PSI - Issue 28

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

121

6

ln(

)

1

P





(5)



ln(

)

1

p





0

0

Probability of the contact bond break due to the one oscillation, 0 p , is defined as a probability of realisation of the critical fluctuation ) ( c p    ( ) ( c p p     0 ). According to Kotrechko et al. (2017), the expression for ) ( c p    is as follows:

    o c









exp

 E k T d ( ) /

  

B



(6)

(

)

p

   

c

  







exp

 E k T d /

  

B

( )   E is the energy fluctuation value:

where T is the temperature; B k is the Boltzmann coefficient;

(7)

( E E u       ( )

) ( ) E u

f

f

where f u is an increase in the contact bond length due to the applied load f F ;

) (   f E u and ( ) f E u are the values

of energy at corresponding displacements. To verify the proposed fluctuation model, we used the results of molecular dynamics simulation of the tension of a carbyne-graphene nanoelement containing a 10-atom carbyne chain at a temperature of 750 K. Despite the fact that the molecular dynamics method covers a relatively small time-scale, for T = 750 K we succeeded to obtain the values of time to the contact bond break within the region of realisation of both “low-energy” and “high-energy” mechanism (Fig. 4). At that, according to the simulation results, transition from the first mechanism to the second occurs when at the value of relative load 0 74 . *  un f F F . This agrees well with the fluctuation model predictions.

Fig. 4 (colour online) Dependence of the lifetime for CGN containing a ten-atom carbyne chain on relative load: lines are the theoretical dependences (modified REBO2 potential with dynamic cut-off function is used, computations are performed for T = 750K).  are the results of MD-simulation;  are their mean values. f F is the applied load; un F is the contact bond strength;

Fig. 5 (colour online) Dependence of the lifetime of a carbyne-graphene nanoelement with a ten-atomic carbyne chain on the value of applied load at temperatures T = 600 K and 1000 K for failure probabilities P of 1%, 50% and 99% (data on the atomic interaction are obtained from the DFT-calculation findings). Designations are the same as in Fig. 4.