PSI - Issue 52

T. Profant et al. / Procedia Structural Integrity 52 (2024) 455–471 T. Profant et al / Structural Integrity Procedia 00 (2023) 000 – 000

469 15

from which the critical ratio , , s ⁄ can be expressed as ( ) ( ) ( ) ( ) ( 2 11 12 2 2 2 11 12 1 , , 2 5 4 3 2 5 4 7 6 3 2 8 8 f I crit s I crit C C K K C     − − − − − − =     



2

8 C C C +

12

.

)( ) 4 I K 

2

2

2

2

2     2

+ − − − +

2

1

−



(52) The critical ratio , , s ⁄ is plotted in Fig.7 and in Fig. 8 for various combinations of the flexoelectric parameters. It can be seen that except for marginal values =±2 is the critical ratio , , s ⁄ greater than 1. Apparently, flexoelectricity tends to reduce the energy release rate. Hence, with the same G c it requires more loading/energy to achieve the minimum condition for the crack to advance if the material is flexoelectric versus when it is not. The “ toughening ” effect of the flexoelectricity is particularly strong for =− 1 and =0.5 , or for =−0.5 and = 1.

1 Fig. 7. Variation of ⁄ with the flexoelectric parameter for several values of the parameter . The remaining parameters are 0 ⁄ =1000 , 0 ⁄ = 0.75, = 0.3.

Fig. 8. Variation of ⁄ with the flexoelectric parameter for several values of the parameter . The remaining parameters are 0 ⁄ =1000 , 0 ⁄ = 0.75, = 0.3.