  In mechanical systems it is of interest to know the onset of fracture in
dependence of the boundary conditions. Here we study a one-dimensional model
which allows for an underlying heterogeneous structure in the discrete setting.
Such models have recently been studied in the passage to the continuum by means
of variational convergence ($\Gamma$-convergence). The $\Gamma$-limit results
determine thresholds of the boundary condition, which mark a transition from
purely elastic behaviour to the occurrence of a crack. In this article we
provide a notion of fracture in the discrete setting and show that its
continuum limit yields the same threshold as that obtained from the
$\Gamma$-limit. Since the calculation of the fracture threshold is much easier
with the new method, we see a good chance that this new approach will turn out
useful in applications.
