Fatigue Damage of Short Fibre-Reinforced Thermoplastics in Crashworthiness Simulation
Abstract
:1. Introduction
1.1. Motivation
1.2. State of the Art and Prior Work
- -
- Onset of local weakening as a result of cyclic deformation, especially starting from the places of greatest stress intensity, the fibre ends.
- -
- Beginning of crack formation.
- -
- Stable crack growth due to cyclic loading. Different effects are to be distinguished, such as separation at the interfaces between fibres and matrix, deformation, and fracture of the matrix between the fibres, fibre pull-out, and fibre breakage.
- -
- Unstable crack growth that leads to the destruction of the material, comparable to the failure in the tensile test.
1.3. Problem Statement and Aims of Work
2. Materials and Methods
2.1. mfkFatiCrash: Considering Fatigue Damage in Crash Simulation
2.2. Description of Material and Specimen Geometry
2.3. Experimental Methods
2.4. Simulation Approach
3. Results
3.1. Validation of Fatigue Life Prediction
3.2. Validation of Damage Progression
3.3. Validation of Bending Strength Prediction
4. Estimation of the Modelling Approach and Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Krivachy, R.; Riedel, W.; Weyer, S.; Thoma, K. Characterisation and modelling of short fibre reinforced polymers for numerical simulation of a crash. Int. J. Crashworthiness 2008, 13, 559–566. [Google Scholar] [CrossRef]
- Pickett, A.K.; Haug, E.; Rückert, J. A fracture damaging law suitable for anisotropic short fibre/matrix materials in an explicit finite element code. Composites 1990, 21, 297–304. [Google Scholar] [CrossRef]
- Guster, C.; Pinter, G.; Mösenbacher, A.; Eichlseder, W. Evaluation of a Simulation Process for Fatigue Life Calculation of Short Fibre Reinforced Plastic Components. Procedia Eng. 2011, 10, 2104–2109. [Google Scholar] [CrossRef]
- Sayers, C.M. Elastic anisotropy of short-fibre reinforced composites. Int. J. Solids Struct. 1992, 29, 2933–2944. [Google Scholar] [CrossRef]
- Kamber, P.; Murri, R.; Gerster, B. Crashtest Gebrauchter Fahrzeuge Mit Airbag; Dynamic Test Center: Vauffelin, Switzerland, 2005; pp. 1–30. [Google Scholar]
- VDI 2223:2004-01; Systematic Embodiment Design of Technical Products. Beuth: Berlin, Germany, 2004.
- Polzer, M.; Bartz, M.; Rothammer, B.; Schulz, E.; Wartzack, S. Tribological behavior of different doped ta-C coatings for slip-rolling contacts with high hertzian contact pressure. Ind. Lubr. Tribol. 2023, 75, 748–757. [Google Scholar] [CrossRef]
- Jackson, K.E.; Fasanella, E.L.; Lyle, K.H. Crash Certification by Analysis—Are We There Yet? In Proceedings of the 57th American Helicopter Society International Annual Forum, Washington, DC, USA, 5 September–5 November 2001; American Helicopter Society: Alexandria, WA, USA, 2011; pp. 549–562. [Google Scholar]
- Schoßig, M.; Bierögel, C.; Grellmann, W.; Mecklenburg, T. Mechanical behavior of glass-fiber reinforced thermoplastic materials under high strain rates. Polym. Test. 2008, 27, 893–900. [Google Scholar] [CrossRef]
- Schmachtenberg, E.; Brandt, M. Mechanical Design of Injection Moulded Parts made of Short-Fibre Reinforced Thermoplastics by Means of Integrative Simulation. J. Polym. Eng. 2006, 26, 179–196. [Google Scholar] [CrossRef]
- Azzi, V.D.; Tsai, S.W. Anisotropic strength of composites. Exp. Mech. 1965, 5, 283–288. [Google Scholar] [CrossRef]
- Liebold, C.; Erhart, A.; Haufe, A. The Significance of the Production Process of FRP Parts for the Performance in Crashworthiness. In Proceedings of the 14th International LS-DYNA Users Conference, Dearborn, MI, USA, 12–14 June 2016. [Google Scholar]
- Gu, G.; Xia, Y.; Lin, C.-h.; Lin, S.; Meng, Y.; Zhou, Q. Experimental study on characterizing damage behavior of thermoplastics. Mater. Des. 2013, 44, 199–207. [Google Scholar] [CrossRef]
- Horst, J.J.; Spoormaker, J.L. Mechanisms of fatigue in short glass fiber reinforced polyamide 6. Polym. Eng. Sci. 1996, 36, 2718–2726. [Google Scholar] [CrossRef]
- Wu, X.-F.; Zholobko, O. Experimental Study of the Probabilistic Fatigue Residual Strength of a Carbon Fiber-Reinforced Polymer Matrix Composite. J. Compos. Sci. 2020, 4, 173. [Google Scholar] [CrossRef]
- Witzgall, C.; Wartzack, S. Experimental and simulative assessment of crashworthiness of mechanically aged shortfibre reinforced thermoplastics. In Proceedings of the 21st International Conference on Engineering Design (ICED 17), Vancouver, BC, Canada, 21–25 August 2017; pp. 279–287. [Google Scholar]
- D’Amore, A.; Grassia, L. Constitutive law describing the strength degradation kinetics of fibre-reinforced composites subjected to constant amplitude cyclic loading. Mech. Time-Depend. Mater. 2016, 20, 1–12. [Google Scholar] [CrossRef]
- Yang, J.N. Fatigue and Residual Strength Degradation for Graphite/Epoxy Composites Under Tension-Compression Cyclic Loadings. J. Compos. Mater. 1978, 12, 19–39. [Google Scholar] [CrossRef]
- Mortazavian, S.; Fatemi, A. Fatigue behavior and modeling of short fiber reinforced polymer composites including anisotropy and temperature effects. Int. J. Fatigue 2015, 77, 12–27. [Google Scholar] [CrossRef]
- Mortazavian, S.; Fatemi, A. Fatigue behavior and modeling of short fiber reinforced polymer composites: A literature review. Int. J. Fatigue 2015, 70, 297–321. [Google Scholar] [CrossRef]
- Mao, H.; Mahadevan, S. Fatigue damage modelling of composite materials. Compos. Struct. 2002, 58, 405–410. [Google Scholar] [CrossRef]
- van Paepegem, W.; Degrieck, J. A new coupled approach of residual stiffness and strength for fatigue of fibre-reinforced composites. Int. J. Fatigue 2002, 24, 747–762. [Google Scholar] [CrossRef]
- van Paepegem, W.; Degrieck, J. Coupled residual stiffness and strength model for fatigue of fibre-reinforced composite materials. Compos. Sci. Technol. 2002, 62, 687–696. [Google Scholar] [CrossRef]
- Shokrieh, M.M.; Lessard, L.B. Progressive Fatigue Damage Modeling of Composite Materials, Part I: Modeling. J. Compos. Mater. 2000, 34, 1056–1080. [Google Scholar] [CrossRef]
- Shokrieh, M.M.; Lessard, L.B. Progressive Fatigue Damage Modeling of Composite Materials, Part II: Material Characterization and Model Verification. J. Compos. Mater. 2000, 34, 1081–1116. [Google Scholar] [CrossRef]
- van Paepegem, W.; Degrieck, J. Effects of Load Sequence and Block Loading on the Fatigue Response of Fiber-Reinforced Composites. Mech. Adv. Mater. Struct. 2002, 9, 19–35. [Google Scholar] [CrossRef]
- van Paepegem, W.; Degrieck, J. Modelling damage and permanent strain in fibre-reinforced composites under in-plane fatigue loading. Compos. Sci. Technol. 2003, 63, 677–694. [Google Scholar] [CrossRef]
- van Paepegem, W. Fatigue damage modelling of composite materials with the phenomenological residual stiffness approach. In Fatigue Life Prediction of Composites and Composite Structures; Elsevier: Amsterdam, The Netherlands, 2010; pp. 102–138. [Google Scholar]
- Witzgall, C.; Wartzack, S. Validation of an approach for the simulation of short fiber reinforced thermoplastics in early design phases. In Proceedings of the DFX 2015: Proceedings of the 26th Symposium Design for X, Herrsching, Germany, 7–8 October 2015; pp. 63–74. [Google Scholar]
- Witzgall, C.; Wartzack, S. An investigation of mechanically aged short-fiber reinforced thermoplastics under highly dynamic loads. In Proceedings of the DFX 2016: Proceedings of the 27th Symposium Design for X, Herrsching, Germany, 5–6 October 2016; pp. 135–146. [Google Scholar]
- Rouchon, J. Certification of large airplane composite structures. Recent progress and new trends in compliance philosophy. ICAS Congr. Proc. 1990, 2, 1439–1447. [Google Scholar]
- Bernasconi, A.; Davoli, P.; Basile, A.; Filippi, A. Effect of fibre orientation on the fatigue behaviour of a short glass fibre reinforced polyamide-6. Int. J. Fatigue 2007, 29, 199–208. [Google Scholar] [CrossRef]
- McNally, D. Short Fiber orientation and its Effects on the Properties of Thermoplastic Composite Materials. Polym.-Plast. Technol. Eng. 1977, 8, 101–154. [Google Scholar] [CrossRef]
- Advani, S.G.; Tucker, C.L. The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites. J. Rheol. 1987, 31, 751–784. [Google Scholar] [CrossRef]
- Folgar, F.; Tucker, C.L. Orientation Behavior of Fibers in Concentrated Suspensions. J. Reinf. Plast. Compos. 1984, 3, 98–119. [Google Scholar] [CrossRef]
- Mortazavian, S.; Fatemi, A. Effects of fiber orientation and anisotropy on tensile strength and elastic modulus of short fiber reinforced polymer composites. Compos. Part B Eng. 2015, 72, 116–129. [Google Scholar] [CrossRef]
- Witzgall, C.; Giolda, J.; Wartzack, S. A novel approach to incorporating previous fatigue damage into a failure model for short-fibre reinforced plastics. Int. J. Impact Eng. 2022, 18, 104155. [Google Scholar] [CrossRef]
- Witzgall, C.; Huber, M.; Wartzack, S. Consideration of cyclic material degradation in the crash simulation of short-fibre-reinforced thermoplastics. Konstruktion 2020, 2020, 78–82. [Google Scholar] [CrossRef]
- Reithofer, P.; Jilka, B.; Fertschej, A. Considering the local anisotropy—Simulation process chain for short and long fibre reinforced thermoplastics. In Proceedings of the CARHS Automotive CAE Grand Challenge, Hanau, Germany, 5–6 April 2017. [Google Scholar]
- Bernasconi, A.; Kulin, R.M. Effect of frequency upon fatigue strength of a short glass fiber reinforced polyamide 6: A superposition method based on cyclic creep parameters. Polym. Compos. 2009, 30, 154–161. [Google Scholar] [CrossRef]
- Chu, T.C.; Ranson, W.F.; Sutton, M.A.; Peters, W.H. Applications of digital-image-correlation techniques to experimental mechanics. Exp. Mech. 1985, 25, 232–244. [Google Scholar]
- Pan, B. Digital image correlation for surface deformation measurement: Historical developments, recent advances and future goals. Meas. Sci. Technol. 2018, 29, 82001. [Google Scholar] [CrossRef]
- Peters, W.H.; Ranson, W.F. Digital imaging techniques in experimental stress analysis. Opt. Eng. 1982, 21, 427–431. [Google Scholar] [CrossRef]
- Weibull, W. The Phenomenon of Rupture in solids. In Ingeniörsvetenskapsakademiens Handlingar; Ingeniörsvetenskapsakademiens: Stockholm, Sweden, 1939; pp. 1–55. [Google Scholar]
- Weibull, W. Fatigue Testing and Analysis of Results; Pergamon Press: Oxford, UK; Elsevier: Oxford, UK, 1961. [Google Scholar]
- Witzgall, C.; Gadinger, M.; Wartzack, S. Fatigue Behaviour and Its Effect on the Residual Strength of Long-Fibre-Reinforced Thermoplastic PP LGF30. Materials 2023, 16, 6174. [Google Scholar] [CrossRef]
Number of Cycles Endured | ||||||
---|---|---|---|---|---|---|
649 | 672 | 792 | 1028 | 1098 | 1124 | 1159 |
Experiment | 649 | 908 | 1269 |
Model Prediction | 595 | 925 | 1282 |
Relative Error, | +8% | −2% | −1% |
Damage | 0 | 0.16 | 0.24 | 0.26 | 0.37 | 0.42 | 0.45 | 0.60 | 0.67 |
---|---|---|---|---|---|---|---|---|---|
Breaking strength, N | 1028 | 861 | 779 | 755 | 647 | 611 | 574 | 437 | 371 |
1017 | 932 | 737 | 737 | 741 | 616 | 597 | 552 | 495 | |
Stiffness, MPa | 1295 | 1106 | 1216 | 1201 | 1007 | 1060 | 1042 | 631 | 546 |
1281 | 1198 | 1150 | 1173 | 1153 | 1068 | 1085 | 796 | 729 | |
Relative error, % | 1.1 | −8.3 | 5.4 | 2.3 | −14.5 | −0.8 | −4.1 | −26.1 | −33.5 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Witzgall, C.; Wartzack, S. Fatigue Damage of Short Fibre-Reinforced Thermoplastics in Crashworthiness Simulation. Appl. Mech. 2023, 4, 1188-1205. https://doi.org/10.3390/applmech4040061
Witzgall C, Wartzack S. Fatigue Damage of Short Fibre-Reinforced Thermoplastics in Crashworthiness Simulation. Applied Mechanics. 2023; 4(4):1188-1205. https://doi.org/10.3390/applmech4040061
Chicago/Turabian StyleWitzgall, Christian, and Sandro Wartzack. 2023. "Fatigue Damage of Short Fibre-Reinforced Thermoplastics in Crashworthiness Simulation" Applied Mechanics 4, no. 4: 1188-1205. https://doi.org/10.3390/applmech4040061