  In order to study the stability of mode-I fracture, we consider a crack
moving along the centerline of a very wide strip and compute its steady-state
response to a small, spatially periodic shear stress. We find that, in the
presence of this perturbation, the crack remains very nearly straight up to a
critical speed $v_c$ of about $0.8\,v_R$, where $v_R$ is the Rayleigh speed.
Deviations from straight-line propagation are suppressed by a factor
proportional to $W^{-1/2}$, where $W$ is the width of the strip. At $v_c$,
however, this suppression disappears and the steady-state crack follows the
wavy curve along which the shear stress vanishes in the unbroken strip. We
interpret this behavior as a loss of stability and discuss its implications for
a more complete dynamical theory of fracture propagation.
