A developed energy-dependent model for studying thermal shock damage and phase transition of composite reinforced panel subjected to lightning strike

Highlights

• Fiber upwarp and swell phenomena are occurred after the failure elements removal.

• The failure materials cause concave pit and bulking damage on composite structure.

• Thermal shock wave causes external and internal damages on composite structure.

• Distribution of equivalent stress is affected serious by fiber direction in the first layer.

Abstract

Lightning strikes generate large amounts of energy. Thus, composite structures subjected to lightning strikes undergo significant physicochemical changes. In this study, the thermal shock damage and three-phase transition of a composite reinforced panel were investigated through a numerical simulation, an experiment, and ultrasonic C-scanning. An anisotropic constitutive model and PUFF equation of state (EOS) were proposed to study the damage behaviors of composite materials. The dynamical damage behaviors and three-phase transition of the composite reinforced panel were simulated using the proposed constitutive model and PUFF EOS. Finally, a lightning experiment and ultrasonic C-scanning were conducted to validate the numerical results. Obvious fiber upwarping and swelling were observed in the numerical simulation. The melted and vaporized materials caused a reverse thermal shock effect, which led to concave pits, buckling and internal damages in the composite reinforced panel. The numerical results were compared with experimental results and scanning results to validate that the proposed constitutive model and modified PUFF EOS can be well used to simulate the dynamical damage behaviors of composite materials. The simulated damage behaviors of the composite reinforced panel agreed well with the behaviors observed in the experiment.

Introduction

Carbon fiber/epoxy composite materials have the advantages of low weight, specific modulus, specific strength, specific stiffness, and designability, which have been widely adopted as the leading materials for the primary bearing structures in aircraft design. The application of composite materials is an important index to evaluate the advancement of the aircraft structures in the 21st century (Gagné and Therriault, 2014). The composite materials are composed of the conductive fibers and insulating resin, so the composite materials exhibit a highly anisotropy in electric conductive on the whole (Todoroki, 2012). Therefore, the composite materials present the low properties in electric conductivity and thermal conductivity compared with traditional metals (such as aluminum alloy and titanium alloy). As the electric conductivity of composite structures is low, and the non-conducting and thermally less stable epoxy resin is used to act as a matrix, thereby leading to the aircraft composite structures to be more vulnerable to catastrophic damage in lightning environment.

Lightning is a common natural phenomenon in the atmospheric environment. It is estimated that the number of thunderstorms in the word is approximately one billion per year, with an average of 2000 thunderstorms per hour. Both military and civil aircrafts inevitably fly in thunderstorm weather. These aircrafts are often struck by lightning when they fly through heavily charged clouds. Data indicate that an aircraft may encounter one lightning strike per 1000–1500 h, which is roughly equivalent to one encounter per year for regular airliners (Bazelyan and Raizer, 2000). Lightning strikes mainly occur at the nose and wing tip. When composite structures are struck by lightning, current flows through the conductive skins and other structures (Larsson et al., 2005). Studies have indicated that the temperature in the center of the discharge channel can reach 20,000–30,000 K (Wang et al., 2018a; Rakov and Uman, 2003). The damage behaviors caused by lightning current conduction within composite structures are called the “direct effects of lightning”. The electromagnetic effects generated by lightning channels are called the “indirect effects of lightning” (Chemartin et al., 2012; Parmantier et al., 2012). “Direct effects of lightning” include fiber sublimation, fiber fracture, resin melting, phase transition, and delamination (Chemartin et al., 2012). “Indirect effects of lightning” include lightning-induced currents and voltages on wiring and electric/electronic equipment (Parmantier et al., 2012). The lightning current is eventually converted into the internal energy of composite materials when it attaches to the surfaces of aircraft structures. The deposited internal energy decreases from the lightning attachment area to the surrounding sides and in the thickness direction, and has a large descending gradient (Shintaro et al., 2018). A solid-liquid-vapor three-phase transition occurs if the specific internal energy is higher than the sublimation energy of composite materials. Therefore, if composite structures are not well-protected, lightning strikes cause severe damage, e.g., thermo-electric damage and physicochemical changes (Gou et al., 2010; Raimondo et al., 2018; Rajesh et al., 2018). The vaporized materials are sprayed rapidly, and a thermal shock wave is then formed on the reminder of the structures, which induces thermal shock damage to the composite materials (Han et al., 2015). The thermal shock wave propagates at a high speed within composite structures and causes tensile and compressive damage. Therefore, the dynamical damage tolerance induced by lightning strikes is an important engineering problem that should be further investigated. Studies on lightning-induced damage and lightning protection of composite structures have been performed by numerous scholars, and the damage mechanisms of the composite materials have been clarified (Ogasawara et al., 2010; Abdelal and Murphy, 2014; Muñoz et al., 2014; Kumar et al., 2020; Sharma et al., 2018; Feraboli and Minller, 2009; Kawakami and Feraboli, 2011; Hirano et al., 2010; Dong et al., 2015, 2016; Li et al., 2016; Yin et al., 2016; Huang et al., 2012). Ogasawara et al. (2010) elucidated the damage behaviors of composite laminate subjected to a simulated lightning current. The results suggested that the Joule heat significantly influenced the damage behaviors of composite laminate. The delamination damage was caused by the resin decomposition and melting. The fiber fracture was attributed to the sublimation of carbon fibers. Abdelal and Murphy (2014) considered the temperature-dependence material properties to study the thermal damage of composite laminate. The results showed that the developed simulation procedure was capable of capturing the decomposition area and temperature profile. Muñoz et al. (2014) studied the thermo-mechanical damage of composite laminate subjected to lightning strikes through an experiment and a numerical simulation. The lightning-induced damage of composite laminate was simulated based on finite element method. The results revealed that the thermal damage was caused by the Joule overheating effect, and the electromagnetic/acoustic pressure was induced by the supersonic expansion of discharge channel. Kumar et al. (2020) reviewed the main affecting factors on the lightning damage to composite structures. The influences of electric conductivity, resin type, stacking sequence, moisture, and pain thickness on lightning damage to composite structure were discussed. Many important suggestions were provided on the future lightning protection design and experiment method. Sharma et al. (2018) manufactured a high-loading MWCNT-reinforced composite using the bucky paper to investigate the flexural, dynamic mechanical, electrical, and electromagnetic interference shielding properties through an experiment. The results highlighted that the flexural strength and storage modulus of MWCNT-reinforced composites increased with an increase in MWCNT content. However, the in-plane conductivity changed little and the through-thickness conductivity significantly increased. The secondary network of MWCNT helped to improve interference shielding property of MWCNT-reinforced composites by providing extra channels for carrier transport. Feraboli and Minller (2009), Kawakami and Feraboli (2011) and Hirano et al. (2010) used a simulated lightning current to study the lightning damage of composite samples. The fundamental damage responses of samples were investigated, and the damage mechanisms of composite materials subjected to different current peaks were compared. Dong et al. (2015, 2016), Li et al. (2016) and Yin et al. (2016) performed many lightning experiments of composite sample. The experimental results indicated that the electric conductivity exerted a heavier effect on lightning damage than thermal conductivity did. Generally speaking, the previous works have important reference value and guiding significance for studying the lightning damage of composite materials. However, the above works mainly focused on the ablation damage of composite materials (Ogasawara et al., 2010; Abdelal and Murphy, 2014; Muñoz et al., 2014; Kumar et al., 2020; Feraboli and Minller, 2009; Hirano et al., 2010; Dong et al., 2015, 2016; Li et al., 2016; Yin et al., 2016). Few studies have been performed on the thermal shock damage and three-phase transition of composite materials. This is because the thermal shock damage and three-phase transition depend on the establishment of a constitutive model and equation of state (EOS) for composite materials. No studies have been performed on the constitutive model and EOS for revealing the dynamical damage mechanism and three-phase transition process of composite materials subjected to lightning strikes. The thermal shock effect of composite materials subjected to lightning strikes is a nonlinear process accompanied by a high-temperature, high-pressure, high-energy, and high-strain rate. Therefore, the thermal shock effects and three-phase transition are important dynamical damage forms and should be investigated further. At present, there are few reports on the constitutive model and EOS of composite materials under a strong radiation environment and mechanical shock. For example, Huang et al. (2011, 2012), Tang et al. (2011), Zhang et al. (2018) and Lukyanov (2008a, 2008b) examined the constitutive model and EOS of composite materials induced by X-Ray, laser, and mechanical shock. Studies have also been performed on the mechanical damage to composite materials subjected to lightning strikes. For instance, Soulas et al. (2018) designed a ball impact experiment to study the lightning damage of composite structures. The deflection, displacement, speed, and delamination area of composite structures were compared between lightning experiment and ball impact experiment. The studies showed that the results achieved in ball impact experiment agreed well with those got in lightning experiment, indicating that the proposed method could be used to reproduce most lightning experiment. Lepetit et al. (2011) studied the thermo-mechanical damage of the protected composite laminate through an experiment and a numerical simulation. The pressure, deflection, and speed of sample were measured through visar. The results highlighted that the speed exhibited first increased and then decreased with an increase in time. The paint layer confined the plasma induced by the sudden Joule heating, which enhanced the stress and damage in composite structures. The surface explosion and thermo-mechanical models were established to simulate the pressure and strain of composite structures. The results found that the numerical results agreed well with experimental results in growing trends, but the paint layer induced a faster increase in pressure and speed. Karch (2013) numerically investigated the thermal-mechanical effect of the protected CFRP laminate subjected to lightning strikes. The finite element model of the protected CFRP laminate was established, and the 2D and 3D calculation results were compared. The results showed that lightning current caused a large temperature gradient and thermal strain, and the thermal strain led to serious mechanical stress and mechanical damage within CFRP laminate. The mechanical damage was mainly caused by C* current component. Then, Karch et al. (2019) proposed a new physical model to compute the elastic response and progressive failure of the protected CFRP laminate. The root radius, near-surface explosion of protection layer, supersonic plasma expansion, magnetic forces, and lightning impact offset were analyzed. Finally, the established physical model was validated through the experiment data that provided by Lepetit et al. (2011). The results revealed that the numerical results agreed well with experimental results, indicating that the proposed physical model can be well used to study the pressure and forces of CFRP laminate. Espinosa (2017) numerically studied the acoustic pressure and Lorentz force of CFRP panels using a coupled electro-thermal-mechanical model. The results showed that the acoustic pressure and Lorentz force also have significant influence on the lightning damage to composite materials. The mechanical analyses in these studies provided important insights regarding the lightning-induced damage to composite materials. However, the foregoing studies did not involve the constitutive model and EOS of composite materials subjected to lightning strikes. The establishment of an accurate constitutive model and EOS can significantly improve the accuracy and reliability of the numerical results. Therefore, it is imperative to study the constitutive model and EOS of composite materials subjected to lightning strikes so that the dynamical damage behaviors can be quantitatively predicted and the three-phase transition mechanisms can be accurately described.

Considering that the constitutive model and EOS of composite materials subjected to lightning strikes have not been investigated, the objective of this study was to examine the thermal shock damage and three-phase transition process of a composite reinforced panel induced by a lightning strike through a numerical simulation, an experiment and ultrasonic C-scanning. First, an anisotropic constitutive model of the composite materials was established. The damage evolutions in the longitudinal, transverse, and shear direction were examined in detail. Expressions for the hydrostatic pressure and deviatoric stress in the elastic and plastic deformation phases were derived, considering the coupling effect of the tolerance law and distortion law. Secondly, the PUFF EOS was introduced to study the three-phase transition of composite materials. The PUFF EOS was then modified according to the stress-strain relationships in the elastic and plastic deformation phases. Third, finite element subroutines based on the theories of the constitutive model and PUFF EOS were developed. The dynamical damage behaviors and three-phase transition of the composite reinforced panel were numerically simulated using the developed finite element subroutines. Finally, a lightning experiment based on the SAE-ARP5416 standard was performed, and the damage forms of the composite reinforced panel were analyzed. Ultrasonic C-scanning was then conducted to examine the internal damage and delamination of the sample after the experiment. The numerical results were compared with the experimental results and scanning results to validate the feasibility of the proposed constitutive model, modified PUFF EOS, and developed subroutines. The achievements of this study can be used to analyze the lightning-induced damage to composite materials from the perspective of the thermal shock and phase transition, and thus have considerable reference value and engineering significance for the lightning protection design of aircraft.