Stratified materials for aircraft structure: thermal effect of lightning impact by numerical simulations

This paper studies the effect of lightning impact on aircraft fuselage made of innovative Carbon Fibers Reinforced Composites (CFRC) panels, as an alternative to traditional metal structures. Metal layers are able to dissipate the current generated by lightning impacting the structure, whereas the multilayer CFRC panels are less conductive and therefore have limited capacity for current dissipation. This study presents a time-varying thermal simulation coupled with an electromagnetic simulation, considering different lightning currents that represent both short strokes (i.e., impulses), and long strokes (i.e., square pulses). In order to compare different stoke shapes, the temperature increment resulting from the lightning impact will be assessed through Finite Element Analysis. This approach allows for an assessment of the impact of different strokes on CFRC panels. The model serves as a starting point for future analyses aimed at comparing different technological solutions, beginning with experimental laboratory tests.


Introduction
Aircraft during cruise may encounter storms, especially when operating at low altitudes such as during landing or take-off.During a storm, experiencing lightning is common as clouds accumulate positive and negative electric charges that, in some conditions, can generate intra-clouds lightning or discharge toward the earth's surface or object with an opposite charge.In fact, thunderclouds are formed by the rise of warm air masses that condense into droplets, forming clouds.As the water rises, it cools to -40°C, leading to formation of ice crystals.These crystals, as they move within the cloud, acquire electrical charges.At lower altitudes, hailstones form as aggregates of these ice crystals.As they move downwards, these hailstones cause droplets condensation on their surface.The ice crystals that break off are lightweight and positively charged, and therefore accumulate in the upper regions of the clouds.Meanwhile, hailstones are heavier and negatively charged, hence they fall in the lower part of the clouds, where negative charges accumulate [1], [2].In general, thunderclouds are located at altitudes ranging from under 2000 m up to a few km above the earth level.During cruise, aircrafts typically fly at altitudes above clouds.Nevertheless, during take -off and landing, it might impact with clouds.Then, aircrafts are susceptible to being struck by lightning, which can potentially cause damage to their structure.The French Office National d'Etudes et Recherches Aérospatiales (the national aerospace research center) estimates that, on average, an aircraft experiences a lightning strike every 1,000 flight hours [3].Lightning strikes are more common at lower altitudes (5000-15000 ft), after the take-off or before the landing (Fig. 1).Over the years, the following direct effects on the exterior of the aircraft related to the lightning impact have been noticed [4]: 1) Burning or melting at lightning strike points; 2) Increase in temperature; 3) Residual magnetism; 4) Acoustic shock effects; 5) Electrical systems failures; 6) Ignition of fuel vapors.For most aircrafts, the fuselage is one of the most vulnerable zones to lightning strikes [3].In general, the fuselage is made of aluminium, and acts like a Faraday cage shielding the passengers and crew from the effects of atmospheric electricity.Nevertheless, the impact of lightning can be destructive and potentially cause irreparable damage to the fuselage.In particular, the impact with the structure may lead to fusion of the metallic coating.To reduce the weight, there has been increasing interest in the literature regarding the use of Carbon Fiber Reinforced Composites (CFRC) for structural aircraft components, including the fuselage [5].However, for the improvement of its electrical performance, the incorporation of conductive nanofiller inside the impregnating matrix have been proposed [6], [7].The effect of such nanofillers and the interaction mechanisms between the different phases in the obtained CFRC are still understudy.A numerical model supporting the experimental results could be useful to advance the understanding of these phenomena.In this paper, the introduction of a CFRC panel for fuselage construction is numerically evaluated in terms of effects related to the lightening impact during landing and take-off.In order to improve the electrical properties of the pristine epoxy resins adopted in the impregnation process, the use of an aeronautic resin filled with electrical conductive multiwall carbon nanotubes up to the percolation content is considered, as in [7].This material is studied for its suitability as structural part, serving as an alternative to metal, and numerically compared with the corresponding behaviour of an aluminium panel with the same final geometry.The proposed CFRC material is modelled as a multilayered sandwich structure, where Carbon fiber and nano-charged resin sheets were superposed in multiple layers, like in [8,9].The resulting multilayer was supposed to be sprayed on the top part with aluminium to create a conductive layer.The final panel was less conductive than metal, but exhibited a very good in-plane and out-of-plane conductivity [7].The paper presents a comparison of the material's response to lightning strikes, considering lightning currents associated with short and long strokes, with different current intensity.A finite element model is numerically solved using COMSOL Multiphysics, a commercial software, accounting for the coupling between electric and thermal equations, as in [8].In particular, this work examines the distribution of scalar potential and temperature field within the CFRC.The analysis is performed by using different stroke-current shapes than in [8] and by taking into account the thermal exchange in different scenarios, i.e. in laboratory conditions and at operational conditions during take-off and landing.

Carbon Fibers Reinforced Composite as Multilayer material
The Carbon Fibers Reinforced Composite (CFRC) is made of two components: a matrix (usually a thermosetting plastic, such as polyester resin, binding the reinforcements together) and a reinforcement, i.e. the carbon fiber, which provides strength to the composite.The material properties depend on these two constituents.Unlike isotropic materials like steel and aluminium, CFRPs have directional strength properties.The reinforcement gives CFRPs strength and rigidity, and contributes to the overall properties, including electrical and thermal ones.The properties of a CFRP depend on the layouts of the carbon fiber and the proportion of carbon fibers and polymer, the latter exhibiting obvious lower performance in terms of electrical and thermal conductivity.Carbon fibers are typically available in a woven form and arranged in layers of a given thickness, referred to as plies.These plies have to be stacked on top of each other to reach the desired dimension.The introduction of the polymeric matrix between these plies binds them, obtaining a final panel with different techniques (in Fig. 2 the case of liquid resin infusion technique from reference [7] is considered as an example).Disregarding the presence of the matrix between the holes inside the carbon-fiber ply, it can be assumed that the resin encapsulating two plies represents three layers of a given thickness.One layer serves as an interlayer between the two plies, while the remaining two layers are the external surfaces of the total structure.In this way, the CFRC can be represented by a multilayer material with (2*numply+1) stacks, where numply is number of plies used in the CFRC production process, having specific characteristics and properties linked to the matrix or to the carbon-fiber ply.In Fig. 3a) and Fig. 3b), domains and boundary conditions settings are shown for the electromagnetic and thermal field, respectively.Moreover, in Fig. 3a) also the rectangular mesh used to discretize the geometry and to solve the coupled electro-thermal model is reported.The geometry of the stratified material is represented as an alternation of epoxy resin layers, 55 μm thick, nanofilled with carbon nanotubes in order to improve the electrical conductivity [10] [11] and layers made of carbon fibres, 150 μm thick, starting from the bottom.The last layer is made of the same charged resin.Finally, the upper and bottom layers are made of 200 μm thick Aluminium.The lightening impact area is represented by a 5 mm long segment (Fig. 3a).The size of the impact area is chosen according to Dehn guidelines [12].The model is discretized by a mapped mesh with 18000 surface elements (Fig. 3a).The electric and thermal material properties relevant for the adopted analysis are reported in Table 1.
In particular, for what concerns the thermal behaviour, the maximum acceptable temperature for aluminium will be the melting point temperature of 660°C.For the resins, the temperature of total mass loss, varying between 600-700°C for the considered reference, will be used, as for the thermogravimetric analysis reported in [13].
Table 1.Electric and thermal properties of the materials; [NU] =not unit, NR=not relevant

Electromagnetic problem
The model in Fig. 3 is used to evaluate the electric potential and temperature in each layer when the lightning current is applied in the impact area, considering one of the time-dependent curves represented in Fig. 4. According to the Dehn guidelines, the parameters of the strokes are reported in Table 2.The adopted stroke behaviour assumes the behaviour of three out of four different parts in which the standard [15] classifies the strokes waveform.In particular, the first short stroke, slower (T1=10μs) and longer (T2=350μs) and with higher amplitude (IMAX=200kA), represents the A part of the standard; the 500 ms long stroke reproduces the C part; the second short stroke considered, faster (T1=0.25μs)and shorter (T2=100μs) and with lower amplitude (IMAX=50kA), represents the final D part of the standard [15].Considering that the current sources are time-dependent, a time transient problem is solved for both the electromagnetic and thermal problems.The scalar electric potential, V, is obtained solving a conduction problem in the electric field vector E: EASN-2023 Journal of Physics: Conference Series 2716 (2024) 012033 where J is the current density vector, D the electric displacement vector, and Je is the current density source applied only on the boundary line marked with the red line in Fig. 3a (boundary condition).
In this way, the domain is energized by a normal current density applied along the line representing the lightning impact segment (as in [8]).The current density value is derived by the current parameters in Table 1, dividing it by the area of the lightning impact.The current source takes one of the shapes in Fig. 4 with the parameters in Table 2.At the bottom line, the potential is constant and fixed at 0 V, a Dirichlet condition.The left boundary side is the symmetry axis, and Neuman boundary conditions (electric field tangent to the boundary line) are applied to the other external sides.

Thermal problem
The electromagnetic solution is the input for the thermal transient problem to evaluate the temperature within the layers of the stratified material.The Fourier equation is solved: where λ is the thermal conductivity [Wm -1 K -1 ], c the specific heat [J/kg/K],  the density of the material [kg/m 3 ], T the temperature [K], P(t) the power density [W/m 3 ] as a function of time, related to the stroke impact.The thermal domain includes all the regions in Fig. 3b.The external sides, except the symmetry axis, are modelled as exchange lines with the environment at the temperature Te, for which convection and radiation coefficients are set as in Table 1.The transient thermal problem is solved as a function of the temperature, providing the electromagnetic power in the domain.In this way, a coupled-field electromagnetic-thermal problem is solved using the Comsol Multyphysics AC/DC module (https://www.comsol.com,COMSOL AB, Stockholm, Sweden).

Results
Simulation results are presented in the following Figures.In Fig. 5a, the electric potential and temperature for the three current strokes in Table 3 are sampled along the three vertical lines at different time steps and computed in a time window chosen according to the input stress.Fig. 5b reports the electric potential for the short stroke 10/350 μs, peak current 200 kA.The intensity is comparable for all the three sampling lines of Fig. 5a.In particular, the inset in Fig. 5b reports a zoom around the maximum of the potential ranging between 6739 and 6744 V; then, it can be considered the same.Fig. 5c-e report the temperature sampled along the lines in Fig. 5a for take-off and landing conditions for the same short stroke.Fig. 5e, zoom of the superposition of temperature along the line at r=10 mm and time step 25.119 μs, shows that the temperature behaviour in landing and take-off conditions are similar but with values about 2% higher reached for the take-off case.Fig. 6 reports the electric potential and temperature values for the short stroke 0.25/100 μs, peak current 50 kA in Table 2, evaluated along the line at r=2.5 mm in the time instant t=125.9μs.The 4000°C temperature is reached after a longer time with respect to the 10/350 μs stroke, peak current 200 kA.Also in this case, the temperature behaviour in landing and take-off conditions is similar, with the takeoff case exhibiting higher values too, but this time of about 3%.In Fig. 5 and 6 the star symbol identifies the epoxy resin and the '+' symbol the carbon fibre layer region, corresponding to linear decreasing slope or constant value region for the potential, or maximum and minimum values for the temperature behaviour, respectively.The temperature in the resin is higher (peaks in the curves) than the one in the carbon fiber (the valleys).The Aluminium layer experiments a temperature lower than the multilayer material and close to 100 °C.Comparing the two short strokes, in Figure 5 and Figure 6, it is evident that the multilayer material experiments different temperature gaps between the epoxy resin layer and the carbon fibre layer.Considering the 10/350 μs stroke, the temperature gap is close to 4000 °C, whereas the gap for the 0.25/100 μs stroke is close to 500 °C.These relevant differences put in evidence that an accurate analysis in terms of maximum temperature value and time instant in which it is reached is needed.The possibility to numerically account for the dynamic electrical and thermal properties of the resin should support the results of experimental tests performed on a similar CFRC. Figure 7 reports the temperature profile on the line at r=2.5 mm in Fig. 5a for the three strokes in Table 3 (Fig. 4) at different time steps.It can be noticed that, with the long stroke, the multilayer material experiences a lower temperature effect.The gap effect, similar to the one visible in the short stroke, is here not visible, whereas a parabolic temperature profile is obtained with a maximum in the central layer.As intuitively suggested, the shape of the input stress influences the electro-thermal behaviour of the system.This means that, if the effect of the standard has to be considered in a suitable experimental test supported by the here presented numerical approach, the input stress has to be properly designed.
Moreover, it has to be noted that, as for short stroke, in the long stroke case the resin temperature is unfeasible too, since the material was already destroyed between 150 ms and 250 ms and before the end of the 500ms long input stress, being overpassed the 600-700°C limit temperature reported in Table 2.Moreover, Figure 7 compares the take-off and landing conditions in two time instants.It is possible to notice that, in the landing condition, the temperature of the material layer is lower with respect to the one at take-off.Therefore, the environmental temperature and heat exchange coefficient influence the final temperature and should be considered in the experimental-to-model analysis in case of laboratory tests.Finally, by considering the time instant at which one of the temperature characteristics for the material-carbon fibre, resin and aluminium-is reached, it is observed that in the examined cases, all the components the multilayer are damaged.The resin is the first material destroyed, followed by the carbon fibre layer.

Conclusion
The effect of lightning impact on the aircraft fuselage made of innovative Carbon Fibers Reinforced Composites (CFRC) panels is numerically analysed by using FEA.In particular, CFRC is studied as multilayer material subjected to electric strokes, modelled by current sources of different shape and defined according to the standard.Time-varying thermal-electromagnetic coupled problems allow comparing the electro-thermal behaviour of the modelled CFRC in response to the assumed different stimuli.The simulation results have shown that the external environment influences the behaviour during landing and take-off, as the external temperature and the exchanging heat capacity are different for all three considered stimuli.In particular, for the short stroke, temperatures in landing and take-off conditions are similar.The temperature in the resin is higher with respect to the one in carbon fiber, whereas the lowest temperature is in the aluminium layer.By considering the maximum temperature of 4000°C, it was found that the two short strokes are different, being the second lower and shorter one capable to reach this maximum in a longer time.Comparing the two short strokes, it is evident that the multilayer material experiments different temperature gaps between the epoxy resin layer and the carbon fibre layer.The possibility to numerically account for the dynamic electrical and thermal properties of the resin should support analysing the results of an experimental test performed on a similar CFRC.Concerning the long stroke case, the multilayer material experiences a lower temperature effect without gap effect between resin and carbon-fiber layer, as in the two short stroke cases.Moreover, it is worth noting that the computed temperatures are unfeasible for the system tested numerically, as the multilayer material representing the CFRC was already destroyed, being the temperature well over the critical value for the material composing the multilayer, e.g. the resin total mass loss.Nevertheless, the numerical approach here introduced can be used to compare different systems up to reaching the maximum temperature allowed, helping to understand which phenomena can be considered triggering the material destruction as a consequence of the lightning strike.Therefore, the model here described represents a starting point for future analyses aimed at comparing different technological solutions, beginning with experimental laboratory tests, and to extract phenomenological information.

Figure 1 .
Figure 1.Scenario of lightning impact on aircraft.

Figure 2 .Figure 3 .
Figure 2. Schema of the liquid infusion techniques (a) in order to obtain the multilayer panel (b) that represents the here considered Carbon Fibers Reinforced Composite (CFRC).Images from [7]2.2.Finite Element Analysis for the numerical study of the lightning phenomenonThe lightning phenomenon and its effect on CFRC are addressed as a Multiphysics problem, involving electromagnetic and thermal fields solved by means of Finite Element Analysis (FEA).As required by FEA techniques, the initial step involves defining the geometry to be analyzed.Fig.3represents the 2D geometry of the axial-symmetric model used in simulations of the CFRC as a multilayer material subjected to lightning strike.The cross-sectional geometry of a sample of the stratified composite material with a diameter of 4 cm is represented.

Figure 4 .
Figure 4. Current source: (a) short stroke waveform and (b) long stroke waveform.Insets are the software created input signal

Figure 5 .
Figure 5. (a) Vertical lines where potential and temperature were sampled.Stroke 10/350 μs (b) Potential along lines in panel (a); Temperature along the vertical lines in panel (a) in (c) take-off and (d) landing conditions at 25.119 μs.(e) Comparison of the temperature along vertical line r=10 mm for landing and take-off conditions.

Figure 6 .
Figure 6.Stroke 0.25/100 μs (a) potential along lines in Fig. 5a and (b) comparison of the temperature along vertical line r=2.5 mm for landing and take-off conditions at 125.9 μs.

Table 2 .
Current source characteristics