Nucleation versus percolation: Scaling criterion for failure in disordered solids

Area of Science:

• Physics of disordered materials
• Solid mechanics
• Statistical physics

Background:

• The mode of failure in disordered solids is critically influenced by the effective range of stress field modifications after local rupture.
• Understanding this range is key to predicting material behavior under stress.

Purpose of the Study:

• To investigate the relationship between the stress field's effective range (R) and the failure mode in disordered solids.
• To determine the critical scaling of R with system size (L) that distinguishes different failure regimes.

Main Methods:

• Utilized a random fiber bundle model as a prototype for disordered solids.
• Analyzed the system's behavior in the large system size limit.
• Examined the scaling of the effective range R with system size L.

Main Results:

• Failure is nucleation-dominated when R scales slower than L^(2/3).
• For faster scaling of R, failure properties shift to a mean-field critical point with uncorrelated damage.
• Precursory avalanches of all sizes are observed in the mean-field limit, even for large systems.

Conclusions:

• The scaling of the stress field's effective range dictates the failure mode in disordered solids.
• The findings provide insights into the transition between nucleation-dominated and mean-field failure regimes.
• Results are expected to apply to systems with finite, normalizable disorder.