Theoretical approach to the ductile fracture of polycrystalline solids

TL;DR

This paper presents a theoretical model demonstrating that polycrystalline solids inevitably fracture after limited plastic deformation due to grain interactions, with predictions aligning well with experimental data.

Contribution

It introduces a novel continuum model of polycrystals that predicts fracture after small strains based on grain sliding and reshaping dynamics.

Findings

Hydrostatic pressure diverges logarithmically with strain

Model accurately predicts strains to fracture in commercial alloys

Grain sliding dominates over reshaping forces during deformation

Abstract

It is shown here that fracture after a brief plastic strain, typically of a few percents, is a necessary consequence of the polycrystalline nature of the materials. The polycrystal undergoing plastic deformation is modeled as a flowing continuum of random deformable polyhedra, representing the grains, which fill the space without leaving voids. Adjacent grains slide with a relative velocity proportional to the local shear stress resolved on the plane of the shared grain boundary, when greater than a finite threshold. The polyhedral grains reshape continuously to preserve matter continuity, being the forces causing grain sliding dominant over those reshaping the grains. It has been shown in the past that this model does not conserve volume, causing a monotonic hydrostatic pressure variation with strain. This effect introduces a novel concept in the theory of plasticity because determines that any fine grained polycrystalline material will fail after a finite plastic strain. Here the hydrostatic pressure dependence on strain is explicitly calculated and shown that has a logarithmic divergence which determines the strain to fracture. Comparison of theoretical results with strains to fracture given by mechanical tests of commercial alloys show very good agreement.