Elastic softening and fracture in randomly perforated solids

TL;DR

This study investigates how random perforations in PMMA affect its mechanical properties, revealing that irregular pore geometries and defect interactions significantly accelerate softening and fracture beyond classical models.

Contribution

It demonstrates that irregular pore shapes and coalescence lead to greater softening and failure than predicted by traditional effective medium theories.

Findings

Young's modulus decreases nearly linearly with porosity but faster than classical predictions.

Critical porosity for zero stiffness is below the percolation threshold due to pore irregularities.

Rupture stress follows a Weibull distribution considering defect size and stress concentration.

Abstract

We study the mechanical response of quasi-brittle polymethyl methacrylate (PMMA) specimens containing controlled random distributions of laser-cut holes. Tensile tests combined with digital image correlation reveal a nearly linear decrease of the Young's modulus with porosity, but with a softening rate far exceeding classical effective medium theory and the Hashin-Shtrikman bound. The extrapolated critical porosity at which the modulus vanishes is well below the 2D percolation threshold, indicating that ideal cylindrical void models fail to capture the observed behavior. Microscopy shows irregular pore geometries and frequent coalescence, which effectively act as crack-like defects and strongly enhance compliance. The rupture stress distributions are well described by a Weibull model accounting for both load-bearing area reduction and stress concentration at hole edges. Digital image correlation reveals heterogeneous but non-localized deformation, with strain increasingly correlated with the hole pattern, indicating a growing influence of defect-induced stress concentrations. These results highlight the dominant role of defect morphology in governing stiffness degradation and fracture statistics in porous quasi-brittle materials.