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

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 23 No. 1 2021 to - 0.58. Comparing this value with the results shown in the table shows that there was an increase in the indicator absolute values by 2 to 5 times. That is why the plasticity of the metal in the experiments increased and it turned out to be suf fi cient for the operation of upsetting without destruction. The results obtained can also be compared with the variant of friction upsetting of a cylindrical billet in a shell while locating the entire assembly on the strikers’ contact surface. This variant leads to a greater amount of metal displacement in the zone of the convexity emergence on the lateral surface [20] and the shell clearance from the billet. In the absence of a pad and the formation of a convex surface, the average normal stresses in this zone can change from the compressive to the tensile ones. The lateral surface of the billet with insuf fi ciently high plasticity can be destroyed. Therefore, the shell should not be exposed to axial stresses. The distribution of the maximum and minimum main stresses is shown in Fig. 3. a b Fig. 3. Distribution of the maximum ( a ) and minimum ( b ) principal stress It can be seen that the scheme of the transverse crack is repeated for the main stresses. Calculating the second main stress enabled calculating the coef fi cient μ σ . The results of calculations of the main normal stresses are shown in Table 2. Ta b l e 2 Principal normal stresses (MPa) and Lode coef fi cient σ 1 / σ 2 / σ 3 / μ σ at relative coordinates z/h r/R 0 0.5 1 1 –92/–92/–205/0.98 –95/–106/–248/0.86 –190/–262/–370/0.2 0.5 –119/–118/–279/0.98 –118/–153/–293/0.60 –39/–90/–219/0.43 0 –148/–148/–310/1.00 –104/–138/–280/0.61 –23/–111/–208/0.05 All the main stresses are negative values, i.e. they are compression stresses. The danger of possible destruction is represented by control points with the lowest modulo of the main stresses. These include the point P7 with coordinates z/h = 0; r/R = 1, here σ 1 = –23 MPa. At the same point, the Lode coef fi cient reaches values close to zero, in contrast to the points located on the axis of the billet, where this coef fi cient is close to one. At a zero value of the Lode coef fi cient, the plasticity is the lowest, as indicated by a number of works [21, 22]. Therefore, the speci fi ed area can be considered a dangerous cross-section in terms of crack formation. As can be seen from all the above illustrations and the results of a real experiment, in the studied upsetting method, there is no shell clearance from the workpiece. During the entire upsetting process, radial compression stresses act on the lateral surface of the billet increasing the plasticity of the metal and allowing the deformation to be carried out without destruction.