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Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms

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International Journal of Fracture Aims and scope Submit manuscript

Abstract

An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks. The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar. The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level. Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed. Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture. This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure.

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Notes

  1. In rock mechanics, cleavage is restricted to splitting along specific crystallographic planes.

Abbreviations

\(\hbox {a}\) :

The notch length

\(A_\mathrm{B}\) :

The cross-sectional area of the bar

\(A_\mathrm{S}\) :

The cross-sectional area of fracture surface

\(A_\mathrm{I} (v)\) :

The function of dynamic fracture

\(b\) :

A material constant

\(\mathrm{B}\) :

The thickness of the specimen

\(C_\mathrm{B}\) :

Longitudinal wave speed of the bar

\(C_\mathrm{L}\) :

Longitudinal wave speed

\(C_\mathrm{R}\) :

Rayleigh wave speed

\(C_\mathrm{S}\) :

Shear wave speed

\(D\) :

Fractal dimensions

\(E\) :

Elastic modulus

\(E_\mathrm{B}\) :

Young’s modulus of the bar

\(G_\mathrm{C}\) :

Quasi-static fracture energy

\(G_{\mathrm{dC}}\) :

Dynamic fracture energy

\(G_\mathrm{d} (t,v)\) :

Dynamic energy release rate

\(I\) :

The moment of inertia

\(K_\mathrm{I}, \, K_\mathrm{I}^{\mathrm{dyn}} (t,v)\) :

Quasi-static, dynamic stress intensity factor

\(K_{\mathrm{IC}}\) :

Fracture toughness

\(K_{\mathrm{Id}}, K_{\mathrm{ID}}\) :

Mode I dynamic crack initiation, growth toughness

\(K_{\mathrm{IIC}}, K_{\mathrm{IId}}\) :

Mode II quasi-static, dynamic fracture toughness

\(\dot{K}_\mathrm{I}^{\mathrm{dyn}}\) :

Dynamic loading rate

\(m\) :

The mass of one fragment

\(P\) :

The load applied on the specimen

\(P_{\max }\) :

The peak applied load

\(r_{OO{'}}\) :

Distance of the translational movement

\(\mathrm{R}\) :

The specimen radius

\(\mathrm{2S}\) :

The specimen span

\(t_\mathrm{f}\) :

The time to fracture

\(T,\, T_{\mathrm{Rot.}},\, T_{\mathrm{Tra.}}\) :

The total, rotational and translational kinetic energies

\(v_0\) :

The theoretical characteristicvelocity

\(v\) :

Crack speed

\(v_{\lim }\) :

The limiting crack speed

\(v_{\max }\) :

The maximum crack speed

\(v_\mathrm{T}\) :

The translational velocity

\(V_{\mathrm{Str.}}\) :

The striking impact speed

\(W_{\mathrm{In.}}, \, W_{\mathrm{Re.}}, W_{\mathrm{Tr.}}\) :

The energies of the incident, reflected and transmitted wave

\(W_\mathrm{S}\) :

The energy absorbed by the specimen

\(Y_\mathrm{I} (\mathrm{S}/R)\) :

The mode-I geometry factor

\(\nu \) :

The Poisson’s ratio

\(\xi \) :

The covering length

\(N(\xi )\) :

The total number of covering box

\(\delta \) :

The critical distance

\(\delta _\mathrm{f}\) :

The displacement of fracture

\(\sigma _{\mathrm{In.}},\, \sigma _{\mathrm{Re.}},\, \sigma _{\mathrm{Tr.}}\) :

The stress measured by gauges on incident, reflected and transmitted bars

\(\omega \) :

The angular velocity

\(\theta \) :

The rotational angle

\(\rho \) :

Density

\(\varOmega \) :

The dissipated energy

References

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Acknowledgments

This work was supported by the Swiss National Science Foundation (No. 200020_129757). The authors thank Prof. Xiao Li and Dr. Changyu Liang of Chinese Academy of Sciences for their help in specimen preparation, Prof. Xibing Li and Dr. Zhiqiang Yin of Central South University for helping us perform experiments with the split Hopkinson pressure bar, Prof. Yang Ju and Dr. Ruidong Peng of China University of Mining and Technology (Beijing) for their help on experiments using the optical profilometry and SEM, and Drs. Daniel Bonamy and Laurent Ponson of the Group Complex Systems and Fracture, CEA-SACLAY, France, for their fruitful discussions on the analysis of fracture surface. The authors would like to thank two anonymous reviewers for their comments that help improve the manuscript.

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Authors and Affiliations

  1. Laboratory of Rock Mechanics (LMR), School of Architecture, Civil and Environmental Engineering (ENAC), École Polytechnique Fédérale de Lausanne (EPFL), 1015, Lausanne, Switzerland

    Q. B. Zhang & J. Zhao

  2. Department of Civil Engineering, Monash University, Building 60, Clayton, Melbourne, VIC, 3800, Australia

    J. Zhao

Authors
  1. Q. B. Zhang
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  2. J. Zhao
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Correspondence to Q. B. Zhang.

Appendix

Appendix

Experimental data under dynamic loading conditions are tabulated in Table 8, including the loading rate \(\dot{K}_\mathrm{I}^{\mathrm{dyn}}\), the time to fracture \(t_\mathrm{f}\), the dynamic crack initiation toughness \(K_{\mathrm{Id}}\), the crack speed \(v\), the dissipated energy \(\varOmega \), the dynamic fracture energy \(G_{\mathrm{dC}}\), the calculated dynamic crack propagation toughness \(K_{\mathrm{ID}}\), and the fractal dimension \(D\).

Table 8 Experimental results of rock materials under dynamic loading conditions
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Table 9 lists the optical and physical properties of the primary minerals in selected four rock types.

Table 9 Summary of the optical and physical properties of primary minerals in selected rock materials
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Zhang, Q.B., Zhao, J. Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms. Int J Fract 189, 1–32 (2014). https://doi.org/10.1007/s10704-014-9959-z

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