From Brittle to Ductile and Back: Reentrant Fracture Transition in Disordered Two-Phase Solids

TL;DR

This study explores how two-phase disordered solids exhibit a reentrant fracture transition from brittle to ductile-like and back to brittle, influenced by phase composition and failure strain mismatch, using a spring network model.

Contribution

It reveals the reentrant fracture transition in two-phase solids and analyzes the underlying mechanisms through avalanche statistics and cluster growth dynamics.

Findings

Reentrant transition from brittle to ductile-like and back to brittle with increasing tough phase.

Change in avalanche exponent indicating a shift in universality class during transition.

Distinct cluster growth mechanisms characterize brittle and ductile regimes.

Abstract

Fracture processes in multi-phase solids are inherently complex due to multiple competing mechanisms. Here, we investigate the elastic and fracture behaviour of two-phase solids, comprising a fragile phase and a tough phase using a disordered spring network model. The macroscopic response is found to depend on the failure strain mismatch, the elastic modulus ratio, as well as the relative composition of the constituent phases. As the proportion of the tough phase increases, the system undergoes a reentrant phase transition in fracture behaviour: from brittle to ductile-like and back to brittle. These transitions are identified through both 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. Analysis of time evolution of cluster characteristics reveals distinct growth mechanisms in the two regimes. In the brittle regime, dominant clusters rapidly absorb other large clusters, keeping the total number of clusters nearly constant. In contrast, the ductile regime is characterised by more gradual coalescence, leading to a decrease in the total number of clusters over time while their average size increases. We provide a physical interpretation of the mechanisms underlying the observed switch in fracture behaviour.