Upper-bound analysis of die corner gap formation for strain-hardening materials in ECAP process

In this paper, the upper-bound solutions proposed by Eivani and Karimi Taheri (2008) to calculate processing force and evaluate die corner angle Ψ formation for distinct friction conditions and tooling geometry during single pass equal channels angular pressed perfectly plastic metals at room temperature were extended to work-hardening metals by using the Hollomon model combined to von Mises isotropic plasticity criterion. Also, plane strain finite-element models were developed to validate the proposed extended analytical solutions by comparing the predictions of angle Ψ, effective plastic strains and pressing force. Mechanical properties of an aluminum Al6070 alloy were considered and its behavior under pressing was evaluated to non-hardening and work-hardening conditions in all performed analyses. The theoretical predictions consistently showed that higher values of die corner angle Ψ and smaller predictions of both effective plastic strains and pressing force are obtained when the work-hardening behavior is included in the models independently of either tribology or tooling arrangements. These aspects were confirmed by comparison with the respective finite-element predictions. In addition, with the proposed upper-bound models it was possible to analyze the dependency of angle Ψ, effective plastic strain and pressing load with the instantaneous workpiece height at the entry surface of deformation zone.