Crack Paths 2006

V ww

Ÿ

TT

T

.

(2)

0 0 T T

c r r

where rc is the critical length parameter.

By solving equation (1) according to (2) gives after rearrangement the following

expression:

1 0

T T

S V c y y

S V

0 0

˜

sin

>

@

. (3)

0 K K I T

cos3 T

1 6 1 T

16 c o s 2 s i n 3 / 2 r

0 2 c o s 2 c o s 6 / 2 0 ¸¹·¨©§ T T c c x x r

II

0

Equation (3) represents a modified M T Scriterion that can be used for determination of

crack propagation angle T0 whenthe crack surfaces are loaded with constant pressure or

sufficiently smooth traction distribution.

Physical length scale rc presents the distance ahead of the crack tip where the fracturing

process is actually initiated. The distance rc is a material parameter, which is very

difficult to determine. Several models have been proposed for its determination. The

model of Larsson and Carlsson [8], which assumed that rc is contained in the region of

constrained yielding, was used to determine the critical distance rc in this paper due to

the availability of necessary material parameters.

N U M E R I CMAOLD E L L IONFGC R A CPKR O P A G A T IPOANT H

Crack propagation of initial surface crack was determined using generalized M T S

criterion (eq. 3). Fracture mechanics parameters stress intensity factor KI, KII and T- stress wer extracted using contour integral, which is implemented in commercial

program A B A Q U[9S]. During the analysis it was assumed that the crack surfaces are

loaded with constant lubricant pressure. Experiments [10] showed that initial surface

crack subjected to rolling-sliding contact and constant internal pressure propagates

under steep angle T0 to the free surface (Figure 2).

T

Figure 2: Influence of constant pressure on crack propagation [10]