Mode I crack tip fields: strain gradient plasticity theory versus J2 flow theory

I hope some of you may find this work interesting. We show, analytically and numerically, that strain gradient plasticity predicts the existence of an inner elastic field adjacent to the crack tip, reminiscent of a dislocation-free zone. The fact that elastic strains dominate plastic strains near the crack tip implies a paradigm-shift with respect to previous crack tip asymptotic studies in plasticity and gradient plasticity, which neglect elastic strains. 

Emilio Martínez-Pañeda, Norman A. Fleck

Mode I crack tip fields: Strain gradient plasticity theory versus J2 flow theory. 

European Journal of Mechanics - A/Solids 75, pp. 381-388 (2019)

https://www.sciencedirect.com/science/article/pii/S0997753818308313

A post-print is available at www.empaneda.com

The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and an inner elastic K field. The inner elastic core significantly influences the crack opening profile. Crack tip plasticity is suppressed when the material length scale L of the gradient theory is on the order of the plastic zone size estimation, as dictated by the remote stress intensity factor. A generalized J-integral for strain gradient plasticity is stated and used to characterise the asymptotic response ahead of a short crack. Finite element analysis of a cracked three point bend specimen reveals that the crack tip elastic zone persists in the presence of bulk plasticity and an outer J-field.