Asymptotic analysis of stresses near a crack tip in a two dimensional colloidal packing saturated with liquid

TL;DR

This paper analyzes the asymptotic stress distribution near a crack tip in a two-dimensional liquid-saturated colloidal packing, relating critical capillary pressure to flaw size and material properties.

Contribution

It provides an asymptotic analysis of crack tip stresses in colloidal packings and links critical capillary pressure to flaw size using Griffith's criterion.

Findings

Derived asymptotic stress distribution near crack tips.

Established relation between critical capillary pressure and flaw size.

Determined maximum flaw size for crack-free packing.

Abstract

The consolidation of colloidal particles in drying colloidal dispersions is influenced by various factors such as particle size and shape, and inter-particle potential. The capillary pressure induced by the menisci, formed between the top layer of particles in the packed bed, compresses the bed of particles while the constraints enforced by the boundaries result in tensile stresses in the packing. Presence of flaws or defects in the bed determines its ultimate strength under such circumstances. In this study, we determine the asymptotic stress distribution around a flaw in a two dimensional colloidal packing saturated with liquid and compare the results with those obtained from the full numerical solution of the problem. Using the Griffith's criterion for equilibrium cracks, we relate the critical capillary pressure at equilibrium to the crack size and the mechanical properties of the packed bed. The analysis also gives the maximum allowable flaw size for obtaining a crack free packing.