A Methodology to Determine the Effective Plastic Zone Size Around Blunt V-Notches under Mixed Mode I/II Loading and Plane-Stress Conditions

Abstract

The determination of the ductile failure behavior in engineering components weakened by cracks and notches is greatly dependent on the estimation of the plastic zone size (PZS) and, particularly, the effective plastic zone size (EPZS). Usually, time-consuming complex elastic–plastic analyses are required for the determination of the EPZS. Such demanding procedures can be avoided by employing analytical methods and by taking advantage of linear elastic analyses. In this sense, this work proposed a methodology for determining the PZS around the tip of blunt V-notches subjected to mixed mode I/II loading and plane-stress conditions. With this aim, firstly, existing approximate mathematical expressions for the elastic stress field near round-tip V-notches reported in the literature are presented. Next, Irwin’s approach (fundamentally proposed for sharp cracks) and a yield criterion (von Mises or Tresca) were applied and are presented. With the aim of verifying the proposed methodology, elastic–plastic finite element analyses were performed on virtual AISI 304 steel V-notched specimens. It was shown that the analytical formulations presented cannot estimate the complete shape of the plastic zone. However, the EPZS, which is crucial for predicting the type of ductile failure in notched members, can be successfully estimated.

Keywords

• round-tip V-notch
• effective plastic zone size
• Irwin’s model
• analytical method
• mixed mode I/II loading
• plane–stress conditions