Comparison of lightning protection performance of carbon/epoxy laminates with a non-metallic outer layer

AS4/3506 carbon/epoxy composite and PCFP properties

Temperature-dependent AS/3506 carbon/epoxy composite properties used in the simulations were obtained from the literature^18–24 (Table 1). The epoxy matrix was assumed to decompose over the temperature range 300–500°C. ^{15 , 16} The composite latent heat of fusion (4.8 × 10³ kJ/kg) ²² associated with matrix decomposition was defined only between 300 and 500°C. The fibers and matrix residue/char were assumed to begin ablating when the local temperature exceeded the fiber sublimation temperature (3316°C ²³ ) and were fully abated at the critical sublimation temperature (3367°C ²⁴ ). Once fiber sublimation began to occur (3316°C), the composite conductivities were assumed to be isotropic as a consequence of irreversible char/residue formation from the matrix. The composite latent heat of vaporization was 4.3 × 10⁴ kJ/kg ²² absorbed between 3316 and 3367°C.

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Table 1.

AS4/3506 carbon/epoxy material properties.^18–21

Temp.	Density a	Specific heat a	Thermal conductivity a			Electrical conductivityb
			Longi.	Trans.	Thick.	Longi.	Trans.	Thick.
(˚C),	(kg/mm3)	(J/kg/K)	(W/mm/K)	(W/mm/K)	(W/mm/K)	(S/mm)	(S/mm)	(S/mm)
11	1.5 × 10−6	1065	4.7 × 10−2	6.8 × 10−4	6.8 × 10−4	35.97	1.15 × 10−3	3.9 × 10−6
350	1.5 × 10−6	2100	2.5 × 10−2	3.7 × 10−4	3.7 × 10−4	35.97	1.15 × 10−3	3.9 × 10−6
510	1.1 × 10−6	2100	1.5 × 10−2	1.8 × 10−4	1.8 × 10−4	35.97	2	2
1000	1.1 × 10−6	5750	1.2 × 10−2	1.3 × 10−4	1.3 × 10−4	35.97	2	2
3316	1.1 × 10−6	5875	1.0 × 10−4	1.0 × 10−4	1.0 × 10−4	35.97	2	2
3367	1.1 × 10−6c	5875 c	1.0 × 10−4c	1.0 × 10−4c	1.0 × 10−4c	1 c	1 c	1.0 × 10−6c

^aMenousek and Monin ¹⁸ and Mueller. ¹⁹

^bGriffis ²⁰ et al. and Fanucci. ²¹

^cProperties determined by the extrapolation of the empirical data over the temperature range (25–3316°C).

Transversely isotropic PCFP comprised short pitch carbon fibers (PCFs) that are 2D, randomly oriented in the in-plane directions. While the in-plane properties of a PCFP layer have been reasonably well characterized by the manufacturer, ²⁵ its through-thickness properties are not well understood due to the difficulty of testing. Thus, several major assumptions about the PCFP have historically been made: (i) both the thermal and electrical conductivity tensors were assumed to be isotropic, (ii) the thermal conductivities were obtained by averaging the axial and radial conductivities of a single PCF, (iii) the in-plane electrical conductivity corresponded to the in-plane conductivity for DONACARBO PCFP (Osaka Gas Chemicals S-259 grade ²⁵ ), and (iv) the PCFP specific heats were assumed to be those of bulk graphite. These assumed properties^25–29 (Table 2) are considered as the “baseline” PCFP properties in this study. In addition, the “baseline” electrical conductance of 2.5 × 10⁷ S/m^{2 27} and thermal gap conductance of 500 W/m² K ²⁹ were assumed between the PCFP and AS4/3506 composite. A more detailed description of PCFP properties was presented previously. ^{15 , 16} In this study, numerical simulations were performed where the baseline PCFP in-plane and through-thickness electrical/thermal conductivities and electrical/thermal gap conductances were each varied by an order-of-magnitude to assess their effects on lightning damage development.

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Table 2.

Baseline PCFP material properties.^25,26,28

Temp.	Density a	Specificheatb	Electricalconductivity c	Thermalconductivity a
(°C)	(kg/mm3)	(kg/mm3)	(S/mm)	(W/mm/K)
25	1.6 × 10−6	803	11.1	0.20
500	1.6 × 10−6	1598	11.1	0.19
100	1.6 × 10−6	1947	11.1	0.17
1500	1.6 × 10−6	2096	11.1	0.16
2000	1.6 × 10−6	2170	11.1	0.15
3000	1.6 × 10−6	2234	11.1	0.12
3316	1.6 × 10−6	2245	11.1	0.11
3367	1.6 × 10−6d	2245 d	11.1 d	0.10 d
4000	1.6 × 10−6d	2245 d	11.1 d	0.10 d

^aOsaka Gas Chemicals. ²⁵

^b Potts.26

^cWang and Chung. ²⁸

^dProperties extrapolated from the empirical data over the temperature range (25–3316°C).

PCFP: pitch-based carbon fiber paper.

Because of its 2D random distribution of PCFs, a typical PCFP displays much higher electrical and thermal conductivities in the in-plane directions than in the through-thickness direction; therefore, the previously mentioned isotropic material assumption is physically unrealistic. The distribution of electrical current flow and heat transfer through an idealized isotropic layer may be profoundly different from those of a more realistic transversely isotropic layer. For instance, protection layers with both high in-plane and through-thickness electrical conductivities lead to lower internal thermal damage development. ^{15 , 16 , 30}

A total of 17 numerical simulations of 50 kA peak current lightning strikes to PCFP-protected AS4/3506 laminates was performed. In the first simulation, the assumed baseline isotropic PCFP properties (Table 2) were employed. In the remaining 16 simulations, the baseline in-plane and through-thickness electrical conductivities, in-plane and through-thickness thermal conductivities, electrical gap conductance, and thermal gap conductance were each successively increased or decreased by an order-of-magnitude. Table 3 contains a summary of the factors used to scale the material properties in each of the 17 simulations. For example, in Case 5, both the in-plane and through-thickness electrical conductivities are 10 times greater than the baseline values (defined in Table 2), while the other properties remain unchanged. In Cases 1–6, the in-plane and transverse electrical conductivities are independently scaled by factors of 1/10 and 10 from the baseline values (Table 2), while holding the thermal conductivities and gap conductances fixed. In Cases 7–12, the in-plane and transverse thermal conductivities are scaled in a similar fashion. Lastly, Cases 13–14 and 15–16 correspond to the cases where the electrical gap conductance and thermal gap conductance, respectively, are scaled accordingly. These simulations can be used to assess the effect of protection layer anisotropy and interfacial properties on lightning damage development.

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Table 3.

16 sets of PCFP properties used in the parametric study.

Propertyset	Electrical conductivity		Electricalgap conductance	Thermal conductivity		Thermalgap conductance
	In-plane	Through-thickness		In-plane	Through-thickness
Baseline	×1	×1	×1	×1	×1	×1
Case 1	×10	×1	×1	×1	×1	×1
Case 2	×0.1	×1	×1	×1	×1	×1
Case 3	×1	×10	×1	×1	×1	×1
Case 4	×1	×0.1	×1	×1	×1	×1
Case 5	×10	×10	×1	×1	×1	×1
Case 6	×0.1	×0.1	×1	×1	×1	×1
Case 7	×1	×1	×1	×10	×1	×1
Case 8	×1	×1	×1	×0.1	×1	×1
Case 9	×1	×1	×1	×1	×10	×1
Case 10	×1	×1	×1	×1	×0.1	×1
Case 11	×1	×1	×1	×10	×10	×1
Case 12	×1	×1	×1	×0.1	×0.1	×1
Case 13	×1	×1	×10	×1	×1	×1
Case 14	×1	×1	×0.1	×1	×1	×1
Case 15	×1	×1	×1	×1	×1	×10
Case 16	×1	×1	×1	×1	×1	×0.1

Note: 16 sets of PCFP properties are obtained by multiplying the baseline properties (Table 2) by the numbers indicated in each row of Table 3.

PCFP: pitch-based carbon fiber paper.

FE lightning strike modeling and boundary conditions

Following the modelling procedure and mesh-sensitivity analysis established in Lee et al., ^{15 , 16} FE models were developed for 150 × 150 mm² AS4/3506 carbon/epoxy laminates with a 0.5 mm thick PCFP protection layer (Figure 1). The AS4/3506 layup was [+45/−45/0₂/90/0₂/−45/+45] with 0.2 mm ply thickness. The uniform FE mesh consisted of eight-node linear coupled electrical-thermal continuum elements with in-plane dimensions, 2.5 × 2.5 mm². Each ply was discretized using a single element through its thickness. ABAQUS surface-to-surface general contact ³¹ was used to define the electrical and thermal gap conductances between the PCFP outer layer and underlying composite.

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Figure 1.

Lightning strike FE model geometry and discretization. FE: finite element.

The lightning strike FE models ^{15 , 16} were used to perform two-step transient analyses: (i) a coupled electrical-thermal analysis to determine the local temperature rise due to Joule heating (resistive) in the first 30 μs after the lightning attachment followed by (ii) a transient heat transfer analysis for 10 s. In a coupled electrical-thermal analysis, Joule heating occurs instantaneously with current passage and heat transfer is almost negligible in this short time span. In contrast, after 10 s, the heat transfer has occurred to the degree that also creates damage to the composite. Each analysis requires assigning either electrical or thermal boundary conditions to calculate the electrical potential, current density, and temperature distributions. The boundary conditions implemented in this FE parametric study were consistent with those used in our recent artificial lightning strike tests (Figure 2).^32,33 In the presence of electrical current (during the coupled electrical-thermal analysis), zero electrical potentials for grounding the current were imposed on all four edges of the simulated composites. Thermal boundary conditions were only applied on the exposed top surface of the PCFP outer layer: (i) radiation boundary conditions (surface emissivity, 0.85 ¹⁸ ; ambient surrounding temperature, 25°C) were employed during all simulations, and (ii) convection boundary conditions (convection coefficient, 200 W/m²/K ³⁴ ) were additionally assigned during the subsequent heat transfer analyses to account for considerable thermal advection. The electrical and thermal boundary conditions used in two-step transient analyses are summarized in Figure 3. Note that the electrical potential boundary condition was not defined in a transient heat transfer analysis due to the lack of electrical current.

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Figure 2.

(a) Experimental lightning test specimen and (b) corresponding composite FE representation of electrical grounding conditions. ^{32 , 33} FE: finite element

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Figure 3.

Electrical and thermal boundary conditions defined in (a) coupled thermal-electrical analyses and (b) subsequent heat transfer analyses.

Simulated impulse current waveforms

The Society of Automotive Engineers (SAE) Aerospace Recommended Practice (ARP) 5412 B ³⁵ provides standard impulse current waveforms consistent with actual lightning strikes (or discharge)

Matrix decomposition prediction criteria

The lightning strike FE models in Lee et al. ^{15 , 16} can be used to calculate the spatially varying local temperature and the corresponding matrix thermal decomposition caused by electrical current at each time increment during the simulations. Irreversible matrix damage (degradation) is modeled by updating the degree of matrix decomposition based on the highest temperature reached at that location. Matrix thermal decomposition was assumed to develop linearly over the temperature range 300–500°C (i.e. between the normalized values of 0 (no damage) at 300°C and 1 (complete matrix decomposition) at 500°C. ^{15 , 16} The predicted matrix decomposition domains using this criteria are consistent with experimental results. ³⁶

Damage in a sacrificial lightning protection layer may be more or less severe than damage in the underlying plies and may require standard repairs. The predicted damage in the PCFP outer layer was not considered in this study, but was considered in our earlier work. ¹⁶ One goal of this work is to assess matrix decomposition in the outermost structural AS4/3506 ply; such plies will experience the most severe thermal damage. Since damage progressively decreases with depth below the surface,^15,16,22,30 outer ply damage can be used to assess the effectiveness of a given lightning protection layer.

FE model validation

Our previously published FE models ^{15 , 16} were successfully validated with laboratory-scale artificial lightning strike tests.^32,33 The FE models predicted CF ablation/sublimation and epoxy matrix decomposition based on the local temperature history. The predicted CF sublimation domain was negligible due to the relatively high sublimation temperature (≥3300°C), compared to epoxy matrix decomposition temperatures (typically, 300–500°C). The time duration that the CFs experience above 3300°C was very short and the dimensions of that very high temperature region were quite small and located near the arc attachment region, which is always the most intensively damaged region experimentally and in our predictions. Therefore, the CF sublimation region was totally encompassed by the widespread matrix damage region. The shape and size of the predicted epoxy matrix decomposition domains agreed fairly well with experimentally measured results. Figure 4 compares actual and predicted lightning damage in the outermost layer of unprotected, copper mesh (CM)-protected, and PCFP-protected similar (AS4/8552) carbon/epoxy laminates subjected to 50 kA nominal peak current.

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Figure 4.

Comparison of actual and predicted lightning damage in the outermost layer of (a) unprotected, (b) CM-protected, and (c) PCFP-protected AS4/8552 carbon/epoxy laminates subjected to 50 kA nominal peak current: the measured peak current is included for clarity. ¹⁵ PCFP: pitch-based carbon fiber paper. CM: copper mesh.

Effect of electrical conductivities on lightning damage development

Damage predicted in the outer +45° ply using the baseline PCFP properties for a composite subjected to a 50 kA peak current is shown in Figure 5(a) and (f). The predicted matrix decomposition in the top +45° ply 30 µs after the initial lightning attachment (i.e. at the end of the coupled electrical-thermal analysis) is shown in Figure 5(a). Matrix decomposition developed in a “figure-eight” configuration, where damage tended to elongate in the direction of the conducting CFs in that ply. Two relatively small regions (“lobes”) with complete matrix decomposition were located adjacent to the attachment point. Given the short time scale involved, such damage is primarily due to Joule heating. In contrast, Figure 5(f) shows the additional predicted matrix decomposition due to conduction after 10 s of transient heat transfer analysis. The damaged region extended significantly in the direction perpendicular to the fibers, and became elliptical in shape. The zone with complete matrix decomposition (red) increased substantially in comparison to that associated with Joule heating. Thus, Joule heating and subsequent heat transfer contribute.

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Figure 5.

Predicted matrix decomposition domains in the top +45° AS4/3506 ply of PCFP-protected composites subjected to 50 kA peak currents (upper figures) after 30 µs of coupled electrical-thermal analysis and (lower figures) after 10 s of transient heat transfer analysis. Damage from various PCFP in-plane and through-thickness electrical conductivities is shown. Note that each figure includes the only varied PCFP in-plane and through-thickness electrical conductivities while all other properties remain the same as the baseline PCFP properties (Table 2). (a) Baseline. (b) In-plane electrical conductivity × 10. (c) In-plane electrical conductivity × 0.1. (d) Through-thickness electrical conductivity × 10. (e) Through-thickness electrical conductivity × 0.1. (f) Baseline. (g) In-plane electrical conductivity × 10. (h) In-plane electrical conductivity × 0.1. (i) Through-thickness electrical conductivity × 10. (j) Through-thickness electrical conductivity × 0.1. PCFP: pitch-based carbon fiber paper

In Figure 5(b) to (e), damage predicted in the outermost AS4/3506 plies after 30 µs of the coupled electrical-thermal analysis is shown for Cases 1–4, respectively, where the PCFP in-plane and through-thickness electrical conductivities were varied (Table 3). Note that baseline PCFP thermal conductivities and gap conductances were used. No matrix decomposition was predicted in the AS4/3506 lamina when the in-plane electrical conductivity of the PCFP outer layer increased by a factor of 10 (Case 1, Figure 5(b)). This makes sense since a PCFP outer layer with higher in-plane electrical conductivity effectively distributes electrical current more rapidly over its surface. This, in turn, results in a lower degree of instantaneous Joule heating in the PCFP outer layer and underlying composite. In contrast, lowering the PCFP in-plane electrical conductivity by an order-of-magnitude (Case 2, Figure 5(c)) resulted in increased Joule heating in the PCFP layer and more thermal damage to the underlying AS4/3506 ply.

When the through-thickness electrical conductivity was increased (Case 3, Figure 5(d) or reduced (Case 4, Figure 5(e)) by an order-of-magnitude from the baseline values, the matrix decomposition domains in the outermost AS4/3506 ply did not appreciably change. Provided the in-plane electrical conductivity is sufficiently high, order-of-magnitude changes in the PCFP through-thickness electrical conductivity did not significantly affect matrix decomposition in the underlying composite. Figure 5(g) to (j) show the matrix decomposition in the top AS4/3506 ply for Cases 1–4 after 10 s of subsequent transient heat transfer analysis. With the exception of Case 1 (Figure 5(g)) where no matrix decomposition occurred due to Joule heating or heat conduction resulting from high PCFP in-plane electrical conductivities, the all remaining cases resulted in a significant increase in thermal damage due to heat conduction. Of course, this affect was much more pronounced for Case 2 (Figure 5(h)) since the PCFP in-plane electrical conductivities were 10 times lower than that for the baseline case (Figure 5(f)). Cases 1 (Figure 5(b) and (g)) and 2 (Figure 5(c) and (h)) clearly underscore the importance of maximizing the in-plane electrical conductivities of the protection layer in order to minimize matrix decomposition in the underlying composite. In essence, protection layers with sufficiently high in-plane electrical conductivities reduce the local electrical current densities and Joule heating in the protection layer and composite, which also leads to less transient heat conduction in the composite.

When both the PCFP in-plane and through-thickness electrical conductivities were simultaneously increased by a factor of 10 (Case 5, Figure 6(a) and (c)), the predicted damage was identical to that for Case 2 (Figure 5(b) and (g)), i.e. no matrix decomposition occurred in the top AS4/3506 ply. Similarly, when these properties were both reduced by an order-of-magnitude from the baseline values, the predicted matrix decomposition to the outermost AS4/3506 ply was a relative maximum (Case 6, Figure 6(b) and (d)), and were virtually the same as Case 2 (Figure 5(c) and (h)). These results further illustrate the importance of high PCFP in-plane electrical conductivity on minimizing thermal damage to composite structures.

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Figure 6.

Predicted matrix decomposition domains in the top +45° AS4/3506 ply of PCFP-protected composites (upper images) 30 µs after being subjected to 50 kA peak currents and (lower images) after 10 s of transient heat transfer analysis. Only PCFP in-plane and through-thickness electrical conductivities are varied, while all other properties remain the same as the baseline values. (a) In-plane and through-thickness electrical conductivity × 10 both. (b) In-plane and through-thickness electrical conductivities × 0.1 both. (c) In-plane and through-thickness electrical conductivity × 10 both. (d) In-plane and through-thickness electrical conductivities × 0.1 both. PCFP: pitch-based carbon fiber paper.

Effect of thermal conductivities on lightning damage development

Lightning is defined as a transient electrical discharge ² that delivers large amounts of electrical energy (instantaneously dissipated as heat energy by Joule heating) to aircraft composites. In addition, dynamic mechanical pressure loads due to arc channel attachment and expansion, arc magneto-hydrodynamic effects, and internal current flow (i.e. magnetic pressure ³⁷ ) can produce significant amounts of mechanical damage. ³⁷ Such mechanical damage is not considered here, but is generally less widespread than thermally induced damage. ³⁸ Electrical current flow, current densities, Joule heating and its corresponding (nearly instantaneous) temperature rise are directly associated with composite electrical conductivities. Once (lightning) the current injection is completed, composite damage may continue due to subsequent heat conduction. In general, Joule heating causes more significant instantaneous damage to composites than does the subsequent damage due to heat conduction. ^{30 , 39}

An additional set of six FE simulations of 50 kA peak current lightning strikes to PCFP-protected AS4/3506 laminates were performed (Cases 7–12, Table 3). In these simulations, the PCFP electrical conductivities, electrical gap conductance, and thermal gap conductance were held at fixed baseline values. The PCFP in-plane and through-thickness thermal conductivities, however, were each independently increased/decreased by one order-of-magnitude from baseline values to assess their effects on thermal damage development in the laminate (Cases 7–10, Table 3). Two additional simulations were performed where the in-plane and through-thickness thermal conductivities were simultaneously increased/decreased 10-fold from baseline values (Cases 11–12, Table 3). As expected in each case, the predicted matrix decomposition due to instantaneous Joule heating at the end of the coupled electrical-thermal analyses (t = 30 μs) was nearly identical to that for the baseline case (Figure 5(a)). This makes sense since relatively little heat conduction can occur during the lightning attachment period of 30 μs. Interestingly, after 10 s of transient heat transfer analysis, the degree of matrix decomposition in the outmost AS4/3506 ply for each case was also nearly identical to the baseline composite (Figure 5(f)). This suggests that the thermal conductivities of the relatively thin PCFP layer do not significantly affect thermal damage development in the underlying laminate. Since Joule heating in the PCFP layer is virtually instantaneous, the interface between the PCFP layer and outermost AS4/3506 ply may essentially act like a temperature boundary condition; heat conduction within the PCFP may play little role on heat conduction and thermal damage in the composite. These results are consistent with the predictions available in literature. ^{40 , 41}

Effect of gap conductances on lightning damage development

Joule heating occurring at the interface between contacted layers (due to the through-thickness current flow) is inversely proportional to the electrical gap conductance. ⁷ A higher electrical gap conductance between the PCFP protection layer and AS4/3506 laminate may cause less Joule heating per unit current flow, leading to potentially less thermal damage in the AS4/3506 plies. In contrast, the through-thickness heat conduction at an interface between contacted layers is proportional to the thermal gap conductance. ⁷ The greater the thermal gap conductance, the more heat is transferred through an interface. Therefore, a lower thermal gap conductance between the PCFP protection layer and composite may lead to reduced thermal damage in the underlying laminate.

A final set of four 50-kA peak current lightning strike simulations were performed where the electrical and thermal gap conductances between the PCFP protection layer and AS4/3506 composite were each independently increased/decreased by one order-of-magnitude from the conductivities were held fixed in the simulations. Figure 5 contains a plot of the predicted matrix decomposition at the end of Joule heating (t = 30 μs) and transient heat conduction analyses (t = 10 s) for each case. For example, Case 13 (Figure 7(a) and (e)) and Case 14 (Figure 7(b) and (f)) correspond to analyses where the electrical gap conductances were increased/decreased 10-fold, respectively, from the baseline values. In both cases, the predicted matrix decomposition was indistinguishable from the baseline case (Figure 5(a) and (f)). Hence, for the intermediate peak current (i.e. 50 kA) and range of electrical properties considered, composite matrix decomposition is relatively insensitive to changes in both through-thickness electrical conductivities (Figure 4) and changes in the electrical gap conductances between the protection layer and laminates (Figure 7(a) and (b)). In essence, the PCFP layer may be too thin for the given variations in through-thickness electrical conductivities to appreciably affect through-thickness current flow. Likewise, the gap between the PCFP and underlying composite may be insufficient to be a significant electrically isolating element over the range of resistance values considered.

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Figure 7.

Predicted matrix decomposition domains in the top +45° AS4/3506 ply of PCFP-protected composites subjected to 50 kA peak currents at the end of coupled electrical-thermal analyses (upper images) and transient heat transfer analyses (lower images). Damage is shown using various PCFP electrical and thermal gap conductances. (a) Electrical gap conductance ·×10. (b) Electrical gap conductance ×0.1. (c) Thermal gap conductance × 1. (d) Thermal gap conductance × 0.1. (e) Electrical gap conductance ·×10. (f) Electrical gap conductance ×0.1. (g) Thermal gap conductance × 10. (h) Thermal gap conductance × 0.1. PCFP: pitch-based carbon fiber paper.

Analogously, in Case 15 (Figure 7(c) and (g)) and Case 16 (Figure 7(f) and (h)), the thermal gap conductance was increased/decreased 10-fold, respectively, from its baseline values. Not surprisingly, at the end of Joule heating (t = 30 μs), the predicted matrix decomposition for the case of increased (Figure 7(c)) or decreased (Figure 7(d)) thermal gap conductance was nearly the same as the baseline case (Figure 5(a)) (i.e. not enough time had transpired for significant heat conduction to occur across the PCFP/laminate interface). At the end of the transient heat transfer analyses (t = 10 s), the predicted size and intensity of the matrix decomposition region associated with a 10-fold increase in thermal gap conductance (Figure 7(g)) were consistent with those for the baseline case (Figure 5(f)). Perhaps for the given intermediate peak current, local temperature distributions, and heat fluxes, the baseline gap properties reasonably approximate perfect interface. When the thermal gap conductance was decreased by an order-of-magnitude, however, the size of the matrix decomposition domain (Figure 7(h)) decreased by roughly 10% relative to the baseline case (Figure 5(d)). This suggests that the interfacial thermal properties between the protection layer and composite may be tailored in order to achieve modest improvement in protection system performance.

Effect of PCFP properties on the through-thickness damage to AS4/3506 laminates

The preceding 17 numerical simulations were used to assess the through-thickness thermal damage penetration (defined as the maximum depth containing matrix decomposition) of PCFP-protected 9-ply AS4/3506 laminates subjected to a 50 kA peak current. The predicted matrix damage obtained using the baseline PCFP properties (Table 2) penetrated the first three plies (i.e. 0.6 mm). Table 4 contains a summary of the number of damaged AS4/3506 plies and total depth of damage penetration for each of the 16 cases considered in the parametric study. Based upon the parametric study, the size, intensity, and depth of penetration of matrix thermal decomposition were driven by the value of the PCFP in-plane electrical conductivity. When the baseline protection layer in-plane electrical conductivity was employed (Cases 3, 4, and 6–16, Table 4), matrix decomposition penetrated through one-third of the laminate, irrespective of the order-of-magnitude changes in PCFP through-thickness electrical conductivity, thermal conductivities, and electrical/thermal gap conductances. Moreover, the size and intensity of the matrix decomposition domain in each ply were essentially the same as for the baseline case (with the exception of a minor reduction in damage size associated with a decrease in thermal gap conductance, Case 16). For the two analyses where the PCFP in-plane electrical conductivity was 10 times greater than the baseline value (Cases 1 and 5), no matrix thermal damage was predicted (Table 4, Figures 5 and 6). Conversely, a 10-fold decrease in PCFP in-plane electrical conductivity (Cases 2 and 6) led to maximal damage in the outermost ply (Figure 5(h) and (d)) and a total penetration depth of penetration of five plies (Table 4). Clearly, maximizing the in-plane electrical conductivity of the protection layer is of paramount importance in reducing underlying thermal damage to composite structures.

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Table 4.

Predicted maximum damage penetration depths of 9-ply PCFP-protected AS4/3506 composites [+45/−45/0₂/90/0₂/−45/+45] subjected to 50 kA peak currents.

Simulation	Number of damaged plies	Max. penetration depth a (mm)	Simulation	Number of damaged plies	Max. penetration depth a (mm)
Case 1	0	0.0	Case 9	3	0.6
Case 2	5	1.0	Case 10	3	0.6
Case 3	3	0.6	Case 11	3	0.6
Case 4	3	0.6	Case 12	3	0.6
Case 5	0	0.0	Case 13	3	0.6
Case 6	5	1.0	Case 14	3	0.6
Case 7	3	0.6	Case 15	3	0.6
Case 8	3	0.6	Case 16	3	0.6

^aMaximum penetration depth is calculated by multiplying the number of damaged layers by the ply thickness (0.2 mm). The predicted damage penetration obtained from baseline PCFP properties (Case 0) was the third layer (i.e. 0.6 mm).

PCFP: pitch-based carbon fiber paper.

The significance of PCFP properties on thermal damage development may be more noticeable at higher peak currents due to increased Joule heating. Three additional FE simulations were conducted using 200 kA peak current lightning strikes to PCFP-protected 9-ply AS4/3506 laminates. In the first simulation, the baseline PCFP properties were used. In the latter two simulations, the PCFP in-plane electrical conductivity was increased one and two orders-of-magnitude from the baseline value. For comparison purposes, a typical copper protection layer has an electrical conductivity 300 (at 1000°C) and 5000 times (at 20°C) greater than the in-plane baseline PCFP property considered in this study. ⁴² Figure 6 shows the predicted matrix decomposition and corresponding through-thickness damage penetration of the three PCFP-protected AS4/3506 laminates subjected to 200 kA peak currents at the end of heat transfer analyses (t = 10 s). When the baseline PCFP properties (Table 2) were employed in the FE model, the matrix decomposition in the top AS4/3506 ply (Figure 8(a)) was far more severe than that obtained from a 50 kA peak current (Figure 5(f)). The size of the damage in the outermost +45° ply was roughly four times larger than for a 50 kA strike and the complete thermal decomposition damage (i.e. red region) penetrated through all nine underlying plies. In contrast, PCFP outer layers designed with the in-plane electrical conductivities 10× (Figure 8(b)) and 100× (Figure 8(c)) greater than the baseline value markedly reduced or completely eliminated matrix decomposition, respectively, resulting from a 200 kA strike. In the former case, a minor amount of matrix decomposition was predicted, but was limited to the outermost AS4/3506 ply (Figure 8(b)). As an aside, the 200 kA peak current is the maximum current specified in SAE ARP 5412 B. ³⁵

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Figure 8.

Matrix thermal decomposition and corresponding damage penetration in PCFP-protected 9-ply AS4/3506 laminates subjected to 200 kA peak currents after 10 s of transient heat transfer analyses. PCFP protection layers designed with (a) baseline in-plane electrical conductivities, (b) 10×, and (c) 100× greater than the baseline values. PCFP: pitch-based carbon fiber paper.

In practice, the PCFP in-plane electrical conductivities can be improved by tailoring the fiber volume fraction and orientation. Alternatively, PCFP can be doped with tiny amounts of highly conductive metallic nanoparticles or coated with such metals to dramatically increase a protection layer’s electrical conductivities without appreciably affecting its mass. Doping may also prove useful in enhancing the electrical/thermal conductivities of the adhesive layer between the protection layer and composite, as well as increasing the conductivities in the outermost composite plies adjacent to the protection layer. Use of conductive adhesives and resins may also lead to improvements in lightning damage resistance. The PCFP represents only one potential carbon-based protection layer. Use of lightweight, thin graphene papers containing exceptionally conductive (in 2-D versus 1-D for nanofibers), high strength, aligned graphene/graphite nanoplatelets may provide an attractive alternative to traditional metallic protection layers. Such options are currently under investigation at Mississippi State University. In addition, through transmission ultrasonic testing combined with destructive sectioning of actual lightning strike test panels is currently underway to clearly understand through-thickness damage development in AS4/3506 composites underneath a PCFP outer layer. This will be discussed in a subsequent publication.