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Pure Mode I Fracture Toughness Determination in Rocks Using a Pseudo-Compact Tension (pCT) Test Approach

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Abstract

Mode I fracture toughness (KIC) quantifies the ability of a material to withstand crack initiation and propagation due to tensile loads. The International Society for Rock Mechanics (ISRM) has proposed four suggested methods for determining KIC. However, these methods present some drawbacks such as insufficient post-peak control, complex sample preparation and considerable material requirements. Here we present an alternative approach, called the pseudo-compact tension (pCT) method, to measure KIC in rocks using disc-shaped specimens loaded in pure tension. The pCT specimen has favourable features such as a simple geometry, small sample volume and minimal machining requirement. The tensile load is transmitted to the specimen through two high-strength, high-stiffness steel jaws that fit into a U-shaped groove cut in the specimen. An additional thin straight notch is introduced to act as a stress concentrator. The crack propagates from the notch tip along the ligament plane, splitting the specimen into two halves. The effects of specimen size and notch length on KIC are determined by testing specimens 100, 50 and 38 mm in diameter with different notch length ratios (0.1 ≤ a/b ≤ 0.4). Tests were performed under ambient conditions and a slow loading rate (0.1 mm/min). Our results show that the pCT method is convenient for the assessment of KIC of both fragile and ductile rocks. The method offers good control even beyond the maximum load, making it possible to study the post-peak behaviour of the material.

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Abbreviations

E :

Young’s modulus

ν :

Poisson’s ratio

σ c :

Compressive strength

σ t :

Tensile strength

σ yield :

Yield stress

n e :

Effective porosity

ρ bulk :

Bulk density

ρ :

Mass density

V p :

Ultrasonic P-wave velocity

V s :

Ultrasonic S-wave velocity

K C :

Fracture toughness

K IC :

Mode I fracture toughness

K I :

Mode I stress intensity factor

Y’ :

Dimensionless stress intensity factor

C i :

Coefficients of the Y’ expression (i = 0–4)

SR:

Short rod

CB:

Chevron bend

CCNBD:

Cracked chevron notched Brazilian disc

SCB:

Semi-circular bend

CT:

Compact tension

pCT:

Pseudo-compact tension

WS:

Wedge splitting

MDCT:

Modified disk-shaped compact tension

R :

Specimen radius

B :

Specimen thickness

D :

Specimen diameter

G w :

U-shaped groove width

G d :

U-shaped groove depth

a :

Notch length

b :

Distance from the base of the groove to the bottom of the specimen

a/b :

Notch length ratio

P :

Load

P max :

Maximum (peak) load

d :

Displacement

d peak :

Displacement at the peak load

σ max :

Applied stress at the maximum load

σ 0 :

Applied stress

COD:

Crack opening displacement

CMOD:

Crack mouth opening displacement

LPD:

Load point displacement

LVDT:

Linear variable differential transducer

AE:

Acoustic emission

FE:

Finite element

FPZ:

Fracture process zone

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Acknowledgements

This work was funded by Repsol S.A., and the support from the Xunta de Galicia, the European Union (European Social Fund—ESF) and the MINECO/AEI/FEDER, UE project BIA2017- 87066-R. The authors would like to thank Dr. Manika Prasad and Kurt Livo (Petroleum Engineering Department, Colorado School of Mines) for their advice and assistance with the micro X-ray computed tomography work. The authors would also like to thank the reviewers for their comments and suggestions that helped to improve the manuscript.

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Authors and Affiliations

  1. School of Civil Engineering, University of A Coruña, Campus de Elviña s/n, 15071, Coruña, Spain

    Andrea Muñoz-Ibáñez & Jordi Delgado-Martín

  2. Structural Impact Laboratory (SIMLab) and Centre for Advanced Structural Analysis (CASA), Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), 7491, Trondheim, Norway

    Miguel Costas

  3. Faculty of Informatics, University of A Coruña, Campus de Elviña s/n, 15071, Coruña, Spain

    Juan Rabuñal-Dopico

  4. Centro de Tecnología de Repsol, Ctra. Extremadura, N-V Km 18, 28935, Móstoles, Spain

    Jose Alvarellos-Iglesias & Jacobo Canal-Vila

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  1. Andrea Muñoz-Ibáñez
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Contributions

JDM, JAI and JCV devised the project and conceptualized the main ideas. JRD designed the electronics and software of the experimental device. MC created the numerical model of the device. AMI performed the experiments and, in cooperation with the rest of the authors, analysed the data. The first draft of the manuscript was written by AMI, and all the authors commented on previous versions of the manuscript. All the authors have read and approved the final version of the manuscript.

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Correspondence to Andrea Muñoz-Ibáñez.

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Muñoz-Ibáñez, A., Delgado-Martín, J., Costas, M. et al. Pure Mode I Fracture Toughness Determination in Rocks Using a Pseudo-Compact Tension (pCT) Test Approach. Rock Mech Rock Eng 53, 3267–3285 (2020). https://doi.org/10.1007/s00603-020-02102-6

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