Strain function analysis method for void closure in the forging process of the large-sized steel ingot

A mathematical methodology for analyzing void closure in the forging process of steel ingot with a large size was proposed from the view of strain function. A numerical simulation of the forging process was established to describe the distribution field of compressive strain within deformed steel ingot. Then the analytic function of compressive strain distribution was given by mathematical fitting on the basis of Gaussian function (including the models without and with void). And finally the quantitative relationship between void closure and compressive strain, namely mathematical expressions of the criterion for central and non-central void closure, was presented by derivation and calculation of this function. The criterion for central and non-central void closure was verified by finite element simulation for a typical steel ingot. This new methodology gives an acute prediction in terms of elimination of void defects, where the deviation is less than 7%.

► A mathematical methodology is proposed to deal with void closure in large forgings.
► Theoretical explanation for the empirical features of void closure has been proposed.
► For models without void, distribution of εz can be given by Gaussian function.
► For void models, distribution of εz can be given by discontinuous Gaussian function.
► The critical condition for void closure within billet can be denoted as ΔL = Δl + d.