Abstract
Fracture growth in underground rock structures occurs under complex stress states, which typically include the in- and out-of-plane sliding deformation of jointed rock masses before catastrophic failure. However, the lack of a comprehensive theoretical and experimental fracture toughness study for rocks under contributions of out-of plane deformations (i.e. mode III) is one of the shortcomings of this field. Therefore, in this research the mixed mode I/III fracture toughness of a typical rock material is investigated experimentally by means of a novel cracked disc specimen subjected to bend loading. It was shown that the specimen can provide full combinations of modes I and III and consequently a complete set of mixed mode I/III fracture toughness data were determined for the tested marble rock. By moving from pure mode I towards pure mode III, fracture load was increased; however, the corresponding fracture toughness value became smaller. The obtained experimental fracture toughness results were finally predicted using theoretical and empirical fracture models.
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Abbreviations
- ENDB:
-
Edge-notched disc bend specimen
- ISENB:
-
Inclined single-edge-notched beam specimen
- MTS:
-
Maximum tangential stress
- MTSED:
-
Maximum tangential strain energy density
- a/t :
-
Crack depth to thickness ratio
- E :
-
Elastic modulus
- G :
-
Strain energy
- K I :
-
Mode I stress intensity factor
- K II :
-
Mode II stress intensity factor
- K III :
-
Mode III stress intensity factor
- K If :
-
Critical mode I stress intensity factor at the onset of fracture
- K IIIf :
-
Critical mode III stress intensity factor at the onset of fracture
- K Ic :
-
Pure mode I fracture toughness
- K IIIc :
-
Pure mode III fracture toughness
- K eff :
-
Effective mixed mode stress intensity factor
- \(M_{13}^{e}\) :
-
Mixity parameter
- P :
-
Applied load
- P c :
-
Critical fracture load
- r, θ :
-
Crack tip coordinate
- R :
-
Disc radius
- 2S :
-
Distance between the bottom supports in the ENDB or ISENB specimen
- S/R :
-
Loading span to radius ratio
- T :
-
Disc thickness
- Y I :
-
Mode I geometry factor
- Y III :
-
Mode III geometry factor
- Z :
-
Parameter showing the location of crack front relative to the mid-section
- α, β :
-
Crack inclination angle
- ε θθ :
-
Strain component in polar system
- σ θθ :
-
Stress component in polar system
- \(\varphi\) :
-
Out-of-plane fracture angle
- ν :
-
Poisson’s ratio
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Acknowledgements
The authors would like to thank Mr. Brent McCleave (Department of Mechanical and Mechatronics Engineering, University of Waterloo) for his help in preparing this paper. We would also like to thank Mr. Farhad Zivari and Mr. Yassin Fotouhi (Machining workshop, School of Industrial Engineering at Iran University of Science and Technology) for their help in manufacturing the test specimens.
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Aliha, M.R.M., Bahmani, A. Rock Fracture Toughness Study Under Mixed Mode I/III Loading. Rock Mech Rock Eng 50, 1739–1751 (2017). https://doi.org/10.1007/s00603-017-1201-7
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DOI: https://doi.org/10.1007/s00603-017-1201-7