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Scaling effect on the mixed-mode fracture path of rock materials

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Abstract

In this paper, a new approach is presented to predict the crack growth path in the rock materials by taking into account the size effect. The proposed approach is an incremental method in which the crack initiation angle for each step is determined from the modified forms of the maximum tangential stress criterion. These modified maximum tangential stress criteria take into account the influence of the higher order terms of the stress series at the crack tip in addition to the singular terms. As an important parameter in the proposed method, the critical distance r c is also assumed to be size dependent. Finally the incremental method is evaluated by experimental results obtained from Guiting limestone and CJhorveh marble specimens reported in the previous studies. It is shown that the proposed approach can predict the fracture trajectory of cracked specimens with different sizes in good agreement with the experimental results when three terms of Williams series expansion are considered for characterizing the stress field around the crack tip.

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Abbreviations

a :

half-crack length in CCCD specimen

A 3, B 3 :

constant coefficients of the third terms in the Williams series expansion

A 3*, B 3*:

non-dimensional forms of A 3 and B 3

CCCD:

center cracked circular disk specimen

f t :

tensile strength

FEOD:

finite element over-deterministic method

FPZ:

fracture process zone

K I :

mode I stress intensity factor

K II :

mode II stress intensity factor

K I*, K II*:

non-dimensional forms of K I and K II

K If :

mode I fracture resistance

MTS:

maximum tangential stress criterion

P :

applied load

P u :

fracture load

R :

radius of CCCD specimens

r, θ:

crack tip coordinate

r c :

critical distance around crack tip

SCB:

semi-circular bend specimen

SED:

strain energy density criterion

T :

T-stress

T*:

non-dimensional form of T

t :

specimen thickness

XFEM:

extended finite element method

α:

crack inclination angle

σθθ :

tangential stress around the crack tip

θ0 :

fracture initiation angle

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  1. Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, 15719-14911, Iran

    J. Akbardoost & A. Rastin

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  1. J. Akbardoost
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Original Text © J. Akbardoost, A. Rastin, 2016, published in Fizicheskaya Mezomekhanika, 2016, Vol. 19, No. 4, pp. 82-91.

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Akbardoost, J., Rastin, A. Scaling effect on the mixed-mode fracture path of rock materials. Phys Mesomech 19, 441–451 (2016). https://doi.org/10.1134/S102995991604010X

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