Fracture and second-order phase transitions

Using the global fiber bundle model as a tractable scheme of progressive fr acture in heterogeneous materials, we define the branching ratio in avalanc hes as a suitable order parameter to clarify the order of the phase transit ion occurring at the collapse of the system. The model is analyzed using a probabilistic approach suited to smooth fluctuations. The branching ratio s hows a behavior analogous to the magnetization in known magnetic systems wi th second-order phase transitions. We obtain a universal critical exponent beta approximate to 0.5 independent of the probability distribution used to assign the strengths of individual fibers.