PSI- Issue 9

Ch.F. Markides et al. / Procedia Structural Integrity 9 (2018) 108–115 Author name / Structural Integrity Procedia 00 (2018) 000–000

115

8

30

0

-30 Transverse-stress σ θ [MPa] 0.025

0.030

0.035

0.040

0.045

0.050

B A

-60

r [m]

Fig. 5. The distribution of the normal transverse stress along x-axis according to the analytic solution (Markides and Kourkoulis 2018).

where the first term in brackets represents the contribution of bending while the second one that of compression. The average fracture force, for all successful tests of the experimental protocol, was equal to about 1.85 kN. Ac cording to Eq.(21) the specific value corresponds to a critical tensile stress (developed at point A) of about 60.0 MPa. This value is in very good agreement with the tensile strength of the specific PMMA batch, which, according to the preliminary direct tension tests, is equal to about 58.5 MPa. It is thus concluded that the CSR test does indeed provide the tensile strength of the material tested. References Akazawa, S., 1943. Splitting Tensile Test of Cylindrical Specimens. Journal of the Japanese Civil Engineering Institute 6(1), 12–19. ASTM E399 - 90, 1997. Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials - A5. Special Requirements for the Testing of the Arc-Shaped Tension Specimen. Carneiro, F.L.L.B., 1943. A New Method to Determine the Tensile Strength of Concrete. In Proceedings of the 5 th meeting of the Brazilian association for technical rules, 3d. section, 16 September 1943, 126–129 (in Portuguese). Fairhurst, C., 1964. On the Validity of the ‘Brazilian’ Test for Brittle Materials. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 1, 535–546. Golovin, Kh., 1882. A Static Problem of the Elastic Body. Minutes of the Technological Institute, St. Petersburg, 1880-1881, St. Petersburg. Hobbs, D.W., 1964. The Tensile Strength of Rocks. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 1, 385–396. Hudson, J.A., 1969. Tensile Strength and the Ring Test. Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 6(1), 91-97. Kuruppu, M.D., Obara, Y., Ayatollahi, M.R., Chong, K.P., Funatsu, T., 2014. ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular Bend Specimen. Rock Mechanics and Rock Engineering 47(1), 267. Love, A.E.H., 2013. A Treatise on The Mathematical Theory Of Elasticity. Cambridge University Press. Markides, Ch.F., Kourkoulis, S.K., 2018. The Stress Field in a Circular Semi Ring Under Simultaneous Bending and Diametral Compression (submitted). Mellor, M., Hawkes, I., 1971. Measurement of Tensile Strength by Diametral Compression of Discs and Annuli. Engineering Geology 5(3), 173–225. Muskhelishvili, N.I., 1963. Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen. Timpe, A. 1905. Probleme der Spannungsverteilung in Ebenen Systemen, Einfach Gelӧst mit Hilf der Airyschen Function. Zeitschrift für Mathematik und Physik 52, 348-383. Volterra, V., 1907. Sur l' Équilibre des Corps Élastiques Multiplement Connexes. Annales scientifiques de l'École Normale Supérieure. 24, 401–517. Wang, Q.Z., Jia, X.M., Kou, S.Q., Zhang, Z.X., Lindqvist, P.A., 2004. The Flattened Brazilian Disc Specimen Used for Testing Elastic Modulus, Tensile Strength and Fracture Toughness of Brittle Rocks: Analytical and Numerical Results. International Journal of Rock Mechanics and Mining Sciences 41(2), 245-253.