Finite-time Singularities in Surface-Diffusion Instabilities are Cured by Plasticity

TL;DR

This paper demonstrates that plasticity in materials prevents finite-time singularities caused by surface diffusion instabilities under stress, transforming potential cusp singularities into regular cracks.

Contribution

It introduces the role of plasticity in curing surface-diffusion instabilities, providing a new understanding of stability in stressed materials.

Findings

Plasticity prevents finite-time cusp singularities.

Instability leads to regular crack formation instead of singularities.

Plastic effects stabilize the surface under non-hydrostatic stress.

Abstract

A free material surface which supports surface diffusion becomes unstable when put under external non-hydrostatic stress. Since the chemical potential on a stressed surface is larger inside an indentation, small shape fluctuations develop because material preferentially diffuses out of indentations. When the bulk of the material is purely elastic one expects this instability to run into a finite-time cusp singularity. It is shown here that this singularity is cured by plastic effects in the material, turning the singular solution to a regular crack.