Title: Macroscopic Modeling of the Linear Viscoelastic Vibration Behavior of Short Fiber Reinforced Plastics

Authors: Fabian Urban and Peter Middendorf

DOI: 10.33599/nasampe/s.20.0015

Abstract: At present, the simulation cannot satisfactorily reproduce the actual vibration behavior of short fiber reinforced plastics. This is because the required viscoelastic material data, in particular damping, is often not available. For this purpose, a new experimental method was developed which can characterize the exact stiffness and damping of the material for a wide frequency range, taking into account environmental conditions such as temperature and humidity as well as fiber orientation. Additionally an orthotropic material model was developed, which can describe the linear-viscoelastic vibration behavior on a macroscopic level with the measured material data and a 2nd order orientation tensor from the injection molding simulation. A validation was performed on cuboid test specimens and engine mounting brackets. Results showed that the approach achieves an accuracy in calculating the resonance frequencies of >4 %. It works with thermoplastics and thermosets without an iterative reverse engineering approach but with a significant effort needed to characterize the materials.

References: [1] Stommel, M., Stojek, M., Korte, W. FEM zur Berechnung von Kunststoff- und Elastomerbauteilen, München: Hanser, 2nd ed., 2018. DOI: 10.3139/9783446452831. [2] Kremer, H. Materialdatenermittlung thermoplastischer Kunststoffe für Körperschallsimulationen auf Basis von Reverse Engineering. PhD thesis, Aachen: Mainz, 2014. [3] Raschke, K., Korte, W. ""Faserverstärkte Motorbauteile besser berechnen."" Kunststoffe 109 (2019): 184–189. [4] Laak, M. op de, Hauth, M. ""Noch schneller zur Zylinderkopfhaube."" Kunststoffe 94 (2004): 126–130. [5] Michaeli, W., Hopmann, C., Kremer, H. ""Materialdatenermittlung für Akustiksimulationen mittels Reverse Engineering: Akustisches Verhalten von Kunststoffen."" Kunststoffe 102 (2012): 5–7. [6] Giersbeck, M., Hornberger, K., Kech, A. ""Virtuelle Bauteilentwicklung."" Kunststoffe 101 (2011): 50–53. [7] Hopmann, C., Michaeli, W., Kremer, H. ""Frequenzabhängiges Verhalten von Kunststoffen."" Kunststoffe 102 (2012): 64–66. [8] Pischinger, S., Michaeli, W., Joerres, M., Steffens, C., Atzler, M., Arping, T. ""Verfahren zur akustischen Simulation von Kunststoffbauteilen."" MTZ - Motortechnische Zeitschrift 70 (2009): 692–701. DOI: 10.1007/BF03225522. [9] Treviso, A., van Genechten, B., Mundo, D., Tournour, M. ""Damping in composite materials: Properties and models."" Composites Part B: Engineering 78 (2015): 144–152. DOI: 10.1016/j.compositesb.2015.03.081. [10] ISO 6721-1, 2019. ""Plastics — Determination of dynamic mechanical properties — Part 1: General principles"" International Organization for Standardization, Geneva, 2019, https://www.iso.org/obp/ui/#iso:std:iso:6721:-1:ed-4:v1:en. [11] ISO 6721-5, 2019. ""Plastics — Determination of dynamic mechanical properties — Part 5: Flexural vibration — Non-resonance method"" International Organization for Standardization, Geneva, 2019, https://www.iso.org/obp/ui/#iso:std:iso:6721:-5:ed-2:v1:en. [12] Menard, K. P. Dynamic Mechanical Analysis: A Practical Introduction, Hoboken: Taylor & Francis, 2nd ed., 2008. DOI: 10.1201/9781420053135. [13] Menges, G., Haberstroh, E., Michaeli, W., Schmachtenberg, E. Menges Werkstoffkunde Kunststoffe, München: Hanser, 6th ed., 2011. DOI: 10.3139/9783446443532. [14] Keuerleber, M. Bestimmung des Elastizitätsmoduls von Kunststoffen bei hohen Dehnraten am Beispiel von PP. PhD thesis, Stuttgart, 2006. [15] Arping, T. W. Werkstoffgerechte Charakterisierung und Modellierung des akustischen Verhaltens thermoplastischer Kunststoffe für Körperschallsimulationen. PhD thesis, Aachen: Mainz, 2010. [16] ISO 6721-3, 1994. ""Plastics — Determination of dynamic mechanical properties — Part 3: Flexural vibration — Resonance-curve method"" International Organization for Standardization, Geneva, 1994, https://www.iso.org/obp/ui/#iso:std:iso:6721:-3:ed-1:v1:en. [17] Berthelot, J.-M., Assarar, M., Sefrani, Y., Mahi, A. E. ""Damping analysis of composite materials and structures."" Composite Structures 85 (2008): 189–204. DOI: 10.1016/j.compstruct.2007.10.024. [18] Bonfiglio, P., Pompoli, F. ""Determination of the dynamic complex modulus of viscoelastic materials using a time domain approach."" Polymer Testing 48 (2015): 89–96. DOI: 10.1016/j.polymertesting.2015.09.016. [19] Crane, R. M., Gillespie, J. W. ""Characterization of the vibration damping loss factor of glass and graphite fiber composites."" Composites Science and Technology 40 (1991): 355–375. DOI: 10.1016/0266-3538(91)90030-S. [20] Ilg, J. Bestimmung, Verifikation und Anwendung frequenzabhängiger mechanischer Materialkennwerte. PhD thesis, München: Dr. Hut, 2015. [21] Belder, K. de, Pintelon, R., Demol, C., Roose, P. ""Estimation of the equivalent complex modulus of laminated glass beams and its application to sound transmission loss prediction."" Mechanical Systems and Signal Processing 24 (2010): 809–822. DOI: 10.1016/j.ymssp.2009.11.001. [22] Cortés, F., Elejabarrieta, M. J. ""Viscoelastic materials characterisation using the seismic response."" Materials & Design 28 (2007): 2054–2062. DOI: 10.1016/j.matdes.2006.05.032. [23] El-Hafidi, A., Gning, P. B., Piezel, B., Belaïd, M., Fontaine, S. ""Determination of dynamic properties of flax fibres reinforced laminate using vibration measurements."" Polymer Testing 57 (2017): 219–225. DOI: 10.1016/j.polymertesting.2016.11.035. [24] Böhm, H. J. ""A Short Introduction to Continuum Micromechanics."" Mechanics of Microstructured Materials. Ed. Helmut J. Böhm. Vienna: Springer Vienna, 2004. pp. 1–40. DOI: 10.1007/978-3-7091-2776-6_1. [25] Mori, T., Tanaka, K. ""Average stress in matrix and average elastic energy of materials with misfitting inclusions."" Acta Metallurgica 21 (1973): 571–574. DOI: 10.1016/0001-6160(73)90064-3. [26] Eshelby, J. D. ""The determination of the elastic field of an ellipsoidal inclusion, and related problems."" Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 241 (1957): 376–396. DOI: 10.1098/rspa.1957.0133. [27] Christensen, R. M. ""A critical evaluation for a class of micro-mechanics models."" Journal of the Mechanics and Physics of Solids 38 (1990): 379–404. DOI: 10.1016/0022-5096(90)90005-O. [28] Kaiser, J.-M. Beitrag zur mikromechanischen Berechnung kurzfaserverstärkter Kunststoffe - Deformation und Versagen. PhD thesis, Saarbrücken, 2013. [29] J. C. Halpin, Kardos, J. L. ""The Halpin-Tsai equations: A review."" Polymer Engineering and Science 16 (1976): 344–352. DOI: 10.1002/pen.760160512. [30] Tandon, G. P., Weng, G. J. ""The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites."" Polymer Composites 5 (1984): 327–333. DOI: 10.1002/pc.750050413. [31] Schöneich, M. M. Charakterisierung und Modellierung viskoelastischer Eigenschaften von kurzglasfaserverstärkten Thermoplasten mit Faser-Matrix Interphase. PhD thesis, Saarbrücken, 2016. DOI: 10.22028/D291-23208. [32] Dassault Systèmes. Abaqus 2018 Theory Guide, 2017. [33] Gieß, M. Untersuchungen zur akustischen Formteilauslegung. PhD thesis, Aachen: Shaker, 2019. [34] Barbero, E. J. Finite element analysis of composite materials using ANSYS, Boca Raton Fla.: CRC Press, 2nd ed., 2014. [35] Advani, S. G., Tucker, C. L. ""The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites."" Journal of Rheology 31 (1987): 751–784. DOI: 10.1122/1.549945. [36] Abdin, Y. Micro-mechanics based Fatigue Modelling of Composites Reinforced with Straight and Wavy Short Fibers. PhD thesis, Leuven, 2015. [37] Kohnke, P. C. ANSYS - engineering analysis system theoretical manual for Rev. 4.4, Houston: Swanson Analysis Systems Inc., 5th ed., 1989. [38] Urban (né Pfeifer), F., Armbruster, B. ""Vorrichtung zur Schwingungsanregung eines Probekörpers."" Patent DE 10 2019 001 226.7, 2019, https://register.dpma.de/DPMAregister/pat/register?AKZ=1020190012267.

Conference: SAMPE 2020 | Virtual Series

Publication Date: 2020/06/01

SKU: TP20-0000000015

Pages: 17

Price: FREE