Strained condition parameters during brass
backward extrusion with a high elongation
coefficient
Shimov G.V., 1, Loginov Y.N.1,2, Bushueva N.I.1, Vorsin А.S.1,3
1
Ural Federal University named after the first President of Russia B.N. Yeltsin, Mira street 19,
Ekaterinburg, 620002, Russia
2
M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences
3
ПАО «Каменск-Уральский завод по обработке цветных металлов»
Annotation. The brass backward extrusion boundary value problem with a elongation
coefficient more than 700 is carried out. This process is consistent with production practices.
The problem is solved using the DEFORM software module by the finite element method. The
displacement velocities, strain rates and degree of strain are calculated. The difference between
extrusion with moderate and high elongation coefficients is revealed. The moderate extraction
coefficients during extrusion results to the formation of a deformation zone which boundaries
which reach the container wall. The use of large extraction coefficients results to the
deformation zone localization near the matrix extrusion die parallel land. The local level strain
rates excess above the value 1000 s-1 is revealed.
1. Previous work
The two-phase brasses pressure shaping is an increased attention object, since in the presence of two
phases due to an additional lever is created to control the properties of the material [1-3]. The twophase brasses have a low ductility level in the hot state with rigid stress state schemes. They are
usually processed not by rolling, but by extrusion. In this case, a high level of compression stresses
increases the paste-forming properties. It is possible to obtain the product without destruction. An
important question is whether the workpiece metal will be partially or completely in the temperature
field corresponding to the high-temperature phase during hot deformation [4,5]. Related studies are
aimed at the fixing possibility of this phase to improve the final product properties [6]. It is important
whether the pressing is carried out in a direct or backward way [7]. The strain rate distribution and
strain distribution during the deformation process is important. It is known that the distribution of
these parameters is extremely heterogeneous from the two-phase brasses’ extrusion. At the same time,
the stress-strain properties level that the metal inherits depends on this distribution. The FEM for
stress-strain state analyses is using by various software modules such as: DEFORM [8], QFORM [9]
etc.
The work aim is to study the distribution of tensor and invariant characteristics of the stress-strain
state by the finite-difference method in the single-channel backward extrusion of a rod made of twophase brass.
1. 1. The calculation method description
The finite element method implemented in the DEFORM software module is used to analyze the
extrusion scheme. The problem statement is carried out in 2D indication. Fig. 1, a shows a general
view of the tools and the workpiece locations. Fig. 1, b shows an enlarged image of the area adjacent
to the matrix extrusion die, with a finite elements mesh on the workpiece body. The tools and
workpieces geometric parameters are represented by the following data: the container diameter Dk =
260 mm, the ingot length L = 750 mm, the ingot diameter D = 250 mm; the parallel land diameter and
length dk = 9,8 мм and 3,0 mm, respectively. Thus, the ratio L/D = 3 is used. It is acceptable for the
backward extrusion scheme since the friction effect on the container walls is leveled here. The
elongation coefficient regarding to container in this case will be the value
= Dk2/dk2 = 2602/9,82 = 704,
(1)
accordingly, the strain degree
ln = 2*ln (Dk/dk) = 6,56.
(2)
The strain degree can also be estimated through the reduction rate over the area:
( - 1) / = 99,85%.
(3)
The latter value indicates that the very high deformations mode is realized in this case. A cylindrical
coordinate system ry is introduced during setting the problem. The following kinematic boundary
conditions for axisymmetric deformation are used:
- for container wall:
𝑉𝑟 = 0; 𝑉𝑦 = 0 ,
(4)
- for matrix extrusion die:
𝑉𝑟 = 0; 𝑉𝑦 = 6 мм/с .
(5)
The index " r "refers to the radial coordinate, the index" y " to the axial coordinate.
The problem scheme statement is shown in Fig. 1.
1
3
2
a
2
b
Fig. 1. The design process scheme (a) and an enlarged image of the metal part adjacent to the matrix
matrix extrusion die with the the finite element mesh display: 1-the wall of the container; 2-the matrix
extrusion die; 3-the workpiece; the arrow shows the the matrix extrusion die movement direction
The statement is carried out with the finite elements number amount 26500. The setting conditions are
as follows: the workpiece material in accordance with the standard DIN_CuZn40Pb with properties in
the temperature range 550…950 ºС. The object type is plastic. The billet heating temperature consist
680 Сº, the heating temperature of the container and matrix extrusion die consist 460 ºС, matrix matrix
extrusion die movement velocity – 6 мм/с (according to the production process data). The friction
coefficient on the matrix extrusion die is 0.2. The heat transfer parameters are set according to the
software module recommendations
2. Calculations results
Fig. 2, a shows the radial component distribution of the displacement velocity. It can be seen that the
the symmetry condition process is satisfied: at the radial coordinate r = 0, the radial velocity Vr is zero.
This velocity on the container wall surface is also consist zero due to the need to meet the condition
that the deformable metal does not penetrate the tool. Figure 2, b shows the modulus of the
displacement velocity vector distribution. The maximum value is close to 4000 mm/s. This value can
also be calculated using the formula Vmax = Vy* = 6* 703 = 4218 mm/s.
a
b
Figure 2. Display of the radial component of the displacement velocity (a) and the modulus of the
displacement velocity vector (b), mm/s
The module of the displacement velocity vector has a maximum just on the extrusion axis in contrast
to the radial component. (Fig. 2, b). This phenomenon is caused by the influence of large movements
along this coordinate. In general, the field of displacement velocities does not extend to the entire the
workpiece volume. It is localized near the matrix extrusion die mouth. This is the difference of
extrusion with a large extraction coefficient.
The strain velocity tensor T characterizes strain of shortening or elongation, as well as shifts in
individual volumes of the deformation zone in contrast to the displacement velocity vector. Fig. 3, a
show the strain rate tensor rr component distribution. The highest values are reached near the matrix
extrusion die parallel land. The component rr is no distribution to the extrusion axis centre in this
case. Invariant value of the strain rate intensity (fig. 3, b) essentially sets the deformation zone
shape: this area can be bounded by a zone with radial curves. This area does not extend to the
container wall. It is localized near the matrix extrusion die mouth in contrast to the case of extrusion
with low and medium elongation coefficient. It should be noted that the strain rate intensity obtained
reaches the value 1400 s-1. This is primarily due to the large values of deformation. Caution is aroused
by the fact that the hardening curves graphs are not usually plotted for such high velocities. At best,
the strain rate in material tests is limited to 100 s-1. Therefore, the calculated data on the strain
resistance are obtained by extrapolating the graphs for moderate velocity values. An important
research area on the rheological materials properties would be to extend the range of strain rates to
1000 s-1. This would improve the calculations performed accuracy.
a
b
Рис. 3. Imaging the strain rate tensor component rr (a) and the strain rate intensity , s -1
3. The production process elements
The paper considers the real situation that occurs during the production of lead brass at the PJSC
"Kamensk-Uralsky non-ferrous metal working plant". Figure 4, a shows a photo of the ingot loaded
into the container and the matrix extrusion die attached to the movable die. Figure 4, b shows the coil
view after extrusion.
a
b
Рис. 4. Ingot and tool assembly during extrusion (a), finished product coil (b)
Conclusions. During the brass extrusion process with large elongation coefficients by the finite
element method, it was revealed that the deformation zone does not reach the walls of the container.
Deformations are localized near the matrix extrusion die mouth. It is established that the strain rates
level exceeds the value of 1000 s-1.
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