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

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 23 No. 1 2021 In the process of upset forging, this is achieved by using shells or clips of various types [4-6]. Besides, the con fi guration of the upsetting tool also matters. For example, with a normal free upsetting, the tool has a working surface, the area of which is obviously larger than the area of the contact surface of the billet, so that the processed metal broadening can occur. Here, the deformation process is hindered only by friction stresses that create additional radial and tangential stresses that increase the hydrostatic pressure. However, the working surface can be con fi gured differently, which creates additional compression stresses and increases the plasticity of the metal. The combination of the billet and the shell creates a bimetal con fi guration; this requires using complex solutions to boundary value problems, which have increasingly been solved by the fi nite element method [7]. The stress state has a great in fl uence on the plasticity of the processed material. This state is described by tensor representation methods, but it is customary to use tensor invariants in one form or another to assess the situation, which eliminates the in fl uence of coordinates on the analysis results. In the sections of deformable body mechanics concerning the in fl uence of the stress state on plasticity, the fi rst stress tensor is used, as well as other invariants [8]; the invariants themselves are transformed into the stress state indicator [9, 10] and the Lode coef fi cient [11, 12]. The use of the shell in earlier studies of the upsetting process was associated with the use of a working tool impact scheme simultaneously on the end of the billet and the end of the shell. Another, newer scheme, according to which the tool acts only on the end of the billet, was tested only experimentally [13]; the scheme enabled obtaining a magnesium billet without destruction and cracks. The invariants of the stress tensor are known to be responsible for increasing the plasticity of the metal in the processes of plastic deformation. The purpose of the work is to mathematically evaluate the invariant parameters of the stress state of the shelled magnesium upsetting process when the tool is applied only to the end of the billet. Research Methodology The experimental part The physical experiments were performed on the forging and pressing equipment of the Mikheev Institute of Metal Physics of the Ural Branch of the RussianAcademy of Sciences, their detailed description is given in a number of publications [13–15]. To avoid self-citation, only the essence of the process is described below. Magnesium of the Mg90 grade according to GOST 804-93 was used as the material of the billet. The following dimensions were taken in the experiment: a billet in the form of a cylinder made of magnesium with a diameter of 21.8 mm and a height of 25 mm, a copper shell has an outer diameter of 48 mm and a height of 29.5 mm, the inner diameter of the shell is equal to the diameter of the magnesium billet. The upsetting was carried out with 25 mm in diameter punches. The absolute compression was 5.9 mm. The diameter of the shell increased to 49.8...50.2 mm at the contact with the strikers and to 52.9...53.2 mm in the middle part. In experiments according to this scheme, there was no destruction of the billet metal revealed, while with a normal upsetting, the billet was destroyed. Calculation This paper deals with a computational experiment, i.e. an assessment of the stress-strain state of the deformation process, whose implementation allowed imposing a certain level of deformation to magnesium billets in the cold state. This estimation was performed by the fi nite element method using the DEFORM software module [16]. The task is to determine the conditions for the absence of cracking, i.e. the destruction of the metal. Further, we will use the basics of the destruction theory expounded, for example, in the book [17]. Destruction occurs when the maximum degree of shear deformation Λ p is exceeded, which, in turn, depends on the stress state index σ /T and the Lode coef fi cient μ σ ; here σ is the mean (hydrostatic) stress, T is the intensity of tangential stresses associated with the stress intensity σ i the ratio