INTRODUCTION

Recent research on the physics of materials and their treatment has focused on the use of external energy to improve product performance. The use of high-density currents in metalworking is of great interest currently, especially in metallurgy, the aerospace industry, and the auto industry [1]. The consequences of applying such currents in the deformation of metallic products include decrease in the metalworking forces and the yield point; increase in plasticity and in rates of aging and recrystallization; decrease in grain size with decrease in the residual stress; and decrease in the elastic recovery [2]. These effects are seen in forging and rolling [3, 4], drawing [5, 6], metalworking [7, 8], bonding [9, 10], sintering [11, 12], and sheet stamping [13–16].

Such electrostimulation was considered in most detail in the reviews [17, 18]. Despite growing interest in the intensification of shape change by means of current pulses, very limited experimental and theoretical information regarding plastic deformation is available, and the physics of plasticization in metals has not been adequately studied. That is delaying the application of promising techniques in practice. In studying electrically stimulated plastic deformation, it may be useful to adopt a synergetic approach, in which plastic flow is regarded as a wave process. This topic was first considered in [19].

In the present work, we regard the wave process in plastic deformation [20] as the motion of an impact-transition wave [21]. We make an analogy with the structure of the impact wave in gases [22]. On that basis, we consider the influence of various physical processes at the impact wavefront on the internal structure of the wavefront. Therefore, in the present work, we study the influence of the electric current on a wave profile of impact-transition type.

EXPERIMENTAL MATERIALS AND METHODS

We investigate 08ps structural steel. Tensile tests are conducted on plane samples in the form of a double blade; the working section is of dimensions 50 × 10 × 2 mm. The samples are cut from cold-rolled strip after annealing in a furnace at 600°C for 60 min. The samples are extended on an Instron 1185 universal test machine at 25°C; the mobile clamp moves at a constant speed of 0.2 mm/min (about 3.3 × 10–6 m/s), as in [20, 23]. To investigate the macroscopic localization of the plastic flow, we use double-exposure speckle interferometry [20]. That technique permits observation of the whole sample (field of view approximately 100 × 100 mm), with resolution of about 1 μm.

Pulsed electric current is supplied from a unipolar-pulse generator [24]. Electrical contact with the sample is ensured by means of self-clamping. Special dielectric bushes provide protection against the current pulses. Sinusoidal current pulses of amplitude 3500 A (175 A/mm2), length 100 ms, and repetition frequency 10 Hz are supplied for 30 s after reaching the yield zone. After a 90-s interval, the current treatment is repeated.

The kinetics of nonuniform plastic deformation is investigated by means of an ALMEC measuring system with photographic image recording and an ALMEC-TV system with digital recording [25]. That permits recovery of the displacement-vector field. From the dependence of the coordinates X of the localized regions on the time t, we determine the spatial λ and time T periods of the corresponding processes. Then we calculate the speed of the localized-plasticity regions.

By infrared thermography, the thermal processes in the sample are studied [26].

The double-exposure speckle recordings, thermal diagrams, and oscillograms are recorded in the yield zone.

RESULTS AND DISCUSSION

In Fig. 1, we show the characteristic stress–strain curve for loading in the presence of pulsed electrical current. We see that the current pulses result in oscillation of the deforming force associated with jumps in the plastic strain. This is consistent with current ideas regarding elastoplastic deformation [1, 2].

Fig. 1.
figure 1

Loading diagram.

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One factor responsible for the decrease in the deforming force under the action of the current is change in temperature of the material. Our thermal data show that a temperature gradient runs from the clamps to the center of the sample (Fig. 2a). The evolution of the temperature fields in regions 2 and 3 (Fig. 2a) over time is shown in Fig. 2b. We note steps in the temperature dependence. The greatest temperature is 351 K in region 2 and 330 K in region 3. Subsequent current application increases the temperature only slightly. Such behavior may be explained in that heat dissipation is not possible when the pulse-repetition frequency is 10 Hz. At the maximum temperature, the deforming force decreases by 7% in the first current-pulse application and by 4% in subsequent applications.

Fig. 2.
figure 2

Temperature distribution in the sample (a); and mean temperature in sectors 2 and 3 (b): (1) sample axis.

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The temperature change due to Joule heating may be calculated from the formula [27]

$$\Delta T = \frac{{{{t}_{1}}f}}{{cm}}R\int\limits_0^\tau i {{(t)}^{2}}dt,$$
((1))

where

$$i(t) = \left\{ \begin{gathered} {{I}_{m}}\sin \left( {\frac{{2\pi }}{T}t} \right),\,\,\,0.1n < t < {{10}^{{ - 4}}} + 0.1n, \hfill \\ {{0.10}^{{ - 4}}} + 0.1n < t < 0.1(n + 1) \hfill \\ \end{gathered} \right.,$$

R = ρl/S; t1 is the time for which a single pulse acts; Im is the current amplitude; n = 0, 1, 2, …; ρ is the electrical resistivity; l is the length of the sample’s working section; S is the cross-sectional area; t is the time; C is the specific heat; T is the period of the pulses; f is the pulse-repetition frequency; and m is the sample mass.

Estimates show that, for 08ps steel (ρ = 1.78 × 10–7 Ω m; C = 482 J/(kg K); density γ = 7843 kg/m3), ΔT = 21 K for a single pulse. That is consistent with the experimental data obtained by the analysis of thermal diagrams: ΔTexp = 30 K. The energy consumed per atom, calculated as the ratio CγΔEexp/N, where N is the number of atoms in the sample, is approximately 10–3 eV. That corresponds to the estimate in [28]. On the other hand, the elastic energy per atom is 10–6 eV [28]. We see that, as a channel for the conversion of electrical energy, structural transformations in the deforming system are faster than heat conduction [28].

One aspect of the restructuring of the deformed system is the appearance of localized plastic-flow waves, in the form of nonuniform distribution of the displacement over the sample. The velocity of the localized regions according to speckle-interferometry data is 0.0925–0.1044 mm/s with no current pulses and 0.1369–0.1722 mm/s with pulses. Thus, the current pulses increase the velocity of the plasticity waves by 65%.

The dependence of the plate velocity on the longitudinal coordinate may be derived from the dependence of the displacement on the coordinate after a specific interval (τ = 10 s), as calculated from the speckle-interferometry data. To determine the velocities, we divide the displacement by the time τ (Fig. 3). As a result, we obtain impact-transition curves. When x = 0, the velocity of the material is zero. That corresponds to the region with the motionless clamp. Beyond the impact transition (on the right side of Fig. 3), the velocity of the material is equal to the extension rate specified by the test machine (Fig. 3a).

Fig. 3.
figure 3

Dependence of the longitudinal velocity on the longitudinal coordinate in the absence of current pulses after 380 (2), 390 (3), 400 (4), and 402 (5) s (a) and in the presence of current pulses after 402 (2), 425 (3), 440 (4), and 450 (5) s (b).

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In the absence of the current pulses (Fig. 3a), the extension rate remains constant. When the current pulses are applied, we note a split in the velocity values (Fig. 3b). That is obvious if we compare curve 5 in Fig. 3a and curve 2 in Fig. 3b, which correspond to the same instant: the onset of the current pulses. Our findings confirm the change in velocity of the slow spontaneous wave when current is applied, which was first noted in [2]. The splitting of the velocity distribution at the mobile clamp has not previously been reported.

CONCLUSIONS

When current pulses are applied, the velocity of the spontaneous plasticity waves increases by 65%. If the experimental data are interpreted in terms of the velocity distribution with respect to the coordinate, the influence of the current pulses on the velocity distribution may be determined. We see that the current pulses split the velocity distribution close to the mobile clamp.