Path independent forming limits in strain and stress spaces

Many practitioners of the metal forming community remain faithful to the idea that strain metrics are useful for formability assessment, while many others who are aware of the limitations of strain metrics are nevertheless reluctant to use stress metrics because of concerns about their practicality. In this work, we review the stress-based forming limit approach and discuss the major history-dependent parameters explicitly accounting for non-linear deformation in the stress space. Then, the parameters are consistently considered in the strain spaces and a new type of forming limit diagram based on a polar representation of the EPS (Effective Plastic Strain) is proposed that has advantages of both stress and strain metrics. The Polar Effective Plastic Strain (PEPS) appears to be an effective solution to the problem of nonlinear effects, with advantages of the familiar strain-based diagram for linear loading, and without the strain-hardening limitations of the stress diagram, or non-intuitive aspects of the alternate Cartesian diagrams based on effective plastic strain.