# On the Influence of Fatigue Damage in Short-Fibre Reinforced Thermoplastic PBT GF30 on Its Residual Strength under High Strain Rates: An Approach towards Simulative Prediction

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modelling of Crashworthiness after Fatigue Damage

#### 2.1. Characterisation of Material Behaviour and Degradation

#### 2.2. Determination of Fatigue Damage

#### 2.3. Determination of Residual Strength

_{T}. A value less than one is recommended for the power p since a value greater than one implies that the strength degrades quicker than the stiffness. Uniaxial fatigue bending studies on plain woven glass/epoxy specimens verified this concept. The model is based on how their stiffness diminishes in general, and delamination mechanisms are ignored in this one-dimensional model. Due to its generality, the model could be transferred to the situation of uniaxial tensile load cases on fibre reinforced thermoplastics.

## 3. Materials and Experimental Studies

- Static and high-speed tensile tests on virgin specimens to ascertain the elastic moduli and strengths of the virgin material with various fibre orientations;
- Destructive cyclic tests to identify the damage progression and orientation angle-dependent S-N curves that represent fatigue behaviour;
- Non-destructive cyclic tests for individual specimen pre-damage;
- Highly dynamic tensile tests on pre-damaged specimens for comparison with the undamaged specimens and for validation of the models used to predict the residual strength.

#### 3.1. High-Speed Tensile Testing

^{−1}. By means of digital image correlation, the actual strain rates were calculated. The force was measured with a piezoelectric force transducer capable of handling loads up to 10 kN. The high-speed test used both virgin specimens and specimens that had already been damaged in earlier non-destructive cyclic tests.

#### 3.2. Cyclic Testing

#### 3.3. Digital Image Correlation

#### 3.3.1. DIC in High-Velocity Testing

#### 3.3.2. DIC in Cyclic Testing

## 4. Results of Experimental Studies and Simulations

#### 4.1. Residual Crashworthiness

^{2}= 0.88 and at the same time confirms van Paepegem’s estimate that this exponent should be below 1 [12].

#### 4.2. Implementation to Simulation

^{2}= 0.98 of the simulative vs the analytical data. Thus, the transfer of material properties might be called functional.

^{2}= 0.983 for the plane of the tensile specimens.

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Bisagni, C.; Walters, C. Influence of impacts on static and low-cycle fatigue characteristics of composite specimens. Int. J. Crashworthiness
**2013**, 18, 139–151. [Google Scholar] [CrossRef] - Steck, P.; Scherb, D.; Miehling, J.; Völkl, H.; Wartzack, S. Synthesis of passive lightweight orthoses considering humanmachine interaction. In DS 119: Proceedings of the 33rd Symposium Design for X (DFX2022), Hamburg, Germany, 22–23 September 2022; The Design Society: Glasgow, UK, 2022; p. 10. [Google Scholar]
- Klein, D.; Witzgall, C.; Wartzack, S. A novel approach for the evaluation of composite suitability of lightweight structures at early design stages. In Proceedings of the International Design Conference, DESIGN, Dubrovnik, Croatia, 19–22 May 2014; pp. 1093–1104. [Google Scholar]
- Hartwich, T.S.; Völkl, H.; Franz, M.; Witzgall, C.; Krause, D.; Wartzack, S. On the necessity of a construction-methodological approach for the time-proof design of endless fiber-reinforced plastic components. In DS 98: Proceedings of the 30th Symposium Design for X, DFX 2019, Jesteburg, Germany, 18–19 September 2019; The Design Society: Glasgow, UK, 2019; pp. 109–122. [Google Scholar]
- Becker, F.; Kolling, S.; Schöpfer, J. Material Data Determination and Crash Simulation of Fiber Reinforced Plastic Components. In Proceedings of the 8th European LS-DYNA Conference, Strasbourg, France, 23–24 May 2011. Hallquist (Ed.). [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 27th Symposium Design for X, Jesteburg, Germany, 5–6 October 2016; pp. 135–146. [Google Scholar]
- Günzel, S. Analyse der Schädigungsprozesse in Einem Kurzglasfaserverstärkten Polyamid unter Mechanischer Belastung Mittels Röntgenrefraktometrie, Bruchmechanik und Fraktografie. Ph.D. Dissertation, Bundesanstalt für Materialforschung und-Prüfung (BAM), Berlin, Germany, 2015. [Google Scholar]
- Bauer, C. Charakterisierung und Numerische Beschreibung des Nichtlinearen Werkstoff- und Lebensdauerverhaltens Eines Kurzglasfaserverstärkten Polymerwerkstoffes unter Berücksichtigung der im μCT Gemessenen Lokalen Faserorientierung; Technische Universität Kaiserslautern: Kaiserslautern, Germany, 2018. [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] - Nutini, M.; Vitali, M. Interactive failure criteria for glass fibre reinforced polypropylene: Validation on an industrial part. Int. J. Crashworthiness
**2017**, 24, 24–38. [Google Scholar] [CrossRef] - Hill, R. The Mathematical Theory of Plasticity; Clarendon Press: Oxford, UK, 1998; ISBN 0198503679. [Google Scholar]
- van Paepegem, W. 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] - 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] - Witzgall, C.; Wartzack, S. Validation of an approach for the simulation of short fiber reinforced thermoplastics in early design phases. In Proceedings of the 26th Symposium Design for X, Herrsching, Germany, 7–8 October 2015; pp. 63–74. [Google Scholar]
- Witzgall, C.; Wartzack, S. Experimental and simulative assessment of crashworthiness of mechanically aged short-fibre reinforced thermoplastics. In Proceedings of the International Conference on Engineering Design, ICED, Vancouver, BC, Canada, 21–25 August 2017; pp. 279–287. [Google Scholar]
- 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] - 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] - 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] - Masendorf, R.; Müller, C. Execution and evaluation of cyclic tests at constant load amplitudes—DIN 50100:2016. Mater. Test.
**2018**, 60, 961–968. [Google Scholar] [CrossRef] - ISO 527-1:2012-06; Kunststoffe—Bestimmung der Zugeigenschaften—Teil 1. Allgemeine Grundsätze; Beuth: Berlin, Germany, 2012.
- Haufe, A.; Schweizerhof, K.; Du Bois, P. Properties & Limits: Review of Shell Element Formulations. In Proceedings of the LS-DYNA Developer Forum, Filderstadt, Germany, 24–25 September 2013. Hallquist (Ed.). [Google Scholar]
- Friedlein, J.; Mergheim, J.; Steinmann, P. Anisotropic plasticity-damage material model for sheet metal—Regularised single surface formulation. Pamm
**2021**, 21, e202100068. [Google Scholar] [CrossRef] - Baltic, S.; Magnien, J.; Gänser, H.-P.; Antretter, T.; Hammer, R. Coupled damage variable based on fracture locus: Modelling and calibration. Int. J. Plast.
**2020**, 126, 102623. [Google Scholar] [CrossRef]

**Figure 5.**Testing equipment: (

**a**) High-speed tensile testing with a Zwick HTM 5020; (

**b**) Cyclic testing with a servo-hydraulic pulser Zwick HCT 25.

**Figure 9.**Comparison between the analytical model and the simulation implementation of the weakened material data.

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

**MDPI and ACS Style**

Witzgall, C.; Steck, P.; Wartzack, S.
On the Influence of Fatigue Damage in Short-Fibre Reinforced Thermoplastic PBT GF30 on Its Residual Strength under High Strain Rates: An Approach towards Simulative Prediction. *J. Compos. Sci.* **2023**, *7*, 23.
https://doi.org/10.3390/jcs7010023

**AMA Style**

Witzgall C, Steck P, Wartzack S.
On the Influence of Fatigue Damage in Short-Fibre Reinforced Thermoplastic PBT GF30 on Its Residual Strength under High Strain Rates: An Approach towards Simulative Prediction. *Journal of Composites Science*. 2023; 7(1):23.
https://doi.org/10.3390/jcs7010023

**Chicago/Turabian Style**

Witzgall, Christian, Patrick Steck, and Sandro Wartzack.
2023. "On the Influence of Fatigue Damage in Short-Fibre Reinforced Thermoplastic PBT GF30 on Its Residual Strength under High Strain Rates: An Approach towards Simulative Prediction" *Journal of Composites Science* 7, no. 1: 23.
https://doi.org/10.3390/jcs7010023