  Multi-phase materials, such as composite materials, exhibit multiple
competing failure mechanisms during the growth of a macroscopic defect. For the
simulation of the overall fracture process in such materials, we develop a
two-phase spring network model that accounts for the architecture between the
different components as well as the respective disorders in their failure
characteristics. In the specific case of a plain weave architecture, we show
that any offset between the layers reduces the delocalization of the stresses
at the crack tip and thereby substantially lowers the strength and fracture
toughness of the overall laminate. The avalanche statistics of the broken
springs do not show a distinguishable dependence on the offsets between layers.
The power law exponents are found to be much smaller than that of disordered
spring network models in the absence of a crack. A discussion is developed on
the possibility of the avalanche statistics being those near breakdown.
