From brittle to ductile and back: Reentrant fracture transition in disordered two-phase solids

Fracture processes in multiphase solids are inherently complex due to multiple competing mechanisms. Here, we investigate the elastic and fracture behavior of two-phase solids comprising a fragile phase and a tough phase using a disordered spring network model. As the proportion of the tough phase increases, the system undergoes a reentrant phase transition in fracture behavior: from brittle to ductilelike and back to brittle. These transitions and the physical interpretation of the underlying mechanisms are identified through avalanche statistics and cluster-size characteristics of broken springs. Notably, the avalanche exponent associated with the majority phase changes universality class during the brittle-to-ductile transition. In the brittle regime, dominant clusters rapidly absorb other large clusters. In contrast, the ductile regime is characterized by more gradual coalescence, leading to a decrease in the total number of clusters over time while their average size increases.