Understanding cracked materials: is Linear Elastic Fracture Mechanics obsolete?

Abstract

AbstractLinear elastic fracture mechanics has enabled the research community to solve a wide variety of problems of practical and scientific interest; however, it has historically suffered from two main shortcomings. Firstly, it predicts physically unrealistic singular stresses and strains at crack tips. Secondly, microstructural effects are lacking, so that a major source of size‐dependent behaviour is not captured. Gradient‐enriched elasticity overcomes both these shortcomings: singularities are avoided, so that crack‐tip stresses can be used to assess integrity, and the inclusion of microstructural terms implies that size effects can be captured. In this investigation, it is shown that gradient‐enriched crack tip stresses can directly be used to model the transition from the short to the long crack regime. The accuracy of this approach was validated by a wide range of experimental results taken from the literature and generated under both static and high‐cycle fatigue loading. This high level of accuracy was achieved without having to resort to phenomenological model parameters: the extra constitutive coefficient was simply the (average) grain size of the material.