Derivation of Equal Area Criterion and its Application to Crack Tip Plastic Zone Analysis

Abstract

A new linear yield criterion, referred to as Equal Area (EA) yield criterion, was derived in Haigh Westergaard stress space based on the projection area of its yielding locus on the π-plane equal to the area of von Mises yielding circle. Under the plane stress and strain conditions the crack tip plastic zone dimensions were calculated based on EA yield criterion and compared with those calculated according to the Tresca and von Mises yield criteria. The results showed that the crack tip plastic zone based on EA yield criterion is similar to that based on von Mises yield criterion, but is much different to that based on Tresca yield criterion. Meanwhile, the influences of Poisson ratio and loading parameter on the crack tip plastic zone were investigated based on EA yield criterion.

Analysis of vertical rolling using double parabolic model and stream function velocity field

“…In order to obtain the results, we use the co-line vector inner product [14][15][16] to integrate the friction power. It is found that…”