Open-die forging experiments using different die geometries under hot isothermal conditions and three-dimensional simulations using rigid-plastic finite-element method were performed to formulate a void-closing behavior using only two factors : the integral of hydrostatic stress and the equivalent strain. First, upsetting, side-upsetting and V-shape die cogging of several cylinders with a spherical void at the center are carried out and the information on the void volume reduction is obtained. Seconds, the same forgings, but without voids is treated numerically and the development of stress and strain at the location of voids is investigated. Then, by combining these results, and using regression analysis, it is found that the void volume reduction is expressed as a polynomial function of the two factors. When the polynomial function is used, various forging methods can be evaluated quantitatively in terms of void-closing behavior. Therefore it is beneficial to optimize the forging process for a large rotor shaft.
