PSI - Issue 43

Jelena M. Djoković et al. / Procedia Structural Integrity 43 (2023) 95– 100 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

99 5

Results for c 1 , d 1 and e 1 are presented in He and Hutchinson (1989) in a tabular form, while they can be approximated with the following expressions, Djokovic (2009):

2 1 − =  +

( e       + + + ) 2 i ln

1 1 2 1

− +

( e e     − −  + ) 3 i i

1 1 4 1

− +

( e e     −  − ) 3 i i

c

,

,

.

(10)

d

=

e

=

1

1

1

3. Results and discussion The two bimaterial combinations were considered, with Young's moduli ratios: E 2 / E 1 = 0.04 and E 2 / E 1 = 25, in the uniaxial tension (perpendicular to the interface) conditions. The considered crack approaching (attacking) angles from material 1 are:  = 0°, 15°, 30°, 45°, 60°, 75° and 90°. Results are shown in Figures 3 and 4 and in Table 1.

Table 1. Results of the possible crack propagation direction. Attacking angle [°] 0 15 30

45

60

75

90

Line number

1

2

3

4

5

6

7

Propagating angle [°] , E 2 /E 1 = 0.04 Propagating angle [°] , E 2 /E 1 = 25

-12.6 12.6

84.6 80.4

88.8 83.4

93.6 95.4

94.8 85.8

94.2 -3.2

90

-1.8

In Figure 3 are shown the propagation directions of a crack approaching the interface from material 1, which is softer than material 2 across the interface, for the moduli ratio E 2 / E 1 = 25. The solid lines denote directions of the crack approaching the interface, while the dashed lines (of the same color) denote the resulting crack propagation directions. As can be seen from Figure 3, when the crack is approaching the interface at a right angle, it will not cross it, but it will bounce back in material 1 and continue to propagate along the path close to the interface, though it might even deflect into the interface it was weak. The same happens with a crack that attacks the interface at an angle of 75°. With further decreasing of the attacking angle, the penetration of the interface occurs and the crack continues to propagate in material 2 across the interface.

Fig. 3. Predicted crack propagation directions

Fig. 4. Predicted crack propagation directions

for the bimaterial combination with E 2 /E 1 = 25.

for the bimaterial combination with E 2 /E 1 = 0.04.

In Figure 4 are shown the propagation directions of a crack approaching the interface from material 1, which is tougher than material 2 across the interface, for the moduli ratio E 2 / E 1 = 0.04. From Figure 4 one can see that the crack coming from the tougher of the two materials will more easily penetrate the interface and continue to propagate in material 2 across it.