Coupled systems mechanics

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Influence of sine material gradients on delamination in multilayered beams

  • Rizov, Victor I. (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy)
  • Received : 2018.02.12
  • Accepted : 2018.12.07
  • Published : 2019.02.25
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Abstract

The present paper deals with delamination fracture analyses of the multilayered functionally graded non-linear elastic Symmetric Split Beam (SSB) configurations. The material is functionally graded in both width and height directions in each layer. It is assumed that the material properties are distributed non-symmetrically with respect to the centroidal axes of the beam cross-section. Sine laws are used to describe the continuous variation of the material properties in the cross-sections of the layers. The delamination fracture is analyzed in terms of the strain energy release rate by considering the balance of the energy. A comparison with the J-integral is performed for verification. The solution derived is used for parametric analyses of the delamination fracture behavior of the multilayered functionally graded SSB in order to evaluate the effects of the sine gradients of the three material properties in the width and height directions of the layers and the location of the crack along the beam width on the strain energy release rate. The solution obtained is valid for two-dimensional functionally graded non-linear elastic SSB configurations which are made of an arbitrary number of lengthwise vertical layers. A delamination crack is located arbitrary between layers. Thus, the two crack arms have different widths. Besides, the layers have individual widths and material properties.

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References

  1. Bensaid, I. and Kerboua, B. (2017), "Interfacial stress analysis of functionally graded beams strengthened with a bonded hydrothermal aged composite panel", Compos. Interf., 24(2), 149-169. https://doi.org/10.1080/09276440.2016.1196333
  2. Bensaid, I., Cheikh, A., Mangouchi, A. and Kerboua, B. (2017), "Static deflection and dynamic behaviour of higher-order hyperbolic shear deformable compositionally graded beams", Adv. Mater. Res., 6(1), 13-26. https://doi.org/10.12989/amr.2017.6.1.013
  3. Bohidar, S.K., Sharma, R. and Mishra, P.R. (2014), "Functionally graded materials: A critical review", Int. J. Res., 1(7), 289-301.
  4. Broek, D. (1986), Elementary Engineering Fracture Mechanics, Springer.
  5. Chakrabarty, J. (2006), Theory of Plasticity, Elsevier Butterworth-Heinemann, Oxford.
  6. Dolgov, N.A. (2005), "Determination of stresses in a two-layer coating", Strength Mater., 37(4), 422-431. https://doi.org/10.1007/s11223-005-0053-7
  7. Dolgov, N.A. (2016), "Analytical methods to determine the stress state in the substrate-coating system under mechanical loads", Strength Mater., 48(5), 658-667. https://doi.org/10.1007/s11223-016-9809-5
  8. 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
  9. Guadette, F.G., Giannapoulos, A.E. and Suresh, S. (2001), "Interfacial cracks in layered materials subjected to a uniform temperature change", Int. J. Fract., 28, 5620-5629.
  10. Hirai, T. and Chen, L. (1999), "Recent and prospective development of functionally graded materials in Japan", Mater. Sci. For., 308-311(4), 509-514.
  11. Hsueh, C.H., Tuan, W.H. and Wei, W.C.J. (2009), "Analyses of steady-state interface fracture of elastic multilayered beams under four-point bending", Script. Mater., 60(8), 721-724. https://doi.org/10.1016/j.scriptamat.2009.01.001
  12. Koizumi, M. (1993), "The concept of FGM ceramic trans", Function. Grad. Mater., 34(1), 3-10.
  13. Lubliner, J. (2006), Plasticity Theory (Revised Edition), University of California, Berkeley, California, U.S.A.
  14. Lukash, P.A. (1998), Fundamentals of Non-Linear Structural Mechanics, Stroizdat.
  15. Markov, I. and Dinev, D. (2005), "Theoretical and experimental investigation of a beam strengthened by bonded composite strip", Reports of International Scientific Conference VSU'2005, 61-68.
  16. 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
  17. Mortensen, A. and Suresh, S. (1995), "Functionally graded metals and metal-ceramic composites: Part 1 processing", Int. Mater. Rev., 40(6), 239-265. https://doi.org/10.1179/imr.1995.40.6.239
  18. Narin, J.A. (2006), "On the calculation of energy release rates for cracked laminates with residual stresses", Int. J. Fract., 139(2), 267-293. https://doi.org/10.1007/s10704-006-0044-0
  19. 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.
  20. Neubrand, A. and Rodel, J. (1997), "Gradient materials: An overview of a novel concept", Zeit. f. Met., 88(4), 358-371.
  21. Rice, J.R. (1968), "A path independent integral and the approximate analysis of strain concentrations by notches and cracks", J. Appl. Mech., 35(2), 379-386. https://doi.org/10.1115/1.3601206
  22. Rizov, V.I. (2017a), "Non-linear analysis of delamination fracture in functionally graded beams", Coupled Syst. Mech., 6(1), 97-111. https://doi.org/10.12989/csm.2017.6.1.097
  23. Rizov, V.I. (2017b), "Non-linear elastic delamination of multilayered functionally graded beam", Multidiscipl. Model. Mater. Struct., 13(4), 434-447. https://doi.org/10.1108/MMMS-10-2016-0054
  24. Rizov, V.I. (2017c), "Delamination of multilayered functionally graded beams with material nonlinearity", Int. J. Struct. Stab. Dyn., 18(4), 1850051.
  25. Rizov, V.I. (2018), "Non-linear fracture analysis of multilayered two-dimensional graded beams", Multidiscipl. Model. Mater. Struct., 14(2), 387-399. https://doi.org/10.1108/MMMS-09-2017-0107
  26. Szekrenyes, A. (2010), "Fracture analysis in the modified split-cantilever beam using the classical theories of strength of materials", J. Phys.: Conf. Ser., 240, 012030.
  27. Szekrenyes, A. (2016a), "Semi-layerwise analysis of laminated plates with nonsingular delamination-the theorem of autocontinuity", Appl. Math. Model., 40(2), 1344-1371. https://doi.org/10.1016/j.apm.2015.06.037
  28. Szekrenyes, A. (2016b), "Nonsingular crack modelling in orthotropic plates by four equivalent single layers", Eur. J. Mech.-A/Sol., 55, 73-99. https://doi.org/10.1016/j.euromechsol.2015.08.005
  29. Uslu Uysal, M. (2017), "Virtual crack closure technique on delamination fracture toughness of composite materials based on epoxy resin filled with micro-scale hard coal", Acta Phys. Polonic. A, In Press.
  30. Uslu Uysal, M. and Guven, U. (2016), "A bonded plate having orthotropic inclusion in adhesive layer under in-plane shear loading", J. Adhes., 92(3), 214-235. https://doi.org/10.1080/00218464.2015.1019064
  31. Uslu Uysal, M. and Kremzer, M. (2015), "Buckling behaviour of short cylindrical functionally gradient polymeric materials", Acta Phys. Polonic. A, 127(4), 1355-1357. https://doi.org/10.12693/APhysPolA.127.1355
  32. Uysal, M. (2016), "Buckling behaviours of functionally graded polymeric thin-walled hemispherical shells", Steel Compos. Struct., 21(4), 849-862. https://doi.org/10.12989/scs.2016.21.4.849