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

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contact bond length 01 a increases almost 2 times, and all other bonds are shortened. At the same time, the total length of nanoelement c remains unchanged. The magnitude of total energy of the system doesn't change either. The latter means that the work of doubling the contact bond length is performed by internal forces. In other words, the accumulated “elastic” energy is “pumped” into the contact bond. This means that the fluctuation-induced instability of the contact bond can act as a “trigger” for the redistribution of accumulated energy, reducing the total energy cost for breaking the bond. DFT-calculations make it possible to determine the level of the lower boundary, min R F , of instability region. When the energy re-distribution is induced by fluctuation, the magnitude of the work of internal forces depends on the level of applied force f F . It means that the current level R F of the IZ lower boundary also depends on the level of acting force f F . Kotrechko et al. (2017) suggested an approximate dependence of R F on the level of applied force f F : 2 2 f un R F F F    (1) where un F is the contact bond strength;  is the coefficient, characterising sensitivity of the IZ width to the magnitude of applied force f F . According to the data of Kotrechko et al. (2019), for carbyne–graphene nanoelements with different length of carbyne chains, the value of  varies within rather narrow range  ≈ 0.85÷0.96.

Fig. 2 (colour online) Force vs. displacement of the contact atom (scheme):

f F is the “applied” force;

f u is the atomic displacement by the force

f F ;

un F is the bond strength;

un u is the displacement corresponding

to the unstable position of an atom;

br u is the displacement corresponding to a bond break;

c  is the critical value of fluctuation at a given load

f F ; un  is the minimal fluctuation required for the bond instability.

The ratio between the magnitude of the applied load f F and the lower boundary of the instability region R F has a key effect on the probability of fluctuation-induced contact bond break. Depending on the relationship between f F and R F , two failure mechanisms are possible [Kotrechko et al. (2019)]: (i) high-energy (at f R F F  ) and (ii) low energy (at f R F F  ). In the first case, the value of critical fluctuation c  exceeds significantly its minimum value ) ( un c un     (Fig. 2) and is predetermined by a level of f F . In this case, the presence of IZ gives rise to a certain decrease in the energy cost of breaking the bond. The degree of this decrease grows with increasing applied load. In the second case, the critical fluctuation c  required to break the contact bond is much smaller. It is equal to the minimum value un  (Fig. 2). This yields a steep increase in the probability of breaking the contact bond, and, accordingly, to a decrease in the lifetime to tenths (hundredths) of a second [Kotrechko et al. (2017)]. From the condition (1) taking into account the value of  , it is possible to estimate the magnitude of the load * f F , upon reaching which there is a transition from a high-energy to a low-energy mechanism: