Structural Engineering and Mechanics

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Examination of contact problem between functionally graded punch and functionally graded layer resting on elastic plane

  • Polat, Alper (Munzur University, Department of Civil Engineering)
  • Received : 2020.04.15
  • Accepted : 2021.01.29
  • Published : 2021.04.25
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Abstract

In this study, continuous contact problem in the functionally graded (FG) layer loaded with a FG flat punch resting on the elastic semi-infinite plane was analyzed by the finite element method (FEM). It was assumed that the shear modulus and density of the layer and punch varied according to exponentially throughout their depth. FG layer's weight was included to the problem and additionally all surfaces were considered as frictionless. Analysis of FG materials was performed with a special macro which was added to the ANSYS program. Firstly, the shear modulus of the punch was considered to be very rigid and the results of initial separation load (λcr) and distance (xcr) were compared with the analytical solution. Afterwards, results obtained from the contact analysis made according to the inhomogeneity parameters (β, γ) between FG punch-FG layer which had been unprecedented in the literature were discussed. As a result, FG punch's stress values at the punch edges where stress accumulations occurred were found to be smaller than the rigid punch. The security of the structure, longer life of the material and ease of production are directly related to the reduction of the stress values. The results obtained in this study are important in this respect. Also this work is the first study that investigates the effect of FG punch on the FG layer.

Keywords

References

  1. Abhilash, M.N. and Murthy, H. (2014), "Finite element analysis of 2-D elastic contacts involving FGMs", Int. J. Comput. Meth. Eng. Sci. Mech., 15(3), 253-7. https://doi.org/10.1080/15502287.2014.882445.
  2. Adams, G.G. and Bogy, D.B. (1976), "The plane solution for the elastic contact problem of a semi-infinite strip and half plane", J. Appl. Mech., 43(4), 603-607. https://doi.org/10.1115/1.3423940.
  3. Adiyaman, G., Yaylaci, M. and Birinci, A. (2015), "Analytical and finite element solution of a receding contact problem", Struct. Eng. Mech., 54(1), 69-85. https://doi.org/10.12989/sem.2015.54.1.069.
  4. ANSYS (2015), Swanson Analysis Systems Inc., Houston PA, USA.
  5. Balci, M.N. (2020), "The effect of punch speed on frictional contact mechanics of finite-thickness graded layer resting on the rigid foundation", J. Brazil. Soc. Mech. Sci., 42, 343. https://doi.org/10.1007/s40430-020-02406-2.
  6. Comez, I. (2019), "Continuous and discontinuous contact problem of a functionally graded layer pressed by a rigid cylindrical punch", Eur. J. Mech. A-Solid., 73, 437-448. https://doi.org/10.1016/j.euromechsol.2018.10.009.
  7. El-Borgi, S., Abdelmoula, R. and Keer, L. (2006), "A receding contact plane problem between a functionally graded layer and a homogeneous substrate", Int. J. Solid. Struct., 43, 658-674. https://doi.org/10.1016/j.ijsolstr.2005.04.017.
  8. El-Borgi, S., Usman, S. and Guler, M.A. (2014), "A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate", Int. J. Solid. Struct., 51, 4462-4476. https://doi.org/10.1016/j.ijsolstr.2014.09.017.
  9. Elloumi, R., Kallel-Kamoun, I. and El-Borgi, S. (2010), "A fully coupled partial slip contact problem in a graded half-plane", Mech. Mater., 42, 417-428. https://doi.org/10.1016/j.mechmat.2010.01.002.
  10. Gecit, M.R. (1986), "Axisymmetric contact problem for a semi infinite cylinder and a half space", Int. J. Eng. Sci., 24(8), 1245-1256. https://doi.org/10.1016/0020-7225(86)90054-6.
  11. Giannakopoulos, A. adn Pallot, P. (2000), "Two-dimensional contact analysis of elastic graded materials", J. Mech. Phys. Solid., 48, 1597-1631. https://doi.org/10.1016/S0022-5096(99)00068-X.
  12. Giannakopoulos, A. and Suresh, S. (1997), "Indentation of solids with gradients in elastic properties: Part ii. axisymetric indenters", Int. J. Solid. Struct., 34(19), 2393-2428. https://doi.org/10.1016/S0020-7683(96)00172-2.
  13. Guler, M.A., Kucuksucu, A., Yilmaz, K.B. and Yildirim, B. (2017), "On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium", Int. J. Mech. Sci., 120, 12-29. https://doi.org/10.1016/j.ijmecsci.2016.11.004.
  14. Gun, H. and Gao, X.W. (2014), "Analysis of frictional contact problems for functionally graded materials using BEM", Eng. Anal. Bound. Elem., 38, 1-7. https://doi.org/10.1016/j.enganabound.2013.10.004.
  15. Karabulut, P.M., Adiyaman, G. and Birinci, A. (2017), "A receding contact problem of a layer resting on a half plane", Struct. Eng. Mech., 64(4), 505-513. https://doi.org/10.12989/sem.2017.64.4.505.
  16. Kaya, Y., Polat, A. and Ozsahin, T.S. (2018), "Comparison of FEM solution with analytical solution of continuous and discontinuous contact problem", Sigma J. Eng. Nat. Sci., 36(4), 977-992.
  17. Kaya, Y., Polat, A. and Ozsahin, T.S. (2020), "Analytical and finite element solutions of continuous contact problem in functionally graded layer", Eur. Phys. J. Plus, 135(1), 1-21. https://doi.org/10.1140/epjp/s13360-020-00138-9.
  18. Liu, T.J., Zhang, C., Swang, Y. and Xing, Y.M. (2016), "The axisymmetric stress analysis of double contact problem for functionally graded materials layer with arbitrary graded materials properties", Int. J. Solid. Struct., 96, 229-239. https://doi.org/10.1016/j.ijsolstr.2016.06.006.
  19. Oner, E., Adiyaman, G. and Birinci, A. (2017), "A continuous contact problem of a functionally graded layer resting on an elastic half-plane", Arch. Mech., 69(1), 53-73. https://doi.org/10.24423/aom.2465.
  20. Oner, E., Yaylaci, M. and Birinci, A. (2015), "Analytical solution of a contact problem and comparison with the results from FEM", Struct. Eng. Mech., 54(4), 607-622. https://doi.org/10.12989/sem.2015.54.4.000
  21. Ozsahin, T.S. (2007), "Frictionless contact problem for a layer on an elastic half plane loaded by means of two dissimilar rigid punches", Struct. Eng. Mech., 25(4), 383-403. 10.12989/SEM.2007.25.4.383.
  22. Polat, A. (2019), "Investigation of the frictionless contact problem in a rigidly supported homogeneous layer by using FEM", Gumushane Universitesi Fen Bilimleri Enstitusu Dergisi, 9(4), 797-807.
  23. Polat, A., Kaya, Y. and Ozsahin, T.S. (2018), "Analytical solution to continuous contact problem for a functionally graded layer loaded throughtwo dissimilar rigid punches", Meccanica, 53(14), 3565-3577. https://doi.org/10.1007/s11012-018-0902-7.
  24. Polat, A., Kaya, Y., Bora, P., Kouider, B. and Ozsahin, T.S. (2019), "Investigation of the contact problem for a partial functionally graded layer by using finite element method", J. Struct. Eng. Appl. Mech., 1(4), 185-193. https://doi.org/10.31462/jseam.2019.01185193.
  25. Polat, A., Kaya, Y., Kouider, B. and Ozsahin, T.S. (2019), "Frictionless contact problem for a functionally graded layer loaded through two rigid punches using finite element method", J. Mech., 35(5), 591-600. https://doi.org/10.31462/jseam.2019.01185193.
  26. Schwarzer, N., Djabella, H., Richter, F. and Arnell, R.D. (1995), "Comparison between analytical and FEM calculations for the contact problem of spherical indenters on layered materials", Thin Solid Film., 270, 279-282. https://doi.org/10.1016/0040-6090(95)06922-4.
  27. Turan, M., Adiyaman, G., Kahya, V. and Birinci, A. (2016), "Axisymmetric analysis of a functionally graded layer resting on elastic substrate", Struct. Eng. Mech., 58(3), 423-442. https://doi.org/10.12989/sem.2016.58.3.423.
  28. Yan, J. and Li, X. (2015), "Double receding contact plane problem between a functionally gradedlayer and an elastic layer", Eur. J. Mech. A/Solid., 53, 143-150. https://doi.org/10.1016/j.euromechsol.2015.04.001.
  29. Yaylaci, M. and Birinci, A. (2013), "The receding contact problem of two elastic layers supported by two elastic quarter planes", Struct. Eng. Mech., 48(2), 241-255. https://doi.org/10.12989/sem.2013.48.2.241.
  30. Yaylaci, M., Adiyaman, G., Oner, E. and Birinci, A. (2020), "Examination of analytical and finite element solutions regarding contact of a functionally graded layer", Struct. Eng. Mech., 76(3), 325-336. https://doi.org/10.12989/sem.2020.76.3.325.
  31. Yaylaci, M., Oner, E. and Birinci, A. (2014), "Comparison between analytical and ANSYS calculations for a receding contact problem", J. Eng. Mech., 140(9). https://doi.org/10.1061/(asce)em.1943-7889.0000781.
  32. Yilmaz, K.B., Comez, I., Guler, M.A. and Yildirim, B. (2019), "Analytical and finite element solution of the sliding frictional contact problem for a homogeneous orthotropic coating-isotropic substrate system", Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik, 99, 1-17. https://doi.org/10.1002/zamm.201800117.