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Transitional failure envelopes of single- and double-walled carbon nanotubes under combined tension-torsion are predicted using classical molecular dynamics simulations. The observations reveal that while the tensile failure load decreases with combined torsion, the torsional buckling moment increases with combined tension. As a result, the failure envelopes under combined tension-torsion are definitely different from those under pure tension or torsion. In such combined loading, there is a multitude of failure modes (tensile failure and torsional buckling), and the failure consequently exhibits the feature of transitional failure envelopes. In addition, the safe region of double-walled carbon nanotubes is significantly larger than that of single-walled carbon nanotubes due to the differences in the onset of torsional buckling.

This work examines the size-dependent elastic and failure properties of single-walled carbon nanotubes (CNTs) with various aspect ratios under simultaneously combined tensiletorsional loads that can widely occur on the nanotubes incorporated in nanometer-scale devices and composite materials; classical molecular dynamics simulations are used. In particular, the effects of coupling between combined loads are investigated carefully, and then the size-dependent failure properties and multiple failure modes are characterized with failure criteria like multiple failure envelopes. These multiple failure modes consist of both the tensile fracture and torsional instability that refer to any actions leading to an inability of CNTs. The observations reveal that while the tensile failure load decreases with combined torsion, the torsional buckling load and shear stiffness increase with combined tension. These effects are due to the coupling between combined loads, and strongly dependent on the size and chirality of CNTs and the ratios of combined loading. This result therefore establishes the multiple failure envelopes, which are definitely different relative to what is predicted under uniaxial tension or torsion.

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