Crack-tip stress evaluation of multi-scale Griffith crack subjected to tensile loading by using peridynamics

TL;DR

This paper introduces a peridynamic method for evaluating crack-tip stress in multi-scale Griffith cracks under tensile loading, addressing limitations of classical elasticity and demonstrating stability and validity through numerical comparisons.

Contribution

It develops a novel peridynamic approach incorporating a scale factor for accurate crack-tip stress evaluation in multi-scale cracks, improving upon traditional methods.

Findings

Method is valid for multi-scale cracks

Stress evaluation tends to be stable with distance

Numerical results agree with Eringen's results

Abstract

Crack-tip stress evaluation has always been a problem in the frame of classical elasticity theory. Peridynamics has been shown to have great advantages in dealing with crack problems. In the present study, we present a peridynamic crack-tip stress evaluation method for multi-scale Griffith crack subject to tensile loading. The bond-based peridynamics is used to calculate the displacement field. Non-local deformation gradient definition from non-ordinary state-based peridynamics is used for stress calculation. Besides, a scale factor is introduced for evaluating crack-tip stress of multi-scale Griffith crack. Numerical results compared with Eringen's results show that this peridynamic crack-tip stress evaluation method is valid for multi-scale cracks, and with the change of distance of material points, the evaluated crack-tip stress tends to be stable.