Mathematical Modeling of Heating and Strain Aging of Steel during High-Speed Wire Drawing

Abstract

In this article, a mathematical model of the wire’s average temperature change in the process of multiple drawing on high-speed straight-line drawing machines has been developed. The calculation results showed that the average temperature of the wire during a drawing at a speed of up to 45 m/s on straight-line drawing machines could reach 400 °C. Deformation heating of the wire during drawing does not exceed 60 °C, and heating due to sliding friction can reach 300 °C, depending on the friction coefficient, which ranges from 0.05 to 0.15. The average strain rates under the conditions of the modern high-speed drawing process reach 7000 s⁻¹. Over the course of the research, it was found that there are no conditions for the occurrence of dynamic deformation aging due to impurity atoms of carbon, nitrogen and oxygen. At the same time, at the temperature and speed parameters of the high-speed wire drawing, conditions are created for the onset of the dynamic strain aging of steel in the presence of hydrogen atoms. Therefore, during heat treatment and pickling, it is necessary to exclude the hydrogenation of steel. It has been established that in order to exclude static strain aging of steel during drawing, it is necessary to prevent heating the wire above 180–200 °C.

1. Introduction

Wire drawing is a process of plastic deformation of metal, during which a round billet, when pulled through a tool called a die, reduces its cross-section and increases its length. A wire is a long metal product with a diameter of 0.005 to 8 mm of a cylindrical or shaped profile, made of steel or non-ferrous alloys [1].

Wire can be obtained through various metal forming processes, namely rolling [2,3], extrusion [4] and drawing [5,6,7], or an effective combination of them. However, drawing remains the most widespread method of wire production [8,9]. Overall, it seems simple, but this is one of the most difficult types of metal forming. The drawing process is influenced by a large number of various factors, such as drawing speed [10], technological lubrication [11,12,13], sub-lubricating layer [14], deformation degree [15,16], drawing die [17] and drawing machine design, etc.

Consumable tools for wire drawing are dies. Recently, the results of studies have been published to determine the optimal parameters of dies in terms of energy consumption [18,19], wear of the die [20], wire quality [21] and other parameters.

The entire history of the development and improvement of metal drawing is mainly associated with a decrease in the negative effect of friction. Research is underway to reduce the negative effect of friction by improving the lubrication coating [22], developing new types of technological lubricants [23], and optimizing the drawing dies [24]. At the same time, its advantages, such as greater accuracy of geometric shapes and high quality of the wire surface, make it competitive with the emergence of new methods and technologies for the production of wire. In the process of drawing, the wire in the die is heated due to the transformation of the deformation work into heat and the action of contact friction. A significant part of the heat (up to 90%) is accumulated by the wire, while the remaining part causes the die to heat up, especially at the metal–die contact [25].

The need to reduce the cost of wire by increasing productivity, as well as the possibility of using more automation in drawing production, leads to an increase in drawing speed. In turn, an increase in the drawing speed has a significant effect on the technological features of the wire drawing process, primarily on temperature conditions. Modern drawing machines include devices and measures to reduce the heating of the wire during the drawing process [26]. To reduce the heating of the wire during the drawing process, water cooling of the inner part of the pulling drums and the outer surface of the clips of the drawing dies in the soap boxes is used.

Much attention is paid to this issue, among other things, because over the past few decades, the equipment used for wire drawing has changed significantly [27]. Drawing machines of the previous generation—pulley wire drawing machines—made it possible to produce wire at a drawing speed of up to 8 m/s. With the development of production automation, which affected wire production, drawing machines of a new generation appeared capable of developing drawing speeds up to 45 m/s [10,28].

Straight-line drawing machines provide a cooling system for pulling drums, drawing dies, the use of new generation lubricants, etc. However, the question remains, which technological and technical parameters of drawing create the conditions for the onset of strain aging of alloys?

Strain aging consists of blocking free dislocations by impurity atoms and inclusions, which in turn leads to an increase in the strain stress and loss of plastic properties [29,30,31,32]. At the same time, one should not forget that strain aging only occurs if:

(1) If a certain number of "fresh" dislocations is introduced into the metal as a result of deformation (or in another way).

(2) The concentration of impurity atoms that can effectively interact with these dislocations exceeds 10^–4 wt %.

A decrease in the mobility of dislocations introduced by deformation due to their blocking by carbon, nitrogen, hydrogen and oxygen atoms is possible only if the dislocation velocity is commensurate with the diffusion rate of impurity atoms determined for a given temperature range and strain rates [7,33].

Previous studies [34,35,36] considered the process of drawing and strain aging during its implementation for the conditions and technologies used earlier. The study [34] evaluated the ductility of carbon steel wire at a strain rate of 10^–4 to 10^–3 s^–1. The paper [35] presents data on the change in the diffusion coefficient depending on the steel temperature. Knowing the value of the diffusion coefficient of hydrogen makes it possible to determine the possibility of blocking dislocations during plastic deformation and premature loss of plastic properties. The study [36] shows the intensity of the temperature increase when the drawing speed changes from 1 to 7 m/s, which corresponds to the drawing machines of the previous generation. The maximum temperature during such drawing does not exceed 70 °C. In studies [37,38], the strain rates were calculated during drawing with a speed of 20 m/s. Using the FEM method, the distribution of strain rates over the wire cross-section was shown with a change in the angle of the die.

The purpose of this study is to determine the conditions for the occurrence of dynamic and static strain aging during steel wire drawing on modern high-speed straight-line machines. The scientific novelty of the study lies in the theoretical analysis of the conditions for dynamic and static strain aging during high-speed wire drawing in monolithic dies.

2. Modeling the Temperature of Wire Drawing on Straight-Line Drawing Machines

A significant part of the work spent on the process of forming is converted into thermal energy, which is accumulated by the metal being processed and heating up the tool. The amount of energy that will be converted into heat significantly depends on the process used to obtain the wire and the technological features during its implementation. Contact friction has the greatest influence on the heating of the metal in the forming process. During rolling and roll drawing, rolling friction is realized, due to which the heating of the metal during deformation is not so significant. In monolithic drawing, due to sliding friction, the heating of the wire and die can be significant. During repeated drawing, the temperature of the wire is determined by two opposite processes: heating in the drawing dies and cooling on the pulling drums.

The model of temperature changes that occur during wire drawing consists of two parts: the first is the influx of heat as a result of the work of friction and deformation forces, and the second is the outflow of heat to the die, to the drum of the drawing machine and the air space of the environment. Let us make a balance of inflow and outflow of heat.

The heat influx is the sum of the heat release caused by the work of deformation and friction at the wire–die contact and the heat brought in from heating in the previous drawing die. The outflow of heat is distributed between the drawing die and the metal. The heat balance during drawing will be as follows:

$$q_{def}+q_{fr}+q_{w/in}=q_{die}+q_{w/out}$$

(1)

where $q_{def}$ is the heat release in the metal caused by the work of deformation, W/m²;

$q_{fr}$—heat release in metal caused by friction, W/m²;

$q_{w/in}$—heat introduced into the deformation zone by the wire from heating in the previous pass, W/m²;

$q_{die}$—heat given off to the die, W/m²;

$q_{w/out}$—heat carried away by the metal, W/m².

When moving the wire from the $i$ die to $i+1$, it loses heat to the environment by convection and radiation. Heat losses from radiation are insignificant, so we neglect this type of loss [1]. To determine the heat loss from convection, we divide the area from $i$ to $i+1$ of the die into three areas (Figure 1).

The heat $q_{w/out}$ is transferred to the environment (Sections I and III) and to the wire drawing drum (Section II) (Figure 1).

$$q_{w/out}=q_I+q_{II}+q_{III}+q_{w/in},$$

(2)

where $q_I,q_{II},q_{III}$ is the heat outflow in the first, second and third areas, W/m².

Hence,

$$q_{df}+q_{fr}+q_{w/in}=q_{die}+q_I+q_{II}+q_{III}+q_{w/out}$$

(3)

The total heating of the wire is determined by adding the average temperature rise over the wire cross-section, caused by the heat of friction and the increase in wire temperature due to plastic deformation:

$$\Delta t=\Delta t_{def}+\Delta t_{fr},$$

(4)

where $\Delta t_{def}$ is the increase in wire temperature due to plastic deformation, °C; $\Delta t_{fr}$ is the average temperature increase over the wire section, caused by the heat of friction, °C.

The increase in wire temperature due to plastic deformation is defined as

$$\Delta t_{def}=\frac{q_{def}}{c\rho },$$

(5)

where $c$ is the heat capacity, J/kg·K; $\rho$ is the metal density, kg/m³.

Heat release in the metal due only to the deformation work, W/m²:

$$q_{def}={\sigma }_s\cdot \ln \mu ,$$

(6)

where ${\sigma }_s$ is the yield strength alloy of the wire, N/m²; $\ln \mu$ is the draw ratio.

The average temperature rise over the wire cross-section caused by the heat of friction is defined as

$$\Delta t_{fr}=t_{\max }\frac{\delta d-{\delta }^2}{0.5d^2},$$

(7)

where $t_{\max }$ is the maximum heating temperature of the surface of the wire and die, °C;

$\delta$—thickness of the metal layer heated near the friction surface, m;

$d$—wire diameter, m.

Then, the maximum heating temperature of the contact surfaces between the wire and the die:

$$t_{\max }=q_{w/out}\times B,$$

(8)

where $B$ is the coefficient determined by the formula

$$B=\sqrt{\frac{4l}{\pi c\rho {\lambda }_{0}v}},$$

(9)

where ${\lambda }_0$ is the thermal conductivity of the die, W/(m·K);

$v$—drawing speed, m/s; $l$—length of the contact zone, m.

The thickness of the metal layer heated near the friction surface

$$\delta =k\sqrt{\frac{{\lambda }_{0}l}{c\rho v}},$$

(10)

where $k$ is a coefficient taken equal to 1.65.

The heat $q_{fr}$ generated as a result of the work of friction forces on the contact surfaces can be divided into the heat $q_{die}$ absorbed by the die and the heat $q_{w/out}$ absorbed by the moving wire.

Heat absorbed by the die, including heat inflow and outflow, contact conditions (i.e., coefficient of friction) and the effect of back tension, is defined as

$$q_{die}=\frac{q_{fr}B-t_{die/out}}{\frac{R}{{\lambda }_1}\ln \frac{R_{out}}{R}+B},$$

(11)

where $t_{die/out}$ is the outside die temperature, °C;

$R_{out}$—outer radius of die, m;

${\lambda }_1$—thermal conductivity coefficient of the wire, W/(m·K);

$R$—arithmetic mean between the input die radius and the output one, m.

$$R=0.5(R_0+R_1)$$

(12)

The heat release in the metal caused by contact friction is defined as

$$q_{fr}=f{\sigma }_{N}v,$$

(13)

where ${\sigma }_N$ is the normal pressure of the metal on the die, MPa;$f$ is the friction coefficient.

The normal pressure of the metal on the die is determined by the formula

$${\sigma }_N=\frac{{\sigma }_{draw}{R}_1^2\sin \alpha }{(R_0^2-R_1^2)\sin (\alpha +arctg(f))},$$

(14)

where $\alpha$ is a die half-angle.

Heat absorbed by moving wire

$$q_{w/out}=\frac{q_{fr}\frac{R}{{\lambda }_1}\ln \frac{R_{out}}{R}+t_{die/out}}{\frac{R}{{\lambda }_1}\ln \frac{R_{out}}{R}+B}$$

(15)

The first area is from the $i$-th die to the drum. In this area, the wire is straight, and the heat exchange between the wire and the environment can be considered as in the case of a longitudinal flow around the cylinder. According to:

$$forRe<{10}^{3}toNu=0.49R{e}^{0.5}$$

$$forRe>{10}^{3}toNu=0.245R{e}^{0.6},$$

where $Re$ is the Reynolds criterion; $Nu$—Nuselt criterion; $L$—length of the wire in the first area, m.

Reynolds criterion:

$$\mathrm{Re}=\frac{vL}{\eta },$$

(16)

where $\eta$ is the kinematic viscosity of air, g·m/s.

Considering the correction factor for the angle of attack of the air flow to the wire, the heat transfer coefficient is determined as

$${\alpha }_k=0.4\frac{Nu{\lambda }_{air}}{d_i},$$

(17)

where ${\lambda }_{air}$ is the thermal conductivity coefficient of air, N·s.

The wire at the end of the first section is cooled to a temperature

$$t_i^I=(t_i-t_{в})\cdot \exp \left(-2Bi\cdot Fo\right)+t_{air},$$

(18)

where $Bi$ is the Biot criterion; $Fo$ is the Fourier criterion; $t_{air}$—ambient air temperature, °С; $\tau$—cooling time, s.

Biot criterion:

$$Bi=\frac{{\alpha }_k}{{\lambda }_{alloy}}\times \frac{d_i}{2},$$

(19)

where ${\lambda }_{alloy}$ is the thermal conductivity coefficient of the drawn metal, W/(m·K).

Fourier criterion:

$$Fo=\frac{{\lambda }_{alloy}\times d_i\tau }{c\rho \times {\left(\raisebox{1ex}{$d_i$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}^2}$$

(20)

The second area is the drum of the drawing machine. The wire on the drum transfers heat to the environment and the drum. We assume that in a stationary process, the wire and the drum have the same temperature; therefore, the calculation of heat losses is carried out as for a vertical cylinder. Considering the correction factor for the angle of attack of the air flow to the drum, the heat transfer coefficient in this section is determined by the formula

$${\alpha }_k^{II}={\phi }_k\times 1.04\times {\lambda }_{air}{\left(\frac{v}{\eta D_d}\right)}^{0.5}{P}_L{}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.},$$

(21)

where $D_d$ is the diameter of the drum, considering the wire located on it, m; ${\phi }_k$—correction factor for the angle of attack of the air flow 90°; $P_L$—Prandtl coefficient for the cooling air.

Correction factor for 90° airflow angle of attack ${\phi }_k=0.55$ and Prandtl factor for cooling air $P_L=0.703$.

The decrease in the wire temperature in the second area:

$$t_i^{II}=(t_i-t_{air})\cdot \exp \left(-2Bi\cdot Fo\right)+t_{air}$$

(22)

The third area is from the point of descent of the wire from the drum to $i+1$ die. The decrease in temperature in the third area is defined as

$$t_i^{III}=(t_i-t_{air})\cdot \exp \left(-2Bi\cdot Fo\right)+t_{air}$$

(23)

Next, you need to combine the two parts of the heat balance. The wire after each drawing in the die is heated and then cooled, more intensively on the drawing machine drum and less intensively when interacting with the environment in the second and third areas. Therefore, before entering the next die, the heating of the wire will be

$$t_{{}_i}^0=t_{i-1}-t_{i-1}^{III},$$

(24)

where $t_{{}_i}^0$ is the temperature of the wire before entering the $i$-th die, °C.

Based on the described technique, a computer program was developed to simulate the temperature regime of multiple drawing. This computer program allows you to estimate the temperature of the wire along the entire drawing route, as well as determine the change in temperature depending on the technological parameters of drawing.

The average wire temperatures for the passes are given in

Table 1. Calculation results average temperature of steel (0.2 wt.% C) wire along the drawing route.

Pass Number	Drawing Route $\mathit{d}$, mm	$\mathbf{Friction}\mathbf{Coefficient}\mathit{f}$
		0.05			0.15
		$\mathbf{Drawing}\mathbf{Speed}{\mathit{v}}_7,\mathbf{m}/\mathbf{s}$
		10	20	45	10	20	45
Billet	3.50	-	-	-	-	-	-
1	3.00	66	63	61	81	74	69
2	2.60	117	117	117	142	136	132
3	2.25	156	164	170	185	187	189
4	1.95	184	200	215	216	227	237
5	1.70	211	235	259	244	264	284
6	1.50	230	262	296	265	293	323
7	1.30	270	310	353	305	340	381

. Since a straight-line drawing machine is used in the studies, the drawing speeds along the route increase in each subsequent die, taking into account the draw ratio according to the law of volume constancy. The drawing speed indicates the speed at the exit of the last (seventh) die. The steel (0.2 wt.% С) billet yield strength was ${\sigma }_s$ = 420 MPa. The calculation results with an error not exceeding 12% are consistent with the results of industrial studies of temperature conditions performed by us earlier [10]. Comparable results were obtained in the study [11].

As follows from the calculation results, when drawing a wire from a steel billet with a yield strength ${\sigma }_s$ = 420 MPa on straight-line drawing machines with a speed of 45 m/s in the last pass, the average temperature of the wire rises to 381 °C. The average temperature of the wire is greatly influenced by the friction coefficient. An increase in the friction coefficient of 0.05 to 0.15 leads to an increase in temperature by 71 °C. The drawing speed also causes the temperature of the wire to rise. With an increase in the drawing speed of 10 to 45 m/s at a friction coefficient $f$ = 0.05, the average temperature rises from 270 °C to 353 °C.

Wire heating during drawing, according to Equation (4), consists of deformation and heating due to friction.

The effect of deformation parameters on deformation heating is shown in Figure 2.

To analyze the effect of technological parameters (die half-angle and friction coefficient) on the maximum temperature that occurs at the wire–die contact, a calculation was performed, the results of which are shown in Figure 3.

The thickness of the surface layer of the metal heated by friction along the drawing route ($f$ = 0.15) is given in

Table 2. Heating of the steel wire surface by friction during drawing.

Drawing Route	3.00	2.60	2.25	1.95	1.70	1.50	1.30
$\mathrm{Maximum}\mathrm{heating}\mathrm{of}\mathrm{the}\mathrm{steel}\mathrm{wire}\mathrm{surface}\Delta t_{fr}$, °С	256	286	305	329	359	397	402
$\mathrm{Thickness}\mathrm{of}\mathrm{the}\mathrm{surface}\mathrm{layer}\mathrm{of}\mathrm{metal}\mathrm{heated}\mathrm{by}\mathrm{friction}\delta$, mm	0.82	0.66	0.53	0.43	0.36	0.28	0.23

.

The calculation results shown in Figure 2 demonstrate that the heating of the wire due to deformation does not exceed 60 °C, but the heating caused by friction at the wire–die contact (Figure 3) with poor preparation of the wire surface and poor-quality technological lubrication can reach 320 °C. It should be noted that with a high friction coefficient, an increase in the die half-angle of 3 to 8° leads to an increase in the maximum temperature by 100 °C.

As the calculation results show, the heating of the wire due to deformation does not exceed 60 °C, but the heating caused by friction can reach 400 °C. The maximum temperatures are localized in the surface layer, but due to the thermal conductivity of the metal, this heat is transferred to the depth of the wire. High-speed drawing processes, even with good heat removal on modern straight-line drawing machines, lead to heat accumulation in the wire and its heating up to 300–400 °C. High-speed drawing should be accompanied by good surface preparation of the workpiece and the use of high-quality lubricants.

3. Conditions for the Development of Dynamic and Static Strain Aging

To calculate the average strain rate $\dot{\epsilon }$ during drawing, the authors in the study [10] propose to use the formula

$$\dot{\epsilon }=6\cdot \tan \alpha \cdot v\frac{\ln \mu }{d\left(\sqrt{{\mu }^3}-1\right)}.$$

(25)

The results of calculating the average strain rate depending on the technological parameters of the drawing process are shown in Figure 4.

As can be seen in Figure 4a, an increase in the drawing speed of 5–45 m/s with a wire diameter of 3 mm and a drawing ratio of 1.35 at different die half-angles leads to an increase in the average strain rate of 276 to 6616 s⁻¹. Only by changing the die half-angle to 3–8° at a drawing speed of 45 m/s does the strain rate increase by 2482 to 6616 s⁻¹, i.e., more than 2.5 times. Less but still significantly, the value of the elongation coefficient also affects the average strain rate (Figure 4b). A drop in the average strain rate by 2916 to 2277 s⁻¹ is observed with an increase in the draw ratio of 1.1 to 1.5 at a drawing speed of 45 m/s. The diameter of the wire being processed has a significant effect on the average strain rate (Figure 4c, so a decrease in the diameter of 6 to 2 mm, other things being equal, leads to an increase in the average speed of 1656 to 4968 s⁻¹, which is a threefold increase. For comparison, Figure 4d shows the technological conditions of the drawing process, under which the average strain rates are in the range of 20–180 s⁻¹. Such significant changes in the strain rate affect the ductility of the alloy and its machinability. It is necessary to determine whether there are prerequisites for the occurrence of dynamic deformation processes of aging since it is the strain rates that play a decisive role in this. The conditions under which dynamic interaction between dislocations and impurity atoms is ensured are determined precisely by the critical strain rate, and as we can see, the spread of these values during drawing is possible from 20 up to 12,000 s⁻¹. The diffusion coefficient is a characteristic that is very sensitive to temperature.

The critical strain rate at which a dynamic interaction between dislocations and impurity atoms is observed is defined as

$${\dot{\epsilon }}_{cr}=2\times {10}^{-2}\times D{\rho }_d$$

(26)

where ${\dot{\epsilon }}_{cr}$ is the rate of plastic deformation, s⁻¹; $D$ is the diffusion coefficient of dissolved atoms, m²/s; ${\rho }_d$ is the dislocation density, m⁻².

The dependence of the diffusion coefficient on temperature obeys the Arrhenius law [39,40]:

$$D=D_0\exp \left(-\frac{Q}{kT}\right)$$

(27)

where $Q$ is the activation energy, eV; $k$ is the Boltzmann constant; $D_0$ is the pre-exponential factor.

This dependence of the diffusion coefficient on temperature has been experimentally confirmed for many systems [39]. The parameters for determining impurity diffusion in α-Fe are presented in

Table 3. Parameters for determining impurity diffusion in α-Fe.

Impurity Atom	The Pre-Exponential Factor ${\mathit{D}}_0,{\mathbf{m}}^2/\mathbf{s}$	Activation Energy $\mathit{Q}$, eV
C	3.96 × 10−7	0.83
N	3.00 × 10−7	0.80
H	4.20 × 10−8	0.04
O	3.78 × 10−7	0.96

[40].

For metal temperatures achieved during wire drawing, the change in diffusion coefficients is shown in Figure 5.

The density of dislocations during plastic deformation, according to [41,42], is in the range of 10¹²–10¹⁵ m⁻² (Figure 6). The maximum density of dislocations during plastic deformation, according to the Bochvar-Oding curve, does not exceed 10¹⁵–10¹⁶ m⁻². A further increase in the dislocation density leads to the formation of cracks.

Substituting the values of the diffusion coefficients for the elements C, N, H and O (Figure 5) and the density of dislocations ${\rho }_d$ = 10¹³ m⁻² in Equation (26), we obtain the dependence of the critical strain rate (Figure 7) for the temperature range calculated for the drawing process under study (Table 1). As we see in Figure 7, the calculated critical strain rate for impurity hydrogen atoms (H) varies in the range of 2000 to 4200 s⁻¹, which corresponds to the strain rate in the drawing process (Figure 4). At the same time, the critical strain rates for C, N, and O impurity atoms are in the range of 0 to 0.07 s. Such strain rates during drawing have not been found. Therefore, hydrogen atoms can be the cause of dynamic strain aging since the strain rates during drawing are commensurate with the critical strain rate for hydrogen atoms. This condition is met at a dislocation density ${\rho }_d$ = 10¹³ m⁻², which corresponds to a degree of deformation of 7% (Figure 6).

As shown in Figure 6, the dislocation density in the drawing process takes values of 10¹²–10¹⁵. According to Equation (26), changing the dislocation density to 10¹² without changing other parameters will allow us to obtain dependences similar to those in Figure 7, with the only difference being that the change in the critical strain rate must be reduced by a factor of 10. Therefore, the critical strain rate for hydrogen atoms will be in the range of 200 to 420 s⁻¹. Increasing the dislocation density up to 10¹⁴ will lead to an increase in the critical strain rate for hydrogen atoms up to 200,000–420,000 s⁻¹. If strain rates of about 200 s⁻¹ can be obtained by drawing with a low drawing speed and small draw ratios (Figure 4d), then strain rates of 200,000 s⁻¹ during drawing are unattainable.

The critical strain rates for impurity carbon, nitrogen, and oxygen atoms do not exceed 7 s⁻¹ at a dislocation density of 10¹⁵.

Consequently, the calculations showed that the conditions for the occurrence of dynamic strain aging could only be created by hydrogen atoms. At the same time, we know that this requires a concentration of hydrogen atoms greater than 10⁻⁴%. The above analysis was conducted for ferrite, i.e., low-carbon steel.

Figure 8 shows the change in the diffusion coefficient depending on the temperature of steel with different structures [35].

The diffusion coefficient for carbon steel varies slightly with temperature and is about 10⁵ m²/s. Substituting this value into Equation (26) shows that, depending on the dislocation density, the critical strain rate varies from 200,000 s⁻¹ and above. There are no such strain rates during the drawing process, so we can talk about the aversion of carbon steel to dynamic strain aging. The diffusion coefficient of pearlite is close to that of ferrite. Therefore, when calculating the critical strain rate, we obtain values of 100 to 200,000 s⁻¹. These values lie in the region of strain rates during drawing. Consequently, pearlite, just like ferrite, in the presence of impurity hydrogen atoms, is prone to dynamic strain aging.

The diffusion coefficient of austenitic steel is very sensitive to temperature. In the temperature range of 20–150 °C, the diffusion coefficient varies from 10^™12 to 10^™7 m²/s. Above a temperature of 150 °C, the diffusion coefficient remains constant. At such values, the critical strain rate varies from 0.2 to 200,000 s⁻¹, depending on the dislocation density and steel temperature. Therefore, austenitic steel is also prone to dynamic strain aging in the presence of hydrogen atoms.

In the process of preparing the workpiece for drawing (heat treatment and etching) and the application of galvanic coatings, steel hydrogenation can occur. Therefore, great attention should be paid to measures that reduce or eliminate steel hydrogenation.

The start time of static strain aging, depending on the steel temperature, varies from several hours to fractions of a second (

Table 4. Start time of static strain aging.

Steel Temperature during Drawing, °С	100	140	180	220	260	300
Start Time, s	7000	3200	200	1.5	0.2	0.004

) [10,14].

From the analysis of Table 1, Table 2 and Table 4, it follows that the heating of the wire during drawing on high-speed straight-line machines provides the conditions for the passage of static strain aging of steel.

To eliminate the conditions for the occurrence of static strain aging of steel, it is necessary to limit the heating temperature of the wire to 180–200 °C.

To do this, it is necessary to pay great attention to the quality of the wire surface preparation before drawing, the properties of technological lubrication, and the cooling of the die and the pulling drum.

It is especially important to avoid winding the finished wire in a warm state onto a spool. A tightly wound wire at a temperature of 100–140 °C will stay on the spool for a long time, and this will allow the processes of static strain aging to take place, which will lead to a loss or decrease in the plastic properties of the wire.

4. Conclusions

The conducted studies have shown:

• A mathematical model has been developed for calculating the wire average temperature during drawing on straight-line drawing machines;
• The calculation results showed that the average temperature of the wire during drawing at a speed of up to 45 m/s on straight-line drawing machines can reach 400 °C;
• Deformation heating of the wire during drawing does not exceed 60 °C, and heating due to sliding friction can reach 300 °C;
• Average strain rates on modern high-speed drawing machines reach 7000 s⁻¹;
• In modern temperature and speed regimes of the drawing process, conditions are created for the occurrence of dynamic deformation aging of steel in the presence of hydrogen atoms;
• During heat treatment and pickling, it is necessary to exclude the hydrogenation of steel;
• To exclude static deformation aging of steel during drawing, it is necessary to prevent heating of the wire above 180–200 °C.