FRACTURING OF BRITTLE HOMOGENEOUS SOLIDS. FINITE SIZE SCALINGS

TL;DR

This study uses a 2D lattice model to analyze crack growth in brittle homogeneous solids under tensile and hydraulic pressures, revealing finite-size effects and the influence of microstructure on scaling behaviors.

Contribution

It provides numerical finite-size scalings for breaking stresses and pressures, highlighting differences between continuum predictions and lattice-based results for hydraulic fracturing.

Findings

Good agreement with continuum theory for tensile cracks

Different finite-size scaling observed for hydraulic fracturing

Microstructure influences the scaling behavior in lattice models

Abstract

Using a two dimensional lattice model we investigate the crack growth under the influence of remote tensile forces as well as due to an internally applied pressure (hydraulic fracturing). For homogeneous elastic properties we present numerical finite-size scalings for the breaking stresses and pressures in terms of crack lengths and lattice sizes. Continuum theory predicts for the tensile and for the pressure problem identical scaling functions. Our findings for the tensile problem are in very good agreement with continuum results. However, for the hydraulic fracture problem we observe a different finite-size scaling. We explicitly demonstrate that the modified scaling is a consequence of the discrete structure of the lattice (micro structure).