  The propagation of (planar) cracks in a heterogeneous brittle material
characterized by a random field of toughness is considered, taking into account
explicitly the effect of the crack front roughness on the local stress
intensity factor. In the so-called strong-pinning regime, the onset of crack
propagation appears to map onto a second-order phase transition characterized
by universal critical exponents which are independent of the local
characteristics of the medium. Propagation over large distances can be
described by using a simple one-dimensional description, with a correlation
length and an effective macroscopic toughness distribution that scale in a
non-trivial fashion with the crack front length. As an application of the above
concepts, the arrest of indentation cracks is addressed, and the analytical
expression for the statistical distribution of the crack radius at arrest is
derived. The analysis of indentation crack radii on alumina is shown to obey
the predicted algebraic expression for the radius distribution and its
dependence on the indentation load.
