Proposal and application of a new yield criterion for metal plastic deformation

Abstract

A new linear yield criterion in terms of principal stresses is developed for the purpose of overcoming the analytical difficulty of mechanical parameters when using the nonlinear Mises yield criterion. This developed yield criterion is established through the parabola interpolation method and the mathematical averaging method, which can be called as the mean influence factor yield criterion, or called MIF yield criterion for short. The yield locus of the criterion on the $$\pi $$-plane is an equilateral and non-equiangular dodecagon, lies between the Tresca and TSS loci, and is very close to the locus of the Mises yield criterion. By comparing with the classical yield criteria, the MIF yield criterion varies linearly with the Lode parameter and has a good accuracy with experimental data. Moreover, based on the flow rule and the geometric projection of the principle stress components, the specific plastic work rate of the yield criterion is also derived. The criterion and its specific plastic work rate are used to solve the limit load of a simply supported circular plate and the forging of a rectangular bar, and both the corresponding analytical solutions are obtained. The theoretical results for the limit load and the forging force are in good agreement with the simulation and experimental data, respectively, and are more accurate than the results calculated from other yield criteria.