Thermomechanical Analysis of an Electrically Assisted Wire Drawing Process

The cold wire drawing process is probably one of the simplest metalworking processes. It reduces the specimen's cross section by pulling the specimen through a single or several converging drawing dies. The main factors that affect the wire drawing process are the type of workpiece material, lubricant, drawing speed, cross-sectional reduction, and the type of drawing die [1]. Due to the cold work, the mechanical properties of drawn wire are changed by having increases in the ultimate tensile stress, yield strength, and the material hardness, while a decrease of the ductility and elongation [2]. In order to enhance the ductility of the wire specimen, it is needed to conduct several annealing treatments during the drawing process. Since these heat treatments increase cost and manufacturing time, hybrid manufacturing processes are currently under research to overcome those shortcomings. A recent review stated that the electrically assisted (EA) techniques are widely used to assist different manufacturing processes [3], such as bending [4,5], wire drawing [6,7], stamping [8], incremental forming [9], machining [10,11], among others.

The aforementioned literature agrees that this hybrid technique brings a great potential because of the change of the mechanical properties and the microstructure characteristics by the in situ electropulses (EPs) influence. In particular, the EPs-assisted wire drawing process has proved to decrease the ultimate tensile stress and to reduce the forming forces necessary to plastically deform the specimens, while increases the material elongation [6,12]. Recently, Jiang et al. [13] and Sánchez Egea et al. [7] showed a modified X-ray pattern in two different wire drawn materials as evident by how the EPs promoted a dynamic recrystallization mechanism in the specimen's microstructure. These results also explained the cause for the enhancement of the formability in the wire drawn specimens.

Despite that most of the literature focused on the experimental analysis of how the mechanical and metallographic properties are affected by the EPs, there are some authors who have developed numerical approximations to describe the impact of EP on mechanical properties. For example, Li and Yu [14] and Tskhondiya and Beklemishev [15] used computational methods to study the plastic behavior affected by EPs. In concordance with their research, this work analyzes the thermomechanical behavior of an electropulsing-assisted drawing process. The formulation of this model is based on a previous study [7], where an increase in the formability of the material and changes in its microstructure were found in 308L stainless steel under the influence of EPs. Some of the main findings from Ref. [7] in terms of the microstructure were dynamic recrystallization, detwinning mechanism, and attenuation in the formation of α martensite. To study how these microstructure changes affect the mechanical properties, like residual stress and plastic strain, it is necessary to achieve a thoroughly experimental and numerical analysis of the in situ EPs consequences on the 308 L stainless steel wire drawing process. Additionally, an instantaneous rise of temperature in the assisted specimen was estimated from an adiabatic condition. To the authors' knowledge, a fully coupled thermomechanical modeling and simulation of EA wire drawing processes has not been explored so far. Hence, the aim of this work has threefold: first, to quantify the influence of EPs on the residual stresses in the wire; second, to assess the performance of two different hardening laws respectively considering rate-independent and rate-dependent material responses; and third, to experimentally validate the temperature rise caused by plastic deformation, frictional, and Joule's heating. The “Experimental Procedure” section presents the methodology undertaken to assess the effect of electroplusing in the wire drawing process of a 308 L stainless steel wire under a specific EP and die configurations. In the process, the drawing force and the bulk temperature were measured. The “Thermomechanical Formulation” section describes the model used in the present work to study the material's performance during this metal forming process. The formulation accounts for elastoplastic behavior of material with isotropic two hardening laws, a rate-independent and a rate-dependent condition. It also considers Coulomb's friction, large strains, Joule's heating, and the thermal contributions of the coupling effects of plastic deformation and friction. This presented numerical approach is investigated in the framework of the finite element method. The “Numerical Simulation” section shows and discusses the results of the EA specimens using two different hardening laws characterized with the experimental measurement of the mean steady-state forming force. Additionally, the microstructure evolution is described in “Experimental Evidences” section to back up the presented thermomechanical model. To sum up, the final statements are listed in “Conclusions” section.

A commercial 308 L stainless steel wires (0.03 wt % C, 19 wt % Cr, 9.7 wt % Ni, 0.45 wt % Si, 1.18 wt % Mn, 0.04 wt % P, 0.03 wt % S, balance Fe) are investigated in the present study. The wire drawing tests were performed in an Instron 4206 universal testing machine using five samples with as-received nominal diameter of 1.60 mm. The output diameter after being wire drawn is 1.47 mm. The wire was drawn in a single pass with the maximum reduction ratio that can be achieved in the conventional drawing (CD) process and a constant velocity of 0.5 m/min, while the cross-sectional area reduction and the semi-angle of the conic die were kept 15.6% and 6 deg, respectively. Fracture of specimens was found when higher, 39.9% and 28.8%, cross-sectional area reductions were conducted. Powder soap lubricated the drawing die during the experiments. The drawing forces were recorded with load cell, sensortronics 98001 model with a resolution of 1 N, connected to the drawing die and the upper clamp of the tensile test machine. The electropulsing effects were achieved via an in-house power supply designed to induce EPs [7,11]. An oscilloscope monitored the electric parameters, like interval, amplitude, and duration of the EPs. All the electric operation parameters are found in Table 1. The forming forces affected by the EPs during the drawing process were measured dedicated force sensor and acquired with a data acquisition card. Ad-hoc nylon collar was designed to isolate the forming die from the tensile test device. The surface bulk temperature variation was continuously traced with a thermocouple (type K). From experimentation, the EA process was decided to take 15 s, because higher durations were found to compromise the strength of the material. An illustrative layout of the EA wire drawing process is shown in Fig. 1.

As explained in the previous work [7], the averaged drawing forces for the conventional drawing and EP processes were obtained from the load–time curve of the tensile test. The recorded forming forces during the experiments conducted in this work are listed in Table 2. The EA process showed lower forces in plastically deforming the specimen to reduce the cross-sectional area. The 11.9% reduction in drawing force is due to the electroplusing effects. As also stated, this hybrid process denotes two effects on the material: lower forming forces for a plastic deformation and a greater elongation that, consequently, improve the material formability.

The maximum bulk temperature measured at the end of the EPs time duration is included in Table 2. This instantaneous temperature of about 200 °C was measured at the exit of the forming die, where the specimen reaches the minimum cross-sectional area and, subsequently, the highest current density. Comparable temperatures were assessed in the literature when using electropulsing treatment [13,16]. In particular, Jiang et al. [13] found a bulk temperature of 205 °C when induced 331 A/mm2 in AZ91 alloy strips, whereas Jiang et al. [16] registered a bulk temperature of 204 °C when induced 150 A/mm2 in 304 stainless steel specimens. The temperatures observed in the assisted specimens are noticeably lower than the temperatures needed for a stress relieving treatment. This lack of stress relieving by thermal softening could be a disadvantage if wire required a higher area reduction, because larger material's formability is obtained when higher temperatures are reached. For stainless steel, temperature is within the range of 450–800 °C for annealing process, while the temperature range of 1100–1400 °C is required for achieving static recrystallization mechanism.

The electropulsing treatment duration was a crucial parameter in this hybrid manufacturing process. An electropulsing duration of 15 s was decided from a series of trials, because it reached the high enough temperature to improve the forming process by decreasing the forming forces, although higher electropulsing durations were found to compromise the strength of the material. Finally, the selection of the isolation system between the lower clamp and the drawing die required a thoughtful design. The polymeric material did not behave as expected and the specimen tends to slip from the lower clamp; consequently, metallic sheet metal trips were used in the interphase of specimen–polymer to improve the effectiveness of gripping.

The proposed thermomechanical model to describe the change of the mechanical response considers only the thermal contribution (Joule effect). Electron wind or magnetoplastic effects were not considered since the microstructure effect associated with these effects is not fully comprehended and described yet. Moreover, according to a recent review [17], electroplastic effect in metallic materials is caused by Joule heating; therefore, the global and local rise of temperature is the major component to affect the mechanical properties compared with the electro wind and magnetic effects.

The main features of the bidirectional thermomechanical model presented in this work to simulate the wire drawing process are summarized in Table 3. Details of a general thermomechanical model can be found in previous works [18,19], though these previous works were not specifically developed for EA. In the governing equations, ▿ is the spatial gradient operator, σ is the Cauchy stress tensor, ρ is the density, c is the specific heat capacity, T is the temperature, q is the heat flux vector, β the conjugate of the thermal dilatation tensor, d is the rate-of-deformation tensor, r is the specific heat source, and r_int is the specific internal heat source. Moreover, J is the determinant of the deformation gradient tensor F, $d=1/2(∇×u˙+u˙×∇)$⁠, the superposed dot stands for time derivative and the subscript 0 is related to the initial condition of a variable. In this framework, the isotropic material performance for this cold work can be assumed by several thermodynamic state variables as the Almansi strain tensor e (⁠$e=1/2(1−F-T⋅F-1)$⁠, where T is the transpose symbol), the temperature and two internal variables, namely the plastic Almansi strain tensor e^p and the effective plastic deformation $e¯p$⁠, whose evolution equations are defined within the context of the associate thermoplasticity theory [20]. In the thermoplastic model, C is the isotropic elastic constitutive tensor, e^th is the thermal Almansi strain tensor (α_th is the thermal dilatation coefficient), $σ¯=3J2$ is the von Mises stress (J₂ is the second invariant of the deviatoric part of σ), $Cy0$ is the yield strength defining the initial material elastic bound, C is the isotropic hardening stress, L_v is the frame-indifferent Lie derivative, and $λ˙$ is the plastic parameter derived from the consistency condition $F˙=0$⁠. Furthermore, k is the thermal conductivity coefficient and γ is the electrical resistivity.

The performance of two hardening laws, a rate-independent and a rate-dependent, respectively given by expressions H₁ and H₂, is particularly assessed in the present work. In these expressions, A^p and B^p are hardening parameters, n^p and m^p are strain and strain-rate sensitivity parameters, ξ is the electroplusing parameter, and j accounts for the equivalent current density. Despite its simplicity, the hardening law H₁ was successfully implemented in others metalworking processes [2]. On the other hand, the rate-dependent hardening law H₂ has been derived taken into account both the influence of internal local stress field on dislocation slipping velocity and the change of the parameters of the thermally activated plastic flow equation when EPs are used [14]. This law adequately describes the electroplusing effect given by a nonlinear relationship for the decrease of the flow stress in terms of the current density. As discussed in Ref. [14], this approach proposes the presence of maximum and minimum thresholds values of j to achieve the electroplusing effect (these two bounds, respectively correspond to D = 2 and D = 1). The inclusion of this law in the described thermomechanical framework is a novel characteristic of this study.

In the contact boundary conditions of the equilibrium and energy balance equations, t_f(i) is the contact traction vector, q_f(i) is the friction normal heat flux, n_(i) is the outward unit normal vector outward unit normal vector of Γ_f(i), a_(i) is the rotation tensor related to the unit tangential vectors of Γ_f(i), p_n is the normal pressure, p_t is the tangential pressure vector, e_(i) is the Vernotte's relative effusivity parameter, and q_c(i) is the conductive normal heat flux described between bodies one and two as $qc(1)=−h(1−2)(T(1)−T(2))$⁠, where h₍₁₋₂₎ is the heat transfer coefficient. The normal gap g_n and the tangential relative position vector g_t between such bodies are given by $gn=n(1)⋅(x(1)−x(2))$ and $gt=a(1)⋅(x(1)−x(2))$⁠, where x is the spatial coordinate vector. Moreover, E_n is the normal rigidity, $gts$ is the tangential slip vector, $‖pt‖=pt⋅pt$ and μ is the friction coefficient.

The thermomechanical formulation briefly aforementioned is solved by using the widely used method of finite elements in agreement with the numerical solution proposed in Refs. [18] and [19].

The wire drawing process described in the Experimental Procedure section is analyzed via the thermomechanical formulation presented above with a threefold objective: estimation of the influence of EPs on the residual stresses in the wire, assessment of the hardening laws H₁ and H₂ (see Table 3), and validation of the thermal values measured underneath of the drawing die.

A uniform mesh consisted of 2000 four-noded isoparametric axisymmetric elements is used in these simulations. A B-bar interpolation method is applied to reach numerical convergence for plastic incompressible approaches [18]. The drawing die is defined as a solid body and composed with two-noded isoparametric elements. This process is characterized by a linear time-dependent and forced displacement at the wire's bottom. The simulations of both hardening laws are conducted using an implicit integration, where the increment of the time step is 0.01 s and the forming velocity is the same as that in the experiments (0.5 m/min). A large specimen's length is selected to adequately accomplish the steady-state behavior during this metal forming process. Therefore, only steady-state results are exhibited in this section.

The material properties taken into account in this thermomechanical approach are summarized in Table 4. Although these parameters are temperature dependent, here are assumed to be constants, because of the low temperature levels found during the experiments. Matweb database was consulted for all these values, except those of the hardening laws and $Cy0$⁠. Tensile experiments of the original material were conducted to estimate the initial yield strength $Cy0$ [7]. EA treatment is presumed not to affect the initial yield strength, as mentioned by Roh et al. [21]. However, EPs denoted a strong impact on the material hardening behavior [22]. In this framework, the method presented here to determine the parameters for the two hardening laws consists in fitting the numerical drawing force to the equivalent experimental average value.

For the hardening law H₁, a linear relationship was considered for this material, because the mechanical parameters, like the initial yield strength and ultimate tensile strength, practically match with this tendency [7]. Only for this law, the hardening parameter A^p was obtained for both the CD and EA processes. For the hardening law H₂, a typical value for the strain-rate sensitivity parameter m^p is adopted [23]. Then, the hardening parameter B^p was fitted with the drawing force of the CD process (i.e., j = 0 which implies D = 1) and, finally, the EA drawing force value is considered to derive the electroplusing parameter ξ. The resulting values obtained with this procedure for both hardening laws are also included in Table 4.

The parameters involved in the thermomechanical boundary conditions are shown in Table 5. The initial wire temperature is assumed as equal to the environmental temperature.

Figures 2 and 3, respectively, show the computed effective plastic strain and equivalent stress distributions along the radial coordinate after the die exit section for three cases: without pulses using the hardening law H₁ and with pulses using the hardening laws H₁ and H₂ (see Table 3). The results indicate that the three studied configurations show similar distributions of effective plastic strain and equivalent stress. The effective plastic strain exhibits the maximum values near the specimen surface, while the minimum values are found in the center of the wire specimen. Comparing the plastic strain values of the process without pulses and with pulses (using the hardening law H₂), the difference is about 5% in average along the radial coordinate distribution. The equivalent stress shows also the same trend for the three configurations but, depending on the radial coordinate position, the stress values bring a wider or smaller difference. Near the center of the specimen, the EA process using both hardening laws exhibit stress values approximately 19% and 9% smaller than that of the CD. These differences increase up to 26% and 10% when the processes are compared with the stresses found at the specimen surface. Therefore, the EA process decreases the equivalent stresses and increases the plastic strain of the wire specimen. Therefore, it could be ensured that the material formability is improved with this hybrid manufacturing process.

The residual equivalent radial stress evolutions in the three cases mentioned previously are plotted in Fig. 4. The residual stress indicates that similar values are found at the surface and at the center of the specimen for the CD process, which are about 850 MPa. The EA process with the hardening law H₂ presents a significant drop of 28% of the residual stress compared with that of the CD process at the surface, while in the center of the specimen, the residual stresses difference decreases to 19%. From the manufacturing point of view, it is desired to have low residual stresses at the specimen surface, to avoid radial cracks that can compromise the specimen strength. The EA process by EPs seems to affect the microstructure, similar to an ultrafast annealing process, where the rise of temperature has an influence on the wire specimen by reliving its internal matrix stresses.

Table 6 shows the computed maximum bulk temperature for the same three cases mentioned previously. It is seen that the effect of the EPs prevails over that of the plastic and frictional heating. This results in a nearly uniform temperature field in the wire for the EA process in which the temperature predictions using both hardening laws reasonably fall within the experimental range shown in Table 2. Moreover, in agreement with Ref. [19], almost negligible thermal expansions were found from the rise of the temperature in the specimens.

Our previous research showed the influence of the electropulsing treatment in the mechanical properties of the wire drawn specimens [7]. Here, the microstructure evolution for the different specimens was studied to experimentally support the proposed thermomechanical model and the numerical results. To do that, manual grinding and polishing steps were conducted up to the size of colloidal particles of 0.05 μm. Then, electron backscatter diffraction analysis was conducted to characterize the specimen's microstructure. The misorientation angle was setup to be ≥15 deg to define high-angle grain boundaries (HAGB) and from 2 deg to 15 deg for low-angle grain boundaries (LAGB).

First, the SEM images were taken to determine the overall grain boundaries and twins organization in the material's microstructure. Figure 5 exhibits the HAGB, LAGB and twins distribution within the specimens' microstructure. All the specimens' microstructures show a great number of curved HAGB that limit nonequiaxial grains preferentially oriented in a direction which indicate a greatly deformed material. Higher densities of LAGB are observed when the EPs were used during the forming process, while a higher number of HAGB are found in CD compared with those of the EA and the as-received specimens. Therefore, the microstructure of the EA specimen exhibits a detwinning process which could stand for a fast stress relieving treatment. Accordingly, Xie et al. [24] described a similar detwinning process in EA magnesium strips after a bending process. In both cases, the analysis of the misorientation angle distributions of the grain boundaries shows an unalike detwinning mechanism when comparing the microstructure of as-received, CD, and EA specimens.

In a second microstructure analysis, higher magnification SEM images were captured to study the LAGB distribution within grains. Figure 6 shows the CD and EA specimens' microstructures where HAGB are plotted with black lines and LAGB are plotted with white lines. The CD specimen exhibits more twins in the overall microstructure, as expected from the cold forming, compared with the EA specimen. Looking within the grain structure, a larger number of LAGB are found in CD respect to EA specimens. In addition, LAGB distribution in the CD specimen tends to orientate in a regular cross-mesh, while in the assisted specimen the mesh tends to orientate in parallel. In the second case, the electropulsing influence seems to affect the formation of the LAGB toward a preferential orientation. Similar results were presented by Song and Wang [25]. They found an annihilation of the twins at inner region of the grains plus a decrease of the grain size, when a cold-rolled process was EA of Ti strips. They stated also that during the recrystallization process the deformed grains are rearranged and the dislocation number is reduced, while the number of effective slip bands increased. Therefore, the lower density of HAGB and the formation of the LAGB toward a preferential orientation could be explained due to two effects: global thermal softening and the local impact of thermal effects (hot-spots). In the first instance, the thermal softening will release the internal stresses and the microstructure will present lower density of twins due to a dynamic recrystallization process, mainly initiated at the grain boundaries due to the localized Joule heating, as investigated by Wang et al. [26] in Mg alloy and Fan et al. [27] in brass alloy. Jiang et al. [16] found that the thermal softening on dislocation hardening is basically to the Joule effect and the electric current do not enhance the activation effect on motion of dislocations when temperature is 204 °C. Hu et al. [28] describe microstructural changes, such as material texture and recrystallization, in Fe-3%Si alloy strip under the influence of electropulsing. They found that grain boundary energy is crucial to enhance the boundary mobility. This mobility is due to the energy accumulation associated with the increase of dislocation and vacancies density at the grain boundaries that force to move them and convert LAGB to HAGB. Additionally, Lu et al. [29] and Conrad et al. [30] studied the microstructure changes in 316 L stainless steel and 7475 aluminum alloy, respectively, and they stated that the electropulsing enhances the dislocation movement through the material lattice, because instantaneous thermal difference (hot-spots) will promote stress—strain fields appears when impurities or material defects are reached that will promote new dislocation generation and helps to dissolve the precipitates and material impurities. At these hot-spots, it is observed local recrystallization areas that have an influence on the crystal orientation and improve the strain accommodation and, consequently, increase the formability of the specimen for future drawing steps. According to this finding, Roh et al. [21] investigated the electropulsing effects in uniaxial tensile test of an aluminum 5052-H32 alloy. Their results show a recrystallization process causing the grain growth, which greatly enhances the material formability when reaching low thermal contribution. Additionally, it is mentioned that the dislocation was annihilated when electric current was applied during plastic deformation because of the temperature. Kim et al. [31] also confirmed that electric current can enhance the atomic diffusion. In their study, it was found an annihilation of dislocations because a current-induced annealing process that occurs when electropulsing is applied to the specimen during plastic deformation without goes beyond the annealing temperature. Finally, Kuang et al. [32] reported electroplastic rolling and warm rolling experiments in Mg alloy. They stated that both processes present different deformation and recrystallization mechanisms and, therefore, different microstructure evolution. The reason is because the electropulsing effects in rolling promote the homogeneity of deformation and dynamic recrystallization and hence the higher activity of micro shear band when low accumulative true strains were studied.

Finally, the material hardness was registered in the center and at the surface of the specimen cross-sectional area. The aim is to analyze the influence of the microstructure changes on the specimen's hardness. Figure 7 shows the hardness of as-received, CD, and EA specimens. Ten measurements were taken for each experimental configuration. Lines within the box plots represent the median; squares represent the average; whiskers represent the tenth and ninetieth percentile; and crosses below and above the box plots represent maximum and minimum sided values. As it is expected, the higher values of hardness nonassisted specimens due to the cold working process. In addition, the hardness results show that as-received and CD specimens present higher values of hardness at the surface compared with those of the inner regions. The contrary happens with the EA specimens. Moreover, the EA specimens show a decrease around 14 and 54 Vickers on average respect to nonassisted drawn wires in the center and at the surface, respectively. The reason of the hardening differences in the center and at the surface could be related to the differences in temperature, due to friction between die and material, and the electrical skin effect. Thus, as smaller are temperature, effective plastic deformation (Fig. 2) and equivalent stress (Fig. 3) in the center of the wire, smaller is the recrystallization ratio and higher is the hardness (Fig. 7). On the contrary, as higher are temperature, effective plastic deformation, and equivalent stress in the surface of the wire, higher is recrystallization ratio and smaller is the hardness, as reported by Steward et al. [33] when studied dynamic recrystallization in 304 stainless steel. Moreover, during CD process the effective plastic deformation and equivalent stress both in the center and at the surface of the wire exhibit similar behavior and higher values comparing with as-received material, as expected in a metal forming process without recrystallization, and much higher comparing with EA process. Consequently, EA process presents a softening by recrystallization (Fig. 6) in the center and at the surface, which is associated with the increase of temperature as a consequence of the Joule effect. Furthermore, this effect is more noticeable in the surface due to the electrical skin effect (Fig. 7). In summary, the electropulsing assistance provoked an ultrafast annealing process in the EA specimens. As it has been aforementioned, the electropulsing treatment has promoted detwinning, has modified HAGB distribution, and seems to reorient LAGB. These changes of the microstructure could explain the decrease of material hardness in both center and surface of the specimen, and the enhancement of the material's ductility and the decrease of the residual stresses. Therefore, all these experimental evidences adequately support the thermomechanical model based on dislocation hardening laws. Additionally, the results observed in the numerical simulation analysis are consistent with the material softening and the detwinning mechanisms.

A thermomechanical model, the numerical simulations, and the microstructure analysis of electrically assisted wire drawn specimens were investigated and the remarks are listed as follows:

1. (1)

   Two hardening laws were proposed to evaluate the numerical forming force to the equivalent experimental results. Both laws have shown to decrease the equivalent and residual equivalent stresses for the EA process.

2. (2)

   The estimated values of the stress under the thermal contribution fit properly with the experimental results found in our previous work [7]. Therefore, the thermomechanical model has proved to be an effective method to estimate the flow stress affected by the electropulsing treatment.

3. (3)

   The electropulsing induce an ultrafast annealing process which, ultimately, decreases the material hardness in the center and at the surface of the specimens. In addition, the electropulsing treatment modifies the distribution of the HAGB and LAGB by promoting a detwinning mechanism.

Future work will consider to examine the residual stress distribution to validate the thermomechanical model proposed here. Moreover, electronic microscopy techniques, such as transmission electron microscopy, will be carried out to examine evidences of whether local rise of temperature at the grain boundaries affects the dislocation density at the material's microstructure and, ultimately, to improve mechanical model.

This work is supported by the Ministry of Economy and Competitiveness of Spain (Reference project DPI2011-26326), the National Fund for Scientific and Technological Development of Chile (Fondecyt project 1130404), and the U.S. Department of Energy (Award No. DE-EE0005764). All the authors who sign this manuscript do not have any conflict of interest to declare.

• Advanced Manufacturing Office (Grant No. DE-EE0005764).

• National Fund for Scientific and Technological Development of Chile (Grant No. 1130404).

• Secretaria de Estado de Investigacion, Desarrollo e Innovacion (Grant No. DPI2011-26326).