Plastic zone size at notch tip in mode I fracture using the modified Irwin’s model and volumetric approach

^a Research Team Materials, Mechanics and Civil Engineering, ENSAAGADIR, 80000, Morocco
^b Polytechnique Agadir, MEER, Universiapolis Bab Al Madina, Agadir 80000, Maroc.

Abstract

At crack tip the stress distribution has singularities (i.e the stress intensity is infinite) which is physically impossible. Irwin realised that the stresses at crack tip are finite and subsequently introduced the Stress Intensify Factor(SIF). This factor is used to determine this plastic zone size. The crack is a special case of the notch. Around the notch, the fracture needs a volume to develop according to the volumetric approach. This volume is characterised by the distance effective Xeff, the stress effective σ_eff and the stress intensity factorK_ρ^I. In This paper a new proposed formula called “Modified Irwin’s Model” based on Irwin’s model can be used to determine the plastic zone size. This new formula will be verified using numerical finite element simulation and validated using the Von-Mises and Tresca Criteria. The Modified Irwin’s Model can be an alternative way to estimate the fracture elaboration zone from the plastic zone.