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Delamination analysis of multilayered beams exhibiting creep under torsion

  • Rizov, Victor I. (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy)
  • Received : 2020.07.21
  • Accepted : 2021.06.23
  • Published : 2021.08.25

Abstract

A delamination analysis of a multilayered inhomogeneous beam structure under linear creep is developed. A viscoelastic model that consists of an arbitrary number of linear springs and linear dashpots is used. The cross-section of the beam is a circle. The beam is made of concentric longitudinal layers. Each layer is continuously inhomogeneous in thickness and length directions. Therefore, the shear moduli and the coefficients of viscosity ofthe viscoelastic model are distributed continuously along the thickness and length of each layer. Two concentric delamination cracks are located arbitrary between layers. The beam is loaded in torsion. Time-dependent solutions to the strain energy release rate for the two delaminations are derived by using the time-dependent strain energy in the beam. The strain energy release rates are derived also by the compliance method for verification. The variation of the strain energy release rate with time due to creep is evaluated. The effects of material inhomogeneity, external loading and delamination length on the strain energy release rate are investigated.

Keywords

References

  1. Akbas, S.D. (2017), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupl. Syst. Mech., 6(4), 399-415. https://doi.org/10.12989/csm.2017.6.4.399.
  2. Akbas, S.D. (2018), "Nonlinear thermal displacements of laminated composite beams", Coupl. Syst. Mech., 7(6), 691-705. https://doi.org/10.12989/csm.2018.7.6.691.
  3. Akbas, S.D. (2019), "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupl. Syst. Mech., 8(5), 459-471. https://doi.org/10.12989/csm.2019.8.5.459 459.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Hutchinson, J. and Suo, Z. (1992), "Mixed mode cracking in layered materials", Adv. Appl. Mech., 64, 804-810.
  10. Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016), "Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties", Adv. Mater. Res., 54, 205-221. https://doi.org/10.12989/amr.2016.5.4.205 205.
  11. Mahamood, R.M. and Akinlabi, E.T. (2017), Functionally Graded Materials, Springer.
  12. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (1999), Functionally Graded Materials: Design, Processing and Applications, Kluwer Academic Publishers, Dordrecht/London/Boston.
  13. 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.
  14. Rizov, V. and Altenbach, H. (2020), "Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length", Frattura ed Integrita Strutturale, 53, 38-50. https://doi.org/10.3221/IGF-ESIS.53.04.
  15. Rizov, V.I. (2017), "Analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non-linearity", Frattura ed Integrita Strutturale, 41, 498-510. https://doi.org/10.3221/IGFESIS.41.61.
  16. Rizov, V.I. (2018), "Analysis of cylindrical delamination cracks in multilayered functionally graded nonlinear elastic circular shafts under combined loads", Frattura ed Integrita Strutturale, 46, 158-17. https://doi.org/10.3221/IGF-ESIS.46.16.
  17. Rizov, V.I. (2018), "Non-linear longitudinal fracture in a functionally graded beam", Coupl. Syst. Mech., 7(4), 441-453. https://doi.org/10.12989/csm.2018.7.4.441.
  18. Rizov, V.I. (2019), "Influence of material inhomogeneity and non-linear mechanical behavior of the material on delamination in multilayered beams", Frattura ed Integrita Strutturale, 47, 468-481. https://doi.org/10.3221/IGF-ESIS.47.37.
  19. Rizov, V.I. (2019), "Influence of sine material gradients on delamination in multilayered beams", Coupl. Syst. Mech., 8(1), 1-17. https://doi.org/10.12989/csm.2019.8.1.001.
  20. Rizov, V.I. (2020), "Delamination of multilayered non-linear elastic shafts in torsion", FME Tran., 48(3), 681-687. https://doi.org/10.5937/fme2003681R.
  21. Tokovyy, Y. (2019), "Solutions of axisymmetric problems of elasticity and thermoelasticity for an inhomogeneous space and a half space", J. Math. Sci., 240(1), 86-97. https://doi.org/10.1007/s10958-019-04337-3.
  22. Tokovyy, Y. and Ma, C.C. (2017), "Three-dimensional elastic analysis of transversely-isotropic composites", J. Mech., 33(6), 821-830. https://doi.org/10.1017/jmech.2017.91.
  23. Tokovyy, Y. and Ma, C.C. (2019), "Elastic analysis of inhomogeneous solids: history and development in brief", J. Mech., 18 (1), 1-14. https://doi.org/10.1017/jmech.2018.57.
  24. 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.
  25. 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.
  26. 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.
  27. Uslu Uysal, M. and Kremzer, M. (2015), "Buckling behaviour of short cylindrical functionally gradient polymeric materials", Acta Physica Polonica, A127, 1355-1357. https://doi.org/10.12693/APhysPolA.127.1355.