Abstract
Success of a hydraulic fracturing operation depends on the height and width of the induced fractures. One of the critical components controlling fracture size is fracture toughness of the formation. In this work, mode I fracture toughness of Berea Sandstone and Mancos Shale is measured by combining semi-circular bend test (SCB) and digital image correlation (DIC). Experiments were carried out in different notch orientations with respect to bedding. DIC is used to measure full-field displacements and to visualize and quantify fracture process zone (FPZ). Full-field displacements from DIC are utilized in Williams’ series solution to extract critical stress intensity factor, or fracture toughness. Accuracy of measuring fracture toughness using DIC displacements depends on area of interest (AOI), field of view (FOV), and the number of terms of solution (N). A parametric study is conducted, allowing to choose an optimal set of these parameters for evaluation of fracture toughness in rock specimens. It is known that fracture toughness values obtained directly from the SCB test, using conventional maximum load method, are underestimated due to the effect of nonlinear behavior caused by the fracture process zone. FPZ length is considered as an increase in the effective crack length. Irwin’s correction for effective crack length is utilized to measure fracture toughness values obtained directly from the SCB test that account for the fracture process zone. Fracture toughness values measured using DIC method and Irwin’s correction method are in a good match for both Berea Sandstone and Mancos Shale. Both methods show higher fracture toughness for samples in arrester orientation. In addition, the results show that FPZ length in Berea Sandstone is much larger than in Mancos Shale.
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Data Availability
All data were obtained from the experiments conducted by the authors.
Abbreviations
- \(a_{0}\) :
-
Initial notch length
- \(a_{{{\text{eff}}}}\) :
-
Effective notch length
- AOI:
-
Area of interest
- B :
-
Thickness of the sample
- CTOD:
-
Crack tip opening displacement
- DIC:
-
Digital image correlation
- \(f_{{\text{I}}} , f_{{{\text{II}}}} , g_{{\text{I}}} , g_{{{\text{II}}}}\) :
-
Known functions of a point k
- FEM:
-
Finite element method
- FOV:
-
Field of view
- FPZ:
-
Fracture process zone
- G :
-
Shear modulus
- \(K_{{\text{I}}}\) :
-
Mode I stress intensity factor
- \(K_{{{\text{IC}}}}\) :
-
Mode I fracture toughness
- \(K_{{{\text{IC}}}}^{{{\text{APR}}}}\) :
-
Mode I apparent fracture toughness
- \(K_{{{\text{IC}}}}^{{{\text{DIC}}}}\) :
-
Mode I fracture toughness obtained from the DIC
- \(K_{{{\text{IC}}}}^{{{\text{IRW}}}}\) :
-
Mode I fracture toughness with Irwin’s correction
- \(K_{{{\text{II}}}}\) :
-
Mode II stress intensity factor
- LEFM:
-
Linear elastic fracture mechanics
- MMTS:
-
Modified maximum tangential stress
- N :
-
Number of terms in solution
- ν :
-
Poisson’s ratio
- rk,θk :
-
Polar coordinates of a point k
- r y :
-
Fracture process zone length
- R :
-
Radius of the sample
- SIF:
-
Stress intensity factor
- STD:
-
Standard deviation
- Tx,Ty,R :
-
Translation and rotation components in displacement equations
- u :
-
Horizontal displacement fields captured by DIC
- UCS:
-
Uniaxial compressive strength
- v :
-
Vertical displacement fields captured by DIC
- Y :
-
Non-dimensional stress intensity factor
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Acknowledgements
The authors are grateful to Mr. Mark LeBlanc, Philip Wortman, Archie Metoyer, and Donatien-Roland Diby for their help in sample preparation and experimental setup. The authors are also grateful to Tuscaloosa Marine Shale Research Group for their feedback and support. This material is based upon work supported by the Department of Energy National Energy Technology Laboratory under Award Number DE-FE0031575 (TUSCALOOSA MARINE SHALE LABORATORY).
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This material is based upon work supported by the Department of Energy National Energy Technology Laboratory under Award Number DE-FE0031575.
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Kramarov, V., Parrikar, P.N. & Mokhtari, M. Evaluation of Fracture Toughness of Sandstone and Shale Using Digital Image Correlation. Rock Mech Rock Eng 53, 4231–4250 (2020). https://doi.org/10.1007/s00603-020-02171-7
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DOI: https://doi.org/10.1007/s00603-020-02171-7