Rock Mechanics and Rock Engineering

, Volume 45, Issue 1, pp 65–74 | Cite as

Typical Upper Bound–Lower Bound Mixed Mode Fracture Resistance Envelopes for Rock Material

  • M. R. M. Aliha
  • M. R. Ayatollahi
  • J. Akbardoost
Original Paper


Mixed mode fracture experiments were conducted on Harsin marble using two disc-shape samples namely the Brazilian disc (BD) and the semi-circular bend (SCB) specimens. For each specimen, a complete fracture toughness envelope ranging from pure mode I to pure mode II was obtained. The experimental results indicate that the mixed mode fracture toughness depends on the geometry and loading conditions such that for any similar mode mixture, the BD test data were significantly greater than the SCB fracture toughness results. Therefore, the conventional fracture criteria which present a unique mixed mode fracture curve, fail to predict the test results. It is shown that a generalized criterion, which takes into account the effects of geometry and loading conditions, is able to provide individual fracture curves for theses specimens with very good estimates for the test results obtained from both BD and SCB specimens. The BD and SCB specimens can be suggested as appropriate specimens for obtaining typical upper bound and lower bound envelopes for mixed mode fracture toughness of rocks.


Marble rock Disc type specimens Geometry effect Mixed mode Lower and upper bound fracture resistance 


  1. Aliha MRM, Ashtari R, Ayatollahi MR (2006) Mode I and mode II fracture toughness testing for a coarse grain marble. J Appl Mech Mater 5–6:181–188CrossRefGoogle Scholar
  2. Aliha MRM, Ayatollahi MR, Pakzad R (2008) Brittle fracture analysis using a ring shape specimen containing two angled cracks. Int J Fract 153(1):63–68CrossRefGoogle Scholar
  3. Aliha MRM, Ayatollahi MR, Smith DJ, Pavier MJ (2010) Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Eng Fract Mech 77:2200–2212CrossRefGoogle Scholar
  4. Al-Shayea NA (2005) Crack propagation trajectories for rocks under mixed mode I–II fracture. Eng Geol 81(1):84–97CrossRefGoogle Scholar
  5. Awaji H, Sato S (1978) Combined mode fracture toughness measurement by the disc test. J Eng Mater Technol 100:175–182CrossRefGoogle Scholar
  6. Ayatollahi MR, Aliha MRM (2007a) Fracture toughness study for a brittle rock subjected to mixed mode I/II loading. Int J Rock Mech Min Sci 44(4):617–624CrossRefGoogle Scholar
  7. Ayatollahi MR, Aliha MRM (2007b) Wide range data for crack tip parameters in two disc-type specimens under mixed mode loading. Comput Mater Sci 38(4):660–670CrossRefGoogle Scholar
  8. Ayatollahi MR, Aliha MRM (2008) On the use of brazilian disc specimen for calculating mixed mode I–II fracture toughness of rock materials. Eng Fract Mech 75:4631–4641CrossRefGoogle Scholar
  9. Ayatollahi MR, Aliha MRM (2009) Analysis of a new specimen for mixed mode fracture tests on brittle materials. Eng Fract Mech 76(11):1563–1573CrossRefGoogle Scholar
  10. Chang SH, Lee CI, Jeon S (2002) Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimen. Eng Geol 66:79–97CrossRefGoogle Scholar
  11. Chong KP, Kuruppu MD (1984) New specimen for fracture toughness determination for rock and other materials. Int J Fract 26:59–62CrossRefGoogle Scholar
  12. Chong KP, Kuruppu MD, Kuszmual JS (1987) Fracture toughness determination of layered materials. Eng Fract Mech 28(1):43–54CrossRefGoogle Scholar
  13. Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng Trans ASME 85:519–525CrossRefGoogle Scholar
  14. Fowell RJ (1994) The use of the cracked Brazilian disc geometry for rock fracture investigations. Int J Rock Mech Min Sci Geomech Abstr 31(6):571–579CrossRefGoogle Scholar
  15. Fowell RJ (1995) ISRM-Suggested methods for determining mode I fracture toughness using cracked chevron notched Brazilian disk (CCNBD) specimens. Int J Rock Mech Min Sci Geomech Abstr 32:57–64CrossRefGoogle Scholar
  16. Funatsu T, Seto M, Shimada H, Matsui K, Kuruppu M (2004) Combined effects of increasing temperature and confining pressure on the fracture toughness of clay bearing rocks. Int J Rock Mech Min Sci 41(6):927–938CrossRefGoogle Scholar
  17. Gómez FJ, Elices M, Berto F, Lazzarin P (2009) Fracture of U-notched specimens under mixed mode: experimental results and numerical predictions. Eng Fract Mech 76(2):236–249CrossRefGoogle Scholar
  18. Hussain MA, Pu SL, Underwood J (1974) Strain energy release rate for a crack under combined mode I and Mode II. Fracture analysis, ASTM STP 560. American Society for Testing and Materials, PhiladelphiaGoogle Scholar
  19. ISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15:99–103Google Scholar
  20. Ke CC, Chen CS, Tu CH (2008) Determination of fracture toughness of anisotropic rocks by boundary element method. Rock Mech Rock Eng 41(4):509–538CrossRefGoogle Scholar
  21. Khan K, Al-Shayea NA (2000) Effect of specimen geometry and testing method on mixed I–II fracture toughness of a limestone rock from Saudi Arabia. Rock Mech Rock Eng 33(3):179–206CrossRefGoogle Scholar
  22. Kharazi B (2008) Mechanical Engineering Department. MSc Thesis, Iran University of Science and Technology, TehranGoogle Scholar
  23. Krishnan GR, Zhao XL, Zaman M, Roegiers JC (1998) Fracture toughness of a soft sandstone. Int J Rock Mech Min Sci 35(6):695–710CrossRefGoogle Scholar
  24. Lim IL, Johnston IW, Choi SK, Boland JN (1994a) Fracture testing of a soft rock with semi-circular specimens under three-point bending, Part 1:mode I. Int J Rock Mech Min Sci Geomech Abstr 31(3):185–197CrossRefGoogle Scholar
  25. Lim IL, Johnston IW, Choi SK, Boland JN (1994b) Fracture testing of a soft rock with semi-circular specimens under three-point bending, Part 2: mixed mode. Int J Rock Mech Min Sci Geomech Abstr 31(3):199–212CrossRefGoogle Scholar
  26. Liu HY, Kous Q, Lindqvist PA, Tang CA (2007) Numerical modelling of the heterogeneous rock fracture process using various test techniques. Rock Mech Rock Eng 40(2):107–144CrossRefGoogle Scholar
  27. Nasseri MHB, Mohanty B (2008) Fracture toughness anisotropy in granitic rocks. Int J Rock Mech Min Sci 45(2):167–193CrossRefGoogle Scholar
  28. Schmidt RA (1980) A microcrack model and its significance to hydraulic fracturing and fracture toughness testing. In: Proceedings of the 21st U.S. rock mechanics symposium, Missouri, Rolla, 27–30 May 1980, pp 581–590Google Scholar
  29. Sih GC (1974) Strain-energy-density factor applied to mixed mode crack problems. Int J Fract 10:305–321CrossRefGoogle Scholar
  30. Smith DJ, Ayatollahi MR, Pavier MJ (2001) The role of T-stress in brittle fracture for linear elastic materials under mixed mode loading. Fatig Fract Eng Mater Struct 24:137–150CrossRefGoogle Scholar
  31. Williams ML (1957) On the stress distribution at the base of a stationary crack. J Appl Mech 24:109–114Google Scholar
  32. Zhao XL, Fowell RJ, Roegiers JC, Xu C (1994) Rock fracture-toughness determination by the Brazilian test. Eng Geol 38(1–2):181–184CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • M. R. M. Aliha
    • 1
    • 2
  • M. R. Ayatollahi
    • 1
  • J. Akbardoost
    • 1
  1. 1.Fatigue and Fracture Laboratory, School of Mechanical EngineeringIran University of Science and TechnologyTehranIran
  2. 2.Welding and Joining Research Center, School of Industrial EngineeringIran University of Science and TechnologyTehranIran

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