  We address the role of the nature of material disorder in determining the
roughness of cracks which grow by damage nucleation and coalescence ahead of
the crack tip. We highlight the role of quenched and annealed disorders in
relation to the length scales $d$ and $\xi_c$ associated with the disorder and
the damage nucleation respectively. In two related models, one with quenched
disorder in which $d \simeq \xi_c $, the other with annealed disorder in which
$d \ll \xi_c$, we find qualitatively different roughening properties for the
resulting cracks in 2-dimensions. The first model results in random cracks with
an asymptotic roughening exponent $\zeta \approx 0.5$. The second model shows
correlated roughening with $\zeta\approx 0.66$. The reasons for the qualitative
difference are rationalized and explained.
