Application of geometric midline yield criterion to analysis of three-dimensional forging

A kinematically admissible continuous velocity field was proposed for the analysis of three-dimensional forging. The linear yield criterion expressed by geometric midline of error triangle between Tresca and Twin shear stress yield loci on the π-plane, called GM yield criterion for short, was firstly applied to analysis of the velocity field for the forging. The analytical solution of the forging force with the effects of external zone and bulging parameter is obtained by strain rate inner product. Compression tests of pure lead are performed to compare the calculated results with the measured ones. The results show that the calculated total pressures are higher than the measured ones whilst the relative error is no more than 9.5%. It is implied that the velocity field is reasonable and the geometric midline yield criterion is available. The solution is still an upper-bound one.