial impact velocity and the known projectile mass, was varied by increasing the impact velocity, and greater levels of damage were obtained as impulse was increased. High-speed camera footage was used to obtain back face mid-point deflection but failed to elucidate the details of the failure processes at low to medium impulse levels.¹⁷

In shock tube apparatus, pressure loading is generated by a rapid release of gas which creates a shock wave that propagates down a tube towards a test specimen. Shukla and co-workers^18–23 have used shock tubes extensively to test composite beams under shock pressure loading. Typically, the specimen is larger than the shock tube diameter^18–23 and is located a few millimetres from the end of the tube – this causes the loading to be concentrated over the central region of the specimen and to be non-uniform around the periphery of the tube. Pressure transducers measure the incident and reflected pressure pulses in close proximity to the test specimens.²² Typical incident and reflected pressure waves have a peak pressure of 1–8 MPa, a steep rise time (typically 60 μs) and a relatively long decay (4–8 ms). The recorded wave speeds vary from 1030 to 1300 m s⁻¹.^18–23 Shock pressure loading is used as a cost-effective, easily controllable alternative to explosive detonation. This technique replicates some of the essential features of the pressure loading that may arise from an unconfined far-field air-blast explosion. The results can be used to indicate the typical failure modes and the dynamic response of composite sandwich structures, although the size of the shock tube is very limited. This approach is useful for validating numerical simulations that require certainty regarding the loading definition, and can also be used to compare materials loaded under similar conditions.

Medium-sized explosive field testing involves the detonation of explosives on the 1–100 kg scale at stand-off distances of several metres.^24–26 Arora et al. ^24,25 performed field tests on composite panels mounted in steel cubicles subjected to blast loading following the detonation of 30 kg C4 charges at stand-off distances of 8 and 14 m. Pressure transducers placed at equal distances from the explosive recorded triangular pressure–time histories that exhibited an almost instantaneous rise time, a relatively slow decay (giving a duration of 6⋅3 ms at 14 m stand-off and 5⋅7 ms at 8 m stand-off), and peak pressures of approximately 200 kPa (14 m) and 800 kPa (8 m).²⁴ High-speed cameras located inside the protected cubicle provided information about the transient response. Digital image correlation (DIC) was employed to obtain transient deflection and strain fields of the composite panels.

Where it is possible to scale the structural dimensions to below 0⋅5 m, laboratory explosive detonation experiments offer a cost-effective alternative to field testing. Explosive charges are typically less than 100 g, and are detonated at distances of up to 500 mm from the test specimen.^27–30 The spatial and temporal characteristics of the blast loading following explosive detonation are controlled by varying the explosive employed, charge geometry, explosive mass, stand-off distance and propagation media. For example, the stand-off distance can be varied to reproduce localised blast loading at close proximity, or increased to produce more uniformly distributed blast loading.²⁹ While much of this type of testing has concentrated on metals and metallic sandwich panels (examples include Refs. 27–29), Langdon and co-workers^31–36 have performed numerous laboratory-scale air-blast experiments on composite materials using these methods.

Polymer composite laminates

When subjected to air-blast loading, fibre-reinforced polymer composite laminates fail in a number of different modes involving a multiplicity of failure mechanisms. Table 1 provides an overview of recent experimental investigations into the air-blast response of polymer composite laminates. Not surprisingly, carbon and glass-fibre laminates have been the subject of most investigations, with a range of matrix types including polyetherimide, epoxy and vinyl ester. Small-scale testing and loading generated by either explosive detonation or shock tube pressure devices are the two predominant test methods.

Table 1.

Summary of air-blast loading experiments on composite materials

Group	Loading type	Structure	Fibre type	Matrix	Failure modes evident
Yahya et al. ^35–38	PE4 detonation, <75 g, 10–200 mm Stand Off Distance (SOD) (near-field)	90 mm dia. panel	Glass Fibre (GF), Carbon Fibre (CF) (woven)	PEI, epoxy	Matrix cracking, delamination, fibre buckling, fibre fracture
Franz et al. ⁴⁰	PE4 detonation, 0⋅4–1⋅2 g, 13 mm dia.	100 mm dia. panels	GF (chopped strand mat)	Polyester	Matrix cracking, delamination, fibre fracture
Comtois et al. ³⁹	PE4 detonation, 0⋅5–1⋅5 g, 54–500 mm SOD	Panel	GF, CF (woven, Unidirectional (UD) cross-ply)	Epoxy	Delamination, fibre fracture
Shukla et al. ^20,48	Shock pressure	Beam	GF	Vinyl ester^20,48 and PU coating²⁰	Delamination, fibre fracture
Ha et al. ⁴²	15⋅88 kg ANFO detonation, 1⋅5 m SOD	As retrofitting layers for concrete panels	CF	Epoxy, PU coating	Prevent cracking of concrete, spalling
von Klemperer et al. ^43,44	PE4 detonation, <10 g, 90 mm SOD (near-field)	90 mm dia. panel	CF	Epoxy and metallic filler powders	Matrix cracking, delamination, fibre fracture
Ravi et al. ⁴⁷	50 mg PETN detonation	Single edge notch specimens (beams)	GF	Polyester	Crack propagation
Dobyns and Avery¹²²	Explosive detonation, 15–25 g, 150–200 mm SOD	Panels	CF	Epoxy	Delamination, fibre fracture

PU: polyurea; CF: carbon fibre; GF: glass fibre; UD: uni-diretional; PEI: Polyetherimide; SOD: stand-off distance; ANFO: ammonium nitrate fuel oil.

A number of investigators have undertaken detailed investigations of the failure processes in air-blast-loaded polymer composite laminates.^35–39 Yahya et al. ^35–37 employed small-scale air-blast loading to characterise the blast resistance of several types of composite material. A number of panels were sectioned, post-testing, in order to elucidate the failure mechanisms occurring within the test samples, and typical examples are shown in Fig. 2.³⁸ At low impulses (below 4 Ns), buckling failure of the top surface fibres as well as extensive fibre fracture in the rear surface plies was observed. Closer inspection shows that there is little, if any, delamination in evidence in these samples. At higher impulses (6⋅1 Ns), fibre damage occurs through the depth of the laminate and a small delamination is evident in the centre of the panel.³⁸ It is likely that the lack of delamination within these panels is a result of the very high interlaminar fracture properties of the laminate. It was also suggested that the absence of delamination may reduce the overall blast resistance of the composite.³⁷ Similar failure mechanisms were noted following testing on a range of glass-fibre-reinforced PEI laminates.^36,37 Figure 3 shows cross-sections of a number of GF/PEI laminates subjected to impulses of up to 9⋅0 Ns. As before, limited delamination in the panel centre, and fibre fracture, is evident in the damaged panels. It was noted that the difference between the impulse required to initiate damage (7⋅9 Ns) and that to effectively destroy the laminate (9 Ns) was small, suggesting that once damage had been initiated, complete failure quickly ensued. Similar observations were made by Tekalur et al. ¹⁹ who observed that a carbon fibre-reinforced vinyl ester composite exhibited little sign of visible damage before complete failure.

Photographs of cross-sections of 4⋅2 mm thick carbon fibre/Polyetherimide (PEI) panels subjected to blast loading

Photographs of cross-sections of glass-fibre/PEI (Polyetherimide) panels subjected to blast loading

Franz et al. ⁴⁰ manufactured and tested both single- and multiple-panel E-glass chopped strand mat/polyester structures using a ballistic pendulum facility. Three predominant failure modes were observed; these being delamination, matrix cracking and penetration. The authors concluded that the blast resistance of structural component could be increased by employing a graded design, whereby the foremost layers offer both high energy absorption characteristics and superior damping properties, whereas the rearmost layers offer a higher flexural rigidity.⁴⁰

Comtois et al. ³⁹ tested relatively thin glass and carbon fibre-reinforced epoxy laminates based on a quasi-isotropic stacking configuration. Following testing, delamination and fibre fracture were observed at the boundaries of the test panels, leading the authors to conclude that the support conditions have a significant effect on the mechanisms of damage development in the panels. The authors observed that there was less fibre damage in the carbon fibre-reinforced composites than in their glass-fibre-reinforced systems.³⁹

A number of researchers have investigated the blast resistance of polyurea (PU)-based polymer composite laminates after it was shown to enhance the properties of concrete structures subjected to explosions.^20,41,42 Tekalur et al. ²⁰ bonded a layer of PU to the face of an E-glass vinyl ester laminate and showed that the presence of such a surface layer resulted in a significant enhancement of the blast resistance of the composite. Ha et al. ⁴² also demonstrated that the incorporation of layer of polyurethane to a carbon fibre-reinforced plastic increased the composites' ability to reinforce concrete structures against blast loading.

Several researchers have investigated the possibility of modifying key properties of polymer composite laminates via the addition of rigid particles (such as metallic fillers,^43,44 carbon nanotubes⁴⁵ or urea formaldehyde⁴⁶). von Klemperer and co-workers^43,44 added copper and aluminium powder fillers to carbon fibre epoxy laminates and showed that the laminates with filler particles outperformed their plain composite counterparts under blast loading conditions (as the damage exhibited by the laminates decreased in the case of those with filler particles). The authors noted, however, that the differences in performance were not significant.⁴³

Ravi et al. ⁴⁷ undertook a fundamental study to investigate the mechanisms associated with dynamic damage growth in modified single edge notch (MSEN) samples, glass-fibre/polyester laminates loaded by stress pulses generated by explosive charges. Here, two explosive charges were detonated simultaneously on the shoulders of the MSEN sample. Detonation of the charges generated compressive stress waves that were subsequently reflected at the free end of the sample generating tensile wave pulses that effectively loaded the sample to failure. The authors studied the effects of notch angle on damage progression by machining pre-cracks at various angles, and found that damage always propagated perpendicular to the loading, regardless of the initial crack orientation. It was also shown that damage was more severe under dynamic loading than in similar samples loaded at quasi-static strain-rates.

Hebert et al. ⁴⁸ studied the shock resistance of polymer composite laminate panels based on glass-fibre-reinforced fibres embedded in vinyl ester and polyurethane resins. The fibre preforms used in the manufacture of the laminates were based on 0 and 90 fibre angles with through-thickness polyester stitching to maintain the orientations of the glass-fibres during lap-up and processing. Three fabric areal densities were considered, with values ranging from 1⋅22 to 3⋅66 kg m⁻². Following manufacture, the panels were placed in a shock tube and subjected to incident pressure of up to 7⋅53 MPa. Damage, in the form of fibre fracture, tended to initiate around the boundaries of the test panels. With increasing shock pressure, delamination extended inwards from the panel boundary. Damage was significantly lower in the polyurethane-based composites, highlighting the impressive energy-absorbing characteristics of the resin.

Composite sandwich panels

Sandwich panels typically comprise a relatively soft core between two stiff outer face sheets. The addition of a core increases the bending stiffness by increasing the second moment of area of the structure without significant weight penalty. Thus, such structures have high specific strength and stiffness, as well as acoustic damping properties, making them attractive materials for transport applications. Sandwich structures, particularly those with Nomex honeycomb cores, are extensively used in aircraft, notable examples being the Boeing 747, 757 and 767 aircraft and the Beech Starship.⁴⁹ Other sandwich structures are also used in the walls of luggage compartments, naval vessels,⁵⁰ surfboards and yachts.⁵¹

There is an enormous possibility for potential combinations of face sheet and cores, including the variation of geometry (thickness of face sheets and core), material (resin, reinforcement, core material), bonding and manufacturing methods. As might be expected from the multiplicity of combinations, research on the blast resistance of composite sandwich panels has been performed on a wide range of panel types with no common material, test method, loading condition or geometry emerging as a benchmark. Table 2 presents a summary of recent experimental investigations into the response of composite sandwich panel to air-blast loading. The investigations reported in the open literature can be grouped into three types – small-scale explosive detonation (near-field) tests, shock tube experiments and large-scale explosive detonation (far-field) tests.

Table 2.

Summary of air-blast loading experiments on sandwich structures

Group	Loading type	Structure	Face sheet material	Core material	Failure modes evident
Shukla et al. ^18–23,52	Shock pressure	Beams	GFVE^18–23,2	Corecell (SAN) foam^{18–21,23,52}	Core compression and cracking, face sheet delamination, deformation
			PU coatings⁵²	Corecell (SAN) foam^{18–21,23,52}
			3D GFVE²²	Polyisocyanurate foam²²
Langdon et al. ^31,53–54	PE4 detonation, <75 g, 10–200 mm SOD (near-field)	90 mm dia. panels	Glass Fibre Epoxy (GFE) Al alloy	Al honeycomb	Core compression and cracking, face sheet delamination, deformation, debonding, fibre fracture, fragmentation
Langdon et al. ^31,53–54	PE4 detonation, <75 g, 10–200 mm SOD (near-field)	200 mm dia. panels	GFVE	Polyvinylchloride (PVC) foam (divinycell)
Arora et al. ^24,25	PE4 detonation, 30 kg at 8–14 m SOD (far-field)	Panels, 1⋅6×1⋅3 m	GFE	Corecell (SAN foam)	Core shear and cracking, face sheet delamination, debonding

GFVE: E-glass-fibre vinyl ester; PU: polyurea.

Shukla and co-workers^18–23,52 performed research into the response of sandwich panels subjected to shock pressure loading. Wang et al. ²¹ reported results from shock tube experiments on sandwich beams with E-glass-fibre vinyl ester (GFVE) face sheets and a Corecell polymeric foam core. The foam core was ‘stepwise graded’ – it comprised three, separate but equal thickness (12⋅7 mm), different density foams.²¹ The three foam densities were 58, 92 and 150 kg m⁻³ and were bonded together in two different configurations, namely, configuration (1) with the foam density (and hence wave impedance) increasing through the core and the low density foam being closest to the loading face (low/middle/high) and configuration (2) where the intermediate density and low density pieces had switched position so that the intermediate density foam was closest to the loading face (middle/low/high). The incident peak pressure was approximately 1 MPa, and the reflected shock peaked at 4⋅8 MPa. Digital image correlation was used to capture the dynamic response of the panels. The energy losses and deformation energies for the two configurations were similar.²¹ The beams exhibited multiple failure modes including core compression, cracking, delamination and inelastic deformation. Large compression was evident in the foam core when the least dense foam was closest to the loading face, improving the performance of configuration (1). Configuration (2) exhibited limited core compression and greater overall damage in the panel.

Gardner et al. ⁵² extended the work of Wang et al. ²¹ by examining the influence of PU interlayers on the shock resistance of GFVE sandwich beams with Corecell foam cores. Here, the thickness of the 150 kg m⁻³ foam used in the previous study was reduced from 12⋅7 to 6⋅35 mm, and a 6⋅35 mm thick PU interlayer was employed, keeping the thickness of the overall sandwich beams consistent with the previous tests by Wang et al. ²¹ In half the tests, the PU layer was placed at the face sheet–foam interface nearest to the loading, and in the remainder of the tests, the PU layer was at the foam–face sheet interface furthest from the shock load. The configurations are shown schematically in Fig. 4. Core compression, face sheet delamination and core cracking were all observed.⁵² It was found that placing the PU interlayer in front of the high density foam (Configuration 2) resulted in greater compression in the foremost foam layers. This lowered the strength of the initial shock wave that reached the rear face sheet, which in turn reduced the in-plane strain and the overall deflection of the panel, relative to Configuration 1. The PU layer redistributed the pressure loading over a wider area when it was placed at the front face sheet–foam interface. The performance was improved when the PU interface was placed at the rear side of the panels. Gardner et al. ⁵² do not present clear comparisons to the results obtained by Wang et al. ²¹ for Configuration 1 to determine if the PU layer offers benefits when compared to the equivalent thickness foam panel baseline. It should also be noted that PU is considerably denser than polymeric foam and would result in a beam that is 24% heavier than those tested by Wang et al. ²¹

Schematics showing the specimen configurations used for shock tests on graded core sandwich structures⁵²

Tekalur et al. ²² studied the effect of stitching a polyisocyanurate foam on the shock resistance of sandwich panels based on three-dimensional (3D) glass-fibre/vinyl ester face sheets. Tests were undertaken on unstitched, partially stitched and densely stitched simply supported panels, where it was shown that through-thickness stitching delayed damage initiation within the volume of the material and increased the shock resistance of the structures.²²

Jackson and Shukla²³ considered the performance of sandwich specimens subjected to sequential impact and air-blast loading. Tests were undertaken on coupons with dimensions 254×102×60 mm having SAN cores and (0°, +45°, 90°, −45°)_s E-glass/vinyl ester skins. Impact tests were conducted at both low and high velocities using a drop-weight impact tower and a Winchester Magnum rifle, respectively. The samples were subjected to between one and five impacts at pre-determined locations. Damage in panels subjected to low impact velocities was localised to the top skin and the foam core, whereas high velocity impact generated damage that was most severe on the exit face. Subsequent blast tests showed that the blast performances of panels previously damaged by high velocity impact loading were superior to those of equivalent panels subjected to prior low velocity impact damage. This is shown in Fig. 5 where the recorded impulse is plotted against the number of prior impacts, from where it is clear that low velocity impact loading is the more detrimental mode of loading.

Impulse generated by blast loading as a function of the number of impacts¹⁷

Langdon et al. ⁵³ compared the blast resistance of aluminium honeycomb sandwich structures based on both glass-fibre-reinforced epoxy and aluminium alloy face sheets. The effect of core thickness on energy absorption was also considered. Damage in the composite-based structures took the form of core crushing and shear failure, debonding at the skin–core interface and cracking of the composite face sheets. It was shown that the composite sandwich panels exhibited smaller permanent displacements than the all-aluminium counterparts. It was also noted that sandwich structures with thicker cores exhibited smaller residual displacements than those with thinner cores [53]. In addition, greater amounts of energy were dissipated in crushing thicker sandwich panels than thinner structures.

Langdon et al. ^31,54 tested glass-fibre vinyl ester composite panels having an equivalent mass to sandwich panels having the same composite in the face sheet and a PVC foam core. The panels had a 200 mm diameter exposed area and were loaded by detonating plastic explosive in close proximity to the panels.^31,54 Delamination of face sheets, core compression, core fragmentation and fibre rupture were observed,⁵⁴ as shown in a typical example in Fig. 6. Finite element (FE) modelling of the panel response was also performed.³¹ The tests showed that, in this particular case, the plain composite panels offered a superior resistance to blast loading because they could be subjected to higher charge mass explosions without rupture.³¹ The FE analysis and the experiments showed that this was because of the higher velocity transferred to the front face sheet during the blast loading, which resulted in face sheet failure. The high velocities caused fibre fracture in the front face sheet, which exposed the soft core to the blast loading, and which further resulted in core fragmentation.³¹

a Cross-section view of a panel with a 200 kg m⁻³ PVC foam core and glass-fibre vinyl ester face sheets subjected to an impulse of 44⋅6 ns; b front face of a panel with a 80 kg m⁻³ PVC foam core and glass-fibre vinyl ester face sheets subjected to an impulse of 23⋅1 ns

Few workers have undertaken experimental tests on large sandwich structures. An exception to this is the work carried out by Arora et al. ^24,25 investigating the blast resistance of large panels. Arora et al. ^24,25 present transient response measurements from blast tests on sandwich panels with E-glass-fibre epoxy face sheets and polymeric foam (Corecell) cores. The panels were considered to be representative of full-scale panels used in marine transport applications, with an exposed area of 1⋅6×1⋅3 m. The panels were loaded by detonating spheres comprising 30 kg of plastic explosive (PE4) at 8 and 14 m from the panel. Transient strain and displacement field data were captured using high-speed photography and DIC.^24,25 In addition, a laser gauge mounted on a steel support was used to obtain the displacement of the centre of each panel, and a pressure gauge was used to record the loading history. Figure 7a shows DIC contour plots of the out-of-plane displacement, the maximum principal strain and the shear strain at various time intervals during the test. The horizontal bar is because of the laser gauge steel support beam. The authors noted that a uniform and symmetrical response was achieved over the panel up to maximum displacement.²⁵ Figure 7b shows the variation of the central deflection with time as determined from both the DIC and laser gauge from where it is clear that the DIC accurately captures the global response. Small discrepancies between the two sets of data were attributed to vibrations in the steel support. Damage initiated on the front face sheet, because of cracking, and was accompanied by localised delamination. Core shear cracking and interfacial failure were also evident. The back face sheets did not exhibit visible tearing and cracking failures.²⁴ The authors highlighted the importance of boundary conditions with regard to blast mitigation.

a Digital image correlation (DIC) analyses; b a plot of pressure–time and displacement–time using both DIC and laser gauge centre point measurements²⁵

Fibre-metal laminates

Recently, there have been a number of investigations into the blast performance of polymer composite and metallic multi-layered systems. Fibre-metal laminates are hybrid structural materials comprising alternating layers of fibre-reinforced polymer composite laminates and thin metallic sheets, most typically glass-fibre-reinforced polymer and aluminium alloy. Fibre-metal laminates were originally developed for the aircraft industry as a lightweight alternative to thick metallic sheets, and have demonstrated excellent fatigue performance⁵⁵ and, in some cases, good impact properties.^56,57

Fibre-metal laminates with thermoset matrices

The only commercially used FML is GLARE©, which comprises thin sheets of aluminium alloy (usually 2024-T3) and layers of S2 glass-fibre-reinforced epoxy resin, as shown in the cross-section of GLARE 3 presented in Fig. 8. Numerous GLARE© variants exist, based on different lay-ups of the unidirectional glass-fibre layers and also the different alloys employed in the FML. GLARE© is used in Airbus A380 aircraft to improve the fatigue properties of its components,⁵⁵ but some GLARE© variants have also demonstrated superior low velocity impact performance and an improved ballistic limit velocity, relative to aluminium structures with an equivalent mass.^56,57

Photograph showing a cross-section view of GLARE 3³²

One variant, GLARE 5, has been certified as a replacement material in unit load devices (aircraft luggage containers that are usually manufactured from aluminium alloy) but is seldom used because of the high cost of GLARE©. Fleisher⁵⁸ showed that a GLARE container was superior to the equivalent aluminium construction, and was able to contain an explosion similar to that which destroyed Pan Am Flight 103 (over Lockerbie, 1988). The absence of detailed experimental procedures has prevented the results from being replicated by others.

Langdon et al. ³² reported results from small-scale blast loading experiments on 200×200 mm GLARE 3 panels. The loading was generated by detonating PE4 discs at a stand-off distance of 200 mm from the panel surface, and directing the blast waves down a square section tube in front of the panel. The PE4 charge height and mass were varied to obtain a range of responses in the panels. The panels exhibited large plastic deformation with a classic yield line formation pattern that would be expected from fully clamped metal plates subjected to uniform loading. Using the dimensionless analysis developed by Nurick et al.,^27,29 the permanent displacements of the GLARE panels were smaller than those for other metals and composites,³² indicating that the material was worthy of further study. However, when the explosive charge was moved closer to the panels, failure was catastrophic because of the highly localised loading and deformation.

Other relevant work reported on GLARE has focussed on dynamic crack propagation and fracture.^59,60 Mediavilla Varas et al. reported results from tests on notched plates subjected to loading arising from an explosive line charge⁵⁹ and demonstrated that both aluminium and GLARE exhibited ductile crack propagation, whereas the CFRP panel exhibited a brittle fracture response. Pressurised barrel test results^59,60 have indicated that higher crack propagation velocities were measured in the CFRP material (up to 2000 m s⁻¹).⁵⁹ The high propagation velocity was attributed to a more brittle failure process in the CFRP compared to that in GLARE and aluminium alloy. This inferior performance was attributed to the lower toughness of the carbon fibre composite.⁶⁰

Fibre-metal laminates with thermoplastic matrices

Fibre-metal laminates manufactured using fibre-reinforced thermoplastic polymers have, in recent years, been attracting significant attention.^61–67 Such laminates are mostly based upon polypropylene, because it is easily recyclable^62,63 and offers good toughness and impact resistance.⁶¹ Langdon and co-workers reported the results from several extensive experimental investigations of polypropylene-based FMLs.^{33,34,64–67} In early work, Langdon et al. ³³ studied small-scale (126×126 mm exposed area) FML panels manufactured from aluminium alloy and three different composite materials. The results indicated that, in a non-dimensional form, the mid-point displacements of the different configurations of FML panel were similar to those obtained from aluminium plates despite differences in failure mechanisms.³³ Subsequent work has examined the blast response of aluminium alloy and woven glass-fibre polypropylene (GFPP)-based FML panels to both localised^31,65–67 blast loading and uniformly distributed⁶⁴ blast loading. The characteristic failure modes of the GFPP-based FMLs were large plastic deformation, front face ring buckling because of localised compressive loading, debonding at the composite–metal interface, rupture and petalling failures.^34,64–67 Delamination failures were not evident in the panels, unlike the FMLs with unidirectional fibre layers. Typical failure modes for blast-loaded FML panels are illustrated in the photographs shown in Fig. 9. Figure 9a–c shows photographs of typical failures in 2/1 configuration FMLs. The panels with unidirectional glass-fibre layers exhibited delamination (as evident in Fig. 9a and b ), whereas the panels with woven fibres do not (shown in Fig. 9c ). In addition, the back faces of FMLs based on unidirectional plies ruptured in the same orientation as the rearmost fibre direction, as shown in Fig. 9b . Debonding, fibre fracture and large inelastic displacement of the aluminium are characteristic failure modes in thicker FML panels, as shown in Fig. 9d .

a Cross-section of a 2/1 FML with unidirectional fibre layers, showing delamination;³³ b back face of a 2/1 FML with unidirectional fibre layers, showing rupture in the direction of the fibres;³³ c cross-section of a 2/1 FML with woven composite layers, showing no delamination failure;³⁴ d cross-section of a ‘thick’ 4/3 FML, showing multi-layer debonding and back face rupture³⁴

Like other panels, spatial distribution of the loading is critical to panel behaviour. Locally loaded panels exhibit fibre fracture and panel rupture in the areas of the highest loading, whereas uniformly loaded FMLs do not exhibit damage localised to the panel centre. Hence, uniformly loaded panels exhibited higher impulses to tearing, and this was evident from the FML test results presented by Langdon et al. ⁶⁴ Debonding occurs in the uniformly loaded FMLs, but is evident across the whole interface and not localised to the centre. A typical example of a uniformly blast-loaded FML panel is shown in the photograph in Fig. 10. Failures are located at both the panel edges and the central region, while the section appears ‘wavy’ because of the elastic rebound of the composite constrained by the plastically deformed aluminium layers. Interestingly, dimensionless analysis techniques showed the mid-point displacements from both the uniform and localised blast tests that exhibited linear trends of increasing normalised displacement with increasing non-dimensional impulse in a similar way to metal plates.^64,66

10.

Photograph of a cross-section from a glass-fibre polypropylene (GFPP)-based fibre-metal laminate (FML) panel subjected to uniformly distributed air-blast loading

Numerical modelling considerations for composite materials

Experimental investigations into the response of composite, sandwich and FML structures have great value in elucidating failure modes, in understanding the mechanics of the blast response and in generating data for systematically evaluating designs and modelling approaches. The development of computer models using FE analysis is a relatively quick and inexpensive process, and can provide additional insights into the response of composite structures, particularly in situations where this can be challenging to measure during experiments. Ideally computational simulations, once properly validated against robust experimental data, can be used for as much of the design process as possible. In such circumstances, only a limited number of material and structural blast tests are required for validation purposes and the design cycle can become more responsive and cost-effective. Once computer models are verified against typical blast tests, covering the upper and lower bound cases, systematically designed parametric studies can be undertaken using validated numerical models. The two main challenges in modelling the response of blast-loaded composite structures are the modelling of the blast loading process and the development of suitable composite material models covering the important failure mechanisms at appropriate strain-rates.

Modelling of blast loads

As described in the Air-blast Loading section, blast loading generated from the detonation of explosives is an extreme dynamic loading event. Owing to the complex nature of the blast event, both spatial and temporal characteristics have to be simplified to capture only the essential features of the loading. For far-field explosions, when the stand-off distance is large, the impulse generated during the positive phase is used and the negative (suction) phase is often ignored, as described in equation (2). 2 where P(t) is the positive pressure as a function of time.

There are various forms of P(t) proposed by different researchers, often described by exponential functions, such as the Friedlander equation expressed in equation (3).^1,68 Some of these are given in Table 2. 3 where b is the decay factor, which is a function of P _SO.

The simplified profile expressed in equation (4) was also used by other researchers.^69–72 A triangular blast and Heaviside pulse were also proposed,^73,74 as described by equation (5). Based on the Friedlander equation in equation (3), a modified Friedlander equation is given in equation (6). For impulsive loading, the exact temporal distribution of the blast loading is of less importance than the spatial distribution of the loading. At large stand-off distances (larger than the greatest dimension of the structure in the path of the blast wave), the spatial distribution is often assumed to be uniform over the incidence face. However, at short stand-off distances, the loading is more localised. 4 where λ is the decay constant. 5 where H(t) denotes the Heaviside step function, δ _b is a tracer that can be taken as 1 or 0 depending on whether the sonic-boom or triangular blast load is considered, and t* denotes the shock pulse length factor. 6 where A is a decay coefficient.

In numerical modelling, there are two approaches to modelling of near-field explosion loading. The first approach is to decouple the loading and the structural response. Typically, a pressure distribution such as that shown in equation (7) is assumed. The pressure function p(r) is a function of radius from the plate centre, and may be based on empirical modelling, blast loading charts, experimental measurements or on independent modelling of the detonation process in a separate code or time-step. 7 where 8

In equation (8), r ₀ is the radius of the explosive disc used in the experiments,³⁴ k is an exponential decay constant, which models the pressure distribution over the exposed area of the plate, and , where L is the length of the panel. The decay constant k that is related to the variation of the total impulse I used in the numerical simulations can be interpolated. The total impulse is defined as 9

For example, Bonorchis and Nurick⁷⁵ proposed the relationship shown in equation (9) for a square plate subjected to a near-field explosion. Karagiozova et al. ^67,76 modelled the blast loading process using Autodyn and fitted a pressure pulse shape function to the predictions from Autodyn. The pulse shape was then imported into ABAQUS/Explicit, which was used to predict the response of blast-loaded FML panels.^67,76 Vo et al. ⁷⁷ also implemented equations (7) and (8) into ABAQUS/Explicit through a user-defined subroutine when modelling the response of blast-loaded FML panels. The less computational expensive ConWep algorithm,⁷⁸ used to describe air-blast loading, is also available in LS-DYNA and ABAQUS/Explicit. Other simplified or idealised pressure–time profiles have been proposed.^79,80

The second approach is to model the blast loading and response in a coupled numerical simulation. This has an advantage, particularly for composites, in cases when the loading imparted to the structure is not entirely impulsive (that is, the structure displaces while the loading is incident on surface and hence changes the loading of the panel because of fluid–structure interaction). At the time of writing, researchers have found that computational codes with specialist Eulerian solvers tend to be better at modelling the loading process but have more limited capability for modelling the complex failure processes and material constitutive models applicable to composite materials. In addition, codes that have developed from Lagrangian solvers are more proficient at modelling the material properties and structural response but less proficient at modelling the blast loading process. However, both the traditionally Lagrangian codes (such as ABAQUS and LS-DYNA) and the more Eulerian-focussed codes (like Autodyn) are improving, and it is only a matter of time when fully coupled blast loading and response simulations will be possible for reasonable computation cost.

Material modelling

Composite structures subjected to blast loading can be modelled based on predicting the blast response of their constituent materials and the nature of the bond between them. Such structures, either laminates or sandwiches, are made of monolithic materials or cellular solids. There are a number of constitutive relationships, failure criteria and damage evolution mechanisms available to determine their corresponding dynamic behaviour under blast loading conditions. In addition, several contact algorithms are also available to model interaction between the constituent materials.

Metals

As metals are not the main focus of this review paper, only a brief summary of two commonly used material models for metals subjected to high strain-rate loading is mentioned herein. The Johnson–Cook constitutive model is perhaps the most widely employed and is often used to describe metal plasticity under large strains, high strain-rate and high temperature conditions.^81,82

The Johnson–Cook damage law⁸² can be used to simulate failure in metals. Both shear failure and tensile failure have been used to simulate the failure mechanisms in aluminium alloys.⁷⁷

In the commonly used elasto-plastic model, the rate-dependent hardening can be expressed as⁸³ (a function of the stress ratio R).

Another constitutive law, namely the Cowper–Symonds relation,⁸⁴ can be employed, if only strain-rate effects are considered, which is given by equation (10). 10 where σ _dy is the dynamic yield stress, and D and n are material constants.

Fibre-reinforced polymers

Fibre-reinforced composite laminates are often modelled as an anisotropic linear elastic material before the onset of damage, followed by damage evolution controlled either by the fracture energy or an element-based failure displacement. A damage mechanics approach may be suitable to predict composite damage in high strain-rate loading conditions, such as blast. Kachanov⁸⁵ and Rabotnov⁸⁶ originally developed the damage mechanics approach, which was initially applied to composites by Frantziskonis.⁸⁷ It can be used to accurately determine the full range of damage in a composite material, from no damage to full damage associated with material disintegration. Neto et al. ⁸⁸ and Krajcinovic⁸⁹ published detailed reviews of the important issues in the area of damage mechanics giving also a historical overview. This approach has been used to predict different composite failure modes, such as matrix cracking, fibre fracture and delamination as well as compression behaviour. Hashin's failure criteria^90,91 are widely used for modelling the onset of damage in fibre-reinforced composites, and are implemented in a 2D form in commercial codes such as ABAQUS and LS-DYNA. These criteria employ four damage initiation mechanisms, i.e. fibre tension, fibre compression, matrix tension and matrix compression. Other mode-dependent failure criteria were also developed by researchers.^92–94 In order to account for through thickness effects, Vo et al. ⁷⁷ implemented Hashin's 3D failure criteria into ABAQUS/Explicit through a user-defined subroutine.

In these failure criteria, the damage variables associated with fibre/matrix tension and compression failure modes need to be calculated in the user-defined code. The degradation of the stiffness matrix⁹⁵ components because of fibre and matrix failure also needs to be updated.

Iannucci⁹⁶ implemented a damage model into the explicit dynamic FE code LLNL DYNA3D⁹⁷ to predict the response of a woven composite on a layer-by-layer basis (2D). The damage parameters were defined as

Fibre-fracture in the local warp fibre bundles for each ply, d ₁

Fibre-fracture in the local weft fibre bundles for each ply, d ₂

Fibre-matrix deterioration because of in-plane shear for each ply, d ₃

The damage variables vary from 0 to 1, with the former representing an undamaged material and the latter complete failure. The damage terms in the stiffness degradation matrix are given in equation (11). 11 where

The superscript zero represents the material properties in the virgin state.

The most simple damage evolution case can be modelled by the negative slope of the equivalent stress–displacement relation after damage initiation occurred, as shown in Fig. 11, with specified fracture energies to account for the energies dissipated during damage. Nahas⁹⁸ conducted a progressive failure analysis based on the failure predictions of a modified maximum strain criterion. The degradation function defined in equation (12) is displayed in Fig. 12. 12

11.

Energy dissipated because of damage

12.

Nahas unloading model

Here, a and n are empirical constants. Iannucci⁹⁶ proposed a 2D damage evolution law for all damage modes in the local coordinate system, given by equation (13). For the initiation of damage, the effective stress needs to be greater than the in-plane lamina strength S _jk. A similar form to equation (13) was also proposed by Nemes.⁹⁹ A thorough review of degradation models for progressive failure of fibre-reinforced polymer composites is given by Garnich and Akula.¹⁰⁰ 13 where d _i are the damage parameters for mode i (i = 1,2,3), and α _i and S _jk (j,k = 11,22,12) are material constants in a simple form.

Cellular solids

Metal foams, PVC foams and honeycombs are cellular solids that can absorb considerable energy through plastic dissipation in compression. Their cellular microstructures enable them to undergo large deformations at nearly constant nominal stress,^101,102 which makes cellular solids ideal choices as core materials for sandwich structures in order to absorb impact and blast energies. Constitutive relations are given in terms of the effective stress¹⁰³ as shown in equation (14). Based on a self-similar yield surface model, Deshpande and Fleck¹⁰⁴ developed a constitutive model to describe a metal foam undergoing continuous crushing, expressed in equation (15). This constitutive model was also used to model a truss core⁹ and an aluminium honeycomb core¹⁰⁵ and PVC foam core^31,106 subjected to blast loading. The modelling of cellular materials is a subject of much current activity, particularly the investigation of stress wave propagation effects in impact and blast-loaded cellular solids. 14 where Y ⁰ is the uniaxial yield stress, r ₁ and r ₂ are the accumulated damage plastic strains, and the remainder are the hardening parameters. 15

Here, α defines the shape of the yield surface, σ _m is the mean stress and σ _y is the yield strength of the foam in uniaxial tension or compression.

Strain-rate dependence

Fibre-reinforced composites are essentially rate-dependent materials and this should be accounted for at high strain-rates, such as under blast loading.^107,108 For glass-based composites, an increase in strain-rate induces an increase in tensile failure stress and strain; however, the initial modulus appears to be unaffected. Figure 13 shows the strain-rate response for the case in which the material constants are set as and S _jk = 610 MPa (equation (13)). The curves are generated via a single element model subjected to varying strain-rates. Based on the works by Yen and Caiazzo,¹⁰⁹ Yen¹¹⁰ and Daniel et al.,¹¹¹ Vo et al. ⁷⁷ considered strain-rate effects in the material properties and strengths using equations (16) and (17). 16 17

13.

Graph of stress versus strain for glass-based composite illustrating the strain-rate dependence under tensile loadings

Here, C ₁ and C ₂ are the strain-rate constants, is the reference strain-rate, {E ₀} are the elastic moduli of {E _RT} at the reference strain-rate and {S ₀} are strength values of {S _RT} at the reference strain-rate.

Numerical modelling investigations

Extensive numerical modelling has been undertaken on structural responses of composite laminates and sandwich structures subjected to blast. The work has been mainly carried out by using commercial codes with built-in constitutive models, failure criteria and damage evolution or by developing in-house programmes.

Fibre-reinforced polymers

A number of workers have attempted to model the blast response of composite plates.^112–116 Turkmen¹¹² used the Runge–Kutta–Verner analysis to solve the equation of motion of curved glass and carbon fibre cylindrical panels and compared the resulting predictions with both experimental data and the results of a FE analysis. Good agreement was obtained between the experimental and predicted responses in the longitudinal direction; however, discrepancies were observed in the circumferential direction. Yuksel and Turkmen¹¹³ extended this work to consider the blast response of laminated GFRP hemispheres, with a qualitative agreement being obtained between the numerical and experimental results. Dolce et al. ¹¹⁴ used a 3D FE analysis to model damage because of an air blast on a carbon fibre-reinforced plastic. The blast load was modelled by assuming a fluid–structure interaction between the Eulerian blast and the Lagrangian structure.¹¹⁴ Agreement between the model and the experimental data was good in terms of both the residual displacements and resulting damage.

Batra and Hassan¹¹⁵ modelled the blast resistance of AS4/PEEK composites using the FE method. The problem formulation included the development of damage as a result of fibre fracture, fibre/matrix debonding, matrix cracking and delamination. They showed that approximately 15% of the total work is dissipated in these failure modes. The model was used to show how the energy absorbed in the various failure modes was strongly dependent on the laminate stacking sequence. Although delamination represented the principal energy-absorbing failure process for many stacking sequences, it was negligible in a [−45, 0, 45, 90] laminate. The authors also investigated the influence of target thickness on delamination in the laminates. It was assumed that the target consisted of four uniform plies with differing thicknesses according to the overall desired laminate thickness. The central deflection of the plate was predicted to decrease exponentially with the target thickness, leading to a similar reduction in the energy dissipated in delamination. Increasing the stiffness of the reinforcing fibre altered the rate of damage development within the target and delayed the onset of matrix cracking.¹¹⁵

Forghani and Vaziri¹¹⁶ developed a user-defined damage model that was implemented into LS-DYNA to simulate the dynamic response of Glass Fire Reinforced Plastic (CFRP) laminates subjected to distributed pressure pulses, with the global structural response captured accurately. Based on the first-order shear deformation plate theory (FSDPT), Icardi and Ferrero¹¹⁷ presented a FE model to study the behaviour of multiple core sandwich composites undergoing blast pulse pressure loading. Hui and Oskay¹¹⁸ developed computational modelling and simulation of woven E-glass-fibre-reinforced vinyl ester (EVE) composites and PU-coated EVE composites subjected to blast loading. Here, the response of the EVE layers is modelled based on a multi-scale computational damage model that includes adiabatic heating and rate dependence in the constituent (i.e. matrix and fibre) behaviour. A multi-scale simulation process was also developed by Kim et al. ¹¹⁹ to model the response of a vehicle with composite armour to the blast loads from an explosive threat.

Sandwich panels

LS-DYNA was also extensively used to model the blast behaviour of skull sandwich structures,¹²⁰ composite laminates^{115,117,121,122,123} and sandwich panels.¹²⁴ Three-dimensional MOSAIC analysis approach was used to investigate the shock loading response of sandwich panels with 3D woven composite skins and a stitched foam core.²² The commercial code ANSYS was also used to develop numerical simulations of laminated composite plates and shells subjected to blast loading.

Several researchers have developed in-house numerical codes to simulate the responses of various types of composite structure under explosive loads. Librescu et al. ^74,125 studied the dynamic behaviour of sandwich panels and the active aeroelastic control of aircraft composite wings to blast loading, with governing equation systems in the von Kármán sense. Sandwich plates/panels subjected to blast loading were also modelled numerically using the basic equations of the dynamic theory of advanced curved panels¹²⁶ and laminated composite rectangular plates.^127,128

Fibre-metal laminates

Modelling the response of FMLs to blast loading is particularly challenging because of the large number of layers, the possibility of multiple failure modes and the difficulties in defining the spatial distribution of the blast loading pressure on the panel surface. Karagiozova et al.,^67,76 working with the GFPP-based FMLs subjected to localised blast loading, showed that the function of the composite is to spread the loading over a wider region of the panel, thus enabling higher energy absorption. Typical simulation results are shown in Fig. 14, which also illustrate the effect of fibre orientation on panel response – the back face debonded shape followed the fibre orientation. The woven composite was simplified as two orthotropic layers. Delamination and interfacial debonding were modelled using cohesive elements. The blast responses of a GLARE fuselage¹²⁹ and GLARE panels¹³⁰ were also simulated using LS-DYNA. Soutis et al. ¹³⁰ used the same approach to model the delamination within clamped quadrangular GLARE panels subjected to air-blast loading. The loading was generated by detonating spheres of C4 explosive 200 mm away from the target plates, and the target plates had an exposed area of 600×600 mm. Aluminium, glass-fibre and GLARE panels were all tested and analysed. The LS-DYNA predictions were compared to blast loading perforation tests, and good correlation was obtained.¹³⁰ A non-linear transient analysis of a FML under blast loads was carried out using the mixed FEM by Aksoylar et al. ¹³¹

14.

a 4/3 FML with fibres oriented at 0° and 90°; b 4/3 FML with fibres oriented at ±45°

Vo et al. ^77,132 have also modelled the low impulse blast and impact behaviour of GFPP-based FMLs following the approach by Karagiozova et al. ^67,76 for modelling the debonding failure. Vo et al. ^77,132 developed a vectorised user material (VUMAT) subroutine and implemented it in ABAQUS/Explicit to model the blast behaviour of a woven GFPP composite in FMLs, with strain-rate effects considered. Numerical simulation results^77,132 compared favourably with experiments reported in Refs. 34, 65 and 66 although there is some difference in the transient response durations between the predictions of Vo et al. ^77,132 and Karagiozova et al. ^67,76 for the same experiments. However, at this stage, no transient response measurements from experiments are available to validate either set of predictions. Vo et al. ¹³² also performed numerical simulations to ascertain the influence of aluminium alloy type on the overall response. Four alloys were investigated. Vo et al. ¹³² showed that mid-point panel displacement could be decreased by increasing the yield stress of the aluminium alloy, but that debonding area increased with alloy yield strength. The influence of aluminium alloy type is illustrated in Fig. 15.¹³²

15.

Simulated displacement–time histories for locally blast-loaded FML panels indicating the influence of alloy type on the structural response, from Vo et al. ⁷⁷

Sitnikova et al. ¹³³ developed an instantaneous failure model to simulate perforation failure of GFPP layers inside FMLs subjected to high impulsive blast loading. A number of dynamic failure scenarios were captured, such as petalling, large tensile tearing and multiple debonding between the aluminium and GFPP layers. Figure 16 shows a typical comparison between the predicted displacement contour plots and the experimental data. The works by Karagiozova et al. ^67,76 and Vo et al. ^77,132 mention the lack of strain-rate-dependent properties for GFPP as a limiting feature in the simulations. Characterisation of the material rate dependence and failure of the interfaces, such as the work by Govender et al. ¹³⁴, should lead to improved modelling capabilities in the near future.

16.

Comparison of predicted displacement contour plots with experimental data¹³³

Outstanding research challenges

One considerable challenge that remains outstanding is the multiplicity of possible threats that could be imposed on composite structures designed to withstand air-blast loading. No standard set of loading definitions that should be designed for currently exists because of the large number of possible threat scenarios that exist, and the considerable challenges in performing large-scale field testing to obtain associated loading characteristics. Academic researchers have developed a large number of test techniques, partly in response to the variety of potential loading sources, but it is unclear how the results from the different test methods can be directly compared. Scaling between laboratory-scale experiments and ‘real life’ is also an outstanding area of research.

There are a number of outstanding challenges in understanding the response of polymer composites to air-blast loading that are at the interface between modelling and experiments. In one sense, these challenges are not unique to either composites or air-blast loading, but the combination of the two areas herein makes the problems particularly difficult to tackle. The outstanding problems in modelling of ultimate failure of woven fibre laminates, FMLs and other sandwich structures under blast loading are largely concerned with accurate definition of loading, high rate material properties and the characterisation of failure.

First, the blast loading characteristics such as pressure magnitude, distribution and loading duration are very difficult to measure precisely. The loading duration relative to the structural response time is of particular importance as it determines whether impulse, pressure magnitude or some combination of these will determine the response and failure. Second, obtaining accurate materials properties is crucial for modelling structural response and failure. A particular challenge is accurate rate-dependent representation of the adhesive layer (1) between the individual composite plies (i.e. delamination failure) and (2) between the metal and composite layers (namely, debonding failure). This covers the definition of rate-dependent normal and shear strength of the cohesive layer used in the modelling of delamination and debonding. Incorrect definition of the debonding and delamination failure causes incorrect energy dissipation within the composite structural model and may even cause a change in the ultimate failure mode simulated. There are two challenges here: the accurate experimental determination of the fracture mode energies and the subsequent challenge of interpreting the data for translation to a failure definition within a numerical simulation. In addition, the accurate rate-dependent elastic properties and ultimate strengths of all the constituent materials play a very important role in modelling of the failure related to high explosive blast. These are also challenging to determine experimentally, noting some recent attempts by Govender et al. ¹³⁴ to address this gap.

Uncertainties in the loading and material definitions make the blast modelling a very challenging task. If some of those dynamic properties are not readily available, another way forward is to undertake inverse modelling to identify reasonable parameters and to compare the related numerical output with the experimental results both qualitatively and quantitatively. However, this requires a lot of CPU time, even using supercomputer, since modelling of debonding and delamination is also a very time-consuming process.

Conclusions

Understanding the blast response and failure of structures based on fibre-reinforced polymer composites is a complicated endeavour. Many possible blast loading scenarios exist, and simple empirical descriptions of the incident pressures on blast-loaded structures are complicated by close proximity detonations (low Hopkinson–Cranz-scaled distances), high degrees of confinement, and geometric variations. Researchers have adopted numerous ways to simulate these loads, including pressure blow down rigs, soft projectile impact, shock tubes, and controlled explosive detonations at various scales.

Recent experimental investigations concerning the blast behaviour of fibre-reinforced polymers and FMLs have shown that the composites are better able to contain explosion loading that is uniformly distributed. In addition to the nature of the loading, the failure progression and ultimate rupture loads of composite materials depend upon many factors, including the materials, geometric configurations, overall panel thickness and stacking sequence. Failure modes in blast-loaded composite and FMLs include delamination, interfacial debonding, fibre fracture, plastic deformation of the metal layers and rupture. Woven composites appear to offer better damage tolerance to blast loading, with fewer delamination failures. Coatings and filler materials could offer a potential improvement in blast response in the future and are avenues of future research. The potential benefits of polymeric sandwich panels are under investigation, but whether the sandwich construction can offer improved blast performance over equivalent mass fibre-reinforced polymers remains an open question.

Numerical modelling work of structures based on fibre-reinforced polymer composite materials subjected to blast loading has been reviewed. Important considerations in modelling are ensuring that the important characteristics of the blast loading are captured, and that the essential failure and response modes can be captured from the chosen material and interface formulations. Spatial distribution of the loading is fundamentally important, particularly in composite materials that display increased sensitivity to highly localised intensive blast loading. Obtaining accurate material parameters (covering rate-dependent plastic hardening, temperature-dependent behaviour and damage) is difficult, particularly for composite materials at high rates of loading.

Much of the published work deals with the blast response at relatively low impulses, conditions that do not cause catastrophic failure in fibre-reinforced composites. Most of the commercially available FE codes have only 2D failure criteria and damage evolution and do not take the structural response through the thickness into account. Debonding and delamination behaviour can be modelled using cohesive elements, but determining the parameters for interfacial failure is challenging and open to interpretation. Therefore, it will be necessary in the future to develop and implement 3D failure criteria and damage evolution laws with appropriate descriptions of high strain-rate dependence to simulate progressive failure of fibres with numerical stability (convergent rate). This also has implication for experimental work, as obtaining rate-dependent material properties is challenging.

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