sentences:  Within the linear region, the electronic properties would be relatively stable under the slightly changing geometry.The energy gaps increase from -0.02 eV to 0.02 eV for the strain between -0.02 and 0.02, which provides the feasibilities for future engineering applications.The tensile strength of the armchair graphene nanoribbons is 175 GPa with the great ductility of 30.26% fracture strain, which shows the greater mechanical properties comparing to the value of 130 GPa and 25% experimentally measured on monolayer graphene.