**Jian Chen 1, Xiaolei Bi 2, Juan Liu <sup>2</sup> and Zhengcai Fu 1,\***


Received: 24 February 2020; Accepted: 19 March 2020; Published: 21 March 2020

**Abstract:** The damage induced by lightning strikes in carbon-fiber-reinforced plastic (CFRP) laminates with fasteners is a complex multiphysics coupling process. To clarify the effects of different lightning current components on the induced damage, components C and D were used in simulated lightning strike tests. Ultrasonic C-scans and stereomicroscopy were used to evaluate the damage in the tested specimens. In addition, the electrothermal coupling theory was adopted to model the different effects of the arc and the current flowing through the laminate (hereinafter referred to as the conduction current) on CFRP laminates with fasteners under different lightning current components. Component C, which has a low current amplitude and a long duration, ablated and gasified the fastener and caused less damage to the CFRP laminate. Under component C, the heat produced by the arc played a leading role in damage generation. Component D, which has a high current amplitude and a short duration, caused serious surface and internal damage in the CFRP laminate and little damage to the fastener. Under component D, the damage was mainly caused by the Joule heat generated by the conduction current.

**Keywords:** Carbon-fiber-reinforced plastics (CFRPs); fastener; arc; Joule heat; finite element analysis (FEA)

## **1. Introduction**

Carbon-fiber-reinforced plastics (CFRPs) have excellent mechanical properties and are widely used in various industries [1–3]. With the massive expansion of wind power and the rapid growth in the number of aircraft, the chances of wind turbine blades and aircraft being struck by lightning have inevitably increased substantially. Because the destructive effects of lightning strikes often lead to serious consequences, research on lightning damage in CFRPs has received unprecedented attention [4–8].

In structural design, depending on the excellent formability of composite materials, the number of fasteners can be reduced by optimizing the design; however, completely eliminating the need for fasteners is difficult. These fasteners have greater electrical conductivity than the other materials in CFRP laminates. Therefore, when a lightning strike occurs, the current is discharged through the fasteners first and then into each layer of the CFRP laminate, which leads to fiber breakage, resin degradation, and internal delamination [9]. In addition, the temperature and air pressure inside the fastener hole will change dramatically during the lightning strike [10], which leads to damage around the hole, loss of fastener support, and weakening of the mechanical and electrical properties of the CFRP [11]. Therefore, research on the damage in CFRPs with fasteners subjected to lightning strikes is the key point of composite lightning protection [10,12].

The duration of a lightning strike is extremely short, during which a large amount of energy is released in an instant, resulting in extremely high temperatures. Observing the damage characteristics near the attachment point of the lightning strike in real time with instruments is difficult. Therefore, finite element analysis (FEA) has become an effective method for studying the damage evolution process of CFRP laminates with fasteners under lightning strikes and for verifying the correctness of the test results. Chemartin et al. [13] used the finite volume method in the time domain and unstructured mesh to establish the mechanism model of CFRPs with fasteners, and simulated the spark phenomenon in fasteners. The research showed that sparking may occur when the current density is greater than 10 kA/mm2. Kirchdoerfer [10] simulated the gas conditions and related local geometric changes in the interior space around the fastener during lightning strikes, and discussed the importance of chemical change modeling in future work. Meanwhile, the electrothermal coupling model is used to investigate the damage of CFRP under lightning strike. Muñoz et al. [14] developed a finite element model to consider the damage sources observed in a lightning strike, such as thermal damage caused by Joule heat. Yin et al. [11] established a three-dimensional electrothermal coupling model of ablation damage of CFRP with fasteners based on the relationship of the energy balance in s lightning strike. The results indicated that fasteners distributed the lightning current to each layer, and a larger conduction current dispersion area led to less damage to the laminate. Abdelal et al. [15] proposed a physical model to predict lightning strike damage for composite materials. The finite element method of non-linear material model was used to analyze composite materials with copper mesh protection. Ogasawara et al. [16] proposed a electrothermal coupling model of angle ply composite laminates, which considered the anisotropic thermoelectric behavior of layer and unidirectional composite laminates. However, their work neglected the arc heat effect in numerical simulation. Dong et al. [17] considered the influence of the arc heat effect and replaced it with heat flux in the models, while the damage to CFRP with fasteners was not mentioned. On the basis of previous work, this paper used the electrothermal coupling module in COMSOL to design simulation models to explore the arc heat and conduction current effects on the damage of CFRP with fasteners, as well as the damage difference under different lightning current conditions.

Experimental investigations are often used to study the damage in CFRP laminates with fasteners subjected to lightning strikes. Previous studies have found a relationship between the damaged area and the mounting depth of the fasteners during a lightning strike. The shallower the mounting depth, the larger the surface damage area [18]. CFRP laminates with fasteners show penetrating damage under lightning strikes, with damage occurring on both sides of the specimen [19,20]. The lightning current component D is influential in developing out-gassing, whereas no out-gassing is observed when component C is used [21]. To make the simulated lightning strikes in the laboratory more closely approximate natural lightning strikes, it is important to ensure that the lightning current waveforms and current amplitudes used in the tests meet the standard requirements [19]. However, in the study of lightning damage in CFRP laminates with fasteners, many of the waveforms and amplitudes used in previous studies did not meet the standard requirements [22,23], and the roles of the arc and conduction current in the process of damage were not clearly distinguished.

In this work, simulated lightning strike tests were performed on CFRP laminates with fasteners using lightning current components C and D, which comply with the standards. Ultrasonic C-scans and stereomicroscopy were used to evaluate the differences in specimen damage under the two components, and an electrothermal coupling model was adopted to verify the test results to study the different effects of the conduction current and arc after the action of lightning current components C and D. The results were compared with the lightning damage of pure CFRP under components C and D [17].

#### **2. Materials and Methods**

#### *2.1. Specimen Preparation*

The material used in this work was a unidirectional carbon fiber prepreg (TC35/FRD-Y360). The specimen dimensions were 250 mm (length) × 250 mm (width) × 2 mm (thickness), and the stacking sequence was 0 ◦ /90◦ /0◦ /90◦ /0◦ /90◦ /0◦ /90◦ /0◦ /90◦ /0◦ /90◦ /0◦ /90◦ /0◦ , creating a total of 15 plies. The diameter of the mounting hole was 8 mm, and the fastener material was stainless steel. Compared with titanium alloy, stainless steel has good electrical conductivity and a lower melting point, which will result in more severe damage during lightning strikes, which is beneficial for observation and analysis. The specimens used in this work were unpainted and unprotected. This structure allowed us to focus on the details of CFRP response to high energy discharge alone [19]. The assembly of the fastener and CFRP laminate is shown in Figure 1a. The tight fitting of the fastener and the CFRP laminate mounting hole can reduce the contact resistance between the two elements. The discharge electrode with a diameter of 8 mm was made of tungsten–copper alloy (W80Cu20) and was positioned directly above the centre point of the specimen, separated from the specimen by a distance of approximately 3 mm. The four sides of the specimen were fixed on a metal plate with detachable copper strips. For reliable grounding, four copper braids were connected at the four corners of the metal plate. The simulated lightning current was injected into the specimen as an arc discharge and then flowed through the metal plate and out through the copper braid. The clamp and connection are shown in Figure 1b.

**Figure 1.** (**a**) Assembly diagram of the CFRP with a fastener; (**b**) the clamp and connection.

#### *2.2. Test setup and waveform*

The lightning current waveforms described in [22] and [23] include four components (Figure 2). Components A, B, C, and D represent the first return stroke, intermediate current, continuing current, and the subsequent return stroke, respectively. These four components can be divided into two categories: (1) short-duration, small-transferred-charge, high-action-integral, high-current-amplitude components A and D; and (2) long-duration, large-transferred-charge, low-action-integral, low-current-amplitude components B and C. To make this study universal, lightning current components C and D were used in the simulated lightning strike test of the CFRP laminates with fasteners. The current amplitude of component C was 200 A, the duration of which could reach 1 s, and the transferred charge was 200 C; the actual test waveform is shown in Figure 3a. The current amplitude of component D was 100 kA, the duration could reach 500 μs, and the action integral was 2.5 <sup>×</sup> 105 <sup>A</sup>2s; the actual test waveform is shown in Figure 3b.

**Figure 2.** Simulated lightning current waveforms in [23].

**Figure 3.** Lightning current waveforms used in the present study: (**a**) component C; (**b**) component D.

#### **3. FEA**

#### *3.1. Electrothermal Coupling Theory*

Because of the short duration of the lightning strike, measuring and observing the damage evolution process is difficult. Therefore, FEA is an effective method for analyzing the process. COMSOL was successfully applied to the finite element simulation of CFRP damage during lightning strikes [10]. The electrothermal coupling module in COMSOL provides a method for analyzing such problems. The module considers both the effect of the electrical conductivity with respect to temperature and the effect of the electric field with respect to the current density.

Herein, a steady-state electrical simulation analysis and a transient thermal simulation analysis are performed in sequence [24]. The lightning current flowing through the CFRP laminate will generate Joule heat, causing the resin to pyrolyze and gasify, which is a typical electrothermal coupling process [25–27]. During this process, the following charge conservation equations need to be followed:

$$\frac{\partial \rho\_{\mathbf{e}}}{\partial \mathbf{t}} + \nabla \cdot \mathbf{j} = 0 \tag{1}$$

where ρ<sup>e</sup> is the charge density and j is the current density inside the material.

The relationship between the current and Joule heat can be expressed as follows:

$$\mathbf{P}\_{\mathbf{c}} = \mathbf{j} \cdot \mathbf{E} = \frac{\mathbf{j}^2}{\sigma} \tag{2}$$

where Pe is Joule heat per unit volume and σ and E are the electric conductivity and electric field intensity per unit volume, respectively.

The heat transfer in the material conforms to Fourier's law. The governing equation of heat balance can be expressed as follows [14,27,28]:

$$
\rho \mathbf{C}\_{\text{P}} \frac{\partial \mathbf{T}}{\partial \mathbf{t}} = \nabla \cdot (\mathbf{k} \nabla \mathbf{T}) + \frac{\mathbf{j}^2}{\sigma} \tag{3}
$$

where Cp is the specific heat capacity at constant pressure, ρ is the density, T is the absolute temperature, and k is the thermal conductivity.

The heat transferred to the material by the arc is equivalent to the heat flux [17], and the heat flux is expressed as follows:

$$\mathbf{Q(r,t)} \approx 10\mathbf{J(r,t)}\tag{4}$$

where t is the time, Q is the heat flux of the lightning arc, and J is the current density on the top of the fastener.

#### *3.2. Finite Element Modeling*

During the lightning strike, the temperature changes drastically, and the thermal conductivity, electrical conductivity, density, and specific heat of the material change significantly with respect to the temperature [15,29,30]. Table 1 shows the material parameters measured by thermogravimetric analysis (NETZSCH STA449F3, Germany) and laser flash thermal conductivity analysis (LFA467, Germany).


**Table 1.** Physical properties of the specimen.

1,2- These parameters are not directly measured but obtained through extrapolation [15,27,31,32].

The parameters of stainless steel fasteners are shown in Table 2.

**Table 2.** Physical properties of stainless steel.


Some assumptions were proposed: no clearance between fastener and composite, and the contact electrical resistance and thermal resistance on the interface were ignored; the delamination caused by Joule heat and the thermal stress inside the specimen was not considered. The stacking sequences and dimensions of the CFRP laminate used in the finite element modeling were the same as those of the specimen. The model is shown in Figure 4. The whole model had 28,157 elements, 28,055 hexahedra, 2,200 edge elements, and 136 vertex elements. The electrical potential boundary of the model was set as follows: the electrical potential of the two parallel sides was 0 V. Heat exchange between the specimen and the environment occurred when the specimen was directly exposed to the air. Therefore, the thermal boundary of the model was set as follows: the thermal radiation emissivity of the top and bottom surfaces was 0.9; the four sides of the model were thermally insulated and did not exchange heat with the external environment; and the environmental temperature was 25 ◦C. The conduction current and heat flux of components D and C were imported into COMSOL and applied on the entire top surface of the fastener. For modeling of different fiber orientations, rotated coordinate systems were used and the material properties of CFRP were assigned to each layer. For each layer, the size of elements increased from the center to the four sides to improve the efficiency and ensure the accuracy at the same time. The maximum and minimum side lengths were 10 mm and 3 mm, respectively. The average element quality was about 0.9. The total time of the transient solver was set according to the duration of the waveform (300 μs for component D and 1 s for component C). In this work, the relative tolerance of the simulation model was 0.01, the tolerance factor was 0.1, the maximum number of iterations was 10, and the termination technique was the tolerance. The simulation was done on a Dell Precision Tower 780 workstation equipped with two E5-2603 CPUs and 48 GB memory, and the longest time consumed about 11 h for a calculation case. In the process of calculation, the temperature distribution and the physical parameters of the materials were monitored by the domain point probes arranged in the model to ensure the convergence of the model.

**Figure 4.** Finite element model and boundary conditions.

In the model, r(t) is the arc channel radius; Q(r, t) is the heat flux obtained by Equation (4), which is used to represent the role of the arc; and I(t) is the conduction current injected into the top of the fastener.

The heat flux radius is assumed to be the same as the fastener radius. When a lightning strike occurs, the lightning current is divided into two parts: one part is attached to the top of the fastener in the form of an arc, whereas the other part is conducted in the fastener and the laminate in the form of conduction current. Therefore, the damage in CFRP laminates with fasteners is caused by the combination of the arc and conduction current. To understand the effect of the arc and conduction current on CFRP damage and to understand the difference in CFRP damage under different lightning current components, we designed three simulation models for each lightning current component, as shown in Table 3.


