Invariant stress state parameters for forging upsetting of magnesium in the shell

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 23 No. 1 2021 3 i T   . (1) The indicator μ σ is determined by the ratio 2 3 1 3 2 1,           (2) where σ i ( i = 1, 2, 3) are the main normal voltages; the voltages are ranked according to the rule σ 1 ≥ σ 2 ≥ σ 3 , i.e. the numbering begins with the maximum voltage and ends with the minimum. The DEFORM system provides for the possibility of calculating the maximum ( fi rst) and minimum (third) main normal voltages, but the second main voltage is not calculated. Therefore, it was determined speci fi cally by calculating the formula 2 1 3 3 ( ).        (3) Another problem is the absence in the list of variables calculated in the DEFORM system: the stress state index σ /T and the Lode coef fi cient μ σ ; they were calculated speci fi cally and brought to a tabular form. Application of a shell and changing the con fi guration of the tool surface was proposed in the scheme of cold upsetting of a magnesium billet to achieve higher plasticity [18]. The difference from the usual schemes of using the shell is that the shell is larger in height than the billet, with the punch not affecting the assembly as a whole, only the billet (Fig. 1, a ). Copper is used as the shell material, its properties are described using reference materials. a b Fig. 1. Photo of the assembly ( a ) and calculation model of the process ( b ) upsetting of a magnesium billet in a shell with an estimation of mean stresses (stress mean) The problem statement included a description of physical and plastic properties based on reference data and the setting of boundary conditions in displacements. We used the model of an isotropic medium with hardening, which is described in the article [19]. Interactions on the contact surfaces are established: billet-strikers, billet-shell. At the contact with the tool, the law of friction is set according to the Coulomb with a coef fi cient of friction being 0.1 since the upsetting was carried out with lubrication. There is no lubrication at the boundary between the workpiece and the shell, and since both materials – copper and magnesium - have increased adhesive properties, the coef fi cient of friction on this surface was assumed to be equal to 0.5. Results and discussion The parameter σ /T is not included in the number of parameters de fi ned by the DEFORM software module, just like the parameter T. For additional calculations, we had to assign control points P1,..., P9,