Crack Paths 2009

[7] and those predicted by means of Eq. (9). In this case the comparison was very

satisfactory and the average error was around 1%.

1.5

KI b π σ

Mastrojannis at al. [7]

Eq.(9)

1.25

α

1

circle

b

ellipse

a

0.75

0

30

60

90

120

150

180

α [deg]

Figure 4. Comparison between the Mastrojannis et al. numerical solution [7] and Eq. (9)

(a/b=1.5; σ is the remotely uniform tensile stress).

Half circle-like sinusoidal contour

This type of crack has a boundary in the form of a half circle and half shape whose polar

equation is given as [7]

(11)

r

=

A

RA

1

+

⎜⎝⎛

−

⎟⎠⎞ sin1

2m2

α

The SIF of the mode I loading which had been numerically solved in Ref. [7] is

compared with Eq. (9) in Fig. 5. The error in the prediction of the maximumSIF was

1.4% while the average error along the whole contour was around 3%.

Remark

In Refs [5, 6, 11] the

4 a r e a was proposed as a parameter which is approximately

along the crack, which can be evaluated as

proportional to the maximumSIF

m a x , I K

1118