  Graphene extraordinary strength, stiffness and lightness have generated great
expectations towards its application in flexible electronics and as mechanical
reinforcement agent. However, the presence of lattice defects, unavoidable in
sheets obtained by scalable routes, might degrade its mechanical properties.
Here we report a systematic study on the elastic modulus and strength of
graphene with controlled density of defects. Counter intuitively, the in-plane
Young modulus increases with increasing defect density up to almost twice the
initial value for vacancy content of ~0.2%, turning it into the stiffest
material ever reported. For higher density of vacancies, elastic modulus
decreases with defect inclusion. The initial increase in Young modulus is
explained in terms of a dependence of the elastic coefficients with the
momentum of flexural modes predicted for 2D membranes. In contrast, the
fracture strength decreases with defect density according to standard fracture
continuum models. These quantitative structure-property relationships, measured
in atmospheric conditions, are of fundamental and technological relevance and
provide guidance for applications in which graphene mechanics represents a
disruptive improvement.
