International Journal of Fracture

, Volume 189, Issue 1, pp 1–32 | Cite as

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

Original Paper


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.


Dynamic loading Rock materials Fracture behaviour Fracture toughness  Micromeasurement Failure mechanisms 

List of symbols

\(\hbox {a}\)

The notch length


The cross-sectional area of the bar


The cross-sectional area of fracture surface

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

The function of dynamic fracture


A material constant


The thickness of the specimen


Longitudinal wave speed of the bar


Longitudinal wave speed


Rayleigh wave speed


Shear wave speed


Fractal dimensions


Elastic modulus


Young’s modulus of the bar


Quasi-static fracture energy


Dynamic fracture energy

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

Dynamic energy release rate


The moment of inertia

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

Quasi-static, dynamic stress intensity factor


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


Dynamic loading rate


The mass of one fragment


The load applied on the specimen

\(P_{\max }\)

The peak applied load


Distance of the translational movement


The specimen radius


The specimen span


The time to fracture

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

The total, rotational and translational kinetic energies


The theoretical characteristicvelocity


Crack speed

\(v_{\lim }\)

The limiting crack speed

\(v_{\max }\)

The maximum crack speed


The translational velocity


The striking impact speed

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

The energies of the incident, reflected and transmitted wave


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

\(\rho \)


\(\varOmega \)

The dissipated energy


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Laboratory of Rock Mechanics (LMR), School of Architecture, Civil and Environmental Engineering (ENAC)École Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland
  2. 2.Department of Civil EngineeringMonash UniversityMelbourneAustralia

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