Buckling and postbuckling of single-walled carbon nanotubes under combined axial compression and torsion in thermal environments

The buckling behavior of single-walled carbon nanotubes under combined axial compression and torsion is investigated by using molecular dynamics simulations, to evaluate interactive buckling loads, and to assess the effect of temperature changes on bucking and postbuckling responses. Simulation results show that both the armchair and zigzag tubes exhibit nonlinear interaction curves at different temperature considered, and the interactive buckling loads are strongly size dependent. The buckling and postbuckling behavior of single-walled carbon nanotubes depends strongly on the temperature. Rise in temperature results in decrease of interactive buckling loads and postbuckling equilibrium paths, and the effect of temperature varies with the value of load-proportional parameter. The results also reveal that the single-walled carbon nanotubes may display two kinds of typical buckling configurations under combined loads, which are characterized by notable features distinct from those presented in pure axial compression or torsion.

Figure 1

Snapshot of the simulation system for (8,8)-tube. The fixed end, loading end, thermostat atoms, and combined loading of axial compression $P$ and torque $M_s$ are indicated.

Figure 2

(Color online) Effect of temperature change on the interaction buckling curves of SWCNTs under combined axial compression and torsion: (a) (8,8)-tube; (b) (14,0)-tube.

Figure 3

(Color online) Effect of nanotube size on the interaction buckling curves of SWCNTs under combined axial compression and torsion: (a) effect of radius, three (6,6), (8,8), and (10,10) tubes with different values of radius being $0.41\mathrm{nm}$, $0.55\mathrm{nm}$, and $0.68\mathrm{nm}$; (b) effect of length, three (8,8)-tubes with different lengths ranging from $3.83\mathrm{nm}\text{to}8.04\mathrm{nm}$.

Figure 4

(Color online) Postbuckling behavior of a (8,8)-tube under combined axial compression and torsion at $800\mathrm{K}$. The notations $A$ and $B$ stand for mechanical loads of pure axial compression and pure torsion, respectively. Curves 1 to 4 correspond to combined loading cases (1: $\mu =11.85$; 2: $\mu =4.70$; 3: $\mu =2.19$; 4: $\mu =0.86$).

Figure 5

(Color online) Postbuckling behavior of a (14,0)-tube under combined axial compression and torsion at $800\mathrm{K}$. The notations $A$ and $B$ stand for mechanical loads of pure axial compression and pure torsion, respectively. Curves 1 to 4 correspond to combined loading cases (1: $\mu =11.85$; 2: $\mu =4.70$; 3: $\mu =2.19$; 4: $\mu =0.86$).

Figure 6

(Color online) Variation of strain energy as a function of axial strain for a (8,8)-tube under combined axial compression and torsion at $800\mathrm{K}$ (1: $\mu =11.85$; 2: $\mu =4.70$; 3: $\mu =2.19$; 4: $\mu =0.86$). The critical points are marked by solid dots.

Figure 7

(Color online) Effect of temperature change on postbuckling behavior of a (14,0)-tube under combined axial compression and torsion: (a) Plots of internal force versus axial strain with $\mu =11.85$; (b) plots of torsional moment versus twist angle per unit length with $\mu =0.86$.

Figure 8

Buckling configurations of a (8,8)-tube at $800\mathrm{K}$. (a) and (e) correspond to pure axial compression and pure torsion, respectively (a: $\epsilon =0.072$; e: $\varphi =16.76\text{degree}∕\mathrm{nm}$). (b)–(d) are for combined axial compression and torsion (b: $\mu =4.70$, $\epsilon =0.073$, $\varphi =3.83\text{degree}∕\mathrm{nm}$; c: $\mu =2.19$, $\epsilon =0.075$, $\varphi =8.90\text{degree}∕\mathrm{nm}$; d: $\mu =0.86$, $\epsilon =0.076$, $\varphi =17.87\text{degree}∕\mathrm{nm}$). The shapes and relative places of corresponding cross-sections for two flattenings are plotted at the bottom of each figure, solid and dash sections represent the upper and lower flattenings, which are marked as $A\text{−}A$ and $B\text{−}B$ in deformed tube structure, respectively.