  We study the stability and roughness of propagating cracks in heterogeneous
brittle two-dimensional elastic materials. We begin by deriving an equation of
motion describing the dynamics of such a crack in the framework of Linear
Elastic Fracture Mechanics, based on the Griffith criterion and the Principle
of Local Symmetry. This result allows us to extend the stability analysis of
Cotterell and Rice to disordered materials. In the stable regime we find
stochastic crack paths. Using tools of statistical physics we obtain the power
spectrum of these paths and their probability distribution function, and
conclude they do not exhibit self-affinity. We show that a real-space fractal
analysis of these paths can lead to the wrong conclusion that the paths are
self-affine. To complete the picture, we unravel the systematic bias in such
real-space methods, and thus contribute to the general discussion of
reliability of self-affine measurements.
