Geomechanics and Engineering

  • 제20권1호
  • /
  • Pages.9-18
  • /
  • 2020
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Measurement of the mixed mode fracture strength of green sandstone using three-point bending specimens

  • Li, Yifan (Department of Mechanical Engineering, University of Bristol) ;
  • Dong, Shiming (College of Architecture and Environment, Sichuan University) ;
  • Pavier, Martyn J. (Department of Mechanical Engineering, University of Bristol)
  • 투고 : 2019.08.29
  • 심사 : 2019.12.23
  • 발행 : 2020.01.10
⟨ 이전 논문 다음 논문 ⟩

초록

Three-point bending specimens have been used to investigate the mixed mode fracture of green sandstone. Dimensionless stress intensity factors and T-stresses were calculated first by using the finite element method for various crack lengths, crack angles and span to length ratios. It is shown that three-point bending specimens can provide the whole range of mode mixities from pure mode I to pure mode II, provided suitable values are chosen for the crack angle and span to length ratio. The fracture test results were also used to compare with predictions of different criteria. These comparisons show that modified criteria including the influence of the T-stress agree better with experiment than the conventional criteria but that no one criterion matches perfectly the test results.

키워드

참고문헌

  1. Akbardoost, J. and Ayatollahi, M.R. (2014), "Experimental analysis of mixed mode crack propagation in brittle rocks: The effect of non-singular terms", Eng. Fract. Mech., 129, 77-89. http://doi.org/10.1016/j.engfracmech.2014.05.016.
  2. Aliha, M.R.M. and Ayatollahi, M.R. (2011), "Mixed mode I/II brittle fracture evaluation of marble using SCB specimen", Procedia Eng., 10, 311-318. http://doi.org/10.1016/j.proeng.2011.04.054.
  3. Aliha, M.R.M. and Bahmani, A. (2017), "Rock fracture toughness study under mixed mode I/III loading", Rock Mech. Rock Eng., 50(7), 1739-1751. https://doi.org/10.1007/s00603-017-1201-7.
  4. Aliha, M.R.M., Ayatollahi, M.R., Smith, D.J. and Pavier, M.J. (2010), "Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading", Eng. Fract. Mech., 77(11), 2200-2212. http://doi.org/10.1016/j.engfracmech.2010.03.009.
  5. Aliha, M.R.M., Bagherifard, S., Akhondi, Sh., Mousavi, S.S., Mousavi, A. and Parsania, H. (2018), "Fracture and microstructural study of bovine bone under mixed mode I/II loading", Procedia Struct. Integrit., 13, 1488-1493. http://doi.org/10.1016/j.prostr.2018.12.306.
  6. Aliha, M.R.M., Bahmani, A. and Akhondi, S. (2015a), "Numerical analysis of a new mixed mode I/III fracture test specimen", Eng. Fract. Mech., 134, 95-110. https://doi.org/10.1016/j.engfracmech.2014.12.010.
  7. Aliha, M.R.M., Bahmani, A. and Akhondi, S. (2015b), "Determination of mode III fracture toughness for different materials using a new designed test configuration", Mater. Des., 86, 863-871. https://doi.org/10.1016/j.matdes.2015.08.033.
  8. Aliha, M.R.M., Hosseinpour, G.R. and Ayatollahi, M.R. (2013), "Application of cracked triangular specimen subjected to three-point bending for investigating fracture behavior of rock materials", Rock Mech. Rock Eng., 46(5), 1023-1034. http://doi.org/10.1007/s00603-012-0325-z.
  9. Aliha, M.R.M., Shaker, S. and Keymanesh, M.R. (2019), "Low temperature fracture toughness study for bitumen under mixed mode I+ II loading condition", Eng. Fract. Mech., 206, 297-309. http://doi.org/10.1016/j.engfracmech.2018.11.037.
  10. Aliha, M.R.M., Sistaninia, M., Smith, D.J., Pavier, M.J. and Ayatollahi, M.R. (2012), "Geometry effects and statistical analysis of mode I fracture in guiting limestone", Int. J. Rock Mech. Min. Sci., 51, 128-135. https://doi.org/10.1016/j.ijrmms.2012.01.017.
  11. Ayatollahi, M.R. and Akbardoost, J. (2012), "Size effects on fracture toughness of quasi-brittle materials-A new approach", Eng. Fract. Mech., 92, 89-100. https://doi.org/10.1016/j.engfracmech.2012.06.005.
  12. Ayatollahi, M.R. and Akbardoost, J. (2013), "Size effects in mode II brittle fracture of rocks", Eng. Fract. Mech., 112, 165-180. https://doi.org/10.1016/j.engfracmech.2013.10.011.
  13. Ayatollahi, M.R. and Aliha, M.R.M. (2005), "Cracked Brazilian disc specimen subjected to mode II deformation", Eng. Fract. Mech., 72(4), 493-503. http://dx.doi.org/10.1016/j.engfracmech.2004.05.002.
  14. Ayatollahi, M.R. and Aliha, M.R.M. (2008), "On the use of Brazilian disc specimen for calculating mixed mode I-II fracture toughness of rock materials", Eng. Fract. Mech., 75(16), 4631-4641. http://doi.org/10.1016/j.engfracmech.2008.06.018.
  15. Ayatollahi, M.R. and Sedighiani, K. (2012), "Mode I fracture initiation in limestone by strain energy density criterion", Theor. Appl. Fract. Mech., 57(1), 14-18. http://doi.org/10.1016/j.tafmec.2011.12.003.
  16. Ayatollahi, M.R. and Sistaninia, M. (2011), "Mode ІІ fracture study of rocks using Brazilian disk specimens", Int. J. Rock Mech. Min. Sci., 48(5), 819-826. https://doi.org/10.1016/j.ijrmms.2011.04.017.
  17. Ayatollahi, M.R. and Zakeri, M. (2017), "An improved definition for mode I and mode II crack problems", Eng. Fract. Mech., 175, 235-246. http://doi.org/10.1016/j.engfracmech.2017.01.027.
  18. Ayatollahi, M.R., Berto, F., Campagnolo, A., Gallo, P. and Tang, K. (2017), "Review of local strain energy density theory for the fracture assessment of V-notches under mixed mode loading", Eng. Solid Mech., 5(2), 113-132. http://doi.org/10.5267/j.esm.2017.3.001.
  19. Ayatollahi, M.R., Moghaddam, M.R. and Berto, F. (2015), "A generalized strain energy density criterion for mixed mode fracture analysis in brittle and quasi-brittle materials", Theor. Appl. Fract. Mech., 79, 70-76. http://doi.org/10.1016/j.tafmec.2015.09.004.
  20. Ayatollahi, M.R., Moghaddam, M.R., Razavi, S.M.J. and Berto, F. (2016), "Geometry effects on fracture trajectory of PMMA samples under pure mode-I loading", Eng. Fract. Mech., 163, 449-461. http://doi.org/10.1016/j.engfracmech.2016.05.014.
  21. Ayatollahi, M.R., Pavier, M.J. and Smith, D.J. (2002), "Mode I cracks subjected to large T-stresses", Int. J. Fract., 117(2), 159-174. https://doi.org/10.1023/A:1020973802643.
  22. Campagnolo, A. and Berto, F. (2017), "Some recent criteria for brittle fracture assessment under mode II loading", Eng. Solid Mech., 5(1), 31-38. http://doi.org/10.5267/j.esm.2016.10.002.
  23. Chang, K.J. (1981), "On the maximum strain criterion-a new approach to the angled crack problem", Eng. Fract. Mech., 14(1), 107-124. https://doi.org/10.1016/0013-7944(81)90021-7.
  24. Chao, Y.J., Liu, S. and Broviak, B.J. (2001), "Brittle fracture: variation of fracture toughness with constraint and crack curving under mode I conditions", Exp. Mech., 41(3), 232-241. http://doi.org/10.1007/BF02323139.
  25. Erdogan, F. and Sih, G.C. (1963), "On the crack extension in plates under plane loading and transverse shear", J. Basic Eng., 85(4), 519-525. http://dx.doi.org/10.1115/1.3656897.
  26. Fowell, R.J., Hudson, J.A., Xu, C., Chen, J. and Zhao, X. (1995), "Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disc (CCNBD) specimens", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 7(32), 57-64. http://dx.doi.org/10.1016/0148-9062(94)00015-U.
  27. Guo, H., Aziz, N.I. and Schmidt, L.C. (1993), "Rock fracture-toughness determination by the Brazilian test", Eng. Geol., 33(3), 177-188. http://doi.org/10.1016/0013-7952(93)90056-I.
  28. Hibbitt, Karlsson & Sorensen, Inc. (2017), Abaqus 6.14 Manual, Version 6.14, Hibbitt, Karlsson & Sorensen, Inc.
  29. Hua, W., Dong, S., Pan, X. and Wang, Q. (2017), "Mixed mode fracture analysis of CCBD specimens based on the extended maximum tangential strain criterion", Fatigue Fract. Eng. Mater. Struct., 40(12), 2118-2127. http://doi.org/10.1111/ffe.12638.
  30. Kumar, C.N.S., Krishna, P. and Kumar, D.R. (2017), "Effect of fiber and aggregate size on mode-I fracture parameters of high strength concrete", Adv. Concrete Constr., 5(6), 613-624. https://doi.org/10.12989/acc.2017.5.6.613.
  31. Li, Y., Dong, S., Li, K. and Hua, W. (2018), "Numerical simulation and experimental study of three-point bending specimen's I/II mixed mode fracture", J. Exp. Mech., 33(4), 557-566. https://doi.org/10.7520/1001-4888-17-040.
  32. Maruvanchery, V. and Kim, E. (2019), "Effects of water on rock fracture properties: Studies of mode I fracture toughness, crack propagation velocity, and consumed energy in calcite-cemented sandstone", Geomech. Eng., 17(1), 57-67. https://doi.org/10.12989/gae.2019.17.1.057
  33. Midhun, M.S., Rao, T.D.G. and Srikrishna, T.C. (2018), "Mechanical and fracture properties of glass fiber reinforced geopolymer concrete", Adv. Concrete Constr., 6(1), 29-45. https://doi.org/10.12989/acc.2018.6.1.029.
  34. Mirsayar, M.M. (2015), "Mixed mode fracture analysis using extended maximum tangential strain criterion", Mater. Des., 86, 941-947. http://doi.org/10.1016/j.matdes.2015.07.135.
  35. Mirsayar, M.M., Berto, F., Aliha, M.R.M. and Park, P. (2016), "Strain-based criteria for mixed-mode fracture of polycrystalline graphite", Eng. Fract. Mech., 156, 114-123. https://doi.org/10.1016/j.engfracmech.2016.02.011.
  36. Mirsayar, M.M., Razmi, A., Aliha, M.R.M. and Berto, F. (2018), "EMTSN criterion for evaluating mixed mode I/II crack propagation in rock materials", Eng. Fract. Mech., 190, 186-197. https://doi.org/10.1016/j.engfracmech.2017.12.014.
  37. Mousavi, S.S., Aliha, M.R.M. and Imani, D.M. (2020), "On the use of edge cracked short bend beam specimen for PMMA fracture toughness testing under mixed-mode I/II", Polym. Test., 81, 106199. https://doi.org/10.1016/j.polymertesting.2019.106199.
  38. Ouchterlony, F. (1988), "Suggested methods for determining the fracture toughness of rock", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 25, 71-96.
  39. Ouchterlony, F. (1990), "Fracture toughness testing of rock with core based specimens", Eng. Fract. Mech., 35(1-3), 351-366. http://doi.org/10.1016/0013-7944(90)90214-2.
  40. Pour, P.J.H., Aliha, M.R.M. and Keymanesh, M.R. (2018), "Evaluating mode I fracture resistance in asphalt mixtures using edge notched disc bend ENDB specimen with different geometrical and environmental conditions", Eng. Fract. Mech., 190, 245-258. https://doi.org/10.1016/j.engfracmech.2017.11.007.
  41. Razavi, S.M.J., Aliha, M.R.M. and Berto, F. (2018), "Application of an average strain energy density criterion to obtain the mixed mode fracture load of granite rock tested with the cracked asymmetric four-point bend specimens", Theor. Appl. Fract. Mech., 97, 419-425. https://doi.org/10.1016/j.tafmec.2017.07.004.
  42. Richard, H.A. and Benitz, K. (1983), "A loading device for the creation of mixed mode in fracture mechanics", Int. J. Fract., 22(2), R55-R58. http://dx.doi.org/10.1007/BF00942726.
  43. Rizov, V. (2013), "Mixed-mode I/II fracture study of polymer composites using Single Edge Notched Bend specimens", Comput. Mater. Sci., 77, 1-6. http://doi.org/10.1016/j.commatsci.2013.04.021.
  44. Schmidt, R.A. (1980), "A microcrack model and its significance to hydraulic fracturing and fracture toughness testing", Proceedings of 21st US symposium on Rock Mechanics, Rolla, Missouri, U.S.A., May.
  45. Shaker, S., Aliha, M.M. andKeymanesh, M. (2019), "Aging effect on combined mode fracture resistance of bitumen", Fatigue Fract. Eng. Mater. Struct., 42(7), 1609-1621. https://doi.org/10.1111/ffe.13003.
  46. Sih, G.C. (1973), "Some basic problems in fracture mechanics and new concepts", Eng. Fract. Mech., 5(2), 365-377. http://doi.org/10.1016/0013-7944(73)90027-1.
  47. Sih, G.C. (1974), "Strain-energy-density factor applied to mixed mode crack problems", Int. J. Fract., 10(3), 305-321. http://dx.doi.org/10.1007/BF00035493.
  48. Singh, R.N. and Sun, G.X. (1989), Relationships Between Fracture Toughness, Hardness Indices and Mechanical Properties of Rocks, Mining Department Magazine, XLI, 49-62.
  49. Smith, D.J., Ayatollahi, M.R. and Pavier, M.J. (2001), "The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading", Fatigue Fract. Eng. Mater. Struct., 24(2), 137-150. http://doi.org/10.1046/j.1460-2695.2001.00377.x.
  50. Wei, M.D., Dai, F., Xu, N.W., Liu, Y. and Zhao, T. (2017), "Fracture prediction of rocks under mode I and mode II loading using the generalized maximum tangential strain criterion", Eng. Fract. Mech., 186, 21-38. http://doi.org/10.1016/j.engfracmech.2017.09.026
  51. Williams, M.L. (1957), "On the stress distribution at the base of a stationary crack", J. Appl. Mech., 24, 109-114. https://doi.org/10.1115/1.3640470.
  52. Yukio, U., Kazuo, I., Tetsuya, Y. and Mitsuru, A. (1983), "Characteristics of brittle fracture under general combined modes including those under bi-axial tensile loads", Eng. Fract. Mech., 18(6), 1131-1158. http://doi.org/10.1016/0013-7944(83)90007-3.

피인용 문헌

  1. Experimental and numerical analysis of mixed mode I/III fracture of sandstone using three-point bending specimens vol.76, pp.6, 2020, https://doi.org/10.12989/sem.2020.76.6.725