Experimental Study of Pipes Extrusion Process by Using Method of Coordinate Grids

The paper presents the results of an experimental study of the pipe extrusion process using the method of coordinate grids. The estimation of influence of separate conditions of friction on the contact surfaces of the deformable material and the pressing tool on metal flow pattern. The calculation of the forming operation is made for extrusion process stages.


Introduction
As it is shown in works (Starostin & Kargin, 1983;Osadchy & Kolikov, 2012), qualitative characteristics of extruded pipes depend on a number of technological parameters. Among them a strain capacity of a work material (Barichko, Kosmatskiy, & Rushchits, 2013;Kosmatskiy, Barichko, & Voskhodov, 2014;Barichko, Kosmatskiy, & Akhmedyanov, 2015;Kosmatskiy, Fokin, & Filyaeva, 2016) and friction conditions on contact surfaces, i.e. a deformed metal -a pressing tool (Manegin & Anisimova, 1978) should be singled out. The studies in the first area are successfully realized due to upsetting tests of cylindrical specimens using a multifunctional complex Gleeble (Barichko, Kosmatskiy, & Rushchits, 2013;Kosmatskiy, Gaslenko, & Tikhonova, 2013;Barichko, Kosmatskiy, & Akhmedyanov, 2015;Kosmatskiy, Fokin, & Filyaeva, 2016). The rationale for choosing a lubricant on the external and internal surfaces of a deformable material raises an unconventional problem. However, friction conditions specify not only qualitative characteristics of pipes of a finished size, but also the maximum load on a deforming instrument of a pipe extrusion press. Thus, an experimental study of the influence of friction conditions on the pattern of metal flow when pressing pattern pipes can ensure in the initial approximation the formation of a scientific and technology-based approach to selection of lubricants during the pipe extrusion. At the same time, the coordinate grid method (CGM) (Del & Novikov, 1979;Kargin & Kargin, 2011) can help justify the choice of boundaries of plastic deformation applied in case of mathematical description of the pipe extrusion process. Besides, the choice in favour of CGM is also justified by the fact that when using it is possible to consider each element of the coordinate grid as an element of the metal flow nucleus undergoing homogeneous strain during the deformation process (Gubkin, 1960).

Method
The billets (С1 grade) 12 quantity and sizes 45 mm in diameter, 40 mm long and with a through hole of 9 mm in diameter were used for physical simulation. The billets were preliminary cut along the centerline in two halves. The coordinate grid consisting of square cells with a way of nearly 5 mm was applied to each cut surface with the help of the EDM machine (see Figure 1).   10 (4,9; 40,5) 2.10 (8,31; 40,54) 3.10 (13,35; 40,5) 4.10 (18,53; 40,54) 5.10 (23,24; 40,54) Subsequently, the billet parts were put together according to a parting plane, previously covered by automobile oil, which protects them from thermal bonding during the extrusion, and jointed together. Using the testing machine by the maximum deformation force of 1.25 MN and corresponding pressing equipment (see Table 2) pattern sleeves were exposed to extrusion in case of production of pattern pipes 25×18 mm in size according to the following schemes: without lubrication (scheme No. 1); lubrication on the contact surface: a mandrel -an internal surface of the sleeve (scheme No. 2); lubrication on the contact surface: a two-part container liner -an external surface of the sleeve (scheme No. 3); lubrication on all contact surfaces (scheme No. 4). To reduce a time interval and consequently improve the reliability of experimental data, used for quantitative assessment of a strained condition, we evaluated three positions of the coordinate grid (see Tables 3 -5), which correspond to well-known stages (Perlin, 1964) of the extrusion process: pressing out (see Figure 2); steady state (see Figure 3); extrusion process end (see Figures 4 -7).   -a hypothesis about the flow non-uniformity in case of correct pressing;

Results
-the maximum speed differential of longitudinal movements is observed in the area before an exit from the deformation zone. When the metal moves towards the exit from the deformation zone, the deformation speed becomes balanced.
-near the contact surface of the deformed metal with the mandrel grids are deformed for a smaller value, as compared to the zone of a matrix funnel, where deformation has a larger value; -in the matrix funnel zone, where deformation has a larger value, the quality of the coordinate grid is unsatisfactory and difficult to replicate. In case of large values of deformation degrees the use of CGM is unacceptable. It is commonly known (Siebel, 1934) that the stress of contact friction ( К τ ) is defined by Siebel's formula: The work of deformation can be defined as: where S σ is a value of metal resistance to plastic shear strain; И ε is a strain intensity; V is the volume of metal where deformation happens.
The strain intensity ( И ε ) is calculated according to the formula (Kolmogorov, 1986): where ρ ε , ϕ ε , Z ε is a normal component of the strain intensity; γ is a tangential component of the strain intensity.
During extrusion there is a non-uniform plastic flow and a value of the strain intensity is different at different points of the deformation zone. Thus, for determination of deformation work we should specify the strain intensity (7), as a function, the volume integral of which, can be used for calculation of deformation work. The analytical determination of the deformation field is not a trivial task. That's why in this case the CGM is applied to determine the deformation strain.

Discussion
To find the strain intensity the components of a deformation tensor should be specified. Therefore, from the plasticity theory (Thomsen, Yang, & Kobayashi, 1969;Kolmogorov, 1986) it is known: where u is displacement of elementary volume.
The metal doesn't flow in a circular motion around an axis of pressing, i.e. displacement: 0 = ∂ ϕ u . As the process is axially symmetrical, the displacement of points and deformation doesn't depend on the ϕ coordinate.
As for derivative determination, a derivative of the constant value is equal to 0 (Fikhtengolts, 2001), namely: Based on the abovementioned, deformation degrees can be defined by formulas: To specify the components of strain intensity coordinates of all points before ( нач ij z , нач ρ ij ) and after deformation ( ij z , ij ρ ) should be defined. After that it is not difficult to determine the average values of height, width and 2 1 , 1 , 1 , , 1 (11) 2 ρ ρ ρ ρ 1 , 1 , 1 1 , , For each cell we define the values of four angles ( ϕ ), applying a relevant formula for determination of angles between vectors a  and b  , where k is an angle number in the cell: The diagram for determination of values reflected in the formulas (11-14) is shown in Figure 8.
As a result, having the information about the strain intensity, it is possible to define the deformation work in each cell: where i,j max ρ is a maximum cell radius: (17) Using the results of coordinate measuring of the coordinate grid nodes, given in Tables 1, 3 -5, we performed calculation of deformation work when manufacturing pattern pipes 25×18 mm in size in accordance to the following schemes: without lubrication (scheme No. 1, see Figure 4); with lubrication on the contact surface: a mandrel -an internal surface of the sleeve (scheme No. 2, see Figure 5); with lubrication on the contact surface: a two-part container liner -an external surface of the sleeve (scheme No. 3, see Figure 6); with lubrication on all contact surfaces (scheme No. 4, see Figure 7). The calculation results are shown in Table 6. The conducted experimental study of pipe extrusion process using the CGM under different friction conditions on the contact surfaces of the deformed metal and the pressing tool has enabled us to draw the following conclusions: -it is obvious that deformation proceeds non-uniformly. At the same time when creating favourable conditions on the contact surfaces owing to lubricants (see Figures 5 -7), the deformed sample is distinguished by uniformity of distribution of the coordinate grid over the wall thickness of a pattern pipe.
-according to Figures 3 -7, the deformed sample has a stagnant zone of metal, geometrically similar to designated zones in case of mathematical simulation of the pipe extrusion process. For illustration purposes, Fig.  9 shows a fragment (1/4 part) of pattern pressing residue formed as a result of pipe extrusion on the pipe extrusion press, 20 MN stress, in the context of Volzhsky Pipe Plant applying a pressure pad of new shaping. As you can see, according to Figure 9, porosity and a fiber structure in the area of press tightening is observed in the macrostructure of pressing residue. In addition, the macrostructure of metal in the contact area with the matrix and the mandrel has a sophisticated fine-grained structure. Figure 9. Macrostructure of a press residue template made of 10Х13Н3 steel -the coordinate grid distribution along the length of pattern pipes (see Figures 5 -7) is characterized by non-uniformity. The front part of pattern pipes isn't worked out to the full through the wall thickness. At the same time, the back part is characterized by a dense structure of the coordinate grid. This as a whole enables one to implicitly judge about possible anisotropy of properties along the body of extruded pipes.
-the use of lubricants on the contact surface: a mandrel -an internal surface of the sleeve will not exert significant influence over pressing force and can be mainly applied for durability of a pressing tool and performance of qualitative characteristics of the internal surface of extruded pipes. Moreover, lubricants, designed for the internal surface of the sleeve, and consequently ensuring a separating layer between the mandrel and the sleeve, in a first place should conform to requirements for thermal properties, namely heat capacity and thermal conductivity, and only after that friction properties.
In conclusion, we should note that when maintaining dynamic and plastic conformity (Chizhikov, 1970) it is possible to use the results of the conducted research based on the CGM under production-line conditions.