PSI - Issue 28

Kotrechko Sergiy et al. / Procedia Structural Integrity 28 (2020) 116–123 Author name / Structural Integrity Procedia 00 (2019) 000–000

120

5



 un F

F    0 71 0 74 . . *

(2)

f

From (2) it follows that in practice it is possible to use not more than ≈70% of contact bond strength. This 30% “loss” of strength is a consequence of the IZ existence.

Fig. 3 (colour online) The dependence of force, total energy and bond lengths on the length of carbyne-graphene nanoelement (scheme): un F is the strength; min R F is the minimum value of lower boundary of the instability zone.

4. Statistical approach to predicting lifetime As noted above, presence of the contact bonds is a specific feature of nanoelements containing nanostructures of different dimensionality. Contact bonds have a minimal strength, therefore, from a mechanical point of view, they are the weakest link in the system. This greatly simplifies prediction of the lifetime of nanoelements, since it is pre determined by the waiting time for a contact bond break. In accordance with this, the probability of a contact bond breaking due to i th its vibration is determined as:

1

i



0 1    (

)

(3)

P p

p

0

i

where 0 p is a probability of the contact bond break due to the one oscillation. Then, the cumulative probability P of bond breaking in time  ( n    0 / ) is:

0          ) ( ) ( p p P P n n i i 0 1 1 1 1 1

 

(4)

0

where 0  is the average time of one oscillation. Dependence (4) can be considered as a statistical law that describes the lifetime of 2D-nanoelements containing contact bonds. Accordingly, the expression for the relative failure waiting time, 0   / , with a given probability P of its realisation may be written as: