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Recalibration and Clarification of the Formula Applied to the ISRM-Suggested CCNBD Specimens for Testing Rock Fracture Toughness

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Abstract

The cracked chevron-notched Brazilian disc (CCNBD) was proposed by the International Society for Rock Mechanics (ISRM) to test the mode I (opening mode) fracture toughness of rock. The test method has been vigorously discussed and debated, despite being the subject of intensive research for decades. The minimum (critical) dimensionless stress intensity factors affiliated with the formula for calculating the fracture toughness using CCNBD specimens with different geometric parameters remain elusive and complex. The matter cannot be resolved by simply replacing the diameter in the original formula with the radius, as claimed by several authors. In this paper, the formula is fundamentally improved, as wide-ranging minimum dimensionless stress intensity factors pertaining to diversified CCNBD geometries are recalibrated by three-dimensional finite element analysis, and an expression with tabulated coefficients is obtained through curve-fitting the data obtained from the numerical calibration. The present results are shown to be more accurate than those in the literature. Furthermore, the importance of the reasonability of the results is highlighted; a comprehensive comparison of different values shows that the upper bounds of minimum stress intensity factors are violated by the above claim. The confusion resulting from the claim is, thus, clarified conclusively.

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Abbreviations

a :

Current crack length

a 0 :

Initial chevron notched crack length

a 1 :

Final chevron notched crack length

a m :

Critical crack length

b :

Width of crack front

B :

Specimen thickness

CCNBD:

Cracked chevron-notched Brazilian disc

CSTBD:

Cracked straight-through Brazilian disc

D :

Specimen diameter

E :

Elastic modulus

K I :

Stress intensity factor of the CCNBD

K IC :

Mode I fracture toughness

K II :

Mode II stress intensity factor

K III :

Mode III stress intensity factor

P :

Load applied on the specimen

P max :

Maximum load

R :

Specimen radius

R s :

Saw radius

SIF:

Stress intensity factor

Y :

Dimensionless SIF of the CSTBD with dimensionless crack length α

\( Y^{*} \) :

Dimensionless stress intensity factor of the CCNBD

\( Y_{\min }^{*} \) :

Minimum (critical) dimensionless stress intensity factor

α :

Dimensionless crack length

α 0 :

Initial chevron notched dimensionless crack length

α 1 :

Final chevron notched dimensionless crack length

α m :

Critical dimensionless crack length

α B :

Dimensionless thickness

γ :

Angle between the tension stress σ and the crack face

μ :

Poisson’s ratio

σ :

Tension stress

ω :

Angle between the x-axis and the direction of projection of the stress on the crack face

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 51179115), State Key Laboratory for GeoMechanics and Deep Underground Engineering (Grant No. K1020), and Doctoral Foundation of the Ministry of Education of China (Grant No. 200806100042).

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Authors and Affiliations

  1. State Key Laboratory of Hydraulics and Mountain River Engineering, Chengdu, 610065, Sichuan, China

    Q. Z. Wang, H. Fan, X. P. Gou & S. Zhang

  2. Department of Civil Engineering and Applied Mechanics, Sichuan University, Chengdu, 610065, China

    Q. Z. Wang, H. Fan, X. P. Gou & S. Zhang

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  1. Q. Z. Wang
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  2. H. Fan
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  4. S. Zhang
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Correspondence to Q. Z. Wang.

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Wang, Q.Z., Fan, H., Gou, X.P. et al. Recalibration and Clarification of the Formula Applied to the ISRM-Suggested CCNBD Specimens for Testing Rock Fracture Toughness. Rock Mech Rock Eng 46, 303–313 (2013). https://doi.org/10.1007/s00603-012-0258-6

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