Quantifying the Influence of Lightning Strike Pressure Loading on Composite Specimen Damage
Abstract
Experimental work has shown that a component of lightning strike damage is caused by a mechanical loading. As the profile of the pressure loading is unknown a number of authors propose different pressure loads, varying in form, application area and magnitude. The objective of this paper is to investigate the potential contribution of pressure loading to composite specimen damage. This is achieved through a simulation study using an established modelling approach for composite damage prediction. The study examines the proposed shockwave loads from the literature. The simulation results are compared with measured test specimen damage examining the form and scale of damage. The results for the first time quantify the significance of pressure loading, demonstrating that although a pressure load can cause damage consistent with that measured experimentally, it has a negligible contribution to the overall scale of damage. Moreover the requirements for a pressure to create the damage behaviours typically witnessed in testing requires that the pressure load be within a very precise window of magnitude and loading area.
Keywords
Lightning strike Pressure loading Composite damage Finite element modelling1 Introduction
Aircraft are on average subjected to lightning strikes once per year or every 1000 flight hours. For legacy metal aircraft when a strike occurs the lightning energy is rapidly conducted away from the attachment point around the aircraft due to the favourable conduction properties of the airframe aluminium materials. However when fibre reinforced plastic composite material is struck by lightning catastrophic damage may occur due to the relatively low conduction properties of the polymer resin constitutive [1]. Thus an additional protection material is required in the material construction, typically a surface metal mesh, to rapidly redistribute the intense charge and reduce the damage.
There is still limited understanding of the damage mechanisms although a number of artificial lightning strike tests have been reported in the literature. Much of this lack of knowledge is due to the speed and intensity of the event which means it is very difficult to take physical measurements near the strike point during the strike. Posttest inspection of the damage is also difficult as there are a number of different surface and internal damage modes, which are difficult to differentiate between in a posttest inspection. A great number of variables are involved in lightning strike testing, the lightning waveform, specimen fixturing and location relative to the discharge probe, the protection system design, the composite materials and their stacking sequence. Together the small number of published test results and the volume of variables included in testing significantly increase the difficulty of establishing generic understanding from individual test results.
The potential of numerical simulations offer many advantages to study lightning strike events and the resultant damage creation. A significant advantage is the potential to scrutinise during the event the internal damage behaviour. In order to achieve this, a complete and accurate understanding of the loading mechanisms is needed in order to harness the significant advances available in composite material damage modelling [2, 3, 4, 5, 6, 7, 8]. This paper assesses the potential contribution of pressure loading to the damage of composite materials during a lightning strike by employing wellestablished and robust modelling approaches for composite damage prediction. The study examines the proposed pressure loads from the literature, modelling a test specimen and test setup with experimentally measured damage. It has been possible to compare the predicted damage considering each proposed load and to compare the predicted damage with the experimentally measured damage. Furthermore the range of loading parameters which result in representative experimental behaviour has been identified and the relative magnitude of damage compared to other loading mechanisms is established (i.e. thermal loading).
2 Background
Lightning is an electrostatic discharge resulting from a buildup of a differential charge between a cloud and earth or between clouds. An aircraft in proximity can become part of the discharge circuit resulting in an aircraft lightning strike. Once a discharge circuit is formed a massive flow of electric current occurs over a very short duration which superheats the conducting channel, forming a highly electrically conductive plasma channel. Where the conducting channel attaches to the aircraft significant local mechanical damage is possible (direct effects). The significant electric pulses passing through the aircraft structure can also interfere with and damage electronic systems etc. (indirect effects). This work specifically focuses on direct effects due to the cost and weight penalties associated with composite material lightning protection via the addition of an embedded surface metal mesh.
Direct lightning loading effects are typically described in two categories: Thermal loading, where the energy sources are the direct plasma heat flux and the Joule heating within the material [9]. Mechanical loading, where the energy sources are related to pressures resulting from arc channel attachment and expansion, along with pressures due to arc magnetohydrodynamic effects. The direct pressures are typically described as a radial pressure shockwave due to the rapid heating of the plasma channel (sometimes termed the acoustic load). An initial longitudinal pressure load is also envisaged as the plasma is formed along the lightning leader circuit. The magnetic induced pressures are due to Ampere’s law and the current streamlines which are attracted and pull together due to the flow in the arc channel which further intensifies the arc channel pressure at the attachment point (magnetic pinch load). In addition the magnetic force induced by the current circulation also induces a mechanical pressure load in the arc column and in specimen material at the attachment point. Furthermore, the electric current flowing in the specimen directly acts to create an additional internal pressure load (termed the magnetic pressure) [9].
From measurements taken on test aircraft flown purposely into active lightning storms [10, 11, 12, 13, 14] the size of lightning impulse currents have been measured and standardised lightning intensity and current waveforms established for laboratory certification testing [15, 16]. A small number of experimental studies have been published on composite materials which loosely adhere to the standardised certification waveforms and test setups. Munoz [17], as far as the authors can find, is the only published work to carry out the full WaveformA load (peak current 200 kA) on a carbon fibre composite specimen. In this case 3 mm thick RTM (Resin Transfer Moulded) epoxycarbon plate specimens were subjected to 200 kA and 100 kA simulated strikes. Kawakami [18, 19] carried out a comprehensive study of damage on press moulded and VARTM (VacuumAssisted Resin Transfer Moulded) epoxycarbon specimens considering a range of current waveforms, material layups  providing detailed descriptions and measurements of resultant damage. Hirano [20] conducted low magnitude simulated strikes (20–40 kA) on pristine unnotched specimens again with a comprehensive description of the resultant damage. Feraboli [21, 22] tested a range of lightning loads (10–50 kA) on pristine, unnotched, quasiisotropic carbon fibre specimens and also investigated the damage effects when the specimens contained fasteners. Hosokawa [23] conducted simulated strikes on sandwich composite specimens (160 kA).
A number of authors have compared lightning strikes with transverse impact tests (Featherston et al., Evans et al. and Soulas et al. [24, 25, 26]). Both lightning strike and transverse impact tests result in significant matrix cracking however the position of damage differs considerably. The matrix cracking damage from a lightning strike test tends to be concentrated over the top plies only, akin to a high speed event with a small contact area, however the lightning strike damage does not occur through the thickness of the specimen, a characteristic not typical of significant transverse impact loading (high or low speed). Other notable works which have examine the damage mechanics and magnitudes include Gammon [27], Gineste [28], Yamashita [29] and Dong [30]. These studies examine individual loading scenarios but do not attempt to quantify how damage changes with load magnitude or load type.
Experimental setups used in the literature
First author  Peak current (kA) / action integral (A^{2} s)  Specimen boundary conditions  Specimen size (mm)  Specimen thickness (mm)  Material  Layup 

Hirano et al. [20]  40 / 22,000  Placed on surface  350 × 350  4.704  IM600/133  [45/0/−45/90]_{4s} 
40 / 18,500  Two edges clamped to base  140 × 140  2.2  T700/2510  [02/902]_{2s}  
80 / 87,000  Two edges clamped to base  356 × 254  4.1  T300 3 K Tow, Resin XB 3518 BD  20 layer twill weave [0/90]  
30 / 23,800  Two edges clamped to base  304.8 × 38.1  2.88  G30–500 12 K Fibre, HTA/7714A Resin  45/02/−45/02/90]_{s}  
Hosokawa [23]  157 /   Placed on surface  150 × 150  1  TR50S Fibre Sandwich panel  Skin, [45/−45], # of plies not known 
Chemartin [9]  200 /   Two edges clamped to base  100 × 100  0.2  Carbon Fibre  – 
Haigh [31]  100 /   Two edges clamped to base  550 × 550  –  Carbon Fibre  6 layer weave 
Munoz [17]  200 /   –  –  –  –  – 
Gou [32]  100 /   Four edges clamped to base  406 × 406  1.778  Unidirectional Carbon Fibre  [0,−45, 90, 45]_{2} 
Evans [25]  100 /   Placed on surface  550 × 550  2  Aluminium 6082T6  n/a 
Featherston [24]   /   Two edges clamped to base  287 × 254  0.6  Aluminium 6082T6  n/a 
Lepetit [33]  98 / 300,000  Two edges clamped to base  450 × 450  2  T700/M21  8 layer quasiisotropic 
Yamashita [29]  1.2 /   Four edges clamped to base  110 × 110  0.8–1.1  CF mat reinforced thermoplastic, Vf = 30%, Polypropylene Resin  n/a 
Three damage areas as identified from experiment with a peak current is 40kA, rise time from 10% to 90% of maximum current is 4 μs and time through to 50% of maximum current is 20 μs
In summary the experimental authors have noted probable or possible causes of the damage. In particular resistive heating is consistently identified to cause a significant amount of the measured damage but does not completely explain all the physical damage witnessed. The discussed pressure loads including the acoustic and magnetic loads are not much studied but these effects are commonly suggested to explain variation in results or the difference between predicted and measured behaviour. Chemartin [9], Gineste [28] and Haigh [31] are some of the few authors to specifically investigate these loads in significant detail. These studies are thus discussed in detail in the following section. The purpose of this study, in contrast to these preceding works, is not to assess a single loading instant but to develop understanding on how the variation of pressure load magnitude and pressure load form influences material damage. With such a developed understanding it will then be possible for the first time to gauge how damage resulting from pressure compares with damage from other load types, e.g. thermalelectric loading, and thus its importance overall to material damage.
3 Pressure Loading Phenomena
Haigh [31] attempted to use special specimen holding fixtures and deflection measurement systems to differentiate experimentally between the impulse loading mechanisms during a simulated test. By striking the specimen directly and striking a metallic bar running above the specimen Haigh recorded equivalent peak deformations, concluding the acoustic load was the dominant loading mechanism. In addition when a lightning arc was configured to pass horizontally above the test setup the peak deformation measurement was more than double indicating the radial magnitude of the acoustic load was significantly greater than the longitudinal magnitude. It is important to note that in these experimental approaches specimen deformations with time is measured and not surface load. Two surface loads could result in equivalent global peak deformations but spread over significantly different areas these could create considerably different damage. Gineste et al. [28] again devises a specific test to characterize the acoustic load once more with a current flow tangentially to a PVC specimen and a displacement measurement system. In this case however a simulation model was used to reverse engineer the lightning strike’s expansion wave to fit the displacement measurements. Gineste [28] states that the values calculated are of the same order of magnitude as those obtained for magnetic pressure as calculated by the theoretic analytic expression [34].
Chemartin et al. [9] observed, using Magnetohydrodynamics (MHD) simulations of the lightning arc plasma, that the Lorentz force and hence the magnetic load is concentrated at the centre of the arc, and reduces to zero at the edge of the arc resulting in a parabolic pressure load. Chemartin’s combined experimental and simulations indicate that both the magnetic and fluid pressure must be taken into account to correctly calculate the specimen deflection during test. In conclusion Chemartin proposes the deflection of unpainted specimens (composite and aluminium) is primarily due to the acoustic load, while for painted specimen consideration of the magnetic pressure is required for realistic prediction of specimen deflection during test.

The denominator numeral varies between authors, while the magnetic pressure equation stipulates that the factor of division is eight: Kawakami [13], Chemartin [9] and Haigh [24] use division factors of two, four and sixteen respectively.

While all other authors have assumed a uniform pressure Chemartin [9], using simulations, has proposed a parabolic equation where the pressure at the arc centre is large and falls to zero at the edge of the arc radius.
Literature proposed lightning strike pressure loads
Electromagnetic ‘Pinch’ Equation  Assumed radius (mm)  Max magnitude for 40kA strike (MPa)  Max magnitude for 200kA strike (MPa)  Electromagnetic ‘Flux’ equation  Expansion shock wave magnitude (MPa)  

Theoretical [34]  \( \frac{\mu_0{i}^2}{8{\pi}^2{R}^2} \)  –  –  –  –  – 
Kawakami [18]  \( \frac{\mu_0{i}^2}{2{\pi}^2{R}^2} \)  1, 2  25  637  –  – 
Chemartin [9]  \( \frac{\mu_0{i}^2}{4{\pi}^2{R}^2}\left[1{\left(\frac{\mu_0{i}^2}{4{\pi}^2{R}^2}\right)}^2\right] \)  5  2  50  \( \frac{\mu_0{i}^2}{4{\pi}^2{R}^2} \)  – 
Munoz [17]  \( \frac{\mu_0{i}^2}{4{\pi}^2{R}^2} \)  5  2  50  \( \frac{\mu_0{i}^2}{4{\pi}^2{R}^2} \)  10 
\( \frac{\mu_0{i}^2}{16{\pi}^2{R}^2} \)  4, 5, 6  0.5  12.7  \( \frac{\mu_0{i}^2}{6{\pi}^2{R}^2} \)  12.7  
Reid [35]  \( \propto \frac{i^2}{d^2} \)  –  –  100  –  10 
Hardwick [36]  –  –  –  100  –  10 
In summary it is not possible to isolate the different proposed aspects of the pressure loads. Authors have until now used novel experimental setups and MHD simulations [37] to understand the loading pressure present during a test. Generally the literature suggests that pressure radically varies in time and magnitude. Table 3 summarises pressure loads proposed in the literature by each author along with the corresponding application radii. Theory is available to calculate the electromagnetic pinching pressure, however authors have modified this to match their experimental and simulation observations and incorporate the other pressure loads.
Rather than explicitly test each proposed load, the effect of varying pressure magnitudes and arc radii will first be investigated separately. The radius will be kept constant (5 mm, [9, 17, 28, 31]) while investigating the effect of varying peak pressure magnitude (based on the magnitudes in the literature). These include the magnitude proposed for Hirano’s current, both around the lower and upper limits, 2 and 50 MPa. Next the peak pressure load will be kept constant while the influence of the radius of loading will be investigated (1 to 5 mm  again covering the magnitudes proposed in the literature and documented in Table 3).
4 Modelling
Advances in numerical modelling techniques, including improved simulation of damage mechanics at micro and macro scale level, have enabled Finite Element methods to predict the damage response of impacted laminates with ever improving levels of accuracy [2, 3, 4, 5, 6, 7, 8]. Various failure criteria can be applied to predict the onset of fibre or matrix failure. Moreover postinitiation energy based or displacement based damage evolution models utilising principles of material degradation have been developed to predict damage progression. Using contact modelling methods to simulate cohesive behaviour at ply interfaces, the initiation and growth of delamination can be predicted from stress and energy based damage evolution and stiffness degradation models.
Model material properties
Properties  

Elastic  E_{1} = 130 GPa E_{2} = E_{3} = 7.7 GPa G_{12} = G_{13} = 4.8GPa G_{23} = 3.8 GPa ν_{12} = ν_{13} = 0.3 ν_{23} = 0.35 
Strength  X_{T} = 2080 MPa X_{C} = 1250 MPa Y_{T} = 60 MPa Y_{C} = 290 MPa S_{12} = 110 MPa 
Delamination Interface  k = 1 × 10^{5} N/mm^{3} \( {\tau}_3^0 \)=20 MPa \( {\tau}_{sh}^0 \)=36 MPa G_{IC} = 0.5 N/mm G_{IIC} = 1.6 N/mm η = 1.45 
Herein the focus will be on modelling a single preceding experimental setup [20] where the specimen is set on a copper plate which acts as an earth and the probe is 2 to 3 mm above the specimen hence the strike occurs near the specimen centre. Loading is thus applied about the specimen centre with the specimen simulated to be laid on top of the plate with material properties of copper. The copper plate is constrained from moving along the zaxis however the composite specimen is free to move. Due to the speed of the event and thus the inertial effects involved the analysis are solved using ABAQUS/Explicit. The modelled specimen is 150 × 100 mm with a ply layup of [45/0/−45/90]_{4s}, matching the global dimensions and laminate stacking sequence of the experimental specimens and enabling straight forward comparison between damage prediction and experimental damage measurement.
5 Results
5.1 General Description of Specimen Behaviour Under Load
Examining Fig. 2 it takes approximately 2.33 × 10^{−6} s for the pressure wave to travel to the back face of the specimen. In general a compressive through thickness strain with a gentle gradient is thus present throughout the specimen thickness soon after the pressure load is applied. The largest strains occur in the through thickness direction with a maximum reached close to the back face of the plate after 6.3 × 10^{−6} s (X marked in Fig. 2). This is due to the combination of the reflected strain wave meeting the oncoming strain wave. The strain at the front surface peaks at a lower magnitude and before the back surface strain peak, approximately occurring around the time of the peak pressure load. Overall the magnitude of the through thickness strain oscillates as the pressure wave reflects off the back and front face of the specimen. The maximum strains occurring are at the plate centre and through the plate thickness due to the localised nature of the loading.
5.2 Influence of Pressure Magnitude (Constant Radius of 5 mm, Varying Peak Load)
Maximum predicted stress in the local ply material axis with constant radius of 5 mm, peak loads 2, 50, 200, 400 MPa
Peak pressure loads  Maximum throughthickness stress σ_{33}  Maximum inplane stress σ_{11}  Maximum inplane stress σ_{22} 

2 MPa  −3.7  −3.5  −1.3 
50 MPa  −88.4  −78.9  −30.4 
200 MPa  −346.9  −291.5  −119.3 
400 MPa  −692.2  −536.9  −238.7 
5.2.1 Intralaminar Failure
In all these simulation cases (with a constant radius and pressure waveform) the dominant lamina stress which causes failure is σ_{33}, while the inplane stress, σ_{11} and the throughthickness shear stress, σ_{13} have a negligible contribution. Moreover the simulation results demonstrate a linear relationship exists between the applied peak pressure load and the maximum throughthickness stress, Table 5, and therefore the maximum stresses for any peak pressure load can be estimated. If we then simplify the Puck matrix compressive failure criteria to a one dimensional stress failure criteria in the throughthickness direction it is possible to calculate the minimum applied peak pressure load (with a fixed radius of 5 mm) which will be sufficient to cause damage, − 167.5 MPa.
The damage through the composite specimen increases with increasing peak pressure magnitude until damage is present throughout the thickness of the specimen. In the case of a peak pressure load of 400 MPa the damage at the surface of the composite specimen is 6 mm, with a damage area of radius 8.4 mm on the bottom surface. In this case due to the magnitude of the applied pressure load, the material fails when the initial stress wave initially propagates through the specimen and therefore failure begins from the top of the plate and propagates down through the plate thickness. Whereas with smaller peak magnitudes, failure begins from the back surface and propagates upwards through the plate thickness. In both cases matrix cracking is predicted by the Puck criteria (as outlined in the Modelling Section, Section 4).
5.2.2 Interlaminar Failure
Predicted delamination initiation with constant radius of 5 mm, peak loads 50, 200 and 400 MPa
Although the employed modelling approach represents a standard method a number of caveats should be considered along with the predictions. In all cases inter and intra lamina damage has been predicted in the immediate vicinity of each other. The modelling strategy employed does not represent interaction between matrix cracking and delamination. Alternative approaches have been proposed to model interaction, e.g. [40, 41], but such models are beyond the scope of this work. In addition delamination initiation is predicted to occur between multiple ply orientations. Although only delamination initiation is predicted care is required with these predictions as the modelled BK material properties are not fully generic and best represent delamination between the plies of a unidirectional laminate. Finally, although Puck’s criterion is widely used for the prediction of matrixdominated damage it does not account robustly for insitu effects (i.e. where the effective shear strength of a ply may be shown to increase when embedded in a multidirectional laminate [4]). Once more advanced techniques have been demonstrated to represent such insitu effects, Catalanotti et al. [42], but again such modelling is beyond the focus of this work.
5.3 Influence of Pressure Radius (Constant Peak Pressure Load 200 MPa, Varying Radius)
5.3.1 Intralaminar Failure
As in the first study the only mode of failure is compressive throughthickness matrix failure which occurs with loading radii of 5 and 3 mm at the back surface of the composite. For both radii, the failure area is again semicircular in shape when viewed in crosssection and circular when viewed from the back surface. Under a load radii of 1 mm intralaminar damage does not occur in the plate but, more significantly, the peak stress in the plate occurs close to the top surface of the specimen as the stress wave does not propagate through the plate.
5.3.2 Interlaminar Failure
Predicted delamination initiation with constant peak load of 200 MPa, load radii 1, 3, and 5 mm
5.4 Comparison with Experimental Results

the peak pressure is greater than that required to cause throughthickness matrix compressive failure,

the radius of loading is sufficiently small so that the pressure wave weakens as it propagates through the thickness of the specimen.
Therefore a pressure wave which causes this type of damage will overwhelm the material upon the initial loading but will not propagate through the plate. If the peak pressure magnitude or radius is too small no damage occurs or if they are too large then damage occurs through the plate thickness. Reconsidering the preceding six simulations only the 1 mm radius loading condition resulted in a stress wave such that the peak stresses occurred close to the top surface. Focusing on these simulation conditions and the two depths of measured lightning damage it is possible to refine the critical peak pressure magnitude and loading radius.
6 Conclusions
A simulation study has been undertaken to examine the proposed lightning strike pressure shockwave loads from the literature using a wellestablished modelling approach for composite damage prediction. The simulations have demonstrated the relationships between the magnitude of the applied pressure, the radius the pressure is loaded over and the internal composite strains and damage behaviour. From the simulations the magnitude of the strain fields and damage behaviour depends on the pressure magnitude but the internal strain waves are not fundamentally changed with this variable. When the radius of loading is varied this influences both the shape and the magnitude of the strains and thus damage behaviour. The arc radius and shock wave pressure required to cause the type of damage witnessed experimentally represents a small subset of the broad range of values proposed in the literature. Given the constraining requirement to only cause damage to the top surface of a specimen and the demonstrated sensitivity of throughthickness compressive stress to the modelled arc channel radius it can be considered unlikely that these conditions are met during each lightning strike test. Moreover the maximum predicted damage radius from simulations (considering both intralaminar and interlaminar damage) is negligible with respect to that measured experimentally. Thus shock wave pressure loading can only be responsible for a small component of the mechanical induced damage witnessed in specimens subjected to lightning strike testing. Based on the results herein electrical loading (and resulting resistive heating) is a significantly greater source of damage than pressure shockwave loading when each loading mechanism is considered in isolation. Given the significant mechanical damage reported experimentally mechanical behaviours associated with resistive heating, such as thermal expansion, and the interaction of loading mechanisms (mechanical and thermalelectric) require greater study to fully understand the damage formation. It is worth reflecting that the simulations represent laboratory test conditions and although there are no scale effects between the simulation and the test arrangement there will be variation between the test environment and test boundary conditions and real world lightning strike events. Thus future work should also establish the sensitivity of damage prediction to the modelled test conditions.
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