The surface-forming energy release rate versus the local energy release rate

TL;DR

This paper compares two types of energy release rates at a crack tip, revealing that stress singularity introduces kinetic energy effects, and recommends using the surface-forming ERR for elastic-plastic fracture analysis due to its simplicity and broad applicability.

Contribution

It clarifies the difference between surface-forming and local ERRs, especially in the presence of stress singularity, and advocates for the surface-forming ERR as a practical fracture criterion.

Findings

Stress singularity causes kinetic energy at the crack tip.

Surface-forming ERR is more suitable for elastic-plastic fracture analysis.

The paper provides a mathematical interpretation of ERR differences.

Abstract

This paper identifies two ways to extract the energy (or power) flowing into a crack tip during propagation based on the power balance of areas enclosed by a stationary contour and a comoving contour. It is very interesting to find a contradiction that two corresponding energy release rates (ERRs), a surface-forming ERR and a local ERR, are different when stress singularity exists at a crack tip. Besides a rigorous mathematical interpretation, we deduce that the stress singularity leads to an accompanying kinetic energy at the crack tip. The local ERR represents the driving force to overcome the surface energy and the accompanying kinetic energy, while the surface-forming ERR represents the driving force to overcome the surface energy only. Their advantages and disadvantages are discussed. We recommend using the surface-forming ERR based fracture criterion for a crack propagation in elastic-plastic materials, since it has a wide applicability and concise formulae which are easy to compute among all energy based criteria.