Appl Compos Mater DOI 10.1007/s10443-017-9588-6

Experimental and Numerical Simulation Analysis of Typical Carbon Woven Fabric/Epoxy Laminates Subjected to Lightning Strike J. J. Yin 1 & F. Chang 1 & S. L. Li 1 & X. L. Yao 2 & J. R. Sun 2 & Y. Xiao 1

Received: 10 January 2017 / Accepted: 16 January 2017 # Springer Science+Business Media Dordrecht 2017

Abstract To clarify the evolution of damage for typical carbon woven fabric/epoxy laminates exposed to lightning strike, artificial lightning testing on carbon woven fabric/epoxy laminates were conducted, damage was assessed using visual inspection and damage peeling approaches. Relationships between damage size and action integral were also elucidated. Results showed that damage appearance of carbon woven fabric/epoxy laminate presents circular distribution, and center of the circle located at the lightning attachment point approximately, there exist no damage projected area dislocations for different layers, visual damage territory represents maximum damage scope; visible damage can be categorized into five modes: resin ablation, fiber fracture and sublimation, delamination, ablation scallops and block-shaped ply-lift; delamination damage due to resin pyrolysis and internal pressure exist obvious distinguish; project area of total damage is linear with action integral for the same type specimens, that of resin ablation damage is linear with action integral, but no correlation with specimen type, for all specimens, damage depth is linear with logarithm of action integral. The coupled thermal–electrical model constructed is capable to simulate the ablation damage for carbon woven fabric/epoxy laminates exposed to simulated lightning current through experimental verification. Keywords Carbon woven fabric/epoxy laminates . Artificial lightning testing . Lightning damage . Numerical simulation

* F. Chang [email protected]

1

College of Aeronautics and Astronautics Engineering, Airforce Engineering University, No.1, Baling St, Xi’an 710038, China

2

The State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiao Tong University, No.28, Xi’an, Xianning St 710049, China

Appl Compos Mater

1 Introduction The carbon fiber reinforced polymer (CFRP) composites, due to its high modulus, high specific strength, good corrosion resistance and outstanding design ability characteristics, have already become a competitive alternative material to aluminum and titanium alloys and are being increasingly used in the territory of aerospace, wind turbines, automotive and other industries. For example, the Boeing 787 Dreamliner and Airbus A350 employ the CFRPs higher than 50% of structure weight [1]. Lightning is a common natural phenomenon, an aircraft may suffer from one lightning strike between each 1000 and 3000 h of flight based on the statistics on airliner, and even once a year especially in the regions with much more lightning storms [2, 3]. However, damage from lightning storms is a major threat to structures made from CFRP because of its bad electric conductivity when compared with traditional metallic structure, which needs careful precaution. When lightning hit metallic structure, lightning current injected into the structure from the lightning attachment point will be conducted away soon and will not cause serious damage. While for composite structures, lightning current could generate vast resistive heating at the lightning attachment point due to the poor electrical conductivity, accompany with the supersonic shockwave with high temperature and magnetic force effects produced by lightning strike arc, the composite structure will be serious damaged as fiber fracture, resin pyrolysis and delamination at the lightning attachment point and nearby region, eventually decrease the mechanical properties of structure and lead to catastrophic consequence [4]. Therefore, clarifying the damage mechanisms and resistance of CFRPs structure subjected to lightning strike show important scientific significance and value to promote the application of CFRP on aircraft. Despite the severity of the lightning damage on CFRPs, there are just a few literatures available regarding to the damage of composite encounter lightning strike, there exist two main reasons: one is that this research is complex due to it refers to the cross discipline between materials and electric major, and impulse current generator, which is used to simulate artificial lightning current, belongs to the territory of power system and with complex structure; another one is that its research progress is confidential to external for some reasons of business and military. According to the pertinent literatures we can get, investigators had carried out some tests to study the damage of composites under the act of lightning. Hirano et al. [5] conducted a series of experimental researches to examine the evolution of damage in graphite/epoxy composite laminates due to lightning strikes by means of visual inspection, ultrasonic testing, micro X-ray inspection and sectional observation, meanwhile, the influence of lightning parameters and specimen size to damage extent were also clarified. Feraboli and Miller [6, 7] did some artificial lightning strike tests to understand the fundamental damage response of both pristine specimens and specimens containing a Hilok stainless steel fastener, damage extent and mechanisms were evaluated via ultrasonic scanning and advanced optical microscope, subsequent mechanical testing to assess the residual tensile and compressive strength and modulus of the materials is performed according to ASTM standards. Furthermore, lightning strike damage was compared with the low velocity impact damage also. Wang FS [8] carried out some impulse electrical current tests for four different types of carbon fiber/ epoxy composite laminates, which are without protection, with full spraying aluminum coating, with local spraying aluminum coating and with spraying aluminum coating on glass cloth pasted to fastener head, respectively, to assess damage degree and effect of lightning strike protection (LSP) design. At the same time with testing, the coupled thermal/electrical simulation analysis of carbon fiber reinforced polymer composites exposed to simulated

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lightning current has been gradually conducted by several scholars. Ogasawara et al. [9] presented a coupled three-dimensional thermal-electrical finite element analysis model based on the ABAQUS thermal-electrical analysis module, to simulate lightning strike damage according to the transient temperature distribution in CFRP and decomposition regulation of resin. Abdelal and Murphy [10] followed the work done by Ogasawara et al. [9], presented a physics based modeling procedure, which uses the Finite Element Method with non-linear material models to represent the extreme thermal material behavior of the composite material (carbon/epoxy) and an embedded copper mesh protection system, to predict the thermal damage of composite material when struck by lightning; Wang FS et al. [11] studied the ablation damage characteristic of carbon fiber/epoxy composite laminate suffered from lightning strike by the coupled thermal–electrical–structural analysis and element deletion, and the influence of thermal/electrical material property to ablation damage were analyzed; A coupled electrical-thermal-pyrolytic model was constructed by Dong et al. [12, 13] to elucidate the damage phenomenon caused by lightning strike, in which the electrical and thermal properties in both out-plane and in-plane directions are modeled as functions of the pyrolysis degree of the composite material. In our previous researches [14, 15], composite lightning strike damage propagation mechanisms and lightning strike ablation damage characteristic of carbon fiber/ epoxy composite laminate with fastener were analyzed through coupled thermal–electrical model. However, all these researches above mainly focus on composite laminate with unidirectional tapes, few researches pay attention to carbon woven fabric/epoxy laminates subjected to lightning strike. Li et al. [16, 17] investigated the damage characteristic of two stacking sequenced carbon woven fabric/epoxy laminates subjected to simulated lightning strike by means of visual inspection, image processing, ultrasonic scanning and scanning electron microscope, and mechanical properties of post-lightning specimens are then assessed. Compared with the general composite laminate with unidirectional tapes, carbon woven fabric/epoxy laminates own excellent in-the-plane strength and impact resistance, and are widely used in manufacture of aircraft. To clarify the damage for carbon woven fabric/epoxy laminates exposed to simulated lightning strike, artificial lightning testing on carbon woven fabric/epoxy laminates were conducted in this paper, damage characteristic, damage model and damage mechanisms were assessed using visual inspection and damage peeling approaches, based on the damage measured results, the relationship between damage size and action integral was elucidated. Finally, a coupled thermal–electrical model was constructed to simulate the ablation damage for carbon woven fabric/epoxy laminates exposed to simulated lightning current, in which electrical conductivity in the thickness direction is a function of the pyrolysis degree of the composite material.

2 Experimental Procedure 2.1 Test Specimens Typical carbon woven fabric/epoxy laminates used in aircraft are prepared for doing the test, and specimens were classified into two categories based on their size: one is 150 mm × 100 mm × 4 mm (named Type 1); another one is 290 mm × 44 mm × 4 mm (named Type 2). The size of the first kind of specimen is selected with reference to ASTM D7137 [18]: the residual strength test standard for polymer matrix composites; and the second kind of specimen is selected with the reference to GB/T3354–2014 [19]: Test method for tensile

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properties of orientation fiber reinforced polymer matrix composite materials. Both the two kinds of specimens with a total of 16 plies carbon woven fabrics is then fabricated, the thickness of each ply is 0.25 mm, ply orientation angle of all the plies are [(0/90F)]. Material used in the test is Hexcel 8552/AS4, the volume fraction of carbon fibers is approximately 55%.

2.2 Lightning Strike Generator and Experimental Setup For the sake of simulating the lightning current, the high impulse current generator developed by Xi’an Jiao-tong University was selected. During the test, fixed the test specimens in the test jig completely, in order to reduce the contact resistance between specimen and test jig, meanwhile, ensure all side surfaces of the specimen with the same electric potential, conductive silver sol is selected to coat on all side surfaces and then covered with copper foil. The location of the copper probe locates upon the center of the specimen and the distance of the specimen from copper probe is set to 1 mm.

2.3 Artificial Lightning Waveform and Test Conditions According to SAE ARP 5412A [20], lightning strike current waveforms to evaluating direct effects are comprised four components (A-D), as shown in Fig. 1. Current components A and D usually are used to do lightning strike tests due to their higher peak current compared with other current components. The double exponential equation mathematical expression of the current components formulated by SAE ARP5412 as following:
iðtÞ ¼ I 0 e−αt −e−βt ð1Þ Where I0 is current constant, α is reciprocal value of wave tail time constant, β is reciprocal value of wave front time constant and t is the time. Furthermore, all the current waveform of double exponential equation can be expressed by parameters T1 and T2, where T1 represent the time to maximum current and T2 represent the time to 50% of the maximum current. Component A (Initial stroke) 200kA

Fig. 1 Simulated normative lightning current waveforms

Current

Component B (Intermediate current) 2kA

Component D (Restrike) 100kA

Component C (Continuing current) 200-800A

A

B

C

<500 s

<0.5ms

0.25
D <500 s

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During the test, lightning current waveform is set to component D, which is the restrike of the lightning infliction according to SAE ARP 5412A [20]. Test conditions and lightning strike parameters for the current experiment are shown in Table 1.

3 Results and Discussion 3.1 Description of the Experimental Phenomenon Tests of the simulated lightning strike in compliance with the conditions in Table 1 had been conducted on 11 specimens, nine for type 1 and two for type 2. During the test, a dazzling white flash and noticeable smoke could be seen on the surface of specimen near the lightning attachment area, meanwhile, a violent explosive sound is heard. At the end of the test, it can be clearly seen that there exist obvious damage in the lightning zone. Measure the transient temperature distribution in the specimens using infrared radiation thermometers ten seconds after the test accompanied, the measured results for specimen B2, B5 and B7 are shown in Fig. 2, from which we can see that there exist large amount of residual heat in specimen, and with the same lighting current waveform, the larger peak current is, the higher maximum residual temperature measured.

3.2 Lightning Strike Damage Characteristic Analysis In order to evaluate the damage characteristic of typical carbon woven fabric/epoxy laminates inflicted from lightning strike, the visual damage appearance of the tested specimen (B4) is compared with other lightning strike literature [5] which conducted lightning test to composite laminate with unidirectional tapes, compared results is shown in Fig. 3. We can see from Fig. 3 that the visual lightning strike damage appearance between carbon woven fabric/epoxy laminate and composite laminate with unidirectional tapes exists distinguishing difference. Visual damage appearance of the former structure form presents circular distribution, and center of the circle locates at the lightning attachment point approximately, however, that of the later structure form presents diamond distribution, and the damage mainly distribute along the fiber direction of the surface layer. For carbon woven fabric/epoxy laminate, fibers distribute uniformly along the direction of warp and weft per layer, hence, in-the-plane of each layers, electrical conductivity along longitudinal and transverse are the same, and when the lightning current injected into laminate, it will be conducted away along longitudinal and transverse direction at the same time, so, its visual damage appearance presents circular distribution. Table 1 The conditions and lightning strike parameters for the current experiment Test condition

1 2 3 4

Specimen type

T1/ T2 (μs)

Peak current (kA)

Action integral (A2s)

Numbering

Type2 Type1 Type1 Type1

10.4/35.2 4.9/19.8 4.9/19.8 4.9/19.8

29.5 31.4 50.2 79.2

24,515 13,596 34,649 87,347

A1 ~ A2 B1 ~ B3 B4 ~ B6 B7 ~ B9

Appl Compos Mater

(a) B2

Max Temp=101.0 Average Temp=95.8 Min Temp=86.5

(b) B5

(c) B7

Max Temp=151.1 Average Temp=121.5 Min Temp=97.9

Max Temp=217.1 Average Temp=158.7 Min Temp=119.2

Fig. 2 Transient temperature distribution in the specimen after lightning strike for carbon woven fabric/epoxy laminate.

For composite laminate with unidirectional tapes, its electrical conductivity along longitudinal direction is much higher than transverse direction in-the-plane of per layer, when the lightning current injected into laminate, it will be conducted away mainly along the longitudinal direction, so, its visual damage appearance presents diamond distribution, and the damage mainly distribute along the fiber direction of the surface layer. The overlaid image of UT scanning and visual damage appearance area for composite laminate with unidirectional tapes inflicted from lightning strike are shown in Fig. 4, the red zone represents internal damage which is got by UT scanning, the gray zone represents external damage which is got by visual inspection, we can see from Fig. 4 that visual damage appearance area is obviously smaller than internal damage. Due to the different layup orientation for each layer in the laminate, when the lightning current conducted to different layers, it will be conducted along different orientations, damage will distribute along the fiber direction, hence, damage projected area for different layers exist dislocations, internal damage presents in the shape of a pair of fans, so, the internal damage territory is larger than external. For the sake of checking the internal damage of carbon woven fabric/epoxy laminate inflicted from lightning strike, delamination damage of specimen B7 was peeled away through external mechanical force, and is shown in Fig. 5. From Fig. 5 we can see that the internal zone of the green dotted line frame represents the visual damage territory, also represents the delamination territory between first and second layers; yellow dotted line frame in Fig. 5 represents the delamination territory between second and third layers. At the center of the specimen, there exist obvious ablation scallops, which penetrate the third layer and reach forth layer. According to the damage appearance in per layer, we can see that damage in the internal

(a) Carbon woven fabric/epoxy laminate

(b) Composite laminate with unidirectional tapes

Fig. 3 Visual damage appearance for different laminate structure form

Appl Compos Mater Fig. 4 The overlaid image of UT scanning and visual damage appearance area [5]

Internal Damage

External Damage

layers also present circular distribution approximately, and the visual damage territory (equal to damage in first layer) wider than any internal damage distribution. At the initial stage of lightning strike, when the lightning current injected into the laminate, it will be conducted in the surface layer firstly, because the electrical conductivity in the thickness direction is much lower than that of in-the-plane, little lightning current will be conducted through the surface layer to second layer until damage penetrate the surface layer, so, damage in surface layer is largest than any internal layer because it conducts away more lightning current. Moreover, layup orientations of all layers are the same, and damage projected areas for different layers will exist no dislocations. Hence, the visual damage territory presents maximum damage scope for carbon woven fabric/epoxy laminate exposed to lightning strike.

3.3 Lightning Strike Damage Mode and Mechanism Analysis The visual appearance of the tested specimens are shown in Fig. 6a–d, each figure represents overhead and side view of the typical result of the specific test condition. Here, Fig. 7 shows a magnified view of lightning strike attachment point for test result with condition 4 (4.9/19.8 μs with peak current of 79.2 kA, B7), which can be regarded as a typical result of an

Fig. 5 Appearance of specimen B7 after delamination damage peeled away

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(a) A2

(c) B5

(b) B2

(d) B7

Fig. 6 Overhead and side view of post-lightning specimens

artificial lightning test, through visual inspection, we can recognize the damage mode and deduce the probable damage mechanisms when carbon woven fabric/epoxy laminate exposed to lightning strike.

Fig. 7 Magnified view of lightning attachment point

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According to the damage appearance in Fig. 7, at the lightning attachment point and nearby region, several typical damage modes can be observed, including resin ablation, fiber fracture and sublimation, delamination, ablation scallops and block-shaped ply-lift. Based on the analysis in literature [9], the mechanisms for laminate delamination damage between two layers during lightning strike can be classified into two main categories: one is delamination due to decomposition of resin; another one is delamination due to internal pressure derived from pyrolysis gases. From Fig. 7, obvious delamination damage can be observed. Red dotted line frame in Fig. 7 represents typical delamination damage territory, which is divided into two parts called A and B by the dotted line J. compared locations C, D, E and F with K, we can see that the color of the former four locations are darker, and exist obvious resin ablation trace. Through the compared results, the above delamination damage mechanisms are experimental verified. Under the act of lightning current, vast resistive heating is generated due to the poor electrical conductivity. As temperature rises through resistive heating, the ablation and pyrolysis of resin advances, the bonding strength between two layers will be descended due to the resin deterioration, and leading to delamination damage eventually, as territory A shown in Fig. 7. Rapid evaporation of the internal resin pyrolysis gases result in an explosive in the vicinity of the lightning strike attachment point, under the act of which the concentrate stress will exist between two layers at the boundary of the delamination damage territory due to decomposition of resin, and new delamination damage will be occurred, as territory B shown in Fig. 7. Meanwhile, under the act of internal pressure, the outer plies will present block-shaped plylift outwards, when the lift extent beyond its limitation, fiber of block-shaped ply-lift will be fractured along the bottom edge, dotted line H and I in Fig. 7 are trace of fiber fracture, meanwhile, also the boundary of second and third layers, first and second layers respectively. Territory in the ellipse dotted line frame in Fig. 7 represents ablation scallops, which is located below the lightning attachment point. Through visual inspection, the ablation scallops penetrate the third layer and reach forth layer, and surface of the forth layer exist ablation trace. In the ablation scallops, there exist many kinds of damage, including resin ablation and pyrolysis, delamination, fiber fracture and sublimation and so on, which can be call comprehensive damage territory. During lightning strike, temperature in this territory was highest and changed promptly, leading to multiple physicochemical and mechanical responses. According to the analysis in chapter 3.2, once penetrability damage exist in the center of surface layer, abundant lightning current can be conducted to the second layer, similarly, little lightning current will be penetrated through the second layer to third layer until damage penetrate the second layer, at this time, lightning current conducted through the surface layer mainly be conducted away along longitudinal and transverse direction in-the-plane of second layer, and causing resin ablation and pyrolysis in second layer. Above descriptions are the current conducted mechanisms when carbon woven fabric/epoxy laminate exposed to lightning strike. On the basis of visual damage appearance in Fig. 7, delamination damage territory due to decomposition of resin and internal pressure exist obvious distinguish, in order to investigate delamination damage proportion of the two mechanisms, adopting the approach of damage peeled away through external mechanical force to analysis the internal damage. Damage appearance and size of specimen A2, B2, B5 and B7 are shown in Fig. 8. In Fig. 8a–c, territory in the outer green dotted line frame is the visual damage zone, also represents the total delamination damage between first and second layer; and color of the territory in the inner yellow dotted line frame is darker than outside, which represents the resin ablation territory in second layer, also represents the delamination damage due to decomposition of resin between

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first and second layer. In Fig. 8d, territory in the larger green dotted line frame is the visual damage zone, also represents the total delamination damage between first and second layer; and color of the territory in the larger yellow dotted line frame is darker than outside, which represents the resin ablation territory in second layer, also represents the delamination damage due to decomposition of resin between first and second layer; territory in the smaller green dotted line frame represents the total delamination damage between second and third layer; and color of the territory in the smaller yellow dotted line frame is darker than outside, which represents the resin ablation territory in third layer, also represents the delamination damage due to decomposition of resin between second and third layer. Based on the measured damage sizes in Fig. 8, delamination damage area due to different mechanisms can be calculated based on ellipse area formula, as is shown in Fig. 9, from which we can see that, for specimen type 2, delamination damage area due to internal pressure is larger than decomposition of resin, there exist obvious boundary effect due to its larger length to width ratio. Under test condition 1, proportion of the delamination damage area due to internal pressure is about 60.9% to the total delamination damage area (specimen A2); for specimen type 1, delamination damage mainly due to decomposition of resin, calculate the average proportion of delamination damage area due to decomposition of resin of specimen B2, B5 and B7, we can get that proportion of delamination damage area due to decomposition of resin is about 60.9% to the total delamination damage area.

Fig. 8 Appearance after delamination damage peeled away

Appl Compos Mater Total Delamination area Delamination area due to decomposition of resin Delamination area due to internal gas pressure

Delamination area (mm2)

2500

Delamination between first and second layer

2000 64.25%

1500 1000

Delamination between second and third layer

39.4%

60.6%

35.75% 50.56% 49.44%

58.91% 41.09%

500

68.94% 31.06%

0

B2

A2

B5 Numbering

B7

B7

Fig. 9 Measured and calculated results of delamination area

3.4 The Relationship between Action Integral and Damage Size According to literature [5, 9, 13], action integral of lightning current is a major parameter to measure composite lightning strike damage degree. Figure 10 shows the relationship between action integral and project area of total damage and resin ablation damage. From fitting curve 1 in Fig. 10 we can see that project area of total damage is linear with action integral for the same type specimens; and from fitting curve 2 in Fig. 10 we can see that project area of resin ablation damage is linear with action integral, more importantly, no correlation with the specimen type. 3000 Project area of total damage Project area of resin decomposition

B7

2500

Project area(mm2)

Fitting curve 1 Fitting curve 2

2000

B7

A2

1500

B5

1000

B5 B2

500

A2

B2

0 0.0

2.0x104

4.0x104

6.0x104

Action integral(A2s) Fig. 10 Relationship between action integral and project area

8.0x104

1.0x105

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According to the appearance after delamination damage peeled away, we can estimate the damage depth of different specimens approximately, typical damage depth under different test conditions is shown in Fig. 11, and abscissa in Fig. 11 is the logarithm of action integral. From Fig. 11 we can see that damage depth is linear with logarithm of action integral, and also no correlation with the specimen type.

4 Coupled Thermal/Electrical Analysis Model 4.1 Problem Description When lightning hit composite structure, lightning current will inject into the structure from lightning attachment point, and generate vast resistive heating due to the poor electrical conductivity of composite, then ablation damage will occur accompany with temperature rises, simultaneously, heat transfer between high-temperature zone and low-temperature zone in composite will appear also. So that, if just take lightning strike ablation damage into account, the essence of composite lightning strike ablation damage analysis process can be simplified into a problem of nonlinear heat transfer which include inner heat source. The coupled thermal-electrical analysis model for composite subjected to lightning current comprises the governing equations of heat transfer, energy transition between electrical and thermal and resin pyrolysis kinetics. The former two governing equations are specified in ABAQUS theory manual [21], and these equations were also adopted in some works [9–15]. According to the simulation work done before, the critical influence factor to affect the accuracy of simulation results is constructing a reliable electrical conductivity model 0.9

D am ag e d ep th (m m )

0.8

Damage depth Fitting curve B7

0.7 B5

0.6 0.5 A2

0.4 0.3 0.2 4.0

B2

4.2

4.4

Equation Weight Residual Sum of Squares Pearson's r Adj. R-Square

y = a + b*x No Weighting 0.00533

E E

Intercept Slope

4.6

Log10(Action integral) Fig. 11 Relationship between action integral and damage depth

0.9833 0.95033 Value Standard Error -2.51948 0.40022 0.67834 0.08877

4.8

5.0

Appl Compos Mater

[9–13]. For CFRP composite laminate, its electrical conductivity is anisotropy, and will be changed accompany with temperature rises, however, experimental data on the electrical conductivity of CFRP composites above 330 °C has already rarely been reported. Ogasawara et al. [9] assumed that the electrical conductivity in the thickness direction changed linearly from 7.64 × 10−7(Ωm)−1 to 0.1(Ωm)−1 between 600 °C to 3000 °C, however, they ignored the correlation between electrical properties and thermal decomposition, which might lead to inaccurate results. Abdelal and Murphy [10] followed the work done by Ogasawara et al. [9], presenting improved methods to model the composite panel subjected to lightning strike, in which temperature-dependent electrical conductivity model referred to literature [22, 23], but it is difficult to convergence during calculation, especially for high lightning current. Dong et al. [12, 13] presented pyrolysis degree-dependent electrical conductivity, and excellent agreement between experimental and numerical results is observed. Wang YQ et al. [24] found that the temperature-dependency of the electrical conductivity for carbon fiber is similar to that of semiconductors, based on the Arrhenius equation, expression of temperaturedependency electrical conductivity for carbon fiber was got, however, the model ignored the influences of resin pyrolysis and ablation scallops to the electrical conductivity in the thickness direction. In this paper, we adopt the electrical conductivity model in literature [12, 13] to do our coupled thermal/electrical analysis, but do some simplified to this model, which will be specified in the next chapter.

4.2 Determination of Pyrolysis-Dependent Electrical Conductivity of Composite Lamina First, the electrical conductivity of the CFRP composites at room temperature is determined using the rule of mixtures [24]:
ð2Þ σ1 ¼ σ f V f þ σm 1−V f Where σ1 is the overall electrical conductivity of the composite lamina in the longitudinal direction (in S/m); σf is the electrical conductivity of carbon fiber (in S/m); Vf is the fiber volume fraction; σm is the electrical conductivity of the polymermatrix (resin) (S/m). For carbon woven fabric/epoxy laminate, the electrical conductivity in the transverse direction σ2 is equal to that in the longitudinal direction, while the electrical conductivity in the thickness direction is around 1 × 10−6 times the electrical conductivity in the longitudinal direction [24]. In literature [12], it is assumed that electrical conductivity in the transverse direction and thickness direction were resin pyrolysis degree dependent and the electrical conductivity in the longitudinal direction kept a constant. In this study, we adopt the same electrical conductivity model, for carbon woven fabric/epoxy laminate, accompany with temperature rises, electrical conductivity in the longitudinal direction and transverse direction keep a constant, and that in the thickness direction changes linearly with the resin pyrolysis degree. Assuming that initial value of the electrical conductivity in the thickness direction is σ3(T0), and electrical conductivity when the resin pyrolysis completely is σ3(Tf), during the

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temperature rises, resin pyrolysis degree is α(T), expression of electrical conductivity in the thickness direction with temperature can be expressed as:

σ3 ðT Þ ¼ σ3 ðT 0 Þ þ αðT Þ σ3 T f −σ3 ðT 0 Þ

ð3Þ

The following empirical equation is often applied for estimating the decomposition kinetics for a thermosetting resin [25].   dα A Ea ¼ exp − ð1−αÞn RT dT β

ð4Þ

Where A is the pre-exponential factor, Eα is the activation energy, R is the universal gas constant (R = 8.314 J/mol/K), β is a constant heating rate, n is the reaction order. Eq. (4) can be integrated by the separation of variables method such that [26]:   dα A t1 Ea α dT ð5Þ ¼ exp − ∫ gðαÞ ¼ ∫0 RT ð1−αÞn β t0 Solve Eq. (5) to get the expression ofα.      1 Ea t A dT ln 1−ð1−nÞ∫t0 exp − αðT Þ ¼ 1−exp RT 1−n β

ð6Þ

The material used in this study is Hexcel 8552/AS4, fiber volume fraction Vf=55%, electrical conductivity for carbon fiber σf=58,823 S/m and electrical conductivity for resin σm=4.9 × 10−16 S/m. Based on Eq. (2) and the relationship between electrical conductivity in the longitudinal direction and thickness direction, AS4/8552 electrical conductivity of carbon woven fabric/ epoxy laminate at room temperature can be calculated, as is shown in Table 2. Value of composite resin decomposition kinetic parameter in Eq. (4) presented as followed: n = 3.5,A = 5.0*1013(1/min),Ea = 180(kJ/mol/K) [9]. Based on Eq. (6), we can get the decomposition degree curves of resin under different temperature rising rate (5 °C/min., 10 °C/min., 20 °C/min., 50 °C/min. And 100 °C/min), which is shown in Fig. 12. From Fig. 12, it can be seen that temperature range of resin decomposition is about 250 °C ~ 700 °C. Resin initial decomposition behavior can be regarded as damage criteria, that is to say, temperature profile greater than 250 °C of simulation result can be regarded as ablation damage. According to literature [10], it is assumed that electrical conductivity in the thickness direction σ3(Tf) =200S/m, and combined Eq. (3), Fig. 12 and Table 2, we can get the electrical conductivity in the thickness direction accompany with temperature rises, as is shown in Fig. 13.

Table 2 AS4/8552 electrical conductivity of carbon woven fabric/epoxy laminate at room temperature Longitudinal(S/m)

Transverse(S/m)

Through-the-thickness(S/m)

σ1= 32500

σ2= 32500

σ2= 3.25×10–2

Appl Compos Mater

Degree of decomposition

1.0 =5 / min

0.8

=10

0.6

/ min

=20

/ min

=50

/ min

=100

/ min

0.4 0.2 0.0 0

500

1000

1500

2000

2500

3000

3500

Temperature/ Fig. 12 Pyrolysis degree curves of resin under diffferent temperature rising rate

4.3 Finite Element Model

Conductivity along thickness direction/Sm-1

According to the test setups in the experimental procedure section, an effective three dimensional thermal-electrical coupling analysis finite element model for carbon woven fabric/epoxy laminate subjected to lightning current is established based on ABAQUS, including two types of specimen. The model contains 16-plies, and each ply is 0.25 mm, the length of the model is 150 mm and the width is 100 mm, ply orientation angle of all the plies are [(0/90F)]. Refine the mesh at the center of the model, each layer of the laminate is explicitly discretized by using 3D element DC3D8E, total number of simulation elements for two types of specimen are 38,400

200 175 150 125 100 75 50 25 0 0

500

1000

1500

2000

2500

3000

3500

Temperature/ Fig. 13 Electrical conductivity in the thickness direction accompany with temperature rises

Appl Compos Mater Table 3 Composite thermal material properties vs. temperature [10] Temperature (°C)

25 343 500 510 1000 3316 >3316

Density (kg/mm3)

Specific heat (J/kg°C)

Longitudinal/Transverse thermal conductivity (W/mm°C)

Through-the-thickness thermal conductivity (W/mm°C)

1.52e-6 1.52e-6 1.1e-6 1.1e-6 1.1e-6 1.1e-6 1.1e-6

1065 2100 2100 1700 1900 2509 5875

0.008 0.02608 0.001736 0.001736 0.001736 0.001736 0.00105

0.00067 0.00018 0.0001 0.0001 0.0001 0.0001 0.001015

and 27,200 respectively. Material properties, such as thermal conductivity, specific heat and density are given in Table 3. The simulated lightning current is located on the top surface center of the specimen. In order to simulate the true test environment, boundary conditions of the simulation model are as follows: electrical potential of the side surfaces are assumed to be zero due to electrically grounded; thermal radiation will occur because of transient heat transmit of the specimen, assuming the upper and side surfaces radiate heat and the bottom surface is adiabatic, the emissivity is 0.9 and the environment temperature is 25 °C. Figure 14 shows the simulation model of a specimen subjected to lightning strike.

5 Simulation Model Verification Coupled thermal/electrical simulation model constructed in the paper just could simulate the ablation damage of the specimen, and unable to simulate the delamination damage and fiber fracture due to internal pressure. Hence, when verify the simulation model, just comparing the ablation damage area between test and simulation results. Test and simulation results under test condition 1 (10.4/35.2 μs with peak current of 29.4kA, A2) are shown in Fig. 15. From Fig. 15a, we can see that surface layer of the laminate was peeled away completely due to the internal pressure, meanwhile, there exist obvious resin ablation trace in the surface center of second layer, and presents circular distribution, and Fig. 14 Simulation model of composite exposed to simulated lighting current

Top surface Thermal radiation Electrical current

Side surface E=0V(electrical discharge to bottom) Thermal radiation

150mm 100mm

Bottom surface Adiabatic

Thermal radiation Emissivity =0.9 Atmosphere T=25

Appl Compos Mater

(a)

Test result

(b)

Simulation result

Fig. 15 Test and simulation results of the second layer for specimen A2

center of the circle locates at the lightning attachment point approximately, the size of the resin ablation territory is about 27.8 mm × 29.8 mm. There also exist ablation scallops in the center zone of the second layer, in which tiny fiber lift will be observed using advanced microscope. Figure 15b shows the ablation simulation results of the front and back surface of the second layer, in which we can see that ablation damage mainly distribute on the front surface of the second layer, and only the center territory of the second layer exist penetrating damage, the ablation damage size on the front surface of the second layer is about 25.5 mm × 29.8 mm. Fig. 16 Simulation ablation damage distribution and size of specimen B2, B5 and B7

(a) B2

(b) B5

(c) B7

Appl Compos Mater Table 4 Test and simulation compared results Numbering

A2 B2 B5 B7

Location

layer2 layer2 layer2 layer2 layer3

Ablation damage of test

Ablation damage of simulation

Size (mm × mm)

Area (mm2)

Size (mm × mm)

Area (mm2)

27.8 × 29.8 23 × 23.5 30 × 33.5 43.3 × 52.5 31 × 31.5

650.32 424.3 788.93 1784.5 766.55

25.5 × 29.8 22.2 × 22.6 29.4 × 32.3 42.8 × 51.1 29.4 × 30

596.52 393.85 745.45 1716.85 692.37

Error (%)

-8.27 -7.18 -5.51 -3.79 -9.68

Figure 16 shows the simulation ablation damage distribution and size of specimen B2, B5 and B7, and test and simulation compared results are shown in Table 4. Based on the compared results in Table 4, ablation damage sizes and damage appearance between test and simulation agree well, and all the errors of ablation damage area between test and simulation are less than 10%. The experimental maximum damage depth is quantified through delamination damage peeled away, as shown in Fig. 17, which is compared to the simulated maximum damage depth. It indicates that the simulation results have a good corresponding to the experimental data. From the above compared results, the model constructed in the paper is capable to simulate the ablation damage of carbon woven fabric/epoxy laminate inflicted from lightning current.

6 Conclusion To clarify the damage for carbon woven fabric/epoxy laminates exposed to simulated lightning strike, artificial lightning testing on carbon woven fabric/epoxy laminates were conducted in this paper, damage characteristic, damage model and damage mechanisms were assessed using visual inspection and damage peeling approaches, based on the damage measured results, the

0.8

Maximum damage depth/mm

Fig. 17 Experiment and simulation comparison of maximum damage depth for different specimens

Experiment Simulation

0.6

0.4

0.2

0.0

A2

B2

B5 Numbering

B7

Appl Compos Mater

relationship between damage size and action integral was elucidated. The following conclusions were obtained: (1)

Compared to the diamond-shaped damage appearance of composite laminate with unidirectional tapes, damage appearance of carbon woven fabric/epoxy laminates presents circular distribution, and center of the circle locates at the lightning attachment point approximately. There exist no damage projected areas dislocations for different layers for carbon woven fabric/epoxy laminates, so, its visual damage territory represents maximum damage scope; (2) The impulse current imitating natural lightning causes visible damage to the carbon woven fabric/epoxy laminates, which can be categorized into five modes: resin ablation, fiber fracture and sublimation, delamination, ablation scallops and block-shaped ply-lift; (3) The influence of resin pyrolysis and internal pressure to delamination damage were clarified. For the specimen with larger length to width ratio, proportion of the delamination damage area due to internal pressure is 60.9% to the total delamination damage area (specimen A2), and for the specimen with smaller length to width ratio, the proportion descend to 39.5% (average proportion of specimen B2, B5 and B7); (4) Project area of total damage is linear with action integral for the same type specimens (type 1), that of resin ablation damage is linear with action integral, but no correlation with specimen type; for all specimens, damage depth is linear with logarithm of action integral. A coupled thermal–electrical model was constructed to simulate the ablation damage for carbon woven fabric/epoxy laminates exposed to simulated lightning strike, in which electrical conductivity in the thickness direction is a function of the pyrolysis degree of the composite material, based on the experimental verification of the ablation damage area, damage appearance and damage depth results, the model constructed in the paper is reasonable to simulate the lightning ablation damage of carbon woven fabric/epoxy laminate. Acknowledgements This study is supported by the National Natural Science Foundation (No: 51477132).

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