  We study how crack buckling affects stress and strain in a thin sheet with
random disorder. The sheet is modeled as an elastic lattice of beams where each
of the beams have individual thresholds for breaking. A statistical
distribution with an exponential tail towards either weak or strong beams is
used to generate the thresholds and the magnitude of the disorder can be varied
arbitrarily between zero and infinity. Applying a uniaxial force couple along
the top and bottom rows of the lattice, fracture proceeds according to where
the ratio of the stress field to the local strength is most intense. Since
breakdown is initiated from an intact sheet where the first crack appears at
random, the onset and mode of buckling varies according to where and how the
cracks grow. For a wide range of disorders the stress-strain relationships for
buckling sheets are compared with those for non-buckling sheets. The ratio of
the buckling to the non-buckling value of the maximum external force the system
can tolerate before breaking is found to decrease with increasing disorder, as
is the ratio for the corresponding displacement.
