Coupled systems mechanics

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Non-linear longitudinal fracture in a functionally graded beam

  • Rizov, Victor I. (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy)
  • Received : 2017.08.21
  • Accepted : 2018.02.05
  • Published : 2018.08.25
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Abstract

Longitudinal fracture in a functionally graded beam configuration was studied analytically with taking into account the non-linear behavior of the material. A cantilever beam with two longitudinal cracks located symmetrically with respect to the centroid was analyzed. The material was functionally graded along the beam width as well as along the beam length. The fracture was studied in terms of the strain energy release rate. The influence of material gradient, crack location along the beam width, crack length and material non-linearity on the fracture behavior was investigated. It was shown that the analytical solution derived is very useful for parametric analyses of the non-linear longitudinal fracture behavior. It was found that by using appropriate material gradients in width and length directions of the beam, the strain energy release rate can be reduced significantly. Thus, the results obtained in the present paper may be applied for optimization of functionally graded beam structure with respect to the longitudinal fracture performance.

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References

  1. Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  2. Ait Atmane, H., Tounsi, A. and Bernard, F. (2015), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84.
  3. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  4. Bohidar, S.K., Sharma, R. and Mishra, P.R. (2014), "Functionally graded materials: A critical review", Int. J. Res., 1(7), 289-301.
  5. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  6. Brajesh, P. and Goutam, P. (2016), "Nonlinear modelling and dynamic analysis of cracked Timoshenko functionally graded beams based on neutral surface approach", J. Mech. Eng. Sci., 230(9), 1468-1497.
  7. Broek, D. (1986), Elementary Engineering Fracture Mechanics, Springer.
  8. Carpinteri, A. and Pugno, N. (2006), "Cracks in re-entrant corners in functionally graded materials", Eng. Fract. Mech., 73(6), 1279-1291. https://doi.org/10.1016/j.engfracmech.2006.01.008
  9. Chakrabarty, J. (2006), Theory of Plasticity, Elsevier Butterworth-Heinemann, Oxford.
  10. Ebrahimi, F. and Barati, M.R. (2016a), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  11. Ebrahimi, F. and Barati, M.R. (2016c), "Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  12. Ebrahimi, F. and Barati, M.R. (2016e), "Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams", J. Mech., 33(1), 23-33.
  13. Ebrahimi, F. and Barati, M.R. (2016f), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  14. Ebrahimi, F. and Barati, M.R. (2016d), "Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment", Int. J. Smart Nano Mater., 7(2), 69-90. https://doi.org/10.1080/19475411.2016.1191556
  15. Ebrahimi, F. and Barati, M.R. (2016g), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Braz. Soc. Mech. Sci. Eng., 39(3), 937-952.
  16. Ebrahimi, F. and Farzamandnia, N. (2016), "Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory", Mech. Adv. Mater. Struct., 24(10), 820-829.
  17. Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng.
  18. Ebrahimi, F. and Salari, E. (2015), "A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position", CMES Comput. Model. Eng. Sci., 105(2), 151-181.
  19. Ebrahimi, F. and Shafiei, N. (2016), "Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy's higher-order shear deformation plate theory", Mech. Adv. Mater. Struct., 24(9), 761-772.
  20. Ebrahimi, F. and Barati, M.R. (2016b), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vibr. Contr., 24(3), 549-564.
  21. Ebrahimi, F., Javad, E. and Ramin, B. (2016), "Thermal buckling of FGM nanoplates subjected to linear and nonlinear varying loads on Pasternak foundation", Adv. Mater. Res., 5(4), 245-261. https://doi.org/10.12989/amr.2016.5.4.245
  22. Erdogan, F. (1995), "Fracture mechanics of functionally graded materials", Comp. Eng., 5(7), 753-770. https://doi.org/10.1016/0961-9526(95)00029-M
  23. 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
  24. Hadji, L. (2017), "Analysis of functionally graded plates using a sinusoidal shear deformation theory", Smart Struct. Syst., 19(4), 441-448. https://doi.org/10.12989/sss.2017.19.4.441
  25. Hadji, L., Khelifa, Z., Daouadji, T.H. and Bedia, E.A. (2015), "Static bending and free vibration of FGM beam using an exponential shear deformation theory", Coupled Syst. Mech., 4(1), 99-114. https://doi.org/10.12989/csm.2015.4.1.099
  26. Hadji, L., Zouatnia, N. and Kassoul, A. (2017), "Wave propagation in functionally graded beams using various higher-order shear deformation beams theories", Struct. Eng. Mech., 62(2), 143-149. https://doi.org/10.12989/sem.2017.62.2.143
  27. 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
  28. Koizumi, M. (1993), "The concept of FGM ceramic trans", Function. Grad. Mater., 34(1), 3-10.
  29. Ke, L.L., Yang, J. and Kitiporncha, S. (2009), "Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening, Compos. Struct., 90, 152-160. https://doi.org/10.1016/j.compstruct.2009.03.003
  30. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Semi-analytical analysis for multi-dimensional functionally graded plates: 3-D elasticity solutions", Int. J. Numer. Meth. Eng., 79(3), 25-44. https://doi.org/10.1002/nme.2555
  31. Lubliner, J. (2006), Plasticity Theory, Revised Edition, University of California, Berkeley, California, U.S.A.
  32. Markworth, A.J., Ramesh, K.S. and Parks, J.W.P. (1995), "Review: Modeling studies applied to functionally graded materials", J. Mater. Sci., 30(3), 2183-2193. https://doi.org/10.1007/BF01184560
  33. 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
  34. Naser, S.A.H. and Sami, T.A. (2017), "Transient thermo-mechanical response of a functionally graded beam under the effect of a moving heat source", Adv. Mater. Res., 6(1), 27-43. https://doi.org/10.12989/amr.2017.6.1.027
  35. 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. Scie. Appl., 2(5), 1708-1718.
  36. Neubrand, A. and Rodel, J. (1997), "Gradient materials: An overview of a novel concept", Zeit. f. Met., 88(4), 358-371.
  37. Paulino, G.C. (2002), "Fracture in functionally graded materials", Eng. Fract. Mech., 69(5), 1519-1530. https://doi.org/10.1016/S0013-7944(02)00045-0
  38. Petrov, V.V. (2014), Non-Linear Incremental Structural Mechanics, M.: Infra-Injeneria.
  39. Rizov, V.I. (2017b), "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
  40. Rizov, V.I. (2017a), "Delamination fracture in a functionally graded multilayered beam with material nonlinearity", Arch. Appl. Mech., 87(6), 1037-1048. https://doi.org/10.1007/s00419-017-1229-x
  41. Rizov, V.I. (2017c), "An analytical solution to the strain energy release rate of a crack in functionally graded nonlinear elastic beams", Eur. J. Mech. A/Sol., 65, 301-312. https://doi.org/10.1016/j.euromechsol.2017.04.005
  42. 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
  43. Upadhyay, A.K. and Simha, K.R.Y. (2007), "Equivalent homogeneous variable depth beams for cracked FGM beams; compliance approach", Int. J. Fract., 144(2), 209-213. https://doi.org/10.1007/s10704-007-9089-y
  44. Zhang, H., Li, X.F., Tang, G.J. and Shen, Z.B. (2013), "Stress intensity factors of double cantilever nanobeams via gradient elasticity theory", Eng. Fract. Mech., 105(1), 58-64. https://doi.org/10.1016/j.engfracmech.2013.03.005