Crack Paths 2009

stress which is parallel to the crack line. To calculate the stresses, finite element method

is successfully used. Other methods of T-stress calculations are presented in Refs. [15

17].

In this paper, the S D Mhas been employed to calculate the T-stress in a notched

body because it is the most simple and widely used. The T-stress for the notch has been

evaluated by experimental and numerical methods.

Numerical determination

The T-stress definition is based on the S D Mas follows

(3)

σ σ yy

(

)0 θ

T

=

.

xx -

=

The T-stress is evaluated using finite element method and computing the difference of

θ=0. It should be noted that the T-stress

principal stresses along ligament for direction

can be evaluated in any direction (table 1).

Table 1. T-stress values according to measurement direction.

θ = 0 θ

= ± π

3 / π θ ± = 2 / π θ ± = 3 / 2 π θ ± =

(

)y

xx 3yyxxσσ−=T3yyxxσσ−=T ()yyTσσ-xx= σ=

σ σ - xx =

T

T

It can be seen that T is not really constant as in theory (Fig. 1).

1000

ter s s , ( M P a )

0

0

-S

a/w=0.1

n o f T

a/w=0.2

a/w=0.3

-1000

E v o lu t io

a/w=0.4

a/w=0.5

a/w=0.6

a/w=0.7

-2000

1E-3

0,01

0,1

1

10

Distance from notch-tip, r(mm)

Figure 1. T-stress distribution along ligament for a roman tile specimen with large

range of the notch aspect ratio [a/t = 0.1-0.7].

For short crack, distribution of the T-stress is stabilised after some distance. For long

crack, T increases linearly with ligament except a region which is close to the crack tip.

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