1. Introduction
It is commonly accepted that the drawing process of round wires is one of the most well-known metal forming processes, both theoretically and technologically, not only due to its circular symmetricity and stationarity but also because many formulas allow for fairly accurate calculations of drawing forces (e.g., Sachs or Siebel equations and analyses), the coefficient of friction, residual stresses in the material, unit pressure values, etc. [
1,
2,
3,
4,
5]. However, throughout the process of manufacturing mostly profiles but also round wires, there are a number of technological difficulties related to the obtaining of the desired mechanical properties, required dimensional tolerances, and satisfactory surface quality. Longitudinal or cross-sectional cracks, which often occur during the process, make the drawn material completely unsuitable for further processing. This phenomenon may transpire mainly due to the loss of metal plasticity, causing well-known drawing defects such as chevron cracks, bulging, or thinning, which are caused by improper technological conditions of the process (e.g., inaccurate deformation coefficient, die angle, coefficient of friction, or velocity field of plastic deformation region) [
6,
7,
8]. Technological aspects of wire drawing failures were analyzed by Raskin et al. [
9] based on 673 wire breaks, which happened in industrial conditions throughout the drawing process of pure copper with the use of a multi-wire drawing machine. They stated that inclusions are the main cause of 52% of wire breaks; however, it is worth noting that as much as 13% of material discontinuities among the tested samples were caused by the aforementioned defects such as chevron cracks, commonly known as central bursts, or cup and cone breaks.
It is assumed that when an elastic–plastic body is subjected to a sufficient stress field, the plastic deformation region is generally accompanied by an elastic deformation region. When considering the wire drawing process, the location of the elastic–plastic region is usually situated inside of the die reduction angle, and to meet the criteria required for material transition to plastic state, it is necessary for it to be entirely proceeded by the elastic state. For the purposes of this analysis, four regions of strains throughout the length of the drawn material were distinguished and are presented in
Figure 1A based on the descriptions made by Knych [
10]: the unloaded region (I); the region of elastic deformation generated behind the elastic–plastic region (II); the elastic–plastic region (III); and the elastic region in which elasticity comes from the drawing force (IV).
Two parallel hypotheses concerning theoretical analysis of the wire drawing process may be considered regarding the classical literature on the subject, i.e., the flat cross-section hypothesis, which assumes that a selected set of points constituting a plane perpendicular to the drawing axis before entering the drawing die will remain at this plane throughout the entire process and after its completion (
Figure 1B); and the spherical boundary hypothesis, which assumes a constant motion field of particles in the deformation region of the die, which means that during the plastic deformation, all points move towards the top of the cone formed by the drawing die (
Figure 1C). Thus, the boundary of the elastic–plastic deformation region is expected to be a plane or a slice of the sphere. Such an assumption allowed for the use of analytical methods to solve problems existing inside of the drawing die.
Regarding more recent scholarly sources, however, attempts have been made to determine the elastic–plastic deformation boundary inside of the die reduction angle, e.g., using the method of characteristics [
11], using the numerical analyses [
12], or with the use of empirical studies such as performed by Dobrov [
13] during the analysis of the shape of the deformation region from the side of the bearing length. The accessible data show that the shape of the elastic–plastic deformation region and, to some extent, the shape of the elastic deformation region related to it may be much more complex than is commonly assumed, and what is more, it may have a significant impact on the nature of the metal flow throughout the drawing process. It is worth noting that the length of the region in the analysis of [
11] reaches a minimum value at the wire drawing axis, and as the deformation, being the result of the adopted process parameters, does not cover the entire material cross-section, it will lead to the forming of the above-described drawing defects, such as chevron cracks.
A wide range of scientific papers concerning the generally understood process of drawing of round wires were written in the 20th and 21st centuries, both in terms of the conventional drawing process and innovative methods, such as accumulated angular drawing (AAD), which tests the influence of the linearity of dies throughout the process; drawing with the use of ultrasound; drawing with an elevated temperature of the die [
14]; or drawing with the use of high-density electric current pulses [
15] or annealing by electropulsing during pure copper wire drawing, which allows the annealing time during the wire drawing process of pure copper to be shortened, and thus does not strengthen the final product [
16]. Lack of strain hardening during the wire drawing process has also been observed after specific heat treatment of other materials [
17]. Many researchers nowadays put more interest in the cryogenic wire drawing process as an alternative process that may increase the material’s mechanical properties, such as ultimate tensile strength, with the cost of higher drawing forces [
3,
18,
19,
20]. In their research paper, Massé et al. [
21] attempted to re-evaluate the optimal drawing angle using finite element method analyses, which led them to conclusions that a lower drawing angle than considered to be optimal in the classic literature allows one to reduce the number of product defects with no significant increase in the drawing force; however, according to the authors, due to the influence of the friction conditions, it seems more advantageous to use a slightly higher drawing angle. Another thought-provoking academic work was conducted by Haddi et al. [
22], who made an attempt to assess the influence of the drawing velocity and the temperature of the process resulting from the friction on the drawing force necessary to carry out the process. They stated that these values differ throughout the process, which is a result of the varying friction coefficient and the nature of metal flow, depending on the drawing velocity. Based on the obtained experimental results, a modification of the Avitzur model was proposed, which, in the opinion of the authors, will allow for the adjustment of the drawing parameters by minimizing the drawing stress of copper-based materials. Another study dealing the influence of die geometry on the drawing force based on numerical simulations was conducted by Sas-Boca et al. [
23], who claimed that both die angle and bearing length have a significant influence on the calculated drawing force values. Results obtained in all these scholarly works show promising possibilities in terms of properties of the final product or decreased drawing force, which in effect would lower the energy expenditure and cause plausible changes in the plastic and elastic deformations of the material. These are, however, considered to be unconventional and difficult to implement in industrial conditions.
Most of the available wire drawing process scientific analyses are based on the rigid-plastic body model. Such simplification does not fully take into account the phenomena occurring in the material before entering the elastic–plastic deformation region inside of the drawing die, and the assumption that the material before entering the die reduction angle is stress-free is not true, as it is obvious that elastic–plastic deformations must be preceded by elastic deformations [
24]. Among research works taking that into account, Martinez et al. [
25,
26] investigated the influence of the wire drawing parameters throughout the process, as well as die geometry on generated heat, friction, and plastic deformations. They confirmed that as a result of the material flowing in the direction of the die axis, the stresses changed from compressive to tensile. What is more, they also noticed that the stresses at the surface of the wire take higher values as the contact length of the material with the die reduction angle decreases, which results in later deformation heterogeneity. They also proved that as the drawing angle increases, the compressive stresses both at the surface and along the axis of the wire increase, and the material shows greater uniformity of the material flow in the radial direction. Additional studies proved that the reduction of the friction coefficient causes an increase in radial deformations. Similar observations have been made when the drawing angle has been changed. The authors of these two works [
25,
26] did not notice any influence of the die geometry on the axial deformations. Skołyszewski et al. [
5], in their research work, investigated the influence of back tension throughout the wire drawing process of steel on recorded stress values and noted that despite the very short length of the region of elastic deformations, its values exceeded several times the value of the metal unit pressure on the wall of the drawing die, which is an extremely dangerous phenomenon during the wire drawing process. They observed, however, that the use of back tension lowered the recorded values at the boundary of the elastic and elastic–plastic deformation regions, which consequently led to lowering the values of unit pressure in the elastic deformation region. The authors in [
27] analyzed the drawing force, stresses, and properties of the final product of the conventional wire drawing process of steel in comparison with the roller dies implemented in the process. The obtained results showed an increase in the drawing force and the die and material temperature throughout the unconventional process along with an increase in recorded stresses and deformation heterogeneity. The authors of this study did not record any changes in the properties of the final product; however, they noticed a significant improvement in the surface quality of the wire obtained with the roller die. Another analytical study in the area of various types of dies and their impact on the process was conducted by Zhang et al. [
28] on aluminum alloy 7A09 with a conical die, single elliptical die, and twin elliptical die. They concluded through their numerical simulations and calculations that the lowest value of the drawing force should be expected when using the twin elliptical die. What is more, they also stated that the minimal values of stress should occur when using dies with an optimum drawing angle, with one additional condition that the angle should increase as the deformation coefficient increases. Some of the few empirical studies in recent years, conducted by Vega et al. [
29] and Tintelecan et al. [
30], proved that the drawing force in the process of copper wire drawing is influenced by the drawing angle, friction coefficient, and bearing length. The authors in [
31,
32,
33,
34] claim that there is a clear connection between the amount of oxygen and therefore copper oxides in the input material on the strength parameters of the materials, and thus the drawing forces, during the process. There is a noticeable modern trend towards lowering the occurring drawing forces, for instance by using various innovative lubricants such as graphite [
35], PTFE [
20], powdered soap [
17], or MoS2 [
3]. Various coating materials and lubricants have been investigated in [
36] in terms of defects occurring on the surface of the wire after the metal forming process, and the authors proved that the smaller the size of the powder, the better the lubrication process. Additionally, they provided evidence that the larger size of the lubricant powder may cause delamination of the coating layer. When considering the surface of the metal wire, it has to be mentioned that microhardness, nanohardness, and Young’s modulus strongly depend on the state of the material surface and change upon contact, as has been proven both experimentally [
37,
38] and in numerical simulations [
39]. In particular, electrical contact and the influence of the electric potential upon contact with other metal on a set of physical and mechanical properties were investigated throughout these research works, as the authors provided evidence that, for example, microhardness may decrease by as much as 8% when the electric potential of ~0.02 V is applied.
There are many scientific works concerning various metal forming processes and the elastic and elastic–plastic deformations occurring during the process, such as electroplasticity-assisted bending process [
40], where the authors reduced the bending force and the elastic restoring force. Thermal elastic–plastic analysis was proposed by Kim et al. [
41] during the friction stir welding process, where they claimed that the proposed parameters during the process would reduce the testing period and the cost of the manufacturing process and increase productivity of electric vehicle battery frames. The authors in [
42] investigated the influence of various strain hardening models under cyclic loading on the elastic–plastic behavior of the material and provided data for further practical applications. These recent works, among many others, prove that elastic and elastic–plastic deformations are recently being given more consideration. Nonetheless, most of the modern research works concerning the wire drawing process and the forces, stresses, and deformations resulting from it are based on numerical and analytical simulations, which necessitate their verification in real conditions, thus proving the innovative approach of the research conducted in this work, which is focused on an empirical attempt to determine the length of the elastic deformation region in the material before entering the drawing die in the process of axi-symmetric wire drawing of ETP grade copper (electrolytic tough pitch). The research was carried out given that, according to the scholars and academics referenced in the introduction, the elastic deformation region may have an influence not only on the drawing force but also on the occurrence of drawing defects caused by heterogeneity of deformation on the cross-section of the final product.
2. Industrial Approach and Application
The focus of the article in on the fundamental research of a cognitive nature and not on application aspects. The conditions of the conducted experiment (velocity of the process and exogenous factors) vary from those in the drawing operations carried out on an industrial scale. Their selection was the key element necessary to isolate the tested parameters, such as the changes in the drawing force and elastic deformation of the material before entering the drawing die, which are normally concealed by changes in the temperature of the material.
Nevertheless, on the basis of the analysis of the conducted research, it is possible to propose a number of significant postulates important from a practical point of view and transfer them (after appropriate verification) to the industrial drawing process.
The observed increase in the drawing force in the non-stationary phase of the drawing process may be associated with the evolution (disappearance) of the elastic deformation region situated in front of the plastic deformation region. Therefore, it may be hypothesized that other process parameters (the presented study proved the influence of the size of the deformation coefficient λ) also have an impact on the shape of the elastic deformation region, and thus on the value of the drawing force in the stationary phase. After empirical verification of this hypothesis, it is possible to search for a new concept of minimizing the force parameters of the drawing process.
As is commonly known, in industrial drawing processes, the elastic back tension of a controlled value is often used in order to reduce the unit pressure of the material on the surface of the drawing die. At the same time, should the critical value be surpassed, it causes a significant increase in the drawing force and lowers the material’s deformability. This back tension is in synergy with the natural region of plastic deformation analyzed in this study. There is a prospective possibility that not only the value of the back tension, but also the elastic deformation region tested in the current work, affects the value and distribution of metal unit pressure on the drawing die’s surface, and thus the wear and tear of the tool or lubricants used. Moreover, the unit pressure and the coefficient of friction determine the temperature gradient across the material cross-section (temperature increase of the surface layer of the tribological origin), which to some extent determines the state of residual stress in the wire after the drawing process.
The studied phenomenon can also be analyzed from the point of view of defects occurring in drawn materials. The classical model of Avitzur’s central burst defects is based on a rigid-plastic body model, while in fact in the observed area of fractures, the material is probably in an elastic state. The elastic deformation region at the axis of the drawn material analyzed in this paper transforms into a new form and cracks appear, which depend not only on the kinematic incompatibility of the velocity field of the material particles, but also on the stress state. Recognition of this phenomenon gives hope for the development of a new mechanism for the emergence of central burst defects, and maybe even for the development of new technological recommendations, making it possible to eliminate the defects in question.
3. Materials and Methods
In order to empirically determine the length of the elastic deformation region generated behind the die in the axi-symmetric wire drawing process of copper, the authors of this paper conducted laboratory tests with as low as possible drawing velocity. Copper wire rod of ETP grade and chemical composition, as specified in
Table 1, was chosen as an input material. Wire rod with a diameter of 20 mm was subjected to a prior wire drawing process on a laboratory draw bench machine in straight sections down to 11.55 mm and 10.5 diameter in 6 and 7 draws, respectively, without intermediate annealing, which assured the hard state of the input material and allowed the influence of strain hardening on the recorded values (approximation to the elastic-ideally plastic body model of the material) to be avoided. The first tests were conducted in order to determine the mechanical properties (ultimate tensile strength, yield strength, Young’s modulus, Poisson’s ratio, Vickers hardness) of the input material with a diameter of 11.55 mm using the uniaxial static tensile test, ultrasonic method, and Vickers hardness test.
The starting point of the conducted research were finite element method (FEM) simulations of the wire drawing process. The strain rates and stresses present at the wire cross-section were analyzed in order to identify elastic–plastic and elastic deformation regions, which functioned as a reference for empirical research conducted in real conditions.
The most important part of the research was the experimental determination of the length of the elastic deformation region and the values of strains occurring in it in order to ensure that the authors carried out wire drawing tests at a very low drawing velocity (measured drawing velocity of the material after exiting the drawing die about 0.1 mm/s) on a testing machine (TIRA GMBH, Schalkau, Germany) with a maximum tensile force possible to be applied equal to 50 kN registered by an independent measuring system fixed with the jaws. The assembly was rigged with mechanical gears. The strain was measured using resistance strain gauges (HBM, Darmstadt, Germany) placed on the samples, as shown in
Figure 2C, with a specially prepared test stand (
Figure 2B), and the values were registered with Spider 8 measuring equipment (HBM, Darmstadt, Germany) and Catman software. This should have partially compensated for the temperature increase caused by the material friction against the die; however, in real conditions it is not possible to completely eliminate temperature increases during plastic working processes, so these values and their influence on the recorded strain values were analyzed using thermocouples, placed as shown in
Figure 2A, and a thermal imaging camera (Optris, GmbH, Berlin, Germany).
Traditionally, the wire drawing process is considered to be stationary, and the macroscopic effect of this stationarity is the constant drawing force necessary to conduct this process. The authors made an assumption that if an elastic deformation region is being generated in the material before entering the die reduction angle, which in any way affects the strength parameters of the process, then from the moment when the material dimensions before the drawing die are smaller than the dimensions of the elastic deformation region, it is expected to have an effect on the drawing force. In order to verify this hypothesis, an analysis of the drawing process was carried out using a drawing die, with a diameter of 10 mm, using two various process parameters, i.e., with the deformation coefficient λ = 1.33 (input material with a diameter of 11.55 mm) and λ = 1.1 after an additional draw of the input material to diameter of 10.5 mm prior to strain gauge measurements, which would allow us to determine the influence of the applied cross-section reduction on the length of the elastic deformations region generated before entering the die reduction angle. An initial estimation of the length of the elastic deformation region was based on the observed increases in the recorded drawing force at the end of the process. More complex analysis of the length of the elastic deformation region was carried out using precise strain gauge measurements. In each case, measurements were made in stationary conditions, i.e., when the strain gauge was placed far from the end of the material, and in non-stationary conditions, i.e., when the strain gauge was placed close enough to the end of the drawn material that the initial estimation based on the drawing force suggested that the length of the material was lower than the expected length of the elastic deformation region. Strain gauges used during analysis measured strains in longitudinal and radial directions.
The last part of the analysis was the Vickers hardness tests performed at the cross-section along the axis of the samples after the drawing process using a TUKON 2500 hardness tester (Buehler, Lake Bluff, IL, USA) with a test load accuracy of +/−1% and an accuracy of the indent’s diameter measurement of 0.02 mm. Starting 0.5 mm from the edge and with the same intervals between measurements, 19 indentations were made on the samples taken from stationary and non-stationary conditions, which allowed for their thorough analysis in comparison with the hardness of the input sample.