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
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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.
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