DOI QR코드

DOI QR Code

On the analysis of longitudinal fracture in functionally graded rods performing non-uniform rotational movement

  • Victor I. Rizov (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy)
  • 투고 : 2024.11.06
  • 심사 : 2025.01.02
  • 발행 : 2025.12.25

초록

Various components of mechanisms and devices that are extensively used in a variety of aerospace and aeronautical applications frequently perform different kinds of movement with acceleration. According to D'Alembert's principle, the acceleration induces forces of inertia that have to be taken into account when analyzing various problems in the area of strength, fracture, stability, durability, reliability, etc. of components of load-bearing engineering structures, machines, mechanisms and devices. Having in mind that functionally graded materials are widely applied for manufacturing of high performance structures in modern aerospace industry, analyzing fracture behaviour of functionally graded structural members represents a problem of the present day. The goal of this paper is to analyze longitudinal fracture in functionally graded rods which perform non-uniform rotational movement around a pinned support. Non-linear viscoelastic rods that are functionally graded along the thickness and length are considered. The problem of determination of the strain energy release rate (SERR) in rods with a longitudinal crack under the action of distributed forces of inertia induced by the normal and tangential acceleration is treated generally (in essence, this is a dynamic problem). The distribution of the forces of inertia in the rod is analyzed. An application of the general approach for solving a particular problem is presented. The solution is confirmed by the integral J. The influence of various parameters of the model is studied. For instance, the influence of the ratio of the values of material parameters on the upper and lower surface of the rotating beam on the SERR is studied in detail. It is found that the SERR is very sensitive with respect to these ratios. A practical application of the solution for determining the boundary value of the parameter involved in the rotation law and the boundary crack length is presented.

키워드

참고문헌

  1. Akbaş, Ş.D., Ersoy, H., Akgöz, B. and Civalek, Ö . (2021), "Dynamic analysis of a fiber-reinforced composite beam under a moving load by the Ritz methodˮ, Math., 9(9), 1048. https://doi.org/10.3390/math9091048.
  2. Amara, K., Bouazza, M. and Fouad, B. (2016), "Postbuckling analysis of functionally graded beams using nonlinear modelˮ, Periodica Polytechnica Mech. Eng., 60(2), 121-128. https://doi.org/10.3311/PPme.8854.
  3. Atmane, H.A., Bedia, E.A.A., Bouazza, M., Tounsi, A. and Fekrar, A. (2016), "On the thermal buckling of simply supported rectangular plates made of a sigmoid functionally graded Al/Al2O3 based material", Mech. Solid., 51, 177-187. https://doi.org/10.3103/S0025654416020059.
  4. Bouazza, M. and Zenkour, A.M. (2020), "Vibration of carbon nanotube-reinforced plates via refined nth higher-order theoryˮ, Arch. Appl. Mech., 90, 1755-1769. https://doi.org/10.1007/s00419-020-01694-3.
  5. Bouazza, M., Zenkour, A.M. and Benseddiq, N. (2018), "Effect of material composition on bending analysis of FG plates via a two-variable refined hyperbolic theory", Arch. Mech., 70(2), 1-23.
  6. Broek, D. (1986), Elementary Engineering Fracture Mechanics, Springer.
  7. Civalek, Ö ., Akbas, S.D., Akgöz, B. and Dastjerdi, S. (2021), "Forced vibration analysis of composite beams reinforced by carbon nanotubesˮ, Nanomater., 11, 571. https://doi.org/10.3390/nano 11030571.
  8. Dastjerdi, S., Akgöz, B., Civalek, Ö ., Malikan, M. and Eremeyev, V.A. (2020), "On the non-linear dynamics of torus-shaped and cylindrical shell structuresˮ, Int. J. Eng. Sci., 156, 103371. https://doi.org/10.1016/j.ijengsci.2020.103371.
  9. Derbale, A., Bouazza, M. and Benseddiq, N. (2021), "Analysis of the mechanical and thermal buckling of laminated beams by new refined shear deformation theoryˮ, Iran. J. Sci. Technol. Trans. Civil Eng., 45, 89-98. https://doi.org/10.1007/s40996-020-00417-6.
  10. 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.
  11. 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.
  12. Dowling, N.E. (2013), Mechanical Behaviour of Materials, Person.
  13. El-Galy, I.M., Saleh, B.I. and Ahmed, M.H. (2019), "Functionally graded materials classifications and development trends from industrial point of viewˮ, SN Appl. Sci., 1, 1378. https://doi.org/10.1007/s42452- 019-1413-4.
  14. Ellali, M., Alazwari, M.A., Bouazza, M., Eltaher, M.E. and Benseddiq, N. (2024), "Effects of changing materials properties for vibration of FGM beam using integral shear deformation model ,ˮ Couple. Syst. Mech., 13, 277-291. https://doi.org/10.12989/csm.2024.13.4.277.
  15. Ellali, M., Amara, K. and Bouazza, M. (2024), "Thermal buckling of porous FGM plate integrated surface bonded piezoelectricˮ, Couple. Syst. Mech., 13(2), 171-186. https://doi.org/10.12989/csm.2024.13.2.171.
  16. Ellali, M., Bouazza, M. and Amara, K. (2022), "Thermal buckling of a sandwich beam attached with piezoelectric layers via the shear deformation theoryˮ, Arch. Appl. Mech., 92, 657-665. https://doi.org/10.1007/s00419-021-02094-x.
  17. Ellali, M., Bouazza, M. and Zenkour, A.M. (2022), "Impact of micromechanical approaches on wave propagation of FG plates via indeterminate integral variables with a hyperbolic secant shear model", Int. J. Comput. Meth., 19(9), 2250019. https://doi.org/10.1142/S0219876222500190.
  18. Ellali, M., Bouazza, M. and Zenkour, A.M. (2023), "Wave propagation of FGM plate via new integral inverse cotangential shear model with temperature-dependent material propertiesˮ, Geomech. Eng., 33, 427-437. https://doi.org/10.12989/gae.2023.33.5.427.
  19. Ellali, M., Bouazza, M. and Zenkour, A.M. (2024), "Hygrothermal vibration of FG nanobeam via nonlocal unknown integral variables secant-tangential shear deformation coupled theory with temperature dependent material propertiesˮ, Eur. J. Mech.-A/Solid., 105, 105243. https://doi.org/10.1016/j.euromechsol.2024.105243.
  20. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshellsˮ, Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
  21. 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.
  22. 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.
  23. Mahamood, R.M. and Akinlabi, E.T. (2017), Functionally Graded Materials, Springer.
  24. 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.
  25. 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.
  26. 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.
  27. Rizov, V.I. (2020), "Analysis of two lengthwise cracks in a viscoelastic inhomogeneous beam structureˮ, Eng. Trans., 68, 397-415. https://doi.org/10.24423/EngTrans.1214.20201125.
  28. Rizov, V.I. (2022), "Effects of periodic loading on longitudinal fracture in viscoelastic functionally graded beam structuresˮ, J. Appl. Comput. Mech., 8(1), 370-378. https://doi.org/10.22055/JACM.2021.37953.3141.
  29. Rizov, V.I. (2024), "The effect of delamination between layers in U-shaped members made of functionally graded multilayered viscoelastic materialsˮ, J. Appl. Comput. Mech., 10, 830-841. https://doi.org/10.22055/jacm.2024.46014.4449.
  30. Rizov, V.I. and Altenbach, H. (2019), "Application of the classical beam theory for studying lengthwise fracture of functionally graded beamsˮ, Technische Mechanik, 39(2), 229-240. https://doi.org/10.24352/UB.OVGU-2019-021.
  31. Rizov, V.I. and Altenbach, H. (2019), "On the analysis of lengthwise fracture of functionally graded round barsˮ, Struct. Integr. Life, 19(2), 102-108.
  32. Rizov, V.I. and Altenbach, H. (2022), "Multilayered non-linear viscoelastic beams subjected to torsion at a constant speed: a delamination analysisˮ, Eng. Ttrans., 70(1), 53-66. https://doi.org/10.24423/EngTrans.1720.20220303.
  33. Saiyathibrahim, A., Subramaniyan, R. and Dhanapl, P. (2016), "Centrefugally cast functionally graded materials-reviewˮ, International Conference on Systems, Science, Control, Communications, Engineering and Technology, 68-73.
  34. 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.
  35. Tokovyy, Y. (2019), "Solutions of axisymmetric problems of elasticity and thermoelasticity for an inhomogeneous space and a half spaceˮ, J. Math. Sci., 240(1), 86-97. https://doi.org/10.1007/s10958-019- 04337-3.
  36. Tokovyy, Y. and Ma, C.C. (2017), "Three-dimensional elastic analysis of transversely-isotropic compositesˮ, J. Mech., 33(6), 821-830. https://doi.org/10.1017/jmech.2017.91.
  37. Tokovyy, Y. and Ma, C.C. (2019), "Elastic analysis of inhomogeneous solids: History and development in briefˮ, J. Mech., 18 (1), 1-14. https://doi.org/10.1017/jmech.2018.57.
  38. Tokovyy, Y. and Ma, C.C. (2021), The Direct Integration Method for Elastic Analysis of Nonhomogeneous Solids, Cambridge Scholars Publishing.
  39. Tokovyy, Y.V. (2023), "Elastic and thermoelastic response of multilayer inhomogeneous hollow cylindersˮ, Mech. Adv. Mater. Struct., 31(17), 3889-3901. https://doi.org/10.1080/15376494.2023.2186548.
  40. Toudehdehghan, J., Lim, W., Foo1, K.E., Ma'arof, M.I.N. and Mathews, J. (2017), "A brief review of functionally graded materialsˮ, MATEC Web Conf., 131, 03010. https://doi.org/10.1051/matecconf/201713103010UTP-UMP.
  41. Varbanov, Chr., Tepavicharov, A. and Ganev, T. (1992), Applied Theory of Elasticity and Plasticity, Technique.
  42. Yildirim, A. and Akgoz, B. (2024), "Buckling behavior of nickel microbeams based on reformulated strain gradient theory",Appl. Phys. A. 130, 832. https://dci.org/101007/s00339-02408013-5. 101007/s00339-02408013-5