Role of spatial patterns in fracture of disordered multiphase materials

Record statistics of fracture in the random spring network model

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 strain interval between successive records of avalanches has a maximum for moderate disorder, thus showing an acceleration in occurrence of records when approaching final fracture. Such a signature is absent for low disorder when the fracture is nucleation-dominated, as well as for high disorder when the fracture is percolation type. We examine the correlation between the record with the maximum waiting strain interval and the crossover record at which the avalanche statistics change from off-critical to critical. Compared to the avalanche exponent crossover based prediction for failure, we show that the record statistics have the advantage of both being real-time as well as being a precursor significantly prior to final fracture. We also find that in the avalanche-dominated regime, the failure strain is at best weakly correlated with the strain at the maximum waiting strain interval. A stronger correlation is observed between the index of the largest record and the index of the record at the maximum waiting strain interval.

Role of composition in fracture behavior of two-phase solids

In a two-phase solid, we examine the growth of a preexisting macroscopic crack based on simulations of a random spring network model. We find that the enhancement in toughness, as well as strength, is strongly dependent on the ratio of elastic moduli as well as on the relative proportion of the phases. We find that the mechanism that leads to enhancement in toughness is not the same as that for enhancement in strength; however, the overall enhancement is similar in mode I and mixed-mode loading. Based on the crack paths, and the spread of the fracture process zone, we identify the type of fracture to transition from nucleation type, for close to single-phase compositions, whether hard or soft, to avalanche type for more mixed compositions. We also show that the associated avalanche distributions exhibit power-law statistics with different exponents for each phase. The significance of variations in the avalanche exponents with the relative proportion of phases and possible connections to the fracture types are discussed in detail.

Interplay between disorder and hardening during tensile fracture of a quasi-brittle solid

We examine the specific role of the interplay between hardening and disorder characteristics of a representative quasi-brittle material on its failure mechanisms using a random spring network model. The model incorporates quasi-brittleness in its spring constants and disorder in the failure strain threshold and is shown to be effective in simulating the experimentally observed tensile and fracture behaviour of a quasi-brittle epoxy resin-based polymer. It is shown that rapid localization of deformation and associated damage growth occurs for a weakly hardening solid while for a linear elastic material, damage nucleates at multiple independent sites, and there is significant growth of damage, independent of other nucleating sites, prior to maximum load. The failure mechanism is shown to crossover from an avalanche-dominated fracture for a linear elastic material to nucleation-dominated fracture for a weakly hardening material.