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The stress-strain response of pristine monolayer graphene under uniaxial loading/unloading over a more extensive size range (100 nm×100 nm) is studied by molecular dynamics simulations, which proves that graphene is perfectly elastic prior to the failure strain. Young's modulus of graphene is calculated by selecting different strain ranges in the elastic region. It is found that Young's modulus is strongly dependent on the strain range. When the selected strain ranges are increased from 0.5% to 8%, Young's modulus of the armchair and zigzag graphene is reduced by approximately 60 GPa and 150 GPa, respectively. Based on the Pearson correlation coefficient method, the linearity of the stress-strain curve during graphene stretching is studied. The elastic region of the tensile curve is divided into the linear elastic region and non-linear elastic region. Simultaneously, the linear elastic limit strains for the armchair and zigzag graphene are defined to be about 2.5% and 1.5%, respectively, and they are independent of the size of graphene. On this basis, the chirality dependence and size effects of Young's modulus, failure strain, and fracture strength of pristine monolayer graphene are investigated. The results show that Young's modulus is dependent on the chiral angle but insensitive to size. The failure strain and fracture strength depend on the chiral angle and have obvious size effects. [ABSTRACT FROM AUTHOR]