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.

Keywords

Extended maximum tangential strain (EMTSN) criterion Mode I fracture resistance Rock Statistical analysis Weibull probability model 

Abbreviations

a

Crack length

am

Critical crack length

a0

Initial length of chevron notch

a1

Final length of chevron notch

Amin

Dimensionless critical stress intensity factor of the CB specimen

B

Thickness of specimen

Br

Biaxiality ratio

Cv

Dimensionless compliance of specimen

D

Diameter of specimen

E

Modulus of elasticity

f

Geometry factor of the SENB specimen

F

Load

Fmax

Fracture load

i

Number of test specimen

k

Shear transfer function

K

Stress intensity factor

Kc

Fracture toughness

KIc

Mode I fracture toughness

KIf

Mode I fracture resistance

Kmin

Location parameter of fracture resistance distribution

K0

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

NI

Shape or geometry factor of the SCCBD specimen

Pf

Failure probability

r

Distance from the crack tip

rc

Critical distance from the crack tip

R

Radius of specimen

S

Support span

Tc

Critical value of T-stress

u

Load-point displacement

W

Height of the CNBB and SENB specimens

Ymin*

Normalized critical stress intensity factor of CCNBD specimen

αr

Normalized critical distance

εc

Critical value of tangential strain

εθθ

Tangential strain

θ

Chevron notch angle

θ0

Direction of fracture in polar coordinates

λ

Shift factor between two sets of data

ν

Poisson’s ratio

σ

Characteristic stress in the specimen

σt

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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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • M. R. M. Aliha
    • 1
  • E. Mahdavi
    • 2
  • M. R. Ayatollahi
    • 2
  1. 1.Welding and Joining Research Center, School of Industrial EngineeringIran University of Science and Technology (IUST)Narmak, TehranIran
  2. 2.School of Mechanical EngineeringIran University of Science and Technology (IUST)Narmak, TehranIran

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