Advances in materials Research

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Elastic-plastic fracture of functionally graded circular shafts in torsion

  • Rizov, Victor I. (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy)
  • Received : 2016.10.15
  • Accepted : 2017.02.08
  • Published : 2016.12.25
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Abstract

Analytical investigations were performed of a longitudinal crack representing a cylindrical surface in circular shafts loaded in torsion with taking into account the non-linear material behavior. Both functionally graded and multilayered shafts were analyzed. It was assumed that the material is functionally graded in radial direction. The mechanical behavior of shafts was modeled by using non-linear constitutive relations between the shear stresses and shear strains. The fracture was studied in terms of the strain energy release rate. Within the framework of small strain approach, the strain energy release rate was derived in a function of the torsion moments in the cross-sections ahead and behind the crack front. The analytical approach developed was applied to study the fracture in a clamped circular shaft. In order to verify the solution derived, the strain energy release rate was determined also by considering the shaft complimentary strain energy. The effects were evaluated of material properties, crack location and material non-linearity on the fracture behavior. The results obtained can be applied for optimization of the shafts structure with respect to the fracture performance. It was shown that the approach developed in the present paper is very useful for studying the longitudinal fracture in circular shafts in torsion with considering the material non-linearity.

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References

  1. Abdelhak, Z., Hadji, L., Daouadji, T. and Bedia, E. (2015), "Thermal buckling of functionally graded plates using an-order four variable refined theory", Adv. Mater. Res., 4(1), 31-44. https://doi.org/10.12989/amr.2015.4.1.31
  2. Ait, Y.S., Ait, A.H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  3. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar, B.O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  4. 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. Brazil. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  5. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  6. Bohidar, S.K., Sharma, R. and Mishra, P.R. (2014), "Functionally graded materials: A critical review", J. Res., 1(7), 289-301.
  7. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on winkler-pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  8. Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  9. 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
  10. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", J. Comput. Methods, 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  11. 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
  12. Chakrabarty, J. (2006), Theory of Plasticity, Elsevier Butterworth-Heinemann, Oxford.
  13. Daouadji, T. and Adim, B. (2016), "Theoretical analysis of composite beams under uniformly distributed load", Adv. Mater. Res., 5(1), 1-9. https://doi.org/10.12989/amr.2016.5.1.001
  14. Daouadji, T., Adim, B. and Benferhat, R. (2016), "Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation", Adv. Mater. Res., 5(1), 35-53. https://doi.org/10.12989/amr.2016.5.1.035
  15. Gasik, M.M. (2010), "Functionally graded materials: Bulk processing techniques", J. Mater. Prod. Technol., 39(1-2), 20-29. https://doi.org/10.1504/IJMPT.2010.034257
  16. Guadette, F.G., Giannapoulos, A.E. and Suresh, S. (2001), "Interfacial cracks in layered materials subjected to a uniform temperature change", J. Fract., 28(1), 5620-5629.
  17. Hadji, L., Khelifa, Z. and Bedia, E.A.A. (2016), "A New higher order shear deformation model for functionally graded beams", KSCE J. Civil Eng., 20(5), 1835-1841. https://doi.org/10.1007/s12205-015-0252-0
  18. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  19. 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
  20. 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", Scripta Mater., 60(1), 721-724. https://doi.org/10.1016/j.scriptamat.2009.01.001
  21. Ivanov, I. and Draganov, I. (2014), "Influence and simulation of laminated glass subjected to low-velocity impact", Mech. Mach., 110, 89-94.
  22. Ivanov, V., Velchev, D.S., Georgiev, N.G., Ivanov, I.D. and Sadowski, T. (2016), "A plate finite element for modelling of triplex laminated glass and comparison with other computational models", Meccanica, 51(2), 341-358. https://doi.org/10.1007/s11012-015-0275-0
  23. Jiao, J., Gurumurthy, G.K., Kramer, E.J., Sha, Y., Hui, C.Y. and Borgesen, P. (1998), "Measurement of interfacial fracture toughness under combined mechanical and thermal stress", J. Electr. Pack., 120(1), 325-349.
  24. Mahi, A., Bedia, E.A.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  25. Markov, I. and Dinev, D. (2005), "Theoretical and experimental investigation of a beam strengthened by bonded composite strip", Proceedings of the International Scientific Conference VSU.
  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 material", Mater. Sci. Appl., 2(5), 1708-1718.
  27. Pei, G. and Asaro, R.J. (1997), "Cracks in functionally graded materials", J. Solids Struct., 34(1), 1-17. https://doi.org/10.1016/0020-7683(95)00289-8
  28. Petrov, V.V. (2014), Non-Linear Incremental Structural Mechanics, M.: Infra-Injeneria.
  29. Rizov, V. and Mladensky, A. (2012), "Crack investigation in bi-layered composite beam of circular cross-section", J. Mater. Sci. Technol., 20(2), 72-83.
  30. Szekrenyes, A. and Vicente, W.M. (2012), "Interlaminar fracture analysis in the GII-GIII plane using prestressed transparent composite beams", Compos. Part A: Appl. Sci. Manufact., 43(1), 95-103. https://doi.org/10.1016/j.compositesa.2011.09.022
  31. Szekrenyes, A. (2010), "Fracture analysis in the modified split-cantilever beam using the classical theories of strength of materials", J. Phys. Conf. Series, 240(1), 012030. https://doi.org/10.1088/1742-6596/240/1/012030
  32. 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
  33. Upadhyay, A.K. and Simha, K.R.Y. (2007), "Equivalent homogeneous variable depth beams for cracked FGM beams; compliance approach", J. Fract., 144(2), 209-213. https://doi.org/10.1007/s10704-007-9089-y
  34. Yeung, D.T.S., Lam, D.C.C. and Yuen, M.M.F. (2000), "Specimen design for mixed mode interfacial fracture properties measurement in electronic packages", J. Electr. Pack., 122(2), 67-72. https://doi.org/10.1115/1.483137
  35. 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

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