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Statistical Analysis of Rock Fracture Toughness Data Obtained from Different Chevron Notched and Straight Cracked Mode I Specimens

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Abstract

In laboratory fracture toughness studies, the crack growth resistance of rock materials may be influenced by different factors such as specimen geometry, loading conditions, and also the type of pre-notch cut in the test sample. In this paper, a large number of mode I fracture toughness experiments are conducted on an Iranian white rock “Harsin marble” with six different mode I specimens. The selected test specimens are in the shape of cylindrical rod, rectangular beam, and circular Brazilian disk containing either chevron notch or straight crack. The effect of specimen geometry and pre-notch type was investigated statistically, and it was found that the average fracture toughness values of notched specimens were higher than those of the similar specimens but containing straight crack. Meanwhile, the scatters of fracture toughness data for chevron notched specimens were smaller than those for the straight cracked samples. For each set of experimental fracture toughness results, probability of fracture was investigated using two- and three-parameter Weibull statistical distributions. Comparison of the Weibull fitted curves for chevron notched and straight cracked samples with the same geometries demonstrated that the discrepancy between the corresponding curves can be described with a good accuracy by a simple shift factor. In addition, using the extended maximum tangential strain criterion which takes into account the influence of both KI and T-stress terms, the statistical fracture toughness data of chevron notched specimens were predicted in terms of the Weibull distribution parameters of the straight cracked specimens.

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Abbreviations

a :

Crack length

a m :

Critical crack length

a 0 :

Initial length of chevron notch

a 1 :

Final length of chevron notch

A min :

Dimensionless critical stress intensity factor of the CB specimen

B :

Thickness of specimen

B r :

Biaxiality ratio

C v :

Dimensionless compliance of specimen

D :

Diameter of specimen

E :

Modulus of elasticity

f :

Geometry factor of the SENB specimen

F :

Load

F max :

Fracture load

i :

Number of test specimen

k :

Shear transfer function

K :

Stress intensity factor

K c :

Fracture toughness

K Ic :

Mode I fracture toughness

K If :

Mode I fracture resistance

K min :

Location parameter of fracture resistance distribution

K 0 :

Scale parameter of fracture resistance distribution

L :

Length of specimen

m :

Shape parameter for describing the scatter of KIf

n :

Total number of tests for each specimen

N I :

Shape or geometry factor of the SCCBD specimen

P f :

Failure probability

r :

Distance from the crack tip

r c :

Critical distance from the crack tip

R :

Radius of specimen

S :

Support span

T c :

Critical value of T-stress

u :

Load-point displacement

W :

Height of the CNBB and SENB specimens

Y *min :

Normalized critical stress intensity factor of CCNBD specimen

α r :

Normalized critical distance

ε c :

Critical value of tangential strain

ε θθ :

Tangential strain

θ :

Chevron notch angle

θ 0 :

Direction of fracture in polar coordinates

λ :

Shift factor between two sets of data

ν :

Poisson’s ratio

σ :

Characteristic stress in the specimen

σ t :

Tensile strength of rock material

CB:

Chevron bend specimen

CCNBD:

Cracked chevron notched Brazilian disk specimen

CNBB:

Chevron notched bend beam

EMTSN:

Extended maximum tangential strain criterion

FPZ:

Fracture process zone

ISRM:

International Society for Rock Mechanics

MTSN:

Maximum tangential strain criterion

SCCBD:

Straight center cracked Brazilian disk specimen

SECRBB:

Single edge cracked round bar bend specimen

SENB:

Single edge notched beam specimen

SIF:

Stress intensity factor

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Authors and Affiliations

  1. Welding and Joining Research Center, School of Industrial Engineering, Iran University of Science and Technology (IUST), Narmak, Tehran, 16846-13114, Iran

    M. R. M. Aliha

  2. School of Mechanical Engineering, Iran University of Science and Technology (IUST), Narmak, Tehran, 16846-13114, Iran

    E. Mahdavi & M. R. Ayatollahi

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  1. M. R. M. Aliha
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  2. E. Mahdavi
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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., Mahdavi, E. & Ayatollahi, M.R. Statistical Analysis of Rock Fracture Toughness Data Obtained from Different Chevron Notched and Straight Cracked Mode I Specimens. Rock Mech Rock Eng 51, 2095–2114 (2018). https://doi.org/10.1007/s00603-018-1454-9

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