  We investigate by means of computer simulations the effect of structural
disorder on the statistics of cracking for a thin layer of material under
uniform and isotropic drying. The layer is discretized into a triangular
lattice of springs. The drying process is captured by reducing the natural
length of all springs by the same factor, and the amount of quenched disorder
is controlled by varying the width {\xi} of the distribution of the random
breaking thresholds for the springs. Once a spring breaks, redistribution of
the load may trigger an avalanche of breaks. Our simulations revealed that the
system exhibits a phase transition with the amount of disorder as control
parameter: at low disorders, the breaking process is dominated by a macroscopic
crack at the beginning, and the size distribution of the subsequent breaking
avalanches shows an exponential form. At high disorders, the fracturing
proceeds in small-sized avalanches with an exponential distribution, generating
a large number of micro-cracks which eventually merge and break the layer.
Between both phases a sharp transition occurs at a critical amount of disorder
{\xi}_c = 0.40 \pm 0.01, where the avalanche size distribution becomes a power
law with exponent {\tau} = 2.6 \pm 0.08, in agreement with the mean-field value
{\tau} = 5/2 of the fiber bundle model. Good quality data collapses from the
finite-size scaling analysis show that the average value of the largest burst
<\Delta_max> can be identified as the order parameter, with {\beta}/{\nu} = 1.4
and 1/{\nu} = 1.0, and that the average ratio <m2 /m1> of the second m2 and
first moments m1 of the avalanche size distribution shows similar behaviour to
the susceptibility of a continuous transition, with {\gamma}/{\nu} = 1.,
1/{\nu} = 0.9. These suggest that the disorder induced transition of the
breakup of thin layers is analogous to a continuous phase transition.
