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Multilayered viscoelastic beam loaded in torsion under strain-path control: A delamination analysis

  • Victor I. Rizov (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy)
  • 투고 : 2023.03.16
  • 심사 : 2023.06.21
  • 발행 : 2024.04.25

초록

This paper is focused on the delamination analysis of a multilayered beam structure loaded in torsion under strain-path control. The beam under consideration has a rectangular cross-section. The layers of the beam are made of different viscoelastic materials which exhibit continuous inhomogeneity in longitudinal direction. Since the delamination is located inside the beam structure, the torsion moments in the two crack arms are obtained by modeling the beam as an internally static undetermined structure. The strain energy stored in the beam is analyzed in order to derive the strain energy release rate (SERR). Since the delamination is located inside the beam, the delamination has two tips. Thus, solutions of the SERR are obtained for both tips. The solutions are verified by analyzing the beam compliance. Delamination analysis with bending-torsion coupling is also performed. The solutions derived are timedependent due to two factors. First, the beam has viscoelastic behavior and, second, the angle of twist of the beam-free end induced by the external torsion moment changes with time according to a law that is fixed in advance.

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참고문헌

  1. Ahmed, R.A., Fenjan, R.M., Hamad, L.B. and Faleh, N.M. (2020), "A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams", Adv. Mater. Res., 9(1), 33-48. https://doi.org/10.12989/amr.2020.9.1.033.
  2. Akbulut, M. and Sonmez, F.O. (2008), "Optimum design of composite laminates for minimum thickness", Comput. Struct., 86(21-22), 1974-1982. https://doi.org/10.1016/j.compstruc.2008.05.003.
  3. Akbulut, M., Sarac, A. and Ertas, A.H. (2020), "An investigation of non-linear optimization methods on composite structures under vibration and buckling loads", Adv. Comput. Des., 5, 209-231. https://doi.org/10.12989/acd.2020.5.3.209 209.
  4. Butcher, R.J., Rousseau, C.E. and Tippur, H.V. (1999), "A functionally graded particulate composite: Measurements and Failure Analysis", Acta. Mater., 47(2), 259-268. https://doi.org/10.1016/S1359-6454(98)00305-X.
  5. Carpinteri, A. and Pugno, N. (2006), "Cracks in re-entrant corners in functionally graded materials", Eng. Fract. Mech., 73, 1279-1291. https://doi.org/10.1016/j.engfracmech.2006.01.008.
  6. Chen, F., Jia, M., She, Y., Wu, Y., Shen, Q. and Zhang, L. (2020), "Mechanical behavior of AlN/Mo functionally graded materials with various compositional structures", J. Alloys. Compd., 816, 152512. https://doi.org/10.1016/j.jallcom.2019.152512.
  7. Chobanian, K.S. (1997), Stresses in Combined Elastic Solids, Science.
  8. Dolgov, N.A. (2002), "Effect of the elastic modulus of a coating on the serviceability of the substrate-coating system", Strength Mater., 34, 153-157. https://doi.org/10.1023/A:1015362426688.
  9. Dolgov, N.A. (2005), "Determination of stresses in a two-layer coating", Strength Mater., 37(2), 422-431. https://doi.org/10.1007/s11223-005-0053-7.
  10. Dolgov, N.A. (2016), "Analytical methods to determine the stress state in the substrate-coating system under mechanical loads", Strength Mater., 48(1), 658-667. https://doi.org/10.1007/s11223-016-9809-5.
  11. Gasik, M.M. (2010), "Functionally graded materials: Bulk processing techniques", Int. J. Mater. Prod. Technol., 39(1-2), 20-29. https://doi.org/10.1504/IJMPT.2010.034257.
  12. Hedia, H.S., Aldousari, S.M., Abdellatif, A.K. and Fouda, N.A. (2014), "New design of cemented stem using functionally graded materials (FGM)", Biomed. Mater. Eng., 24(3), 1575-1588. https://doi.org/10.3233/BME-140962.
  13. Hirai, T. and Chen, L. (1999), "Recent and prospective development of functionally graded materials in Japan", Mater. Sci. Forum, 308-311(4), 509-514. https://doi.org/10.4028/www.scientific.net/MSF.308-311.509.
  14. Hsueh, C.H., Tuan, W.H. and Wei, W.C.J. (2006), "Analyses of steady-state interface fracture of elastic multilayered beams under four-point bending", Scripta Mater., 60, 721-724. https://doi.org/10.1016/j.scriptamat.2009.01.001.
  15. Hutchinson, J.W. and Suo, Z. (1992), "Mixed mode cracking in layered materials", Adv. Appl. Mech., 64, 804-810. https://doi.org/10.1016/S0065-2156(08)70164-9.
  16. Madan, R., Saha, K. and Bhowmick, S. (2020), "Limit speeds and stresses in power law functionally graded rotating disks", Adv. Mater. Res., 9(2), 115-131. https://doi.org/10.12989/amr.2020.9.2.115.
  17. Mahamood, R.M. and Akinlabi, E.T. (2017), Functionally Graded Materials, Springer International Publishing, Cham, Switzerland.
  18. Markworth, A.J., Ramesh, K.S. and Parks, Jr.W.P. (1995), "Review: Modeling studies applied to functionally graded materials", J. Mater. Sci., 30(3), 2183-2193. https://doi.org/10.1007/BF01184560.
  19. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (1999), Functionally Graded Materials: Design, Processing and Applications, Springer, New York, NY, USA.
  20. Nemat-Allal, M.M., Ata, M.H., Bayoumi, M.R. and Khair-Eldeen, W. (2011), "Powder metallurgical fabrication and microstructural investigations of aluminum/steel functionally graded material", Mater. Sci. Appl., 2(5), 1708-1718. https://doi.org/10.4236/msa.2011.212228.
  21. Nguyen, S.N., Lee, J. and Cho, M. (2015), "Efficient higher-order zig-zag theory for viscoelastic laminated composite plates", Int. J. Solids Struct., 62, 174-185. https://doi.org/10.1016/j.ijsolstr.2015.02.027.
  22. Nguyen, S.N., Lee, J., Han, J.W. and Cho, M. (2020), "A coupled hygrothermo-mechanical viscoelastic analysis of multilayered composite plates for long-term creep behaviors", Compos. Struct., 242, 112030. https://doi.org/10.1016/j.compstruct.2020.112030.
  23. Nikbakht, S., Kamarian, S. and Shakeri, M.A. (2019), "A review on optimization of composite structures Part II: Functionally graded materials", Compos. Struct., 214, 83-102. https://doi.org/10.1016/j.compstruct.2019.01.105.
  24. Radhika, N., Sasikumar, J., Sylesh, J.L. and Kishore, R. (2020), "Dry reciprocating wear and frictional behaviour of B4C reinforced functionally graded and homogenous aluminium matrix composites", J. Mater. Res. Technol., 9, 1578-1592. https://doi.org/10.1016/j.jmrt.2019.11.084.
  25. Rizov, V. (2023), "Delamination analysis of multilayered functionally graded beams which exhibit non-linear creep behavior", J. Appl. Comput. Mech., 9(4), 935-944 https://doi.org/10.22055/jacm.2023.42743.3969.
  26. Rizov, V.I. (2018), "Non-linear fracture in bi-directional graded shafts in torsion", Multidiscip. Model. Mater. Struct., 14, 387-399. https://doi.org/10.1108/MMMS-12-2017-0163.
  27. Rizov, V.I. (2020), "Longitudinal fracture analysis of continuously inhomogeneous beam in torsion with stress relaxation", Struct. Integr. Proc., 28, 1212-122. https://doi.org/10.1016/j.prostr.2020.11.103.
  28. Rizov, V.I. (2021), "Delamination analysis of multilayered beams exhibiting creep under torsion", Coupl. Syst. Mech., 10, 317-331. https://doi.org/10.12989/csm.2021.10.4.317.
  29. Rizov, V.I. (2022), "Effects of periodic loading on longitudinal fracture in viscoelastic functionally graded beam structures", J. Appl. Comput. Mech., 8(1), 370-378. https://doi.org/10.22055/JACM.2021.37953.3141.
  30. Rizov, V.I. and Altenbach, H. (2023), "Fracture analysis of inhomogeneous arch with two longitudinal cracks under non-linear creep", Adv. Mater. Res., 12(1), 15-29. https://doi.org/10.12989/amr.2023.12.1.015.
  31. Saiyathibrahim, A., Subramanian, R. and Samson Jerold Samuel, C. (2019), "Processing and properties evaluation of centrifugally cast in-situ functionally graded composites reinforced with Al3Ni and Si particles", Mater. Res. Express, 6(11) 1165a8. https://doi.org/10.1088/2053-1591/ab4c9f.
  32. Shrikantha Rao, S. and Gangadharan, K.V. (2014), "Functionally graded composite materials: An overview", Proc. Mater. Sci., 5(1), 1291-1299. https://doi.org/10.1016/j.mspro.2014.07.442.
  33. Tilbrook, M.T., Moon, R.J. and Hoffman, M. (2005), "Crack propagation in graded composites", Compos. Sci. Technol., 65, 201-220. https://doi.org/10.1016/j.compscitech.2004.07.004.
  34. Toudehdehghan, J., Lim, W., Foo, K.E., Ma'arof, M.I.N. and Mathews, J. (2017), "A brief review of functionally graded materials", MATEC Web Conf., 131, 03010. https://doi.org/10.1051/matecconf/201713103010.
  35. Uslu Uysal, M. (2016), "Buckling behaviours of functionally graded polymeric thin-walled hemispherical shells", Steel Compos. Struct., 21(1), 849-862. https://doi.org/10.12989/scs.2016.21.4.849.
  36. Uslu Uysal, M. and Guven, U. (2015), "Buckling of functional graded polymeric sandwich panel under different load cases", Compos. Struct., 121, 182-196. https://doi.org/10.1016/j.compstruct.2014.11.012.
  37. Uslu Uysal, M. and Guven, U. (2016), "A bonded plate having orthotropic inclusion in adhesive layer under in-plane shear loading", J. Adhes., 92, 214-235. https://doi.org/10.1080/00218464.2015.1019064.
  38. Uslu Uysal, M. and Kremzer, M. (2015), "Buckling behaviour of short cylindrical functionally gradient polymeric materials", Acta Phys. Polon., A127, 1355-1357. https://doi.org/10.12693/APhysPolA.127.1355.
  39. Zubchaninov, V.G. (1990), Fundamentals of Theory of Elasticity and Plasticity, Vishaya Shcola, Minsk, Belarus.