Abstract
An analytical study of the strain energy release rate for an inhomogeneous beam structure with a lengthwise crack subjected to non-linear creep is developed. The beam is inhomogeneous along its length. Two cases are analysed (material with identical creep behaviour in tension and compression, and material with asymmetrical creep behaviour). Since the stress cannot be determined explicitly from the non-linear stress-strain-time relationship, an approach for obtaining of time-dependent solutions of the strain energy release rate is developed by expressing the z-coordinate as a function of the stress. The analysis indicates that the asymmetrical creep behaviour leads to an increase in the strain energy release rate.
Keywords:
beam structure, non-linear creep, lengthwise crackReferences
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3. Tutuncu N., Temel B., An efficient unified method for thermoelastic analysis of functionally graded rotating disks of variable thickness, Mechanics of Advanced Materials and Structures, 20(1): 38–46, 2013, https://doi.org/10.1080/15376494.2011.581413
4. Arefi M., Rahimi G.H., Non linear analysis of a functionally graded beam with variable thickness, Scientific Research and Essays, 8(6): 256–264, 2013, https://doi.org/10.5897/SRE10.342
5. Arefi M., Nonlinear analysis of a functionally graded beam resting on the elastic nonlinear foundation, Journal of Theoretical and Applied Mechanics, 44(2): 71–82, 2014, https://doi.org/10.2478/jtam-2014-0011
6. Arefi M., Elastic solution of a curved beam made of functionally graded materials with different cross sections, Steel and Composite Structures, 18(3): 659–672, 2015, https://doi.org/10.12989/scs.2015.18.3.659
7. Akbaş Ş.D., Nonlinear static analysis of functionally graded porous beams under thermal effect, Coupled Systems Mechanics, 6(4): 399–415, 2017, https://doi.org/10.12989/CSM.2017.6.4.399
8. Akbaş Ş.D., Nonlinear thermal displacements of laminated composite beams, Coupled Systems Mechanics, 7(6): 691–705, 2018, https://doi.org/10.12989/CSM.2018.7.6.691
9. Akbaş Ş.D., Hygro-thermal post-buckling analysis of a functionally graded beam, Coupled Systems Mechanics, 8(5): 459–471, 2019, https://doi.org/10.12989/CSM.2019.8.5.459
10. Miyamoto Y., Kaysser W.A., Rabin B.H., Kawasaki A., Ford R.G., Functionally Graded Materials: Design, Processing and Applications, Kluwer Academic Publishers, Dordrecht/London/Boston, 1999.
11. Mahamood R.M., Akinlabi E.T., Functionally Graded Materials, Springer, 2017.
12. Bohidar S.K., Sharma R., Mishra P.R., Functionally graded materials: A critical review, International Journal of Research, 1(7): 289–301, 2014, https://journals.pen2print.org/index.php/ijr/article/view/378
13. Markworth A.J., Ramesh K.S., Parks Jr.W.P., Modelling studies applied to functionally graded materials, Journal of Materials Science, 30(9): 2183–2193, 1995, https://doi.org/10.1007/BF01184560
14. Gasik M.M., Functionally graded materials: bulk processing techniques, International Journal of Materials and Product Technology, 39(1–2): 20–29, 2010, https://doi.org/10.1504/IJMPT.2010.034257
15. Hsueh C.H., Tuan W.H., Wei W.C.J., Analyses of steady-state interface fracture of elastic multilayered beams under four-point bending, Scripta Materialia, 60(8): 721–724, 2006, https://doi.org/10.1016/j.scriptamat.2009.01.001
16. Hutchinson J.W., Suo Z., Mixed mode cracking in layered materials, Advances in Applied Mechanics, 29: 63–191, 1991, https://doi.org/10.1016/S0065-2156%2808%2970164-9
17. Carpinteri A., Pugno N., Cracks and re-entrant corners in functionally graded materials, Engineering Fracture Mechanics, 73(10): 1279–1291, 2006, https://doi.org/10.1016/j.engfracmech.2006.01.008
18. Tilbrook M.T., Moon R.J., Hoffman M., Crack propagation in graded composites, Composites Science and Technology, 65(2): 201–220, 2005, https://doi.org/10.1016/j.compscitech.2004.07.004
19. Yang J., Chen Y., Free vibration and buckling analyses of functionally graded beams with edge cracks, Composite Structures, 83(1): 48–60, 2008, https://doi.org/10.1016/j.compstruct.2007.03.006
20. Rizov V.I., Statically undetermined functionally graded beam under torsion: A longitudinal fracture analysis with considering creep, AIP Conference Proceedings, 2557(1): 040006-1, 2022, https://doi.org/10.1063/5.0104158
21. Rizov V.I., Continuously inhomogeneous beam structure with creep: a longitudinal crack study, Structural Monitoring and Maintenance, 8(1): 111–124, 2021, https://doi.org/10.12989/smm.2021.8.1.111
22. Narisawa I., Strength of Polymer Materials [in Russian], Chemistry Publishing House, Moscow, 1987.
