Effective strain based on shear and principal strains in equal channel angular extrusion with outer curved corner

In this paper, with introducing and based on a new configuration of equal channel angular extrusion (ECAE) process, nominated as multi-stage equal channel angular extrusion, two relationships are derived to calculate the effective strain based on shear and principal strains. First, a solution is presented for evaluating the effective strain in multi-stage ECAE dies consisting of two or more ECAE sub-dies. Then, the solution is extended to calculate the effective strains in ECAE dies with outer curved corner. The effective strain based on shear strains shows an exact agreement with previously published results. The derived relationships were compared with each other, with the relationships derived by other researchers and with experimental results. It was observed that the agreement between the two theoretical relationships increases by increasing the outer curved corner. The largest difference between these two relationships is ⩽4% for ϕ = 90° and ψ = 0. In both of the derived relationships the agreement between experimental and theoretical results increases as the outer curved corner angle increases. Moreover, the effective strain based on principal strains is in a more agreement with experimental results.