A criterion for void closure in the porous model during the forging of steel ingot and its application

•A criterion for multiple void closure is presented by derivation of the strain function.•The criterion provides a new method in terms of elimination of void defects within ingot.•The closure of each void is independent, but not accumulated in the porous model.•The critical amount of strain for two-dimensional void closure is given as 0.5 from elastic theory.•The criterion for three-dimensional void closure can be given as εZ0(Z1)⩾0.61. In this paper, on the basis of the new mathematical method formerly proposed, i.e., strain analysis method, (Chen et al., 2013), the criterion for multiple void closure was presented by mathematical derivation of the strain function. It indicates that the closure of each void is independent, but not accumulated in the porous model. Therefore, the criterion for single void closure formerly proposed can be completely applied on the porous model. Also, the criterion for two-dimensional void closure was derived from the elastic theory in the present paper. On this basis, the criterion for three-dimensional void closure applied on the practical process was discussed. It is shown that the deviation between them is less than 18%. Finally, this criterion for three-dimensional void closure was validated by numerical simulations for a typical steel ingot. It illuminates that with the criterion for void closure in the porous model, not only comparatively accurate results but also simplified model with voids are obtained in terms of prediction for void closure. It provides a new method with extensive application prospect for the optimization of the forging process.