Crack Paths 2009

− Under mixed mode loading the minimumenergy density criterion and the maximum

tangential stress criterion predict almost the same fracture initiation angle for pointed

V-notches and cracked plates;

− For pointed V-notches the two criteria loose the independency of the distance r, at

which the fracture angle is evaluated;

− The variation of the assessed fracture angle as a function of the distance r is greater

for 2α=60° and 2α=90° than for t 2α=30°; in the last case the influence of the distance

is very weak;

− The comparison between experimental angles and theoretical values is satisfactory for

the crack case and less satisfactory for the other cases.

Table 3. Mixed mode. Comparison between experimental and theoretical initial crack

angles, P M M tAested at -60°C (ν=0.4), distance r in (mm).

2α b1 ϕ1 ϕ2 ϕ3 <ϕ>

ϕ according to Erdogan-Sih [11]

ϕ according to Sih [12]

0 -3 19.1 16.4 17.6 17.7

23.7

23.4

0 3 31.2 25.7 25.6 27.5

32.5

32.0

0 9 37.3 -

- 37.3

38.2

37.7

0 18 37.5 41.5 42.2 40.4

40.3

40.0

0 27 45.7 40.0 43.5 43.1

40.2

39.8

0 36 36.4 35.0 46.3 39.2

40.3

39.9

2α b1 ϕ1 ϕ2 ϕ3 <ϕ> r = 0.035 0.05 0.1 0.2 0.3 1 0.035 0.05 0.1 0.2 0.3 1

30 1 12.9 14.8 7.7 11.8

8.5 8.8 9.4 10.0 10.4 11.6 8.6 8.9 9.5 10.1 10.5 11.7

60 1 11.9 15.8 14.3 14.0

4.9 5.3 6.1 7.1 7.8 10.0 4.7 5.1 5.9 6.8 7.4 9.6

90 1 5.2 5.9 6.2 5.8

4.6 5.2 6.6 8.5 9.7 14.5 3.9 4.4 5.6 7.2 8.2 12.3

30 9 19.7 29.7 24.3 24.6

17.2 17.3 18.3 19.4 20.1 22.1 16.7 17.2 18.2 19.2 19.9 21.8

60 9 14.6 27.5 21.9 21.3

10.4 11.2 12.9 14.7 15.9 19.9 10.0 10.7 12.3 14.1 15.2 18.8

90 9 17.4 16.8 21.1 18.4

7.4 8.4 10.6 13.3 15.2 21.5 6.2 7.1 9.0 11.3 12.9 18.5

2α m ϕ1 ϕ2 ϕ3 <ϕ> r = 0.035 0.05 0.1 0.3 0.5 1 0.035 0.05 0.1 0.2 0.3 1

30 18 54.2 59.5 59.9 57.9

36.8 37.5 38.8 40.0 40.8 42.8 36.1 36.8 38.1 39.5 40.3 42.7

60 18 47.8 49.2 48.3 48.4

25.9 27.3 30.0 32.7 34.3 38.7 24.4 25.7 28.3 31.1 32.7 37.8

90 18 40.8 33.1 36.3 36.7

16.7 18.5 22.4 26.4 28.8 35.4 14.2 15.8 19.3 23.2 25.6 33.8

30 9 63.3 69.2 64.3 65.6

50.1 50.5 51.4 52.2 52.6 53.9 52.7 53.5 54.9 56.3 57.1 59.5

60 9 43.0 49.6 56.3 49.6

40.1 41.3 43.4 45.4 46.4 49.2 39.7 41.2 44.4 47.7 49.6 55.5

90 9 49.1 49.4 45.1 47.9

28.9 30.9 34.7 38.1 39.9 44.2 25.7 28.0 32.8 38.0 41.4 52.1

The initiation fracture angles have been evaluated considering the influence of the non

singular stress term (T-stress), as suggested for the crack case by Ayatollahi and Aliha

[10]. Table 4 summarises the results only for 2α =30° and the notches shown in Fig. 1b.

The introduction of the T-stress modifies the results of Table 3 but the differences are

low in the close neighbourhood of the notch tip.

Table 4. P M M tAested at -60°C (ν=0.4). Effect of the T-stress on initial crack angle

ϕ according Erdogan-Sih [11]

ϕ according to Sih [12]

2α m ϕ1 ϕ2 ϕ3 <ϕ> r= 0.035 0.05 0.1 0.2 0.3 1 0.035 0.05 0.1 0.3 0.5 1

T-stress = 6 M P a

T-stress = 6 M P a

30 18 54.2 59.5 59.9 57.9

38.5 39.4 41.4 43.7 45.1 50.1 37.4 38.3 40.2 42.2 43.5 47.8

T-stress = 8 M P a

T-stress = 8 M P a

30 9 63.3 69.2 64.3 65.6

52.3 53.1 54.7 56.6 57.7 61.7 53.9 54.8 56.6 58.4 59.6 63.1

998