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

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Abstract

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.

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Abbreviations

MTS:

Maximum tangential stress

ECT:

Edge cracked triangular

FE:

Finite element

GMTS:

Generalized maximum tangential stress

CZM:

Cohesive zone model

SED:

Strain energy density

a :

Crack length for ECT specimen

a/W :

Crack length ratio in the ECT specimen

r, θ :

Crack tip coordinates

t :

Specimen thickness

E :

Elastic modulus

T :

T-Stress

T * :

Normalized T-stress

2W :

Edge length of square plate

θ 0 :

Crack initiation direction

σ θθ :

Tangential stress component

ν :

Poisson’s ratio

K I :

Mode I stress intensity factor

K II :

Mode II stress intensity factor

K Ic :

Mode I fracture toughness

P :

Applied load

P cr :

Critical fracture load

r c :

Critical distance from the crack tip

Y I :

Mode I geometry factor

Y II :

Mode II geometry factor

α :

Crack inclination angle

σ θθc :

Critical tangential stress

σ t :

Tensile strength

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Authors and Affiliations

  1. Welding and Joining Research Center, Iran University of Science and Technology, Narmak, 16846-13114, Tehran, Iran

    M. R. M. Aliha

  2. Fatigue and Fracture Lab, Iran University of Science and Technology, Narmak, 16846-13114, Tehran, Iran

    M. R. M. Aliha, Gh. R. Hosseinpour & M. R. Ayatollahi

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  1. M. R. M. Aliha
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  2. Gh. R. Hosseinpour
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  3. M. R. Ayatollahi
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Correspondence to M. R. M. Aliha.

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Aliha, M.R.M., Hosseinpour, G.R. & Ayatollahi, M.R. Application of Cracked Triangular Specimen Subjected to Three-Point Bending for Investigating Fracture Behavior of Rock Materials. Rock Mech Rock Eng 46, 1023–1034 (2013). https://doi.org/10.1007/s00603-012-0325-z

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