Rock Mechanics and Rock Engineering

, Volume 46, Issue 5, pp 1023–1034 | Cite as

Application of Cracked Triangular Specimen Subjected to Three-Point Bending for Investigating Fracture Behavior of Rock Materials

  • M. R. M. Aliha
  • Gh. R. Hosseinpour
  • M. R. Ayatollahi
Original Paper


Numerical and experimental studies were performed on a new fracture test configuration called the edge cracked triangular (ECT) specimen. Using several finite-element analyses, the fracture parameters (i.e., K I, K II, and T-stress) were obtained for different combinations of modes I and II. The finite-element results show that the ECT specimen is able to provide pure mode I, pure mode II, and any mixed-mode loading conditions in between. Also, a series of mixed-mode fracture experiments were conducted on Neiriz marble rock using the proposed specimen. Furthermore, the generalized maximum tangential stress (GMTS) criterion was used to predict the experimental results. The GMTS criterion makes use of a three-parameter model (based on K I, K II, and T) for describing the crack tip stresses. Due to the significant positive T-stresses that exist in the ECT specimen, typical minimum fracture toughness values were expected to be obtained when the ECT specimen is used. The direction of fracture initiation and the path of fracture growth were also obtained theoretically using the GMTS criterion, and good agreement was observed between the experimental fracture path and theoretical simulations. The fracture study of this specimen reveals that the ECT specimen can be also used in mixed-mode fracture studies of rock materials in addition to the conventional circular or rectangular beam test samples.


Neiriz marble Triangular specimen Finite-element analyses Mixed-mode loading Fracture experiments 



Maximum tangential stress


Edge cracked triangular


Finite element


Generalized maximum tangential stress


Cohesive zone model


Strain energy density

List of Symbols


Crack length for ECT specimen


Crack length ratio in the ECT specimen

r, θ

Crack tip coordinates


Specimen thickness


Elastic modulus




Normalized T-stress


Edge length of square plate

Greek Letters


Crack initiation direction


Tangential stress component


Poisson’s ratio


Mode I stress intensity factor


Mode II stress intensity factor


Mode I fracture toughness


Applied load


Critical fracture load


Critical distance from the crack tip


Mode I geometry factor


Mode II geometry factor


Crack inclination angle


Critical tangential stress


Tensile strength


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Copyright information

© Springer-Verlag Wien 2012

Authors and Affiliations

  • M. R. M. Aliha
    • 1
    • 2
  • Gh. R. Hosseinpour
    • 2
  • M. R. Ayatollahi
    • 2
  1. 1.Welding and Joining Research CenterIran University of Science and TechnologyTehranIran
  2. 2.Fatigue and Fracture LabIran University of Science and TechnologyTehranIran

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