Meso-scale size effects of material heterogeneities on crack propagation in brittle solids: Perspectives from phase-field simulations

TL;DR

This study uses phase-field simulations to analyze how meso-scale heterogeneities in brittle solids influence crack propagation, revealing optimal inclusion sizes and configurations for enhancing toughness based on the K-dominance zone.

Contribution

It introduces a systematic phase-field simulation approach to optimize mesoscale heterogeneity design for improved crack resistance in brittle composites.

Findings

Matching inclusion size to the K-dominance zone enhances toughening.

Lower volume fractions can improve toughness if inclusion size exceeds the K-zone.

Designing heterogeneities based on K-zone estimates can optimize strength and toughness.

Abstract

Brittle solids are often toughened by adding a second-phase material. This practice often results in composites with material heterogeneities on the meso scale: large compared to the scale of the process zone but small compared to that of the application. The specific configuration (both geometrical and mechanical) of this mesoscale heterogeneity is generally recognized as important in determining crack propagation and, subsequently, the (effective) toughness of the composite. Here, we systematically investigate how dynamic crack propagation is affected by mesoscale heterogeneities taking the form of an array of inclusions. Using a variational phase-field approach, we compute the apparent crack speed and fracture energy dissipation rate to compare crack propagation under Mode-I loading across different configurations of these inclusions. If fixing the volume fraction of inclusions, matching the inclusion size to the K-dominance zone size gives rise to the best toughening outcome. Conversely, if varying the volume fraction of inclusions, a lower volume fraction configuration can lead to a better toughening outcome if and only if the inclusion size approaches from above the size of the K-dominance zone. Since the size of the K-dominance zone can be estimated \textit{a priori} given an understanding of the application scenario and material availability, we can, in principle, exploit this estimation to design a material's mesoscale heterogeneity that optimally balances the tradeoff between strength and toughness. This paves the way for realizing functional (meta-)materials against crack propagation in extreme environments.