Crack Paths 2012

intensity factors, the finite element results showed that the first non-singular stress term

also has a significant value of 0.18 M P aat the tip of initial crack. This value was also

obtained directly from the A B A Q UsSoftware using the contour-integral method. It is

now well established that the sign and magnitude of the T-stress can affect noticeably

the onset of fracture as well as the direction of mixed mode fracture [12-15].

Accordingly, the conventional fracture criteria that are based only on the stress intensity

factors and ignore the effect of T-stress may not provide accurate estimations for the

fracture behaviour of the cracked structures. Thus, a modified mixed mode fracture

criterion called the generalized maximumtangential stress (GMTS)is employed in the

next section for evaluating the onset of rock slope failure. This criterion uses a three

parameter (KI, KII and T) model for predicting the load bearing capacity and the

direction of fracture initiation [12].

M I X EMD O D CER A CGKR O W TC RHI T E R I O N

The G M T Scriterion takes into account the influence ofT-stress in addition to the mode

I and modeII stress intensity factors. Hence in comparison with the conventional M T S

criterion, this criterion uses a more accurate description for the tangential stress VTT in

front of the crack tip under mixed modeI/II loading as [16]: T T

2 1 2 r O T K

T T

K

(3)

2 s i n s i n 2 3 2 c o s 2 c o s

» ¼ º « ¬ ª

1

VTT where r and are the crack tip co-ordinates, T is a non-singular and constant stress term

2S r

which is independent of the distance from the crack tip, usually called the T-stress. It

depends on the geometry and loading conditions and its magnitude may vary in a wide

range for different cracked bodies and structures. O(r1/2) represents the remaining terms

of the series expansion which are negligible near the crack tip. The G M T Scriterion

proposes that the crack growth initiates radially from the crack tip along the direction of

maximumtangential stress To. Also the crack extension takes place whenthe tangential

stress VTT along To and at a critical distance rc from the crack tip attains a critical value

VTTc . Both rc and VTTc are assumed to be material constants. According to the G M T S

criterion [12], the direction of fracture initiation angle To and the onset of mixed mode

I/II brittle fracture can be found from:

T T S T T c r T 0

sin cos 2 3 1 6 1 c o s 3 s i n 0 0 K K

0 VT TT T T w

(4)

w

0

Ÿ

0

>

@

2 0

T r

K

T

K

T

K

T

S c »

ª

º

Ic

(5)

0 2 cos 2 23

sin

0 2cos

2 s i n 2 T

0

,

,,

0

« ¬

¼

More details about how Eqs. (4) and (5) are derived can be found in Smith et al. [12]. If

the effect of T in Eqs. (4) and (5) is ignored, the G M T Scriterion will be identical to the

conventional M T Scriterion. Based on the G M T Scriterion, a negative T-stress in a

cracked geometry increases the mixed mode I/II fracture resistance and conversely a

positive T-stress decreases it [12]. Similarly, the angle of mixed modefracture initiation

decreases when the T-stress is negative and increases for those situations where the T

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