Crack Paths 2009

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

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

O (r1/2) represent the remaining terms of the series expansion and are negligible near the

crack tip. Accordingly, the direction of fracture initiation (θ0) can be determined based

on the generalized M T Scriterion as [9]:

− −

= π θ θ θ θ c r T +

K K

(3)

∂ < ⇒ σ θθ

σ

∂

( cos 2 3 1 6 1 c o s 3 s i n 0 0 0 Ι Ι 0 Ι ) ] 0 2 s i n

θθ

[

= 0

,

0

2

2

θ

∂ θ

∂

θ θ =

0

By ignoring the effect of T-stress in Eq. (3), the generalised M T Swill be identical with

the conventional M T Scriterion. Generally, the mixed mode crack initiation angle

θ0 increases for

decreases for those specimens having a negative T-stress and conversely

the specimens with a positive T-stress. Therefore, unlike the conventional M T Scriterion

the generalised M T Scriterion can predict different values of θ0 for any mode mixity

and for any cracked geometry. In the next section the the generalised M T Scriterion is

used to predict the observed results.

DISCCUSSION

In order to use the generalized M T Scriterion (Eq. 3), three parameters, KI, KII and T,

should be knownfor any test specimen and for various modemixities. These parameters

for the C C C Dand S C Bsamples are[6]:

∗

C C C D for aPRT R B









(4)

Y RPRBBa a i π π

π

K

T

i

specimen





  

  

( )





specimen

2

i

III,

=





∗

R B P T





for SCB



2

,

 =

 

=

−

 





where YI,YII and T* are the normalized forms of KI, KII and T, respectively. These

parameters are functions of crack length ratio (a/R), crack initiation angle (or mode

mixity) and also the location of loading supports (S/R in the S C B specimen). The

variations of YI,YII and T* for the tested C C C Dand S C B specimens made of limestone

rock are given in Fig. 4 for various combinations of modeI and modeII.

By introducing the corresponding values of KI, KII and T for each specimen and any

required mode mixity, the direction of the initial fracture angle was determined from

θ0 in both C C C Dand S C Bspecimens a fixed value of rc = 1.2 m m

Eq. 3. To predict

was selected and assumed to be the size of fracture process zone in the limestone. This

value was assumed to be constant for all mode mixities. The measured fracture

initiation angles and the predictions using the generalized M T Scriterion for both C C C D

and S C Bsamples are shown in Fig. 5.

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