Phonon softening and failure of graphene under tensile strain

• We show that phonon instabilities are responsible for the mechanical failure of graphene over a wide range of tensile strain directions.
• We demonstrate how phonon softening develops and finally triggers mechanical failure under tensile strain.
• We find out there are two types of phonon instabilities and either of them leads to mechanical failure depending on the direction of tensile strain.

Phonon softening of graphene under tensile strain is investigated based on ab initio density functional theory calculations. We demonstrate that, over a wide range of tensile strain directions, the strain-induced enhancement of phonon softening can give rise to phonon instabilities resulting in a mechanical failure of graphene. It is shown that there are two types of instabilities associated with phonons near K and Γ points, respectively, which induce symmetry-breaking structural distortions, and both of them lead to mechanical failure prior to the elastic failure commonly expected when the structural symmetry is retained.