Abstract
Over the years, various models have been developed to predict the fatigue behavior in fibre reinforced plastics. Recently, a new fatigue damage model (FDM) was developed. The FDM relates the energy dissipated in the quasi-static case to the energy dissipated under a cyclic loading. The model is based on evolution laws for fatigue based degradation and is more physically oriented than most models as it has an energy based methodology and takes into account Puck’s failure modes for the degradation of strength and stiffness. Since it is based on a macro-mechanical analysis scale and uses a block wise loading approach, the FDM can be applied to arbitrary structures and consideration of a large number of cycles is also possible with this model. Moreover, phenomena such as stress redistribution and sequence effects occurring under fatigue conditions can also be analyzed. Originally, the FDM was based on a two-dimensional (2D) formulation and implemented within layer-based shell elements. In the present work, an extended version of the FDM is presented. The extended version comprises a three-dimensional (3D) formulation and a finite element implementation based on solid elements. The extended FDM is used for numerical simulations of the very high cycle fatigue behavior of laminates for specific reference cases such as four-point bending based cyclic loading. Results obtained from the original FDM (2D FDM) and the present work (3D FDM) are compared and in a final step compared with the results obtained from experiments in a four-point bending test.
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References
[1] H. Krueger: ‘Ein physikalisch basiertes Ermüdungsschädigungsmodell zur Degradationsberechnung von Faser-Kunststoff-Verbunden’, PhD thesis, Raimund Rolfes, editor. Institute of Structural Analysis, University of Hanover, Germany, 2012. (ISSN 1862-4650)
[2] H Krueger, R Rolfes: ‘A physically based fatigue damage model for fibre-reinforced plastics under plane loading.’, Int. J. Fatigue, 2015, 70, 241-251.
[3] A. Puck and H. Schuermann: ‘Failure analysis of FRP laminates by means of physically based phenomenological models’. In: M. J. Hinton, A. S. Kaddour, P. D. Soden: ‘Failure Criteria in Fibre Reinforced Polymer Composites: The World-wide Failure exercise (WWFE)’, Oxford, UK, Elsevier Science Ltd., 2004. (ISBN 0-08-044475)
[4] A. Puck: ‘Festigkeitsanalyse von Faser-Matrix-Laminaten – Modelle für die Praxis’, Munich, Germany, Carl Hanser Verlag, 1996. (ISBN 3-446-18194-6)
[5] M. Knops: ‘Analysis of Failure in Fibre Polymer Laminates – The Theory of Alfred Puck.’, Berlin, Germany, Springer-Verlag, 2008. (ISBN 978-3-540-75764-1)
[6] OptiDAT: ‘Optimat Blades Database, database reference document, R. Nijssen. OB_TC_R018 rev. 004, Ver. 1.9.6’, WMC, Netherlands, June 2006, https://www.wmc.eu/optimatblades_optidat.php.
[7]D. Pfanner: ‘Zur Degradation von Stahlbetonbauteilen unter Ermüdungsbeanspruchung’, PhD thesis, Institute of Structural Engineering, Ruhr-University Bochum, VDI Verlag GmbH, Germany, 2003. (ISBN: 3-18-318904-6)
[8] H. Krueger, R. Rolfes and E. Jansen: ‘An Innovative Energy-Based Fatigue Approach for Composites Combining Failure Mechanisms, Strength and Stiffness Degradation’, Proceedings of the International Conference on Fatigue of Composites (ICFC5), October 2010, University of Aeronautics and Astronautics, Nanjing, China.
[9] A. Hillerborg, M. Modeer and P. E. Petersson: ‘Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements’, Cement Concrete Research, 1972, 6, 773-782.
[10] P. Maimi, P. Camanho, J. A. Mayugo, C. G. Davila: ‘A continuum damage model for composite laminates, Part I: Constitutive model, Part II: Computational implementation and validation’, Mechanics of Materials, 2007, 39, 10, 897-919.
[11] R. Pölling: ‘Eine praxisnahe, schädigungsorientierte Materialbeschreibung von Stahlbeton für Strukturanalysen’, PhD thesis, Ruhr-Univerity Bochum, Books on Demand GmbH, Germany, 2001. (ISBN 3-83-11-1473-0)
[12] K. L. Reifsnider, K. Schulte and J. C. Duke: ‘Long Term Fatigue Behavior of Composite Materials’, Long-term Behavior of Composites, 1983, ASTM STP 813, 136-159.
[13] A. L. Gagel: ‘Über die Schädigung und Degradation von Glasfaser-Multiaxialgelege verstärktem Epoxid unter mechanischer Last’, PhD thesis, Hamburg University of Technology, Karl Schulte (ed.), TuTech Innovation GmbH, Hamburg, Germany, 2007. (ISBN 978-3-930400-91-1)
[14] K. Schulte: ‘Compressive Static and Fatigue Loading of Continuous Fibre-reinforced Composites’, Compres-sion Response of Composite Structures, 1994, ASTM STP 1185, 278-305.
[15] G. L. W. E. GmbH: ‘Richtlinie für die Zertifizierung von Windenergieanlagen’, Hamburg, Germany, 2003.
[16] J. R. Vinson, R. L. Sierakowski: ‘The behavior of structures composed of composite materials’, Dordrecht, Netherlands, Martinus Nijhoff Publishers, 1986. (ISBN 90-247-3125-9)
[17] R. M. Christensen: ‘Tensor Transformations and Failure Criteria for the Analysis of Fiber Composite Materials’, J. Comp. Mater., 1988, 22(9), 874-897.
[18] P. D. Soden, M. J. Hinton and A. S. Kaddour: ‘Biaxial test results for strength and deformation of a range of E-glass and carbon fibre reinforced composite laminates: failure exercise benchmark data’, Comp. Sci. Technology, 2002, 62, 12-13, 1489-1514.
[19] T. J. Adam and P. Horst: ‘Experimental investigation of the very high cycle fatigue of GFRP [90/0] s cross-ply specimens subjected to high-frequency four-point bending.’, Comp. Sci. Technology, 2014, 101, 62-70.
[20] P. Lorsch, T. J. Adam, M. Zeisberg, M. Sinapius, P. Horst, R. Rolfes, P. Wierach and H. Krüger: ‘Investigating the VHCF of composite materials using new testing methods and a new fatigue damage model’, 6th International Conference on VHCF, October 2014, Chengdu, China.
[21] S. Hartmann and R R. Gilbert: ‘Identifiability of material parameters in solid mechanics’, Archive of Applied Mechanics, 2017, https://doi.org/10.1007/s00419-017-1259-4.
[22] I. Koch, M. Zscheyge, K. Tittmann and M. Gude: ‘Numerical fatigue analysis of CFRP components’, Comp. Structures, 2017, 168, 392-401.
[23] T. Kant and K. Swaminathan: ‘Estimation of transverse/interlaminar stresses in alaminated composites – a selective review and survey of current developments’, Comp. Structures, 2000, 49, 65-75.
[24] S. B. Dong, K. S. Pister, R. L. Taylor: ‘On the theory of laminated anisotropic shells and plates’, Journal of Aeronautical Sciences, 1962, 29, 8, 969-975.
[25] E. Reissner, Y. Stavsky: ‘Bending and stretching of certain types of heterogeneous aelotropic elastic plates’, ASME Journal of Applied Mechanics, 1961, 28, 402-408.
[26] M. D. Aydn: ‘3-D Nonlinear Stress Analysis on Adhesively Bonded Single Lap Composite Joints with Different Ply Stacking Sequences’, The Journal of Adhesion, 2008, 84, 15-36.
[27] C. H. Wang and L. R. F. Rose: ‘Determination of triaxial stresses in bonded joints’, International Journal of Adhesion and Adhesives, 1997, 17, 17-25.
[28] M. Y. Tsai, J. Morton, F. L. Mathews : ‘The effect of a spew fillet on adhesive stress distributions in laminated composite single – lap joints’, J. Comp. Mater., 1995, 29, 1254-1275.
[29] R. Gutkin, S. Costa and R. Olsson: ‘A physically based model for kink-band growth and longitudinal crushing of composites under 3D stress states accounting for friction’, Comp. Sci. Technology, 2016, 135, 39-45.
[30] Z. Hashin and A. Rotem: ‘A fatigue criterion for fibre reinforced composite materials’, J. Comp. Mater., 1973, 7, 4, 448-464.
[31] K. L. Reifsnider and Z. Gao: ‘A micromechanics model for composites under fatigue loading’, Int. J. Fatigue, 1991, 13, 2, 149-156.
[32] T. P. Philippidis and A. P. Vassilopoulos: ‘Fatigue strength prediction under multiaxial stress’, J. Comp. Mater., 1999, 33, 17, 1578-1599.
[33] I. P. Bond : ‘Fatigue life prediction of GFRP subjected to variable amplitude loading’, Composites Part A, 1999, 30, 8, 961-970.
[34] Y. Liu and S. Mahadevan: ‘Stochastic fatigue damage modelling under variable amplitude loading’, Int. J. Fatigue, 2007, 29, 1149-1161.
[35] J. N. Yang, D. L. Jones, S. H. Yang and A. Meskini: ‘A stiffness degradation model for graphite/epoxy laminates’, J. Comp. Mater., 1990, 24, 7, 753-769.
[36] W. Hwang, K. S. Han: ‘Fatigue of composites – fatigue modulus concept and life prediction’, J. Comp. Mater., 1986, 20, 2, 154-165.
[37] G. R. Ahmadzadeh, A. Shirazi and A. Varvani-Farahani: ‘Damage assessment of CFRP [90/±45/0] composite laminates over fatigue cycles’, Appl. Comp. Mater., 2011, 18, 559-569.
[38] A. Varvani-Farahani, H. Haftchenari and M. Panbechi: ‘An energy-based fatigue damage parameter for off-axis unidirectional FRP composites’, Comp. Structures, 2007, 79, 381-389.
[39] M. M. Shokrieh and L. B. Lessard: ‘Multiaxial fatigue behavior of unidirectional plies based on uniaxial fa-tigue experiments, Part 1: modelling’, Int. J. Fatigue, 1997, 19, 3, 201-207.
[40] P. M. Barnard, R. J. Butler and P. T. Curtis: ‘The strength-life equal rank assumption and its application to the fatigue life prediction of composite materials’, Int. J. Fatigue, 1988, 10, 3, 171-177.
[41] J. R. Schaff and B. D. Davidson: ‘Life prediction methodology for composite structures (Part I-constant amplitude and two-stress level fatigue; Part II-spectrum fatigue)’, J. Comp. Mater., 1997, 31, 2, 128-181.
[42] T. P. Philippidis and V. A. Passipoularidis: ‘Residual strength after fatigue in composites: theory vs. experiment’, Int. J. Fatigue, 2007, 29, 2104-2126.
[43] J. Bartley-Cho, S. G. Lim, H. T. Hahn and P. Shyprykevich: ‘Damage accumulation in quasiisotropic graph-ite/epoxy laminates under constant-amplitude fatigue and block loading’, Comp. Sci. Technology, 1998, 58, 9, 1535-1547.
[44] A. Varvani-Farahani and A. Shirazi: ‘A Fatigue Damage Model for (0/90) FRP Composites based on Stiffness Degradation of 00 and 900 Composite Plies’, Journal of Reinforced Plastics and Composites, 2007, 26.
[45] F. Wu and W. Yao: ‘A fatigue damage model of composite materials’, Int. J. Fatigue, 2010, 32, 134-138.
[46] H. Mao and S. Mahadevan: ‘Fatigue damage modeling of composite materials’, Comp. Structures, 2002, 58, 405-410.
[47] S. Subramanian, K. L. Reifsnider and W. W. Stinchcomb: ‘A cumulative damage model to predict the fatigue life of composites laminates including the effect of a fibre-matrix interphase’, Int. J. Fatigue, 1995, 17, 5, 343-351.
[48] J. A. Epaarachchi and P. D. Clausen: ‘A new cumulative fatigue damage model for glass fibre reinforced plastic composites under step/discreter loading’, Composites Part A: Applied Science and Manufacturing, 2005, 36, 9, 1236-1245.
[49] H. A. Whilworth: ‘A stiffness degradation model for composite laminates under fatigue loading’, Comp. Structures, 1997, 40, 2, 95-101.
[50] S. Shiri, M. Yazdani and M. Pourgol-Mohammad: ‘A fatigue damage accumulation model based on stiffness degradation of composite materials’, Materials and Design, 2015, 88, 1290-1295.
[51] W. Van Paepegem and J. Degrieck: ‘A new coupled approach of residual stiffness and strength for fatigue of fibre-reinforced composites’, Int. J. Fatigue, 2002, 24, 747-762.
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Madhusoodanan, H., Jansen, E., Rolfes, R. (2018). A physically based fatigue damage model for simulating three-dimensional stress states in composites under very high cycle fatigue loading. In: Christ, HJ. (eds) Fatigue of Materials at Very High Numbers of Loading Cycles. Springer Spektrum, Wiesbaden. https://doi.org/10.1007/978-3-658-24531-3_24
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