Record statistics based prediction of fracture in the random spring network model

Abstract: We study the role of record statistics of damage avalanches in predicting the fracture of a heterogeneous material under tensile loading. The material is modeled using a two-dimensional random spring network where disorder is introduced through randomness in the breakage threshold strains of the springs. It is shown that the waiting time between successive records of avalanches has a maximum for moderate disorder, thus showing an acceleration of records with impending fracture. Such a signature is absent for low disorder strength when the fracture is nucleation-dominated, and high disorder strength when the fracture is percolation type. We examine the correlation between the record with the maximum waiting time and the crossover record at which the avalanche statistics change from off-critical to critical. Compared to the avalanche based predictor for failure, we show that the record statistics have the advantage of both being real-time as well as able to predict final fracture at much smaller strains. We also show that in the avalanche-dominated regime, the failure strain is shown to have a linear relation with the strain at the maximum waiting time, making possible a quantitative prediction.