Advances in materials Research

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Fracture analysis of inhomogeneous arch with two longitudinal cracks under non-linear creep

  • Victor I. Rizov (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy ) ;
  • Holm Altenbach (Lehrstuhl fur Technische Mechanik, Fakultat fur Maschinenbau, Otto-von-Guericke-Universitat Magdeburg)
  • Received : 2022.02.23
  • Accepted : 2022.04.28
  • Published : 2023.03.25
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Abstract

In this paper, fracture analysis of a continuously inhomogeneous arch structure with two longitudinal cracks is developed in terms of the time-dependent strain energy release rate. The arch under consideration exhibits non-linear creep behavior. The cross-section of the arch is a rectangle. The material is continuously inhomogeneous along the thickness of the cross-section. The arch is loaded by two bending moments applied at its end sections. The mechanical behavior of the material is described by using a non-linear stress-strain-time relationship. The two longitudinal cracks are located symmetrically with respect to the mid-span of the arch. Due to the symmetry, only half of the arch is considered. Time-dependent solutions to strain energy release rate are obtained by analyzing the balance of the energy. For verification, time-dependent solutions to the strain energy release rate are derived also by considering the time-dependent complementary strain energy. The evolution of the strain energy release rate with the time is analyzed. The effects of material inhomogeneity, locations of the two cracks along the thickness of the arch and the magnitude of the external loading on the time-dependent strain energy release rate are evaluated.

Keywords

Acknowledgement

The financial support provided by the German Academic Exchange Organization (DAAD) for the research stay of the first author (V.I.R.) in Department of Engineering Mechanics, Institute of Mechanics, Otto-von-Guericke-University, Magdeburg, Germany is gratefully acknowledged.

References

  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. Altunsaray, E. (2017), "Static deflections of symmetrically laminated quasi-isotropic super-elliptical thin plates", Ocean Eng., 141, 337-350. https://doi.org/10.1016/j.oceaneng.2017.06.032.
  3. Altunsaray, E. and Bayer, I. (2014), "Buckling of symmetrically laminated quasi-isotropic thin rectangular platesˮ, Steel Compos. Struct., 17, 305-320. https://doi.org/10.12989/scs.2014.17.3.305.
  4. Altunsaray, E., unsalan, D., Neser, G., Gursel, K.T. and Taner, M. (2019), "Parametric study for static deflections of symmetrically laminated rectangular thin plates", Scientif. Bull. Mircea cel Batran Naval Academy, 22, 1-12. https://doi.org/10.21279/1454-864X-19-I1-041.
  5. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundationˮ, Arab. J. Geosci., 11, 232. https://doi.org/10.1007/s12517-018-3579-2.
  6. Butcher, R.J., Rousseau, C.E. and Tippur, H.V. (1999), "A functionally graded particulate composite: Measurements and failure analysisˮ, Acta. Mater., 47(2), 259-268. https://doi.org/10.1016/S1359-6454(98)00305-X.
  7. 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.
  8. 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.
  9. Gasik, M.M. (2010), "Functionally graded materials: bulk processing techniquesˮ, Int. J. Mater. Prod. Technol., 39(1-2), 20-29. https://doi.org/10.1504/IJMPT.2010.034257.
  10. Hedia, H.S., Aldousari, S.M., Abdellatif, A.K. and Fouda, N.A. (2014), "New design of cemented stem using functionally graded materials (FGM)ˮ, Biomed. Mater. Eng., 24(3), 1575-1588. https://doi.org/10.3233/BME-140962.
  11. Hirai, T. and Chen, L. (1999), "Recent and prospective development of functionally graded materials in Japanˮ, Mater Sci. Forum, 308-311(4), 509-514. https://doi.org/10.4028/www.scientific.net/MSF.308-311.509.
  12. Kishkilov, M. and Apostolov, R. (1994), Introduction to Theory of Plasticity, UACEG.
  13. Madan, R., Saha, K. and Bhowmick, S. (2020), "Limit speeds and stresses in power law functionally graded rotating disksˮ, Adv. Mater. Res., 9(2), 115-131. https://doi.org/10.12989/amr.2020.9.2.115.
  14. Mahamood, R.M. and Akinlabi, E.T. (2017), Functionally Graded Materials, Springer.
  15. Markworth, A.J., Ramesh, K.S. and Parks, Jr. W.P. (1995), "Review: Modeling studies applied to functionally graded materialsˮ, J. Mater. Sci., 30(3), 2183-2193. https://doi.org/10.1007/BF01184560.
  16. 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.
  17. 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 materialˮ, Mater. Sci. Appl., 2(5), 1708-1718. https://doi.org/10.4236/msa.2011.212228.
  18. Rabenda, M. (2015), "Analysis of non-stationary heat transfer in a hollow cylinder with functionally graded material properties performed by different research methods", Eng. Trans., 63, 329-339. 
  19. Rabenda, M. (2016), "The analysis of the impact of different shape functions in tolerance modeling on natural vibrations of the rectangular plate with dense system of the ribs in two directions", Vib. Phys. Syst., 27, 301-308.
  20. Rabenda, M. and Michalak, B. (2015), "Natural vibrations of prestressed thin functionally graded plates with dense system of ribs in two directionsˮ, Compos. Struct., 133, 1016-1023. https://doi.org/10.1016/j.compstruct.2015.08.026.
  21. Rizov, V. and Altenbach, H. (2020), "Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam lengthˮ, Frattura ed Integrita Strutturale, 53, 38-50. https://doi.org/10.3221/IGF-ESIS.53.04.
  22. Rizov, V.I. (2020), "Longitudinal fracture analysis of inhomogeneous beams with continuously changing radius of cross-section along the beam lengthˮ, Strength Fract. Complex., 13, 31-43. https://doi.org/10.3233/SFC-200250.
  23. Rizov, V.I. (2020a), "Inhomogeneous multilayered beams of linearly changing width: a delamination analysisˮ, IOP Conf. Ser.: Mater. Sci. Eng., 739, 012004. https://doi.org/10.1088/1757-899X/739/1/012004.
  24. Rizov, V.I. (2022), "Analysis of the strain energy release rate for time-dependent delamination in multilayered beams with creepˮ, Adv. Mater. Res., 11, 41-57. https://doi.org/10.12989/amr.2022.11.1.041.
  25. Saiyathibrahim, A., Subramaniyan, R. and Dhanapl, P. (2016), "Centrefugally cast functionally graded materials-review", International Conference on Systems, Science, Control, Communications, Engineering and Technology, 68-73.
  26. Shrikantha Rao, S. and Gangadharan, K.V. (2014), "Functionally graded composite materials: an overviewˮ, Procedia Mater. Sci., 5(1), 1291-1299. https://doi.org/10.1016/j.mspro.2014.07.442.
  27. Sofiyev, A.H., Alizada, A.N., Akin, O., Valiyev, A., Avcar, M. and Adiguzel, S. (2012), "On the stability of FGM shells subjected to combined loads with different edge conditions and resting on elastic foundationsˮ, Acta Mech., 223, 189-204. https://doi.org/10.1007/s00707-011-0548-1.
  28. Sofiyev, A.H. and Avcar, M. (2010), "The stability of cylindrical shells containing an FGM layer subjected to axial load on the Pasternak foundationˮ, Eng., 2, 228-236 https://doi.org/10.4236/eng.2010.24033.
  29. Uslu Uysal, M. (2016), "Buckling behaviours of functionally graded polymeric thin-walled hemispherical shellsˮ, Steel Compos. Struct., 21(1), 849-862. https://doi.org/10.12989/scs.2016.21.4.849.
  30. Uslu Uysal, M. and Guven, U. (2015), "Buckling of functional graded polymeric sandwich panel under different load casesˮ, Compos. Struct., 121, 182-196. https://doi.org/10.1016/j.compstruct.2014.11.012.
  31. Uslu Uysal, M. and Guven, U. (2016), "A bonded plate having orthotropic inclusion in adhesive layer under in-plane shear loadingˮ, J. Adhes., 92, 214-235. https://doi.org/10.1080/00218464.2015.1019064.
  32. Uslu Uysal, M. and Kremzer, M. (2015), "Buckling behaviour of short cylindrical functionally gradient polymeric materialsˮ, Acta Physica Polonica, A127, 1355-1357. https://doi.org/10.12693/APhysPolA.127.1355.
  33. Wu, X.L., Jiang, P., Chen, L., Zhang, J.F., Yuan, F.P. and Zhu, Y.T. (2014), "Synergetic strengthening by gradient structureˮ, Mater. Res. Lett., 2(1), 185-191. https://doi.org/10.1080/21663831.2014.935821.