  Free-standing graphene is inherently crumpled in the out-of-plane direction
due to dynamic flexural phonons and static wrinkling. We explore the
consequences of this crumpling on the effective mechanical constants of
graphene. We develop a sensitive experimental approach to probe stretching of
graphene membranes under low applied stress at cryogenic to room temperatures.
We find that the in-plane stiffness of graphene is between 20 and 100 N/m at
room temperature, much smaller than 340 N/m (the value expected for flat
graphene). Moreover, while the in-plane stiffness only increases moderately
when the devices are cooled down to 10 K, it approaches 300 N/m when the aspect
ratio of graphene membranes is increased. These results indicate that softening
of graphene at temperatures less than 400 K is caused by static wrinkling, with
only a small contribution due to flexural phonons. Together, these results
explain the large variation in reported mechanical constants of graphene
devices and paves the way towards controlling their mechanical properties.
