A weighted average yield criterion and its applications to burst failure of pipeline and three-dimensional forging

Abstract

By weighting the Tresca and TSS yield criteria with the golden ratio 0.618, a linear yield criterion, called WA yield criterion for short, is proposed as a linear function of the principal stress components σ1, σ2, and σ3. The shear yield stress for the proposed yield criterion is also calculated, whose value is very close to that of the Mises yield criterion. The yield locus of the proposed yield criterion on the π-plane is described in geometry and proved to be a dodecagon with the same side length of 0.4148σs and two intersection angles of 140.4° and 159.6°. To verify the proposed yield criterion, a comparison is made between the calculated stress difference ratio and the available experimental data, and a good agreement is found. By applying the WA yield criterion to the prediction of burst pressure for pipelines, the present yield criterion is found to be the best one. Moreover, the specific plastic work rate (SPWR) of the WA yield criterion is also derived and applied to a three-dimensional forging accounting for bulge. Through the derived SPWR, an analytical solution of the forging forces is obtained, and an experiment of forging pure lead is performed. Comparison of the present calculated forging forces with the present experimental data of pure lead forging as well as the other theoretical ones clarifies that the present SPWR has the superiority of predicting the forging forces. In addition, the dominant parameters that affect the burst pressure of pipelines and the stress state coefficients of the 3D forging are discussed systematically.