In this study, the plasticity behavior of an AZ31B magnesium alloy subjected to short-duration (100 *μ*s), high-frequency (120–800 Hz) pulsed current was investigated using tensile tests. The key finding is that the effect of pulsed current on plastic deformation goes beyond the Joule heating effect. In our experiments, the frequency was adjusted to maintain a constant effective current density and, thus, the same Joule heating effect. A comparison with continuous current having the same Joule heating effect was made as well. It was observed that when the peak current density is higher than a critical value, a higher peak current density will yield a more significant reduction in flow stress even though the thermal heating effect is the same. This critical current density decreases with the increase in the effective current density. Pulsed current with a higher peak current density can more effectively reduce the dislocation density through electric-induced annealing, induce more severe grain rotation, and, thus, lower the resistance for dislocations to pass through barriers like grain boundaries, resulting in a more significant flow stress reduction. X-ray diffraction characterizations were also conducted for the deformed specimen to show that a higher peak current density induces more severe grain rotation and, thus, more effectively decreases dislocation density.

## INTRODUCTION

Recently, pulsed electric current with short pulse duration (50–200 *μ*s) and high frequency (100–500 Hz) has been integrated into the manufacturing process for metals in order to improve their plasticity. For example, Sánchez Egea *et al.*^{1} and Wang *et al.*^{2} observed that electropulsing (EP) can decrease the cutting force and improve surface finish in the turning process, while Kuang *et al.*^{3} reported that electropulsing can reduce crack formation and significantly improve formability in rolling. Electropulsing has also been reported to produce a deeper plastically affected layer in metals subjected to ultrasonic impact treatment.^{4}

The improvement in formability in electropulsing-assisted deformation processes is attributed to the reduction in flow stress as a result of the pulsed current. However, a continuous current can also be used to decrease flow stress and, thus, improve metal formability in the manufacturing process. For example, Perkins *et al.*^{5} and Jones *et al.*^{6} studied electrically assisted metal forging using continuous current. It was found that the applied electric current significantly increases the forgeability. Reduced springback in sheet metal bending has also been reported.^{7–9} Note that the power supply for a microsecond pulsed current is much more complex as compared to that of continuous current. Therefore, it would be logical to ask: “Why is pulsed current needed when continuous current can produce the same result? What are the advantages of a microsecond pulsed current in comparison with a continuous current that would justify the expense in terms of electric power supply?”

To answer the above two fundamental questions, it is necessary to investigate the efficiency of flow stress reduction by pulsed current in comparison with continuous current. The effect of continuous current on flow stress reduction has been widely documented,^{10–13} but only a few studies have focused on the effect of microsecond pulsed current on metal flow stress. Sprecher *et al.*^{14} studied the effect of high density (1000 A/mm^{2}) and short duration (60 *μ*s) pulsed current on the flow stress of aluminum and copper. It was argued that the electric current enhanced the dislocation mobility and, thus, decreased the flow stress. In their study, only a single pulse, instead of multiple pulses, was used. While single pulse is fine for scientific studies, multiple pulses are needed to maintain low flow stress for forming applications. Salandro *et al*.^{15} and Ross *et al*.^{11} studied the effect of pulsed current on the flow stress of aluminum and titanium alloys. However, the pulse duration used in their studies was very long (1 s or longer),^{11,15} resulting in low instantaneous current density compared with a microsecond pulsed current. Thus, the effect should not be significantly different from that of a continuous current. Zhang *et al.*^{16} studied the tensile behavior of Inconel 718 subjected to a short-pulse (60 *μ*s) high-frequency (100 Hz) pulsed current. It was observed that if the frequency is kept constant, flow stress decreases with an increase in peak current. With a constant pulsing frequency, the effective current increases with peak current, leading to a more significant thermal effect and, thus, a lower flow stress. Thus, the lower flow stress in their study is mostly attributed to the thermal effect.

Compared with continuous current, pulsed current with the same effective current density, and, thus, the same heating effect, has a much higher peak current density. It was reported that there exists a critical current density below which the effect on dislocation mobility is negligible.^{17} It is possible that a pulsed current can more effectively reduce flow stress as compared to a continuous current with the same effective current density. In this work, for the first time, we have tested this hypothesis by comparing the flow stress of metallic samples subjected to pulsed current and continuous current with the same effective current density. Pulsed current with a short pulse duration (100 *μ*s) and high frequency (100–800 Hz) was used in this study. The flow stress behaviors of metals subjected to different electric currents, including continuous current and pulsed current, were evaluated using tensile tests. Comparison with a continuous current having the same effective current density was made to investigate the advantages, if any, of using a pulsed current. Based on the experimental results, the mechanisms of physics behind the flow stress reduction were analyzed and discussed. X-ray diffraction (XRD) was also conducted for the tensile test specimens to gain insight into the effect of pulsed current on grain orientation and dislocation density during plastic deformation.

## EXPERIMENTAL SETUP

The experimental setup for this study is shown in Fig. 1(a). The magnesium alloy AZ31B was selected because its electroplastic behavior has been widely studied.^{18,19} In the experiment conducted in the study, AZ31B specimens having a gauge length of 8 mm and a cross-sectional area of 4 mm^{2} [Fig. 1(a)] were used. To eliminate the effect of precipitates on the flow stress, the specimens were solution treated at 420 °C for 2 h, followed by water quenching prior to tensile testing. Two electrodes were connected to two ends of the tensile specimens. Electric insulation was used between the tension grip and the specimens. An infrared camera was used to measure the temperature of the sample as shown in Fig. 1(a). An oscilloscope was used to monitor the pulse duration, frequency, peak current, and effective current of the pulsed current. The pulse current profile, which has a sinusoidlike shape, is schematically illustrated in Fig. 1(b), where *I _{RMS}* is the effective current density calculated from the root mean square (RMS) of the current. The electric current was turned on 180 s before applying the tensile load to ensure that the temperature is stabilized. The tensile tests were then conducted using a constant strain rate of 0.002 s

^{−1}. The average of 10 tests for each condition was reported.

## EXPERIMENTAL RESULTS

The effective current density *J _{RMS}* and the peak current density

*J*are the most important parameters for electropulsing. The effective current density determines the average energy input, while the peak current density determines the instantaneous energy input. While the effective current density was found to be extremely important for the 5052-H32 aluminum alloy in the work of Roh

_{P}*et al.*,

^{20}the effect of peak current density on the flow stress reduction was not studied. In this study, a much shorter pulse duration (∼100

*μ*s) was used, resulting in a much higher instantaneous current density. As mentioned before, the aim of this work is to explore the advantages, if any, of pulsed current over continuous current to determine its effectiveness in reducing flow stress. Pulsed current has a higher peak current density than that of continuous current when the effective current density is the same. Therefore, by keeping the effective current density constant, the effect of peak current density on the flow stress reduction can be studied.

First, the effect of peak current density was investigated by comparing the stress–strain curve for specimens tested at different peak current densities while the effective current was kept constant. The five sets of pulsed current and the two sets of continuous current parameters used in this work are listed in Table I. The evolutions of maximum temperature of the gauge length of the tensile samples are plotted in Fig. 2(a). For the five sets of pulsed current, different peak current densities were used, and the frequency was adjusted to keep the effective current density constant (*J _{RMS}* = 24 A/mm

^{2}), resulting in the same heating effect as observed in Fig. 2(a). A continuous current (DC1) with the same effective current density (24 A/mm

^{2}) was also used. Theoretically, DC1 should result in the same heating effect as the five sets of pulsed current if the electric resistance is unchanged. However, as observed in Fig. 2(a), using DC1 resulted in a lower temperature as compared to the five sets of pulsed current. This result can be explained by the fact that the dynamic resistance of metals is higher under pulsed current than under continuous current based on the Drude model for electric resistance, $\rho =\rho 0[1+(\pi itd\tau )2]$, where $\rho 0$ is the resistance under continuous current, $td$ is the pulse width, and $\tau $ is the mean free time between ionic collisions. To keep the contribution from the thermal effect to the flow stress reduction constant, the DC current was adjusted to 101 A, corresponding to a current density of 25.25 A/mm

^{2}. As shown in Fig. 2(a), DC2 and the five sets of pulsed current have the same heating effect. Note that DC2 has a slightly higher effective current density than the five sets of pulsed current.

. | DC1 . | DC2 . | EP1-i . | EP1-ii . | EP1-iii . | EP1-iv . | EP1-v . |
---|---|---|---|---|---|---|---|

J (A/mm_{RMS}^{2}) | 24 | 25.3 | 24 | 24 | 24 | 24 | 24 |

J (A/mm_{p}^{2}) | 24 | 25.3 | 123 | 132.5 | 224 | 300 | 360 |

Frequency (Hz) | NA | NA | 790 | 650 | 260 | 160 | 120 |

. | DC1 . | DC2 . | EP1-i . | EP1-ii . | EP1-iii . | EP1-iv . | EP1-v . |
---|---|---|---|---|---|---|---|

J (A/mm_{RMS}^{2}) | 24 | 25.3 | 24 | 24 | 24 | 24 | 24 |

J (A/mm_{p}^{2}) | 24 | 25.3 | 123 | 132.5 | 224 | 300 | 360 |

Frequency (Hz) | NA | NA | 790 | 650 | 260 | 160 | 120 |

The engineering stress–strain curves for the tensile test specimens are plotted in Fig. 2(b). It can be clearly observed that all electropulsing (EP) currents exhibit a significantly lower flow stress compared with that of DC current, except EP1-i and EP1-ii. The EP current set EP1-v, which has the highest peak current density (360 A/mm^{2}), exhibits the lowest flow stress and, thus, the most significant flow stress reduction. When the peak current density is gradually decreased from 360 A/mm^{2} to 132.5 A/mm^{2}, the flow stress increases gradually. When the peak current density reaches 132.5 A/mm^{2}, the flow stress is close to that of DC1. Note that continuous current can be regarded as a special EP case with infinite frequency but a much lower peak current. Based on the results shown in Fig. 2(b), one can see that if the peak current density is higher than the critical value (around 132.5 A/mm^{2} for this case), pulsed current can more effectively reduce the flow stress as compared to continuous current, even though the effective current density, and, thus, the thermal heating effect, is the same. For the five sets of pulsed current, the higher the peak current density, the more significant the reduction in flow stress.

The tensile strengths (ultimate strength) of the AZ31B magnesium alloy under different EP conditions with the same bulk temperature are plotted in Fig. 3. It is clear from Fig. 3 that the tensile strengths decrease once the peak current density $JP$ is greater than 132.5 A/mm^{2} (EP1-ii), and a linear relationship between tensile strength and $JP$ exists for the current density range studied in this work. That is to say, when the peak current density reaches the critical value (132.5 A/mm^{2}), the tensile strength decreases linearly with the peak current density. Roh *et al.*^{20} found that the drop in stress was proportional to the square of the effective current density *J _{RMS}* and was independent of the peak current density. It is possible that the peak current density used in their study (120 A/mm

^{2}) was below the threshold value for the material studied (5052-H32 aluminum alloys).

Based on the experimental results presented in Figs. 2(b) and 3, it was found that there exists a critical peak current density. When the peak current density (*J _{P}*) is higher than this critical value, a higher

*J*can induce an additional drop in flow stress, even though the effective current density (

_{P}*J*), and, thus, the bulk temperature, remains constant. This critical peak current density might be affected by material properties as well as the effective current density (

_{RMS}*J*). To further investigate the critical peak current density, we repeated our experiment using different effective current densities. For convenience, the sets of EP parameters used in this work are denoted as EPk-j (where

_{RMS}*k*= 1 – 4,

*j*= i –

*v*). The corresponding frequencies, peak current densities, and effective current densities are illustrated in Figs. 4(a) and 4(b). The EP parameters can be divided into four groups according to the effective current density (

*J*): 24.0 A/mm

_{RMS}^{2}, 22.5 A/mm

^{2}, 20.5 A/mm

^{2}, and 18.5 A/mm

^{2}. For each group (from EPk-i to EPk-v, where

*k*= 1 – 4), the peak current densities increase from EPk-i to EPk-v (

*k*= 1 – 4), while the frequency was adjusted to obtain a constant

*J*.

_{RMS}Tests for the first group (EP1-i to EP-v) were already completed, and the results are plotted in Figs. 2 and 3. We then tested the other three groups of parameters, which have lower *J _{RMS}*, to determine their capacity to reduce the flow stress. The engineering stress–strain curves for EPk-j (where

*k*= 2 – 4,

*j*= i –

*v*) are plotted in Figs. 5(a)–5(c). It can be seen that, except for EP4-j (where

*j*= 1 –

*v*), where the effective current density equals 18.5 A/mm

^{2}, the highest peak current density results in the lowest flow stress. This is consistent with the results for the first group (EP1-i to EP-v), as shown in Figs. 2 and 3. However, when the

*J*is equal to 18.5 A/mm

_{RMS}^{2}[Fig. 5(c)], the stress–strain curves are nearly coincident, and no additional drop in stress due to the increase in

*J*was observed.

_{P}In Fig. 6(a), the tensile strengths (ultimate strength) of the specimens are plotted as a function of the peak current density for all sets of EP parameters. It can be observed that when *J _{RMS}* is higher than 18.5 A/mm

^{2}, the tensile strength decreases almost linearly with

*J*. It can also be observed that the critical peak current density for different

_{P}*J*decreases with the effective current density [Fig. 6(b)]. When

_{RMS}*J*= 18.5 A/mm

_{RMS}^{2}, it seems as though the critical peak current density is higher than that in all EP4 sets. This could explain the almost identical stress–strain curves in Fig. 5(c), as the peak current densities used in all EP4 sets have not reached the critical peak current density to induce additional reduction in the flow stress. The critical peak currents

*J*at different effective current densities

_{Pc}*J*(24.0 A/mm

_{RMS}^{2}, 22.5 A/mm

^{2}, 20.5 A/mm

^{2}, and 18.5 A/mm

^{2}) are indicated in Fig. 6(b) using blue circles. It can be seen that with a higher

*J*, a lower critical peak current density is required. An exponential curve fitting is also plotted along with the experimental data in Fig. 6(b). The curve fitting equation is described as follows:

_{RMS}where *J _{Pc}* is the critical peak current density and

*a*(799.3 A/mm

^{2}) and

*b*(0.00313 mm

^{4}/A

^{2}) are fitting constants. Based on this empirical equation, the critical current density is 271 A/mm

^{2}, a density that is higher than that used in all EP4 sets.

Based on our experimental results, we observed the effect of effective current density and peak current density on the flow stress reduction. There exists a critical peak current density for additional flow stress reduction. When the peak current density is higher than the critical density, the tensile stress decreases almost linearly with the peak current density. In addition, this critical peak current density is dependent on *J _{RMS}*. To take into account the additional softening induced by the pulsed current, a factor

*f*is proposed. The flow stress $\sigma f$ can be written as

_{ep}where $\sigma fe(JRMS)$ is the flow stress affected by the thermal effect from the electric current without considering the effect from peak current density, and *f _{ep}* is a factor that considers the effect of peak current density on the reduction in flow stress. The factor

*f*can be extracted from experimental data as illustrated in Fig. 7. It is clear that

_{ep}*f*is a linear function of the peak current density, and it is also affected by

_{ep}*J*as the slope changes with

_{RMS}*J*(i.e., the higher the

_{RMS}*J*, the steeper the slope).

_{RMS}## DISCUSSION

In order to explain the additional flow stress reduction related to peak current density, the effects of EP on dislocation generation and movement should be considered, as plastic deformation in metals is accomplished through dislocation movement. Based on the Taylor strengthening equation,^{21,22} the flow stress $\sigma f$ of metallic materials can be described as

where $\alpha $ is a dimensionless constant, *b* is Burger’s vector, $\mu $ is the shear modulus, *M* is the Schmid factor, and $\rho $ is the dislocation density. The electric current is unlikely to affect the extrinsic material constants like $\alpha $, b,^{23} or the shear modulus $\mu $.^{17} Therefore, it is important to understand how pulsed electric current affects the dislocation density and the Schmid factor *M*.

It was reported^{24,25} that a higher peak current density could lead to more effective annealing and, thus, a lower dislocation density. As a result, a more significant flow stress reduction can be achieved at a higher peak current density based on Eq. (3). Thus, we used XRD study to evaluate the relative dislocation density of the samples after loading to 5% engineering strains (tensile tests were stopped after the strain is reached). Four groups of samples were tested: (1) without electric current, (2) DC1 (*J _{P}* = 24 A/mm

^{2}), (3) EP1-ii (

*J*= 132.5 A/mm

_{P}^{2}), and (4) EP1-v (

*J*= 360 A/mm

_{P}^{2}). For each group, fives samples were studied to ensure data reliability.

The XRD patterns are shown in Fig. 8(a). The relative dislocation densities were evaluated by comparing the full width at half maximum (FWHM) values of the XRD peaks. Typically, higher FWHM values represent smaller grain size and/or higher dislocation density. It is unlikely for the grain size to change significantly after tensile testing at around 150 °C; thus, higher FWHM values indicate higher dislocation density. The results in Fig. 8(b) show that FWHM values for pulsed current (EP1-ii and EP1-v) are smaller than those for DC1. The EP samples with the highest peak current density (360 A/mm^{2} in EP1-v) have the lowest FWHM values for all five XRD peaks and, thus, the lowest dislocation density. This means that during tensile tests, EP current is more effective in annihilating dislocations than continuous current, and this dynamic dislocation annihilation is responsible for, at least partially, the most significant reduction in flow stress.

In addition, grain rotation, which also affects flow stress, could also be facilitated by EP. It has been reported that grain rotation can be induced by the electric field in various metals, such as aluminum,^{26–28} copper,^{29,30} and tin $(\beta -Sn)$.^{31,32} Recently, it was found that EP, with a peak current density of 10.18 A/mm^{2}, which was much lower than that used in our study, can induce grain rotation and produce crystalline texture in duplex steel at room temperature.^{33} Note that grain rotation can directly affect the flow stress by changing the Schmid factor. In polycrystalline metals without preferred orientation, the crystals are randomly distributed, yielding an average Schmid factor. If favorable orientation is achieved during deformation, the Schmid factor will increase significantly and, thus, much a lower flow stress will result.

Crystalline orientation can be determined from the intensity ratio of the diffraction line.^{34,35} The XRD patterns shown in Fig. 8(a) were analyzed to observe the change in grain orientation. Note that the crystallographic orientation can be observed by examining the shift in the peak intensity ratio of the XRD patterns.^{36} As the α(0002) peak and the $\alpha (001\xaf1)$ peak are the two major peaks, the ratios of the intensity of the α(0002) peak and that of the $\alpha (001\xaf1)$ peak were calculated and shown in Fig. 9(a). It can be noticed that the ratios for both EP sets (EP1-ii and EP1-v) are much higher than those for DC current and EP1-V is higher than EP1-ii. This suggests that EP current with a higher peak current density is more effective in inducing grain orientation, even though the effective current density is the same. By increasing the Schmid factor, grain rotation can lower the flow stress.

To better understand how electric current induces grain rotation, a schematic of dislocation pileups and current concentration is illustrated in Fig. 9(b). Grain boundaries have a relatively large misorientation and, thus, large resistance for dislocation transmission.^{37,38} With the accumulation of plastic strain, the dislocations accumulate in grains I and II and, thus, results in even higher electric resistance. The increased electric resistance introduces a higher local electric current density (*j*_{1} and *j*_{2}) along the grain boundary at grain I and grain II than that in grain III (*j*_{3} and *j*_{4}), because electric current tends to avoid regions with high electric resistivity. Under this condition, the imbalance in the electric field *E* at each side of the grain boundary results in a driving force for grain rotation, making dislocation slip transmission across the grain boundaries easier. It was proposed in our previous simulation work that the EP-induced grain rotation could also be driven by the difference in the electric field *E* between two adjacent grains as a result of material heterogeneity at the grain boundary.^{39} By decreasing localized dislocation accumulation around grain boundaries, a more significant reduction in dislocation density and flow stress can be achieved.

It should be noted that a critical peak current density exists for grain rotation, and this current density must be high enough for the grains to overcome the resistance to rotation.^{33} It was reported^{17,40} that the dislocation mobility increases linearly with electric current density when it reaches a critical value. This can potentially explain the existence of critical peak current density needed to observe any additional flow stress reduction in metals subjected to EP. For AZ31B in this study, the critical peak density is around 130 A/mm^{2} (with *J _{RMS}* = 24 A/mm

^{2}), which is a very high current density. For a continuous current with such a high level of current density, resistive heating will be significant and the thermal effect will dominate. For pulsed current use in this study, the temperature can be kept at around 150 °C. This reveals the advantages of using a pulsed current: the peak current density is high enough to assist dislocation movement and, thus, lower the flow stress; at the same time, the effective current density can be kept sufficiently low so as to avoid excessive resistive heating. This results in a significant enhancement of plasticity without a significant temperature increase in EP-assisted plastic deformation. For a pulsed current and a continuous current with the same effective current density, the pulsed current would be more effective in reducing the flow stress if its peak current is higher than the critical value. For the pulsed current, the peak current is high enough to mobilize pinned dislocations. Once mobilized, these dislocations can accommodate plastic deformation until all mobile dislocations are pinned, when another electric pulse is needed to activate the pinned dislocations. By manipulating the EP conditions so that they match with plastic deformation, the flow stress can be significantly decreased without a significant increase in temperature. On the other hand, a continuous current does not have any electric energy spikes, though it can still assist dislocation motion to a certain extent. Its instantaneous energy density has not reached the critical value needed to mobilize some pinned dislocations, even though the total amount of energy supplied is the same. As a result, a similar level of bulk heating is observed, even though the reduction in flow stress is significantly different. It should be noted that other factors may also contribute to reducing the flow stress. For example, it has been reported that electric current may reduce the stress needed to generate dislocations from dislocation sources, such as the grain boundary and pre-existing dislocations.

^{40–42}Note that further studies are needed to reveal the fundamental mechanisms behind electroplasticity in metals subjected to

*μ*s, high peak current density, and high frequency pulsed current. This study, however, serves as a first attempt in that direction.

## CONCLUSION

In conclusion, we have demonstrated that pulsed current can more effectively reduce the flow stress in the AZ31B magnesium alloy compared with a continuous current having the same bulk heating effect. There exists a critical peak current density below which the pulsed current does not induce any additional reduction in flow stress. The electric-induced annealing and the EP-induced grain rotation, which can reduce the flow stress during plastic deformation, can be more significant under a higher peak current, as suggested by our experimental observations. These findings imply that a pulsed current can be more efficient in reducing the flow stress than a continuous current having the same bulk heating effect. Note that compared with continuous current, pulsed current was not observed to increase the ductility in this study. Decreasing the flow stress alone, however, can benefit many deformation based processes, such as laser shock peening. The significance of this finding lies in the prospect that by using a pulsed current with a high peak density, it is possible to significantly reduce the flow stress while keeping the bulk temperature relatively low, potentially eliminating the drawbacks associated with high-temperature forming operations and thermomechanical processes. Even though a more in-depth investigation is needed to reveal the fundamental mechanisms in electroplasticity in metals subjected to EP, this study serves as a first attempt to study the effect of peak current density on flow stress reduction.

## ACKNOWLEDGMENTS

The authors are grateful for the financial support of this research from the National Science Foundation (NSF) Faculty Early Career Development Program (Award No. CMMI 1847247).