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Experimental analysis of the extension to shear fracture transition in a rock analogue material using digital image correlation method

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Abstract

This paper presents the results of axi-symmetric extension tests on a Rock Analogue Material that showed a continuous transition from extension fracture to shear fracture with an increase in compressive stress. The analysis used non destructive full-field experimental methods—digital image correlation (DIC), as well as the post-mortem specimens observation. When the mean stress was small, the fractures formed through the mode I cracking at tensile equal to the material tensile strength with smooth surfaces. These surfaces became rougher or delicate plumose patterns as the mean stress increased. Fracture angles also increased progressively from extension fractures to shear fractures. Hybrid fractures formed under mixed tensile and compressive stress states and presented plumose patterns on the rupture surface. DIC results showed the localisation of tensile deformation and the acceleration of deformation at the zone that induced the fracture. The fracture caused a reduction of deformation in the surrounding areas, which showed a release of elastic energy stored in the material during the propagation of fracture.

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Abbreviations

\(\sigma _1\), \(\sigma _2\), \(\sigma _3\) :

Principal stress

\(\sigma _{m}\) :

Mean stress

q = \(\sigma _1 - P_c\) :

Deviatoric stress

\(P_c\) :

Confining pressure

\(\Psi \) :

Angle between fracture/band and \(\sigma _1\) direction

E :

Young’s modulus

\(\nu \) :

Poisson’s ratio

\(\rho \) :

Density

\(\varepsilon _{ax}\) :

Axial strain

\(\tilde{\varepsilon }_{ax}\) :

Nominal axial strain

\(\varepsilon \) :

Volumetric strain

\(\sigma _{ax}\) :

Axial stress

\(\sigma _{ax}^{c}\) :

Axial stress at central section of dog-bone sample

\(\sigma _{ax}^{ex}\) :

Axial stress at extremity of dog-bone sample

\(\sigma _{ax}^{rup}\) :

Axial stress at failure

\(\sigma _{ax}^{pk}\) :

Axial peak stress

\(\sigma _{t}\) :

Uniaxial tensile strength

\(S_c\) :

Area at central section of dog-bone sample

\(S_{ex}\) :

Area at extremity of dog-bone sample

\(S_{rup}\) :

Area of the fracture surface

\(F_{ax}\) :

Applied force on the sample

GRAM1:

Granular Rock Analogue Material 1

\(\beta \) :

Dilatancy factor

DIC:

Digital image correlation

C:

Correlation coefficient

\(X_{i}\), \(x_{i} = \phi _0(X_{i})\) :

Coordinates (in pixels) of homologous points in the reference and deformed images

\(\phi _0\) :

Transformation function

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Acknowledgements

We would like to thank Chemenda A.I. and P. Vacher for discussions related to this paper, J. Ambre for assistance in the laboratory. This work was supported by the Côte d’Azur Observatory, the Region Provence Alpes Côte d’Azur and GeoFrac-Net Consortium.

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Authors and Affiliations

  1. The University of Danang - University of Technology and Education, 48 Cao Thang street, Da Nang City, Vietnam

    Huyen Thi Phuong Tran

  2. HCMC University of Technology and Education, Ho Chi Minh City, Vietnam

    Hung Sy Nguyen

  3. ESPACE Laboratory UMR 7300, Université Côte d’Azur, 06200, Nice, France

    Stéphane Bouissou

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  1. Huyen Thi Phuong Tran
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Tran, H.T.P., Nguyen, H.S. & Bouissou, S. Experimental analysis of the extension to shear fracture transition in a rock analogue material using digital image correlation method. Int J Fract 243, 91–104 (2023). https://doi.org/10.1007/s10704-023-00734-7

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