Barton, Janice M

Carloni, Lisa

Harrell, Timothy M.

Thomsen, Ole Thybo

This paper presents a coupled thermal-electric-mechanical model to predict the delamination damage of a Carbon Fiber Reinforced Polymer (CFRP) material when subjected to a lightning strike. A Finite Element Model (FEM) is used to predict the heat response of the CFRP material by solving the Joule heating governing equations. The results of the heat response are coupled with thermal stresses to predicte interlaminar stresses. A bilinear traction law is used to predict the delamination of the laminate. Solutions to the model are developed using a time dependent simulation with the 10/350?s standard waveform to mimic a typical lightning strike on a wind turbine blade in accordance to IEC61400 section 24 Ed 1.0. The time dependent model implements damage criteria and is able to identify damaged elements. The COMSOL software engine was used to derive the results from the thermal-electrical-mechanical model. The final result is a delamination map of the CFRP panel subjected to a lightning discharge

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                          Harrell, T. M., Thomsen, O. T., Barton, J. M., & Carloni, L. (2018).Delamination prediction on CFRP materials subjected to a lightning strike.Paper presented at 18th European Conference on Composite Materials -ECCM18, Athens, Greece.Peer reviewed versionLink to publication record in Explore Bristol ResearchPDF-documentUniversity of Bristol - Explore Bristol ResearchGeneral rightsThis document is made available in accordance with publisher policies. Please cite only the publishedversion using the reference above. Full terms of use are available:http://www.bristol.ac.uk/pure/about/ebr-termsECCM18 - 18th European Conference on Composite Materials  Athens, Greece, 24-28th June 2018 1 Timothy M. Harrell, Ole Thybo Thomsen, Janice M. Dulieu-Barton and Lisa Carloni   DELAMINATION PREDICTION ON CFRP MATERIALS SUBJECTED TO A LIGHTNING STRIKE  Timothy M. Harrell1, Ole Thybo Thomsen1, Janice M. Dulieu-Barton11, and Lisa Carloni2  1University of Southampton, Faculty of Engineering and the Environment, University Road, Southampton, UK Email: T.M.Harrell@soton.ac.uk, Web Page: http://www.sparcarb.com  2Global Lightning Protection Services A/S, Hededhusene, DK    Keywords: Lightning Damage, Wind Turbine Blades, Delamination, Multiphysics modeling, Joule Heating    Abstract This paper presents a coupled thermal-electric-mechanical model to predict the delamination damage of a Carbon Fiber Reinforced Polymer (CFRP) material when subjected to a lightning strike.  A Finite Element Model (FEM) is used to predict the heat response of the CFRP material by solving the Joule heating governing equations.  The results of the heat response are coupled with thermal stresses to predicte interlaminar stresses. A bilinear traction law is used to predict the delamination of the laminate. Solutions to the model are developed using a time dependent simulation with the 10/350µs standard waveform to mimic a typical lightning strike on a wind turbine blade in accordance to IEC61400 section 24 Ed 1.0. The time dependent model implements damage criteria and is able to identify damaged elements. The COMSOL software engine was used to derive the results from the thermal-electrical-mechanical model. The final result is a delamination map of the CFRP panel subjected to a lightning discharge.  1. Introduction  Carbon fiber composite materials are increasingly being used in the wind turbine, aerospace, and automotive industries to reduce the structural weight of components as a result of their high strength to weight and stiffness to weight ratios.  However, the anisotropic material properties of Carbon Fiber Reinforced Polymers (CFRP), specifically their electrical and thermal conductivities, create challenges when protecting structures from lightning strike. Exposing CFRP to electric currents from lightning discharges can cause significant damage to CFRP structures. A coupled thermal-electric-mechanical model is developed, based on the Joule heating governing equations [1], which predicts the delamination damage in a CFRP materials when subjected to a lightning strike.  The Joule heating model uses the Finite Element Method (FEM) to predict the temperature distribution through the CFRP material and the mechanical model calculates the thermal stresses which when used with cohesive zone elements predict delamination. Solutions for the model are obtained using a time dependent simulation with current inputs that mimic the 10/350 standard waveform used to test wind turbine blades according to the IEC61400 section 24 Ed 1.0 [2]. The cohesive zone elements are used to predict the extent of delamination.  2. Numerical Analysis Method  A thermal electrical mechanical model is employed to analysis the damage of CFRP materials due to a lightning strike. The damage simulation indicates the areas at the interlaminar surface which have become delaminated. The corresponding model does this by calculated a Joule heating (thermal-ECCM18 - 18th European Conference on Composite Materials  Athens, Greece, 24-28th June 2018 2 Timothy M. Harrell, Ole Thybo Thomsen, Janice M. Dulieu-Barton and Lisa Carloni electrical effects) and combining those effects to calculate the stresses induced by thermal stresses. Both of these models were calculated through the use of the commercial finite element software COMSOL.  The phenomena of a lightning strike on a CFRP composite involves significant complexity that cannot be dealt with accurately by simplified analytical methods.  Therefore, the governing equations and the associated boundary and initial conditions will be solved through the use of a finite element model.  The finite element modelling has been completed using the commercial code COMSOL 5.3 [3].  The finite element formulation adopted is summarized from two COMSOL reports [4], [5].  2.1.  Coupled Thermal Electrical Mechanical Model  The thermo-electric portion of the model is determined through the Joule heating equation.  Joule heating is the phenomena where a resistive object is heated when subject to current. A Joule heating model is constructed by coupling of the Seebeck, Peltier, and the Thomson effects. The governing equations are listed below, according to [5].  The electric balance equations are:  −∇ ∙ (𝜎𝜎∇𝑉𝑉) = 0 (1) where 𝜎𝜎 is the electric conductivity and 𝑉𝑉 is the electric potential.    The heat transfer equations are shown in equation (2):  𝜌𝜌𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕+ ∇ ∙ 𝑞𝑞 = 𝑄𝑄 𝑞𝑞 = −𝜅𝜅∇𝜕𝜕 + 𝑃𝑃𝑃𝑃 (2) where 𝜌𝜌 is the density, 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 is the specific heat of the CFRP. 𝜕𝜕 is the temperature, 𝜕𝜕 is time, 𝑞𝑞 is the heat flux, Q is the Joule heating equation (𝑄𝑄 = 𝑃𝑃 ∙ (−∇𝑉𝑉)), 𝜅𝜅 is the thermal conductivity, 𝑃𝑃 is the Peltier coefficient, and J is the current density. Since we will be investigating CFRP composite materials, the Peltier and Seebeck coefficients are have to be specified such that the anisotropic properties are represented.  The constitutive relations are:   𝑞𝑞 = [𝑃𝑃]𝑃𝑃 − [𝜅𝜅]∇𝜕𝜕 𝑃𝑃 = [𝜎𝜎](𝐸𝐸 − [𝑆𝑆]∇𝜕𝜕) 𝐷𝐷 = [𝜀𝜀]𝐸𝐸 (3) where [𝑃𝑃] is now the Peltier coefficient, [𝜅𝜅] is now the thermal conductivity, [𝜎𝜎] is now the electric conductivity, [𝑆𝑆] is now the Seebeck coefficient, 𝐷𝐷 is the electric flux density, [𝜀𝜀]is the dielectric permittivity.  2.2.  Thermal Stress Analysis  The temperature field from the Joule heating model are used to calculate the stresses induced by thermal expansion on the CFRP material. The equations governing the thermal stress are describe by  ∇[𝑐𝑐∇𝑢𝑢 + 𝛼𝛼∆𝜕𝜕] = 0 (4) where 𝑐𝑐 is the stiffness matrix, 𝑢𝑢 is the displacement field, 𝛼𝛼 is the thermal expansion coefficient, and ∆𝜕𝜕 the change in temperature.  2.3.  Cohesive Zone Elements  The interlaminar zones are modelled by cohesive zone elements. The separation of these regions are simulated by a bi-linear traction law. The traction law is presented in Figure 1 where 𝜏𝜏 is the traction, 𝜏𝜏0 is initial traction strength, 𝛿𝛿 is the opening displacement between interfaces, 𝛿𝛿0 is the critical opening displacement, 𝛿𝛿𝑓𝑓 is the fracture displacement, 𝐾𝐾 is the initial interface stiffness, and 𝐺𝐺𝐶𝐶 is the critical energy release rate. ECCM18 - 18th European Conference on Composite Materials  Athens, Greece, 24-28th June 2018 3 Timothy M. Harrell, Ole Thybo Thomsen, Janice M. Dulieu-Barton and Lisa Carloni  Figure 1. Bilinear traction separation law The implementation of these cohesive zone elements will allow for the delamination prediction. The delamination will be predicted by stresses in the interface region which are larger than the initial traction strength. The elements which are greater than these values will then follow the bilinear traction law until the critical separation is reach and the element is considered to be completely delaminated or in other words does not contribute to the stiffness.  2.4.  Numerical Model  The numerical model is a flat composite panel with a four unidirectional ply layup ([0]4).  The model is a quarter plate model measuring 20cm wide x 25cm long x 4mm thick. The outside edges are grounded, fixed and allowed thermal radiation. The inner edges are symmetric boundary conditions. On the top surface a circular surface is applied with normal current density set to the 10/350μs waveform divided by the area of the surface. The top and bottom surface are set to radiate heat. Figure 2 shows the geometry and applied boundary conditions.  Figure 2. Thermal-electrical-mechanical quarter plate model with applied boundary conditions The waveform is modelled by discrete points to mimic the 10/350μs waveform shown in Figure 3. The orange line indicates the lightning current discrete points used while the blue marks indicate a typical 10/350μs waveform.  ECCM18 - 18th European Conference on Composite Materials  Athens, Greece, 24-28th June 2018 4 Timothy M. Harrell, Ole Thybo Thomsen, Janice M. Dulieu-Barton and Lisa Carloni  Figure 3. Normalized waveform used to model the lightning current into the structure The model was run for two example lightning cases 20 kA and 60 kA.  2.5.  Material Properties  The material properties were based on assumed properties for composite materials. Table 1 indicates the thermal and electrical materials properties used.  Table 1. Thermal-electrical material properties for FEM model  Direction Thermal Conductivity [W/(m K)] Density [g/cm3] Heat Capacity [J/(g K)] Electrical Conductivity [S/m] Longitudinal 120 1.15 1.1 40000 Transverse 10.22 500 Through-thickness 10.22 500  Table 2 shows the mechanical properties used.  Table 2. Mechanical material properties for FEM model Direction Young's Modulus [Gpa] Direction Shear Modulus [Gpa] Coefficient of Thermal Expansion [10-6 ε/K] Longitudinal (1) 120 12 5.6 -0.76 Transverse (2) 13 13 1.93 36.34 Through-thickness (3) 13 23 1.93 35.96  Table 3 shows the traction properties used for the delamination modeling.  Table 3. Traction properties for FEM model Characteristic Stiffness [Gpa] Mode I Maximum Traction  [Mpa] Mode II Maximum Traction  [Mpa] Mode I Critical Energy Release Rate [Mpa] Mode II/III Critical Energy Release Rate [Mpa] 9 80 110 400 1800 ECCM18 - 18th European Conference on Composite Materials  Athens, Greece, 24-28th June 2018 5 Timothy M. Harrell, Ole Thybo Thomsen, Janice M. Dulieu-Barton and Lisa Carloni 3. Results and Discussion  The results of the 20kA waveform delamination analysis are shown in Figure 4. The figure shows the interface damage indicated by the element which were larger than the critical energy release rate. These elements are shown with a value of 1 in the figure and the undamaged interface is shown with a zero. As can be seen in the plot, the with a 20kA strike for the average composite non-toughened, no protected CFRP the first layer is delaminated.  Figure 4. Delamination of different ply layers for a 20kA 10/350 waveform  The results of the 100kA waveform delamination analysis are shown in Figure 5. As can be seen in the figure, there is a significant increase in delaminated from a 100kA strike for the average composite non-toughened, no protected. All interfaces have indicated delamination and become progressively smaller the further into the panel thickness.  Figure 5. Delamination of different ply layers for a 100kA 10/350 waveform ECCM18 - 18th European Conference on Composite Materials  Athens, Greece, 24-28th June 2018 6 Timothy M. Harrell, Ole Thybo Thomsen, Janice M. Dulieu-Barton and Lisa Carloni 4. Conclusions  The paper presents the results of a lightning strike delamination damage in CFRP panels. A coupled thermal-electrical-mechanical FE model implemented in the software tool COMSOL has been presented. The model is based on the assumption that the damage source of Joule heating (or resistive heating) can cause delamination in a CFRP material. The paper presents two different kilo-amperage results of delaminated interlaminar layers from a lightning strike.  Acknowledgments  This work was sponsored by the Marie Skłodowska Curie Actions, Innovative Training Networks (ITN), Call: H2020-MSCA-ITN-2014, as part of the 642771 “Lightning protection of wind turbine blades with carbon fiber composite materials” SPARCARB project.  References  [1] L. Chemartin et al., “Direct Effects of Lightning on Aircraft Structure : Analysis of the Thermal, Electrical and Mechanical Constraints,” J. Aerosp. Lab, no. 5, pp. 1–15, 2012. [2] IEC 61400: Wind turbines – Part 24 Lightning protection. 2010. [3] COMSOL, COMSOL v5.2a: User’s Guide. Burlington, MA, 2015. [4] M. Jaegle, “Multiphysics Simulation of Thermoelectric Systems - Modeling of Peltier-Cooling and Thermoelectric Generation,” COMSOL Conf. 2008 Hann., no. 6, p. 7, 2008. [5] S. P. Yushanov, L. T. Gritter, J. S. Crompton, and K. C. Koppenhoefer, “Multiphysics Analysis of Thermoelectric Phenomena,” in Seventh Annual Conference on Multiphysics Modeling and Simulation, 2011, pp. 1–11.   

Delamination prediction on CFRP materials subjected to a lightning strike

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Delamination prediction on CFRP materials subjected to a lightning strike

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