DOI QR코드

DOI QR Code

Fracture analysis of functionally graded beams with considering material non-linearity

  • Rizov, Victor I. (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy)
  • Received : 2016.08.02
  • Accepted : 2017.08.04
  • Published : 2017.11.25

Abstract

The present paper deals with a theoretical study of delamination fracture in the Crack Lap Shear (CLS) functionally graded beam configuration. The basic purpose is to analyze the fracture with taking into account the material non-linearity. The mechanical behavior of CLS was described by using a non-linear stress-strain relation. It was assumed that the material is functionally graded along the beam height. The fracture was analyzed by applying the J-integral approach. The curvature and neutral axis coordinate of CLS beam were derived in order to solve analytically the J-integral. The non-linear solution of J-integral obtained was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, crack location along the beam height and material non-linearity on fracture behavior were evaluated. The J-integral non-linear solution derived is very suitable for parametric studies of longitudinal fracture in the CLS beam. The results obtained can be used to optimize the functionally graded beam structure with respect to the fracture performance. The analytical approach developed in the present paper contributes for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.

Acknowledgement

Supported by : UACEG

References

  1. Anlas, G., Santare, M.H. and Lambros, J. (2000), "Numerical calculation of stress intensity factors in functionally graded materials", Int. J. Fract., 104(1), 131-143. https://doi.org/10.1023/A:1007652711735
  2. Bohidar, S.K., Sharma, R. and Mishra, P.R. (2014), "Functionally graded materials: A critical review", Int. J. Res., 1(7), 289-301.
  3. 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
  4. Chakrabarty, J. (2006), Theory of Plasticity, Elsevier Butterworth-Heinemann, Oxford.
  5. Dolgov, N.A. (2005), "Determination of stresses in a two-layer coating", Streng. Mater., 37, 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", Streng. Mater., 48, 658-667. https://doi.org/10.1007/s11223-016-9809-5
  7. Erdogan, F. (1995), "Fracture mechanics of functionally graded materials", Compos. Eng., 5(7), 753-770. https://doi.org/10.1016/0961-9526(95)00029-M
  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. Gu. P. and Asaro, R.J. (1997), "Cracks in functionally graded materials", Int. J. Solid. Struct., 34(1), 1-17. https://doi.org/10.1016/0020-7683(95)00289-8
  10. 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
  11. Hutchinson, W. and Suo, Z. (1992), "Mixed mode cracking in layered materials", Adv. Appl. Mech., 64(1), 804-810.
  12. Koizumi, M. (1993), "The concept of FGM ceramic trans", Function. Grad. Mater., 34(1), 3-10.
  13. 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
  14. Lubliner, J. (2006), Plasticity Theory, Revised Edition, University of California, Berkeley, CA.
  15. 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
  16. 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
  17. 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.
  18. Neubrand, A. and Rodel, J. (1997), "Gradient materials: An overview of a novel concept", Zeitschrift fur Metallkunde, 88(4), 358-371.
  19. Niino, M., Hirai, T. and Wanatabe, R. (1987), "The functionally gradient materials", J. Jpn. Soc. Compos. Mater., 13(1), 257. https://doi.org/10.6089/jscm.13.257
  20. Parvanova, S.L., Dineva, P.S. and Manolis, G.D. (2013), "Dynamic behavior of a finite-sized elastic solid with multiple cavities and inclusions using BIEM", Acta Mech., 224, 597-618. https://doi.org/10.1007/s00707-012-0759-0
  21. Parvanova, S.L., Dineva, P.S., Manolis, G.D. and Kochev, P.N. (2014), "Dynamic response of a solid with multiple inclusions under anti-plane strain conditions by the BEM", Comput. Struct., 139, 65-83. https://doi.org/10.1016/j.compstruc.2014.04.002
  22. 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
  23. Petrov, V.V. (2014), Non-linear Incremental Structural Mechanics, M., Infra-Injeneria.
  24. Suresh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Materials, IOM Communications Ltd., London.
  25. Szekrenyes, A. (2012), "J-integral for delaminated beam and plate models", Periodica Polytechnica, Mech. Eng., 56(1), 63-71. https://doi.org/10.3311/pp.me.2012-1.10
  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. 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
  28. 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