contributions of lightning current pulses to mechanical ...

2015 International Conference on Lightning and Static Electricity (Toulouse, France)

CONTRIBUTIONS OF LIGHTNING CURRENT PULSES TO MECHANICAL DAMAGE OF CFRP STRUCTURES C. Karch*, R. Honke†, J. Steinwandel*, and K.W. Dittrich# * Airbus Group Innovations, 81663 Munich, Germany, † University of Applied Sciences, 95028 Hof, Germany # Airbus Defence and Space, 85077 Manching, Germany

Keywords: Lightning Damage, Direct Effects, CFRP

radial direction. The increase in the arc root radius during the pulsed current component depends also on the surface coating of the test sample [10]. The presence of a dielectric layer generally restricts the expansion of the arc root radius. CFRP structures are usually protected by expanded (copper) foils (ECF) that are laminated on the top by an epoxy resin. This specific design of lightning protection layer helps to dissipate the lightning strike energy. Since the electrical resistivity of ECF is generally 2 orders of magnitude smaller than that of CFRP the lightning current flows almost completely within the ECF not affecting directly the CFRP structure. This is supported by experimental results for the arc root behaviour of the transient lightning current components on protected CFRP samples [8]. As shown in Figure 1 the arc root expands radially continuously removing the metallic protection from the top of the CFRP sample.

1 Abstract The lightning direct effects on metallic materials are described within a thermo-electrical framework that has been extended to describe the thermo-mechanical damage of continuous lightning current components of CFRP structures. It is shown, that the thermo-electrical approach needs to be supplemented or even replaced by force concepts for describing mechanical damage of CFRP structures caused by the transient lightning current components. An analysis of the damage mechanism of CFRP structures due to transient lightning strike current components is given with focus on the main non-thermal damage mechanisms: the magnetic forces, the shock waves due to supersonic channel expansion, and the shock waves due to near surface-explosions. Moreover, a numerical model for the arc root radius expansion during the transient lightning current component is developed as well.

2 Introduction Although the basics of the fundamental description of the physics of a lightning strike to protected CFRP composite structure are known, there is still a need for reliable models that can predict the response and damage of CFRP structures caused by transient lightning current components. The thermal load of the plasma channel and of the Joule resistive heating result in melting and / or vaporization of metallic material and epoxy resin. Moreover, the thermal load can result in elastic distortion and fracture of brittle CFRP structures as well. The thermo-electrical approach has already been extended to describe the thermo-mechanical damage of continuous lightning components of protected CFRP structures [16]. However, there is a strong need to develop reliable mechanical based concepts for describing damage of composite structures caused by transient lightning currents. The main task of the present study is to clarify the nature and magnitude of different non-thermal damage mechanisms of protected CFRP structures caused by transient lightning strike current components.

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Figure 1. Plasma formation on a surface protected CFRP sample. The image sequence is 4.76 µs [8]. The plasma formation was caused by a D current lightning waveform discharge; the CFRP sample was protected with ECF 195.3 g/m2 and coated with 200 µm thick PU-paint [8]. A typical final state of the metallic protection layer after lightning current discharge is shown in Figure 2a. The visual inspection and X-ray analysis clearly reveals the removed part of the metallic protection from a CFRP sample [34]. In case of not “too thick/heavy” dielectric coatings there is a strong relationship between the area of the damaged coating and removed metallic protection (as indicated in Figure 2b). In the following two different approaches for the estimation of the time-dependent behaviour of the arc root radius of

3 Arc Root Radius Experimental evaluation of the arc attachment during the lightning pulsed current components on composite samples show that the arc root generally continuously expands in the

1


where ϕ is the electric potential, σ the tensor of electric conductivity, ρ the density and cp the specific heat. The term qVeq accounts for thermal transfer from the plasma channel. The literature gives values for Veq between 8 and 14 V, depending on the material, polarity of the electrode, and the experimental conditions. Recently, Landfried et al. [19] determined Veq of a copper anode submitted to a nonstationary electric arc in air to be about 12 V. Equations (2) and (3) are solved for cylindrical geometries using a cell centred finite volume (FV) approach. The resulting system of ordinary differential equations for the cell temperatures is solved with standard ODE-solvers in Matlab®. The source term qVeq is a surface heat flux term for the FV cells next to the degradation surface: Veq (4) qeq  σ     dS  S

lightning pulse currents without taking into account the effects caused by dielectric surface coatings are described. b

Figure 2. a) Visual-visible damage and b) X-ray analysis of the removed metallic protection [34]. 3.1 Braginskii’s Model of the Plasma Channel Radius The Braginskii model of the plasma channel expansion is based on the assumption that the current flowing through gas heats and expands the channel at supersonic velocity driving a cylindrical shock wave. The considered heat losses are due to thermal radiation, the thermal conduction during the short period of the plasma channel can be completely neglected [5]. Moreover, the pressure, the temperature, and the plasma density are constant over the cross section of the plasma channel. The entire temperature drop occurs in a thin shell where the radiation is absorbed. The channel radius rC(t) increases with respect to time and is obtained from

where ΔΩ is a cell volume and ΔS denotes the surface parts of that cell adjacent to the arc root plasma. The boundary conditions for the electric potential below the arc root is J( t ) σ   . (5)  RR2 ( t ) In the following we consider a CFRP laminate disk with 1.5 mm thickness and 200 mm diameter covered with a 3CU7100FA or 2CU4-100FA ECF, respectively. The structure is exposed to a 100kA, 12/36 μs waveform. The initial temperature is 293.16 K and an initial arc root radius (RR) of 0.5 mm is assumed. In the present work, RR is defined to be at the surface location where the temperature drops below the degradation temperature. Hence, RR is calculated and not assumed to be constant as in similar studies, see e.g. [20] and [25]. Reasonable choices for appropriate degradation temperature are the fusion temperature, or the evaporation temperature. Here, the fusion temperature of copper was chosen, since the calculated degraded (melted) areas correspond fairly well with experimental data for the removed copper [17].

1/ 3 t

  2/3 r (t)   4 2 (1)   J   d ,    0   0 where 0 is the undisturbed gas (air) density and J(t) is the magnitude of the arc current.  is a dimensionless constant which depends on gas properties and somewhat on the current rise time and is usually taken to be about 4.5. The electric conductivity of the plasma channel  is assumed to be time (temperature) independent and can be approximately set to be around 2.22 x104 S/m [5]. The Braginskii approach has often been used for an estimation of spark channel radius; see e.g. [23], [32], [33]. In the following the fast lightning current waveform D is described by a 12/36 s double-exponential function with a peak current of 100 kA. The radius of the hot plasma channel can easily be calculated using eq. (1). The time-averaged value of the plasma channel radius is around 33 mm. The corresponding channel expansion velocity can be calculated directly from eq. (1) as well. The channel expands with an average velocity of around 270 m/s. The Braginskii approach gives the values of the plasma channel radius and channel expansion velocity for the case of unrestricted free space plasma expansion. 2 C

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Figure 3. Numerical results (3CU7-100FA) for the fusion radius Rmelt for the 12/36 μs pulse current waveform and for three different values of Veq.

3.2 Degradation Area Approach Within the degradation area approach a homogeneous surface current within the root radius is considered as the source for Joule heating. The root radius is determined by defining a degradation temperature above which the material is assumed to turn to plasma properties. The short time scale of the process allows for neglecting heat diffusion. Hence, charge and energy conservation for solids read as  σ    0 (2)

 c p T t    σ    qVeq

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The results for the radius of the melted surface area, which is identical to RR when larger than 0.5mm, are depicted in Figure 3 and Figure 4 for three different values of Veq. The influence of the equivalent voltage drop on the final melted area is clear, but moderate. For small periods, Veq appears to be a main contribution to the fusion of the copper volume below the initial root radius. For 3CU4-100FA the root radius is significantly below the Braginskii radius.

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removed by the Joule’s resistive heat of the lightning current load; see e.g. [2], [8] and Figure 2. The initial root radius (of the plasma channel created during the forgoing streamerleader transition phase) is assumed to be 0.5 to 1.0 mm, see e.g. [3] and [13]. The maximum magnetic pressure of 12/36 s lightning current D waveform is plotted as a function of time in Figure 6a for both ECF 2CU4-100FA and 3CU7-100FA. The peak pressure of 0.53 (0.99) MPa occurs at around 1.6 (1.4) s when the ECF 2CU4-100FA (3CU7-100FA) is used. At this time RR has the value of 5.75 (3.75) mm. The plotted data indicate that the magnitude of the magnetic pressure decreases rapidly after peak pressure time. The magnetic force acting on a disk shaped sample with edge radius R=225 mm is plotted in in Figure 6b. The magnetic force has a maximum of 693(786) N at around 10.2 (10.4) s when the expanded copper foil 2CU4-100FA (3CU7-100FA) is used. This times corresponds to the arc root radius of about 24 (18) mm. The estimated total magnetic impulse for the given 12/36 s lightning current D waveform and the degradation arc root radius is rather small, round 0.016 (0.019) Ns .

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Figure 4. See Figure 3, but for 2CU4-100FA protection. For the thin protection layer (Figure 4), RR(t) is similar to the Braginskii-Radius. Hence, for a lower surface specific weight of Cu protection than for 2CU4-100FA, the Braginskii’s approach can be used to define the RR(t). The time dependence of RR should not be ignored, as it influences electric breakdown via confinement of the current density at early time stages and serves as an important input for the calculation of the magnetic forces and shockwave analysis.

4 Magnetic Forces In case of protected CFRP structures the lightning current flow is mainly constrained within the high-conduction protection layer [14]. The currents flow from the plasma channel into the metallic protection layer through the arc root surface with arc root radius RR. The thin protection layer can formally be split into two regions: region 1 which corresponds to the sample under the arc root (0