Abstract
In addition to the macroscopic component geometry, a morphological microstructure model and material models for all individual phases of the material are required as input data to apply multi-scale methods. However, the advantage is that complicated mechanical coupon tests on the composite material can be avoided. This chapter explains the computation of morphological and material parameters on the example of short glass fibre reinforced polymers. The fibre orientation is the most important geometrical micro-structural parameter which has to be computed from µCT scans, whereas other micro-structural parameters (e.g. fibre length distribution and diameter) are a priori known. State-of-the-art methods for estimating local fibre orientations based on 3D image data are used to determine this essential microstructure feature depending on the sample position w.r.t. the flow front. After that the generation of virtual microstructures with the same morphological parameters as the µCT scans is considered. In the second part of this chapter, the identification of the material parameters is described for the polymer polybutylene terephthalate (PBT). All necessary parameters of a rate-independent elastoplastic model with damage are computed from cyclic tensile tests with increasing load amplitudes. Finally, the validation of the morphological and material models are illustrated by using an FFT-accelerated pseudo-spectral method as micro-scale solver.
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References
Baur, E., Osswald, T.A., Rudolph, N., Brinkmann, S., Schmachtenberg, E. (eds.): Saechtling Kunststoff Taschenbuch, 31st edn. Hanser (2013)
Fisher, N., Lewis, T., Embleton, B.: Statistical Analysis of Spherical Data. Cambridge University Press, Cambridge, UK (1987)
Frangi, A., Niessen, W., Vincken, K., Viergever, M.: Multiscale vessel enhancement filtering. In: Proceedings of the Medical Image Computing and Computer-Assisted Intervention, pp. 130–137 (1998)
Fraunhofer ITWM, Department of Image Processing: MAVI—modular algorithms for volume images. http://www.mavi-3d.de (2005)
GeoDict.: www.geodict.com. Accessed 16 Jan 2019
Ju, J.: On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects. Int. J. Solids Struct. 25(7), 803–833 (1989)
Kabel, M., Böhlke, T., Schneider, M.: Efficient fixed point and Newton-Krylov solvers for FFT-based homogenization of elasticity at large deformations. Comput. Mech. 54(6), 1497–1514 (2014)
Kouznetsova, V., Brekelmans, W., Baaijens, F.: An approach to micro-macro modeling of heterogeneous materials. Comput. Mech. 27(1), 37–48 (2001)
Kröner, E.: Bounds for effective elastic moduli of disordered materials. J. Mech. Phys. Solids 25(2), 137–155 (1977)
Lippmann, B., Schwinger, J.: Variational principles for scattering processes. Phys. Rev. 79, 469–480 (1950)
Moulinec, H., Suquet, P.: A fast numerical method for computing the linear and nonlinear mechanical properties of composites. Comptes rendus de l’Académie des sciences. Série II, Mécanique, physique, chimie, astronomie 318(11), 1417–1423 (1994)
Moulinec, H., Suquet, P.: A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput. Methods Appl. Mech. Eng. 157(1–2), 69–94 (1998)
Mura, T.: Micromechanics of Defects in Solids, 2nd, revised edn. Mechanics of Elastic and Inelastic Solids. Martinus Nijhoff Publishers, Dordrecht (1987)
Niedziela, T., Strautins, U., Hosdez, V., Kech, A., Latz, A.: Improved multiscale fiber orientation modeling in injection molding of short fiber reinforced thermoplastics: simulation and Experiment. Int. J. Multiphys. Special Edition: Multiphys. Simul. Adv. Methods Ind. Eng. 357–366 (2011)
Ohser, J., Schladitz, K.: 3D Images of Materials Structures: Processing and Analysis. Wiley VCH (2009)
Onate, E. (ed.): Multiscale modeling of progressive damage in elasto-plastic composite materials (2014)
Otsu, N.: A threshold selection method from gray level histograms. IEEE Trans. Syst. Man Cybern. 9, 62–66 (1979)
Schneider, R., Weil, W.: Stochastic and Integral Geometry. Probability and Its Applications. Springer, Heidelberg (2008)
Spahn, J., Andrä, H., Kabel, M., Müller, R.: A multiscale approach for modeling progressive damage of composite materials using fast Fourier transforms. Comput. Methods Appl. Mech. Eng. 268, 871–883 (2014)
Stoyan, D., Kendall, W., Mecke, J.: Stochastic Geometry and Its Applications, 2nd edn. Wiley, Chichester (1995)
Wirjadi, O.: Models and algorithms for image-based analysis of microstructures. Ph.D. thesis. Technische Universität Kaiserslautern (2009)
Wirjadi, O., Schladitz, K., Easwaran, P., Ohser, J.: Estimating fibre direction distributions of reinforced composites from tomographic images. Image Anal. Stereol. 35(3), 167–179 (2016)
Zeller, R., Dederichs, P.H.: Elastic constants of polycrystals. Phys. Status Solidi (b) 55(2), 831–842 (1973)
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Andrä, H., Dobrovolskij, D., Schladitz, K., Staub, S., Müller, R. (2019). Modelling of Geometrical Microstructures and Mechanical Behaviour of Constituents. In: Diebels, S., Rjasanow, S. (eds) Multi-scale Simulation of Composite Materials. Mathematical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-57957-2_3
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