Polarization dependence of laser interaction with carbon fibers and CFRP Christian Freitag,1,2,* Rudolf Weber,2 and Thomas Graf 2 1

Graduate School of Excellence advanced Manufacturing Engineering GSaME, Universität Stuttgart, Nobelstraße 12, 70569 Stuttgart, Germany 2 Institut für Strahlwerkzeuge IFSW, Universität Stuttgart, Pfaffenwaldring 43, 70569 Stuttgart, Germany * [email protected]

Abstract: A key factor for laser materials processing is the absorptivity of the material at the laser wavelength, which determines the fraction of the laser energy that is coupled into the material. Based on the Fresnel equations, a theoretical model is used to determine the absorptivity for carbon fiber fabrics and carbon fiber reinforced plastics (CFRP). The surface of each carbon fiber is considered as multiple layers of concentric cylinders of graphite. With this the optical properties of carbon fibers and their composites can be estimated from the well-known optical properties of graphite. ©2013 Optical Society of America OCIS codes: (140.0140) Lasers and laser optics; (140.3390) Laser materials processing.

References and links 1.

R. Weber, C. Freitag, T. V. Kononenko, M. Hafner, V. Onuseit, P. Berger, and T. Graf, “Short-pulse laser processing of CFRP,” Phys. Procedia 39, 137–146 (2012). 2. C. Freitag, V. Onuseit, R. Weber, and T. Graf, “High-speed observation of the heat flow in CFRP during laser processing,” Phys. Procedia 39, 171–178 (2012). 3. R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia 12(2), 302–307 (2011). 4. D. Herzog, P. Jaeschke, O. Meier, and H. Haferkamp, “Investigations on the thermal effect caused by laser cutting with respect to static strength of CFRP,” Int. J. Mach. Tools Manuf. 48(12-13), 1464–1473 (2008). 5. A. Goeke and C. Emmelmann, “Influence of laser cutting parameters on CFRP part quality,” Phys. Procedia 5, 253–258 (2010). 6. P. Morgan, Carbon Fibres and their Composites (CRC Press, 2005). 7. W. P. Hoffman, W. C. Hurley, P. M. Liu, and T. W. Owens, “The surface topography of non-shear treated pitch and PAN carbon fibers as viewed by the STM,” J. Mater. Res. 6(08), 1685–1694 (1991). 8. F. R. Barnett and M. K. Norr, “A three-dimensional structural model for a high modulus pan-based carbon fibres,” Composites 7(2), 93–99 (1976). 9. A. Borghesi and G. Guizzetti, “Graphite (C),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, 1991). 10. A. B. Djurisic and E. H. Li, “Optical properties of graphite,” J. Appl. Phys. 85(10), 7404–7410 (1999). 11. J. Lekner, “Reflection and refraction by uniaxial crystals,” J. Phys. Condens. Matter 3(32), 6121–6133 (1991). 12. D. Ségur, Y. Guillet, and B. Audoin, “Picosecond ultrasonics on a single micron carbon fiber,” J. Phys. Conf. Ser. 278, 012020 (2011).

1. Introduction CFRP has recently gained a lot of attention especially regarding lightweight construction in industrial applications. The laser as a well automatable, noncontact tool without wear has a large potential for processing of CFRP. To explore this potential a detailed consideration of the fundamental mechanisms of the interaction between laser radiation and carbon fibers is necessary. In addition to the thermal considerations on heat conduction, sublimation of the fibers, and decomposition of the matrix material [1–5], an exact quantitative knowledge of the polarization- and wavelength-dependent absorption of the laser beam in the material is required in the first place. In the special case of CFRP this needs to take into account the rather complex composite structure of the material. To this end we propose a simplified model for the material and derive the optical properties of the carbon fibers necessary to calculate the absorption from the well-known optical properties of graphite.

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Received 16 Oct 2013; revised 18 Nov 2013; accepted 20 Nov 2013; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001474 | OPTICS EXPRESS 1474

2. The material 2.1 Carbon fibers In this study we consider High Tensity (HT) carbon fibers based on Polyacrylnitril (PAN). PAN based carbon fibers are composed of turbostratic carbon [6]. The carbon atoms form a network of regular hexagons that are arranged in almost parallel layers. This makes the crystal structure of turbostratic carbon similar to the crystal structure of graphite although there are some differences: The interlayer distance of for PAN based carbon fibres is typically 0.355 nm, which is 0.0196 nm larger than in graphite due to additional types of bonds and the atomic lattice in the turbostratic layers may include some cluster defects [7]. The outermost shell of PAN based carbon fibers can approximately be described as regular concentric cylinders of turbostratic carbon [8]. The close similarity of the crystal structures of turbostratic carbon and graphite led us to the assumption that the optical properties of the concentric turbostratic carbon cylinders of the carbon fibers can be approximated by the better known properties of graphite. Due to the anisotropy of graphite, where the spacing between two parallel graphite layers is about 2.7 times larger than the distance between neighboring carbon atoms within the layers, the optical properties depend on the orientation of the electric field with respect to the optical axis c of the graphite layers [9]. For the complex refractive index No = no-i·ko of the ordinary beam we have used the experimental data of graphite reported in [9]. The complex refractive index Ne = ne-i·ke of the extraordinary beam was calculated following the model described in [10]. The values of no,e and ko,e are shown in Fig. 1(a) as a function of the wavelength. The absorptivity A of a material can be derived from the reflected part R and transmitted part T. Since the absorption length in graphite is in the range of 12 nm for wavelengths relevant for laser material processing, the transmission can be neglected and the absorptivity A can be approximated by A = 1-R = 1-r2. To calculate the reflection amplitudes rs for the polarization perpendicular to the plane of incidence and rp for the polarization parallel to the plane of incidence in the following we used the equations derived for the reflections at uniaxial birefringent materials by J. Lekner in [11].

Fig. 1. a) Values of n and k of the complex refractive index of graphite for E┴c derived from experimental data presented in [9] and the model reported in [10]. b) Corresponding absorptivity of graphite for different wavelengths for radiation at normal incidence.

The absorptivity AG of pure graphite for an orientation of the electric field perpendicular to the symmetry axis of the graphite layers (E┴c) and at normal incidence is shown in Fig. 1(b) as a function of the wavelength.

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Received 16 Oct 2013; revised 18 Nov 2013; accepted 20 Nov 2013; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001474 | OPTICS EXPRESS 1475

2.2 Matrix material In the following we consider CFRP material with a volume content of the matrix of 40%. The matrix is the thermoset material MGS RIM 135. The absorption coefficient of this material has been measured to be always less than 0.1 mm−1 in the whole spectral range between 400 nm and 1400 nm. The thickness of the matrix layers on top and between the carbon fibers is less than about 50 µm. Following the Beer-Lambert law, the absorbed intensity in the matrix material hence is less than about 0.5% and is therefore neglected for the following considerations. The refractive index of the surrounding matrix needs however to be considered to calculate the reflectivity and absorptivity on the carbon fibers. The refractive index of RIM 135 is nS≈1.55 according to the specifications of the manufacturer. In case of non-infiltrated carbon fiber preforms the volume between the fibers is filled with air (nS equal to 1). 3. Model for the absorptivity of carbon fibers and CFRP 3.1 Absorptivity of a single carbon fiber As a consequence of the nearly circular cross-section of the carbon fibers, the cylindrical fibers absorb light at all angles of incidence ranging from −90° to + 90° across their irradiated circumference, as shown in Fig. 2(a). As the diameter of carbon fibers typically is much smaller than the diameter of the laser beam, the fibers absorb radiation simultaneously at all angles of incidence.

Fig. 2. a) The incident radiation hits the surface of the carbon fibers at different angles of incidence depending on the position with respect to the fiber axis. b) Absorptivity on a carbon fiber with a radius of 4 µm at a wavelength of 515 nm for light polarized parallel and perpendicular to axis of the carbon fiber, respectively.

Calculating the local absorptivity on the surface of the carbon fibers for a wavelength of 515 nm leads to the local absorptivity distributions shown in Fig. 2(b). It is noted, that the polarization perpendicular (parallel) to the fiber axis is parallel (normal) to the plane of incidence. For a polarization parallel to the carbon fiber axis the highest absorptivity is found in the center of the surface facing the incident beam. In contrast, for a polarization perpendicular to the carbon fiber axis, the absorptivity has its maximum near the edge of the irradiated carbon fiber. The mean absorptance Aav of one single carbon fiber is obtained by averaging the absorptivity over the whole surface of the fiber and leads to the behavior shown in Fig. 3.

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Received 16 Oct 2013; revised 18 Nov 2013; accepted 20 Nov 2013; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001474 | OPTICS EXPRESS 1476

Fig. 3. Average absorptance of a single carbon fiber as a function of wavelength. The surrounding medium is air.

3.2 Absorptance for multiple carbon fibers For typical material processing situations the relevant quantity is the absorptance of several carbon fibers taking into account multiple reflections of the incident radiation between them. In order to calculate the resulting absorptance by means of raytracing we consider the model arrangement of three carbon fibers shown in Fig. 4(a). The radius r of the carbon fibers is 4 µm. The distance d between the carbon fibers was chosen to be 1.152 µm as this gives a volume content of the carbon fibers in the material of 60% which is a typical value for CFRP. Due to symmetry considerations only light rays incident between x = 0 and x = r + d/2 are considered. Taking into account the absorptivity and reflectivity at each reflection on the carbon fibers the total absorptance was calculated for a large number of equidistant light rays. Light rays propagating into the material after the multiple reflections on the three considered fibers are assumed to be completely absorbed. The other rays are followed until they are reflected back from the assumed sample surface (into the half space y>0) in Fig. 4(a). The resulting total absorptance of carbon fibers in air averaged over all parallel rays incident between x = 0 and x = r + d/2 is shown in Fig. 4(b).

Fig. 4. a) Arrangement of carbon fibers used to calculate the absorptance of multiple fibers. Exemplarily the multiple reflection of a light ray incident at x = 3,764 µm is shown. b) Average absorptance for multiple carbon fibers calculated by means of ray tracing for different wavelengths.

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Received 16 Oct 2013; revised 18 Nov 2013; accepted 20 Nov 2013; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001474 | OPTICS EXPRESS 1477

3.3 Absorptance of a single carbon fiber and CFRP The additional matrix material RIM 135 has a twofold impact on the total absorptance. First, an additional reflection of the incident laser light occurs at the interface between air and matrix material. With the known optical properties of RIM 135 the reflectivity of this surface amounts to 4.65%. Second, the higher refractive index of the matrix material as compared to air leads to a slight increase of the absorptivity on the carbon fibers at every reflection leading to an overall increase of the total absorptance. As a consequence of the birefringent properties of graphite, a local minimum of the absorptivity at angles of incidence near the Brewster angle can be observed for the polarization perpendicular to the fiber axis as shown in Fig. 5(a) for a wavelength of 1064 nm. This local minimum is only observed with the increased refractive index of the surrounding matrix material and is not noticeable in Fig. 2(b), where the birefringent fiber was surrounded by air with a refractive index of 1. The impact of the birefringence was also found to be more pronounced for longer wavelengths. The resulting total absorptance of CFRP taking into account multiple reflections between the fibers with the model described above is shown in Fig. 5(b) for wavelengths between 400 nm and 1400 nm since the absorbed intensity in the matrix material can be neglected in this spectral range. The difference between the absorptance for polarizations parallel and perpendicular to the carbon fiber axis is reduced by the increased refractive index of the matrix.

Fig. 5. a) Absorptivity on a single carbon fiber with a radius of 4 µm surrounded by matrix material with a refractive index of n = 1.55 at a wavelength of 1064 nm for light polarized parallel and perpendicular to axis of the carbon fiber, respectively. b) Average absorptance at normal incidence on CFRP with RIM 135 as matrix material for different wavelengths calculated with the simplified model discussed in the text.

4. Experimental verification As a simple validation of the ray tracing calculation, the grayscale values of microscope images of bare carbon fibers were analyzed using polarizing filters. The bare carbon fibers were illuminated by an un-polarized white light source and examined by means of a microscope camera to record the images shown in Fig. 6. For the polarization perpendicular to the carbon fibers (Fig. 6(a)) significantly less light is reflected than for the polarization parallel to the carbon fibres (Fig. 6(b)). The average greyscale value of the image with the polarization perpendicular to the fiber orientation (Fig. 6(a)) amounts to 62% of the value for the parallel polarization. This is in satisfactory agreement with the ratio of the reflectance that can be read from the calculated absorptance shown in Fig. 4(b). For the visible wavelengths range between 380 and 780 nm the ratio of the two reflectance values (pol. perpendicular to fibers and pol. parallel to fibers) is 77%.

#199638 - $15.00 USD (C) 2014 OSA

Received 16 Oct 2013; revised 18 Nov 2013; accepted 20 Nov 2013; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001474 | OPTICS EXPRESS 1478

Fig. 6. a,b) Images taken with an optical microscope. A polarization filter was placed in front of the camera system. Figure 6(a) shows an image taken with light polarized perpendicular to the carbon fiber axis. Figure 6(b) shows an image taken with light polarized parallel to the carbon fiber axis.

4. Discussion Only little data is available in literature on the complex index of refraction of carbon fibers. For UMS40 carbon fibers a complex refraction index of nCF = 2.3-i·0.6 at a wavelength of 796 nm is reported in [12]. For a single carbon fiber this would lead to an increased absorptivity of 82% at normal incidence as compared to the absorptivity of 67% calculated using the complex refraction indices no and ne of graphite. The presented investigations show that for wavelengths in the UV to NIR, the absorptance of the two polarization direction parallel and perpendicular to the fiber differ at most by 8%. Since this difference is comparatively small, the influence of the polarization on laser processing of carbon fibers and CFRP should not be significant at these wavelengths. Other effects such as the heat accumulation [1,2] have very likely a much stronger impact on the laser ablation process of carbon fibers and CFRP. Since the relative difference between the two polarization states is largest for long wavelengths (10.6 µm), an influence of the polarization state is most likely for these wavelengths. The applied raytracing calculations not only allowed the consideration of multiple carbon fibers in the presented model, but also showed significant scattering of light perpendicular to the carbon fiber axis. This could also be an additional damaging mechanism when laser processing carbon fibers or CFRP. 5. Summary A theoretical model to calculate the absorptance of carbon fibers and CFRP was presented. It is based on the assumption, that carbon fibers can be represented by concentric cylinders of multiple graphite layers near the surface where the interaction with the light occurs in the beginning of the process. Due to the circular cross-section of the carbon fibers, the absorptance was calculated as an average over multiple, equidistant, parallel light rays using the equations derived by Lekner [11] for the reflectivity on uniaxial birefringent materials. It was found that the total absorptance is larger than 70% for wavelengths in the UV, VIS and NIR and drops to less than 40% for a wavelength of 10.6 µm (CO2-Lasers). The absorptance for light polarized perpendicular to the carbon fibers was shown to be larger than for light polarized parallel to the fibers which was confirmed by a polarized microscope measurement of the reflectivity. Acknowledgments The authors would like to thank the Graduate School of Excellence advanced Manufacturing Engineering GSaME of the University of Stuttgart for the funding of this work and the Institute for Laser Technology in Medicine and Measurement Technique (ILM) of the Ulm University for the measurement of the absorption coefficient of the matrix material RIM135.

#199638 - $15.00 USD (C) 2014 OSA

Received 16 Oct 2013; revised 18 Nov 2013; accepted 20 Nov 2013; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001474 | OPTICS EXPRESS 1479

Polarization dependence of laser interaction with carbon fibers and CFRP.

A key factor for laser materials processing is the absorptivity of the material at the laser wavelength, which determines the fraction of the laser en...
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