Advances in materials Research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Continuously inhomogeneous beam with longitudinal vertical cracks: an analytical investigation

  • Rizov, Victor I. (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy)
  • Received : 2020.08.03
  • Accepted : 2021.03.27
  • Published : 2021.06.25
⟨ Previous Next ⟩

Abstract

The present paper is concerned with fracture analysis of an inhomogeneous beam with three longitudinal vertical parallel cracks. The three cracks are located symmetrically with respect to the mid-span. A notch is cut-out in the lateral surface of the beam in the mid-span. Only half of the beam is considered due to the symmetry. The material is continuously inhomogeneous in the width direction of the beam. Besides, the material exhibits non-linear elastic mechanical behavior. The three cracks are located arbitrary in the width direction so as the cross-sections of the four crack arms have different width. The longitudinal fracture behavior is studied in terms of the strain energy release rate. Three solutions to the strain energy release rate are derived by differentiating the complementary strain energy with respect to the areas of the three cracks. The strain energy release rate is determined also by analyzing the balance of the energy for verification. Further verifications are carried-out by applying the J-integral approach. The influences of the locations of the three cracks, the material inhomogeneity and the beam geometry on the longitudinal fracture behavior are appraised. Results of analyses of a beam that is continuously inhomogeneous in both width and length directions are also presented.

Keywords

References

  1. Al-Khanbashi, A. and Hamdy, A.E. (2004), "Fracture mechanics approach to predict delamination lifetime in Mode II under constant loads", J. Adhes. Sci. Technol., 18, 227-242. https://doi.org/10.1163/156856104772759430
  2. Broek, D. (1986), Elementary Engineering Fracture Mechanics, Springer.
  3. Butcher, R.J., Rousseau, C.E. and Tippur, H.V. (1998), "A functionally graded particulate composite: Measurements and Failure Analysis", Acta. Mater., 47(1), 259-268. https://doi.org/10.1016/S1359-6454(98)00305-X
  4. Dolgov, N.A. (2002), "Effect of the elastic modulus of a coating on the serviceability of the substrate-coating system", Strength Mater., 34(2), 153-157. https://doi.org/10.1007/s11223-005-0053-7
  5. 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
  6. 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
  7. Gasik, M.M. (2010), "Functionally graded materials: bulk processing techniques", Int. J. Mater. Product Technol., 39(1-2), 20-29. https://doi.org/10.1504/IJMPT.2010.034257
  8. 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
  9. Her, S.C. and Su, W.B. (2015), "Interfacial fracture toughness of multilayered composite structures", Strength Mater., 47(1), 186-191. https://doi.org/10.1007/s11223-015-9646-y
  10. Klingbeil, N.W. and Beuth, J.I. (1997), "Interfacial fracture testing of deposited metal layers under fourpoint bending", Eng. Fract. Mech., 56, 113-126. https://doi.org/10.1016/S0013-7944(96)00109-9
  11. Mahamood, R.M. and Akinlabi, E.T. (2017), Functionally Graded Materials, Springer.
  12. Markworth, A.J., Ramesh, K.S. and Parks, W.P. (1995), "Review: modeling studies applied to functionally graded materials", J. Mater. Sci., 30(3), 2183-2193. https://doi.org/10.1007/BF01184560
  13. 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.
  14. 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. Applicat., 2(5), 1708-1718. https://doi.org/10.4236/msa.2011.212228
  15. Popov, E.P. (1998), Engineering Mechanics of Solids, Pearson.
  16. Rizov, V.I. (2016), "Elastic-plastic fracture of functionally graded circular shafts in torsion", Adv. Mater. Res., Int. J., 5(4), 299-318. https://doi.org/10.12989/amr.2016.5.4.299
  17. 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/IGF-SIS.41.61
  18. 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, 158-177. https://doi.org/10.3221/IGF-ESIS.46.16
  19. 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
  20. Rizov, V.I. (2020), "Longitudinal fracture analysis of inhomogeneous beams with continuously changing radius of cross-section along the beam length", Strength Fract. Complex.: Int. J., 13, 31-43. https://doi.org/10.3233/SFC-200250
  21. 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
  22. Rudih, O.L., Sokolov, G.P. and Pahomov, V.L. (1998), "Introduction to non-linear structural mechanics", IASV, Moscow, Russia.
  23. Simsek, M. (2012), "Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods", Computat. Mater. Sci., 61, 257-265. https://doi.org/10.1016/j.commatsci.2012.04.001
  24. Simsek, M. (2015), "Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions", Compos. Struct., 133, 968-978. https://doi.org/10.1016/j.compstruct.2015.08.021
  25. Simsek, M., Kocaturk, T. and Akbas, D. (2013), "Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory", Compos. Struct., 95, 740-747. https://doi.org/10.1016/j.compstruct.2012.08.036
  26. Tilbrook, M.T., Moon, R.J. and Hoffman, M. (2005), "Crack propagation in graded composites", Compos. Sci. Technol., 65(2), 201-220. https://doi.org/10.1016/j.compscitech.2004.07.004
  27. Tokovyy, Y. (2019), "Solutions of axisymmetric problems of elasticity and thermoelasticity for an inhomogeneous space and a half space", J. Mathe. Sci., 240(1), 86-97. https://doi.org/10.1007/s10958-019-04337-3
  28. Tokovyy, Y. and Ma, C.C. (2008), "Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders", J. Eng. Math., 61(3), 171-184. https://doi.org/10.1007/s10665-007-9154-6
  29. Tokovyy, Y. and Ma, C.C. (2013), "Three-dimensional temperature and thermal stress analysis of an inhomogeneous layer", J. Thermal Stress., 36(2), 790-808. https://doi.org/10.1080/01495739.2013.787853
  30. 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
  31. 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
  32. Wu, X.L., Jiang, P., Chen, L., Zhang, J.F., Yuan, F.P. and Zhu, Y.T. (2014), "Synergetic strengthening by gradient structure", Mater. Res. Lett., 2(1), 185-191. https://doi.org/10.1080/21663831.2014.935821
  33. Yokozeki, T, Ogasawara, T. and Aoki, T. (2008), "Correction method for evaluation of interfacial fracture toughness of DCB, ENF and MMB specimens with residual thermal stresses", Compos. Sci. Technol., 68, 760-767. https://doi.org/10.1016/j.compscitech.2007.08.025