  We study the effect of the sample thickness in planar crack front propagation
in a disordered elastic medium using the random fuse model. We employ different
loading conditions and we test their stability with respect to crack growth. We
show that the thickness induces characteristic lengths in the stress
enhancement factor in front of the crack and in the stress transfer function
parallel to the crack. This is reflected by a thickness-dependent crossover
scale in the crack front morphology that goes from from multi-scaling to
self-affine with exponents in agreement with line depinning models and
experiments. Finally, we compute the distribution of crack avalanches which is
shown to depend on the thickness and the loading mode.
