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Theoretical analysis of tensile stresses and displacement in orthotropic circular column under diametrical compression

  • Received : 2010.06.18
  • Accepted : 2011.01.03
  • Published : 2011.05.10

Abstract

This paper shows the solution for an orthotropic disk under the plane strain condition obtained with complex stress functions. These stress functions were induced by Lekhnitskii and expanded by one of the authors. Regarding diametrical compression test, the finite element method poses difficulties in representing the concentrated force because the specimens must be divided into finite elements during calculation. On the other hand, the method shown in this study can exactly represent this force. Some numerical results are shown and compared with those obtained under the plane stress condition for both stress and displacement. This comparison shows that the differences between the tensile stresses occurred under the plane strain condition and also that the differences under a plane stress condition increase as the orthotropy ratio increases for some cases.

Keywords

References

  1. Cai, M. and Kaiser, P.K. (2004), "Numerical simulation of the Brazilian test and the tensile strength of anisotropic rocks and rocks with pre-existing cracks", Int. J. Rock Mech. Min., 41, 450-451. https://doi.org/10.1016/j.ijrmms.2003.12.111
  2. Cauweleart, F.V. and Eckmann, B. (1994), "Indirect tensile test applied to anisotropic materials", Mater. Struct., 27, 54-60. https://doi.org/10.1007/BF02472820
  3. Chen, C.S., Pan, E. and Amadei, B. (1998), "Determination of deformability and tensile strength of anisotropic rock using brazilian tests", Int. J. Rock Mech. Min., 35, 43-61. https://doi.org/10.1016/S0148-9062(97)00329-X
  4. Claesson, J. and Bohloli, B. (2002), "Brazilian test: stress field and tensile strength of anisotropic rocks using an analytical solution", Int. J. Rock Mech. Min., 39, 991-1004. https://doi.org/10.1016/S1365-1609(02)00099-0
  5. Exadaktylos, G.E. and Kaklis, K.N. (2001), "Applications of an explicit solution for the transversely isotropic circular disc compressed diametrically", Int. J. Rock Mech. Min., 38, 227-243. https://doi.org/10.1016/S1365-1609(00)00072-1
  6. Exadaktylos, G.E. (2001), "On the constraints and relations of elastic constants of transversely isotropic geomaterials", Int. J. Rock Mech. Min., 38, 941-956. https://doi.org/10.1016/S1365-1609(01)00063-6
  7. Jianhon, Y., Wu, F.Q. and Sun, J.Z. (2009), "Estimation of the tensile elastic modulus using Brazilian disc by applying diametrically opposed concentrated loads", Int. J. Rock Mech. Min., 46, 568-576. https://doi.org/10.1016/j.ijrmms.2008.08.004
  8. Kawakubo, S., Tsutsumi, T. and Hirashima, K. (1996), "Stress and displacement fields for an anisotropic elliptical disk subjected to arbitrary loads at boundary", Trans. JSME Series A, 62, 1626-1633. (in Japanese)
  9. Lavrov, A. and Vervoort, A. (2002), "Theoretical treatment of tangential loading effects on the Brazilian test stress distribution", Int. J. Rock Mech. Min., 39, 275-283. https://doi.org/10.1016/S1365-1609(02)00010-2
  10. Lekhnitskii, S.G. (1968), Anisotropic Plate, Gordon & Breach, New York.
  11. Lemmon, R.K. and Blackketter, D.M. (1996), "Stress analysis of an orthotropic material under diametral compression", Exp. Mech., 36, 204-211. https://doi.org/10.1007/BF02318008
  12. Markides, C.F., Pazis, D.N. and Kourkoulis, S.K. (2010), "Closed full-field solution for stresses and displacements in Brazilian disk under distributed radial load", Int. J. Rock Mech. Min., 47, 227-237. https://doi.org/10.1016/j.ijrmms.2009.11.006
  13. Sokolnikoff, I.S. (1956), Mathematical Theory of Elasticity, McGraw-Hill, New York.
  14. Tavallali, A. and Vervoort, A. (2010), "Effect of layer orientation on the failure of layered sandstone under Brazilian test conditions", Int. J. Rock Mech. Min., 47, 313-322. https://doi.org/10.1016/j.ijrmms.2010.01.001
  15. Timoshenko, S.P and Goodier, J.N. (1970), Theory of Elasticity, McGraw-Hill, New York.
  16. Tsutsumi, T. and Hirashima, K. (2000), "Analysis of orthotropic circular disks and rings under diametrical loading", Struct. Eng. Mech., 9(1), 37-50. https://doi.org/10.12989/sem.2000.9.1.037