Effects of electrical pulse on metal deformation behaviors

As a kind of special energy field assisted plastic forming, electric pulse assisted plastic forming combines multiple physical fields, such as thermal, electrical, magnetic and mechanical effects, has multiple effects on metal. It has a good industrial application prospect in the fields of directional microstructure regulation of materials and preparation of new materials. The flow stress of metal materials can be effectively reduced by electro-pulse assisted forming. The action mechanism of pulse current includes thermodynamics (Joule heating effect) and kinetic (pure electro-plastic effect or athermal effect). Thermodynamically, electric pulses can be used to provide the energy for dislocation migration and atomic diffusion, and aid in microstructure changes such as recrystallization, phase transition and microcrack healing of metals. In terms of dynamics, electric pulse has an effect on the speed and path of dislocation structure evolution. On this basis, a series of theoretical models for accurately predicting the flow stress of materials in electrically assisted forming process were formulated by combining the stress–strain constitutive relationship considering the temperature rise effect and the pure electro-plastic effect. The accuracy of the predicting model is greatly enhanced by the introduction of electrical parameters. The mechanism for electrically assisted forming was further revealed.


Introduction
In the modern manufacturing industry, metals are widely used for various parts and products.The formability of metal is closely associated with the forming method [1,2].Hot forming is widely used to decrease the deformation resistance of materials and ensure good quality of products [3].A given combination of thermosdynamic parameters leads to a specific microstructure evolution of metal materials, and the microstructure changes of metal during hot forming will affect the formability of metal [4][5][6].In the traditional hot forming process, most of the heat generated by energy is not used efficiently in the process of heating and cooling for a long time because of the the adoption of furnace heating.This contradicts the goal of improving process energy efficiency.Electrically assisted forming (EAF) provides a feasible alternative method to achieve the coordinated control of metal formability and energy consumption simultaneously.
EAF involves applying current during material deformation.The flow stress of the metal material is reduced [7,8] and its plasticity capacity is improved [9][10][11] during the EAF process.Troiski first proposed this effect in 1963, known as the electro-plastic effect (EPE) [12].Troiski discovered that the strain hardening rate of Zn crystal and its plasticity increased significantly when the high-speed electron flow was irradiated along the slip system direction.Subsequently, Conrad et al [13,14] carried out experiments on the rheological stress, stress 2. Theory of electrical pulse on metal 2.1.Action mechanism of electrical pulse on metal Numerous studies have revealed that the influence of electric pulse on homogeneous metal materials is mainly to facilitate the evolution of material microstructure or to reduce the flow stress during deformation by stimulating the dislocation behavior [26].There are three important theories concerning the influence of pulse current, which are described below:

Local joule heating
Because of the resistance of the metal itself, the current through the metal will produce Joule heat.The temperature rise induced by Joule heat plays an essential role in the softening of the material.Local Joule heating theory is a kind of theory based on the high resistivity of crystal defects.It not only has a definite physical model, but also can explain qualitatively the acceleration behavior of dislocation motion caused by electrical pulse.The basic point of this view is that electric pulse generate transient local high temperature at the defects because of the large local resistivity at lattice distortions such as crystal defects (dislocation, grain boundary and second phase) of the material, which result in rapid dislocation movement, as illustrated in figure 1.The local heating theory of electric pulse at the crystal defect can explain the non-polar behavior of electric pulse action and can explain almost all the previous reports of electric pulse accelerated microstructure evolution and electro-plastic phenomena of homogeneous metal materials.The local Joule heat theory of electric pulse has a definite physical model and can explain the motion behavior of dislocation acceleration qualitatively.
Experimental evidence suggests that Joule heat during EAF is the main mechanism of electric pulse action [27].Researchers have performed precise temperature measurements on samples treatedwith electrical pulses, rebuilt the corresponding material model, and subsequently corrected experimental data to simulate the Joule heating effect.Mathematical models were used to represent Joule heating, convection from the outer surface of the specimen, and heat conduction along the axial direction of the specimen to the instrument fixture.Since heat loss is usually ignored in current pulses, the change in temperature rise ΔT can be evaluated by equation (1) [27] or (2) [28].
Where, J and j is the current density, ρ is the electrical resistivity, V is the volume of conductive part, and Δt is the acting time of the current, m is the quality of conductive part, c and c p is the specific heat and d is the density of the material.
Zhang et al [27] conducted electrically assisted tension experiments on Ni-based high temperature alloys at different current densities.The results showed that there is a local Joule heating effect at defects and at large second equal lattice distortion.This indicated that the local Joule heating effect is a critical factor affecting the macroscopic and microscopic behavior of Ni-based alloys during electrically assisted tensile processes.McNeff et al [29] studied the EPE of Haynes 230 material and found that the collision between electrons and ions caused Joule heat.Yang et al [30] systematically studied the electroplasticity of high entropy alloy Al0.6CoCrFeNiMn by using electroassisted uniaxial tensile.They concluded that the local Joule effect is the primary factor which affects the electroplasticity of this material, where the local Joule heating effect facilitates dislocations to undergo slip, thereby inhibiting dislocation multiplication.

Electronic wind
The electron wind theory explains the interaction between drifting electrons and dislocations, as shown in figure 2. Experiments on the effects of short time and high strength pulsed current on the macroscopic mechanical properties of materials have shown that electrical pulses can greatly reduce the flow stress and increase the fatigue life of materials.Short pulse processing time can effectively suppress the thermal effect of electric pulse, while instantaneous high-intensity current pulse can highlight the influence of electronic wind on material mechanics.According to the electron wind theory, the kinetic energy of high-speed electrons can induce a change in dislocation behavior by generating electron wind forces on the dislocations [8].
The electron wind theory can explain the proportional relationship between the athermal effect of electrical pulses and the current density observed in tension or stress relaxation experiments.However, the proportional coefficient calculated theoretically is 3~5 orders of magnitude lower than that measured experimentally, indicating a significant difference between theoretical calculation and experiment [31].
Classical electron-dislocation interaction models include (3), ( 4) and (5) proposed by Kravchenko [32], Klimov et al [33] and Roschupkin et al [34], respectively.The force l f ed of per unit length acting on the dislocation can be expressed as: Where, J is the current density, b is the Burgers vector, m * is the effective electron mass, e is the electron charge, n is the electron density, h is the Planck's constant, E F is the Fermi energy, e n is the electron velocity, F n is the Fermi velocity, and d n is the dislocation velocity.
The 'electron wind' theory proposed by Kravchenko explains the effects of pulsed currents on dislocations as mechanical forces and stresses [28].Zhao et al [35] studied the plastic deformation of Ti-Al alloy under pulsed current and found that its ductility increased when the current was introduced, because of microstructure reconstruction in the presence of electric current.Pulsed current can change the defect structure of the material from local plane slip to uniform wave slip during deformation, improving its ductility.Xiao et al [36] studied the mechanical property changes and dislocation density evolution of 5052 aluminum alloy under the action of electric current.The motion of dislocations is promoted by the current, resulting in increased plastic deformation ability of the material at RT.Under the action of current, the dislocation density is reduced and the dislocation structure is rearranged, as shown in figure 3(d) [37].The dislocation structure changes from a different direction to a direction parallel to the current after the action of the current, which is observed on both sides of the metal and at the interface.

Magnetic field depinning
Dislocation depinning because of a a magnetic field is a theory proposed based on the influence of magnetic field on the structure of dislocation core, which holds that the promoting effect of electrical pulse on dislocation behavior should mainly be attributed to the magnetic field caused by current rather than the electronic wind force.The schematic diagram of dislocation depinning due to a magnetic field is shown in figure 4. The magnetic field unpinning theory posits that the induced magnetic field caused by current can change the core structure of the dislocation, causing chemical bond breakage near the dislocation pinning point and facilitating the dislocation to break away from the pinning point [38].The magnetic field unpinning effect is non-polar, and the movement direction of the dislocation does not change with the change of the magnetic field direction.This theory explains the magnetoelastic effect well, and the flow stress decrease caused by the magnetic field unpinning is close to the experimental value in order of magnitude [39].However, it is not applicable to all materials and cannot explain the occurrence of increased deformation resistance in some metallic materials when a magnetic field is applied.Magnetic fields can affect dislocation unpinning by changing the occupation of the singlet (S) and triplet (T) states of atoms in the dislocation core [40,41].The T state is higher in energy in general and is much easier to escape from than the S state, so the unpinning rate increases substantially in magnetic fields.The contribution of magnetic field to EPE is shown in equation (6) [40].
Where s D is pressure drop, s* is effective shear stress, j is current density, j 0 is characteristic current density.This formula is only a general form, and the specific form should be related to the experimental conditions and materials.
Fan et al [42] investigated the magnetoplastic effect in the EPE by introducing pulsed currents in Ni-718.The skinning effect was first verified by calculating the skinning depth [43], as follows: Where f is the pulse frequency, m is the permeability, and r is the resistivity.Through calculation, the skin depth is 13.9 μm, which is close to the sample cross-section diameter of 30 μm. Figure 5 shown the current distribution at 200A/1500Hz.The current at the surface of the specimen is larger than that at the central region, and the current localization phenomenon occurs on the surface of the specimen.From the combination of  experimental and simulated data, it is concluded that the skinning effect is produced on the specimen under the action of current.
The magnitude of the force on the dislocation under the action of the magnetic field is given by the following equation [44] : In the formula, where H is the direction of magnetic field intensity, B is the magnetic induction intensity, α is the Angle between H and the dislocation, β is the angle between H and the dislocation, and as shown in the figure 6: By fixing H and β values at 45°and 90°respectively, the distribution diagram as shown in figure 7 is obtained.Under experimental conditions, the maximum value is 0.068 Mpa.It is found that the minimum chamber stress required when the dislocation in Ni-718 superalloy is driven from the glide plane {111} to the glide direction {110} as proposed by Nabrro et al [45] cannot be reached.Therefore, under experimental conditions, the magnetic field excited by the pulse current has little driving effect on the dislocation motion in terms of force.This finding may be consistent with the paramagnetic theory proposed by Golovin et al above.

Influence factors of electrical pulse on metal
However, manyresearches have shown that the influence of pulsed current on the micro structure of the material is complex and there is a lack of unified electric pulse theory to explain the mechanism of electric pulses on the microstructure of materials [5,46].The uncertainty of the action mechanism of electrical pulse is mainly reflected in the following aspects: First, a variety of physical effects are produced by an electrical pulse in the  material (including heat, electricity, magnetism, force) [47], and the diversity of physical effects makes it difficult to identify the major controlling factors that affect the microstructure/properties of the material; Second, the specific physical effects produced by electric pulses will have different influence laws on different materials (different chemical compositions or phase structures) [48][49][50][51][52][53]; Third, even for the same influence law under a particular physical effect, the specific mechanism of action is not very clear.The EPE can be affected by variousfactors, such as frequency, current density, current duty cycle, grain size, pulse width [54-58], etc.
For example, the temperature curve of TA2 was influenced by frequency during EAF.At low frequency, the temperature curve showed an evident sawtooth waveform, while the temperature curve climbed swiftly during the beginning stage and gradually stabilized during the latter stage under medium frequency.In case of high frequency, the sample temperature was too high to fuse in advance.Moreover, the flow stress of TA2 decreased with small fluctuation under current.As the pulse width and current density increase, a greater drop in flow stress curve is observed [59].
There is an obvious pure electro-plastic effect when the current density applied to the material is above a certain threshold (10 3 -10 4 A mm -2 for pure metals, 40-70 A mm -2 for alloys), flow stress is decreased and deformation capacity is increased [26,60,61].Some high-strength aluminum alloys can also exhibit EPE at low current density, as reported by Clifton et al [62] who observed the electroplasticity of Al7050 at a current density of 0.035-0.1A mm -2 , much lower than the previously reported a threshold of 10 A mm -2 .The law of electroplastic effect varies greatly under different influential factors when the materials are different.For instance, as the frequency and current density increase, the plasticity of the copper plate first increases and then decreases.As the pulse width increases, the plasticity of copper plate increased all the time [46].The influence of pulsed current on the mechanical properties of materials also differs at different pulse current densities.The forming limit of the sheet is a relatively important property index during the forming process, which can reflect the maximum deformation of the sheet before the plastic destabilization [63].Ghiotti et al [64] studied the influence of direct current (DC) density on the forming limit of AA1050-H24 sheet.The forming limit property is shown by the fracture strain.Different fracture strains show different EPE, with the fracture strain reaching a maximum at a current density of 5 A mm -2 .
The ratio of thermal and EPE is significantly affected by the percentage of grain boundaries of different grain sizes and the defect density present during the application of current.Stolyarov et al [65] investigated the influence of current duty cycle to the microstructure, microhardness, and tensile deformation behavior of coarse crystalline (CG) and ultra-fine crystalline (UFG) titanium by varying the current density and the pulse duration.Under the action of low duty cycle pulse current, the flow stress of CG and UFG titanium decreases with the change of current density and duration and the reduction of flow stress of CG titanium is lower than that of UFG titanium.Chen et al [66] conducted electroassisted micro-tensile experiments on 50 μm coarse crystal (CG-Ti) and 95 nm Nano-Ti to investigate the change in mechanical properties of the material and the fracture mechanism.When deformation occurs in the presence of current, stress reduction is demonstrated in both Nano Ti and CG Ti, and the flow stress reduction of nano-Ti is greater than that of CG-Ti.The experimental results showed that the pulsed current had a more pronounced inhibitory effect on the vacancy proliferation of nano-Ti than CG-Ti.It can be concluded from experimental fracture analysis that CG-Ti exhibits dimple or microporous coalescence fracture, while Nano-Ti exhibits quasi-cleavage fracture.Nafiseh et al [47] studied the effect of pulse current type on the microstructure of AA2024 during v-bending.It is worth noting that components formed by sinusoidal pulse currents had smaller grain sizes and lower low-angle grain boundary volume fractions compared to square pulse currents, which can better enhance the formability of the material.
It has been shown that pulsed currents also facilitate the preferential growth of intermetallic compounds (IMCs) with high electrical conductivity, which affects both growth rate and growth direction.Feng et al [67] reported that the growth rate of Cu 6 Sn 5 grains with higher resistance was lower than that of the grains with lower resistance under the action of current.Liang et al [68] used the phase field model to study the growth behavior of intermetallic compounds under the action of electric current, finding that intermetallic grains with higher electrical conductivity preferentially grow along the electron flow.Current can not only affect the growth of intermetallic compounds, but also improve their plastic deformation ability.Han et al [69] studied the EPE of Fe-6.5 wt%Si with an intermetallic ordered phase, and eliminated the influence of thermal effect by reducing the temperature variation of the sample through air cooling.The electrical pulse significantly increases the dislocation mobility, which further decreases the yield strength and increases the elongation accordingly.Pulsed currents can boost the forming properties of materials with intermetallic compounds.Lu et al [70] investigated Al 3 Ti alloy, an intermetallic compound, and selected electrical pulse treatment with different parameters.The grain size of Al 3 Ti alloy after electrical pulse treatment was significantly increased than that of traditional heat treatment, and the grain size increased with the increase in electrical pulse frequency.The fracture form of Al 3 Ti alloy changed from intrinsic brittle fracture to quasi-dissociative fracture, and its plastic deformation ability improved after electrical pulse processing (EPT).Therefore, EPT can be used as a novel method to improve the plastic deformation ability of Al 3 Ti alloy.

Constitutive model of metal in electric pulse
The constitutive model can theoretically provide a basis for the actual forming process, thereby achieving more accurate and higher quality forming [71].Researchers have established electroplastic constitutive models for different materials, each with its own characteristics and scope of application, as shown in table 1.However, there is no unified electroplastic constitutive model to explain the EPE in the EAF.
Up to now, the experimental method to explore the EPE is simply to test the comparison between Joule heating effect and other effects [72][73][74][75][76].The extent of the EPE can be empirically determined by comparing a heating test at a matched temperature with an electrically assisted process, but requires more work to devise experiments.It is difficult to test the dynamic effects of electroplasticity directly at microscopic or atomic scales by experimental methods.In contrast, theoretical models can predict partial EPE with relative accuracy.Models of related theories, including thermal effects, electron winds and magnetic plasticity theories, are used in the restof this paper.
What noticeable is that pulse current can improve the plasticity, decrease the flow stress and promote dislocation annihilation in materials such as Mg alloy [77,78], Cu alloy [79], Al alloy [80,81], Ti [1110] and stainless steel [18,82].The anisotropy of metallic material characteristic of microhardness levels or distribution can be eliminated by the annealing effect induced by electrical pulses [8].
Ao et al [83] investigated the behavior of deformation of Ti-6Al-4V during electric pulse assisted incremental forming (EAIF).It was discovered out that the fracture depth and limit of the forming angle of Ti-6Al-4V changed with the root mean square (RMS) of the current density, as shown in figure 8(a).The forming limit of Ti-6Al-4V improved as the current density increased.The maximum forming limit of the alloy sheet has increased by 417.9% compared with no pulse current.At the optimum forming limit of RMS current density, specimens failed because of breakdown caused by the combined effect of thinning plates and high electrical pulses, resulting in small holes without fracture, as shown in figure 8(b).Studies by other researchers have not observed such electrical breakdown failures [83].
Another study on Ti-6Al-4V shown that suitable electric pulse parameters can decrease deformation force [84].Figures 9(a) and (b) illustrated the variation of deformation force with electrical parameters.As it can be seen, the deformation force of the material reduced at the same process height owing to pulse current.The vertical deformation force in the material decreases significantly as the peak current density and frequency increased.In addition, the friction coefficient decreased with the increase of current density and frequency, as shown in figures 9(c) and (d).As we all know, the forming limit of material will improve with the reduction of friction coefficients.The reduction of friction will lead to a lower stress state.The smaller the friction, the smaller the shear across the thickness along the radial direction, which delays the occurrence of fracture.
The metal temperature during EAF will rise rapidly because of the resistance.Therefore, the flow stress model based on temperature effect, considering the factors such as strain, strain rate, etc have been proposed.The Johnson-cook model suitable for large metal deformation, high strain rate and high temperature is proposed by Johnson and Cook [28]: Where, A is the yield strength; B, n is the strain strengthening parameter; C is the strain rate sensitive parameter; ⁎  e is the relative strain rate; T * is the dimensionless temperature and T is the linear function of temperature, is the room temperature and T m is the softening temperature; m is the temperature effect index.
However, it is essential to evaluate anew the effect of temperature on the mechanical behavior of the EAF since no reduction in stress can be observed in samples that are cooled to near RT.Meanwhile, the role of temperature is often omitted when invoking the theory of electro-plasticity.Magargee et al [49] predicted the commercial pure Ti plate stress reduction induced by the application of direct current using the improved Hollomon model and Johnson-Cook model.They also calculated the increase in the temperature of relevant Joule heating in the EA axial tension test.The results shownthat the thermal-mechanical coupling model could predict the mechanical behavior of Ti alloy in EA tension and compression experiments effectively.It was found that the higher the current density and the temperature, the lower the stress while the higher the plasticity of Ti alloy during EAF, as shown in figure 10.Both models could better fit the regularity of stress and strain.Among them, the Johnson-Cook model was closer to explaining the stress softening process.The specific constitutive relationship as shown in equation (10) [49]: Where,  e is equal effect rate of change; 0  e is the plastic strain rate; α, β is the temperature dependent coefficient; T m is the melting temperature, and T R is the reference temperature.
The electron wind theory is introduced AZ31B It is related to the mean dislocation density Al2052 Dislocation density model Lee et al [50] found that the Johnson-Cook model could not fully explain the stress reduction in the plastic deformation stage during the tension process that a single pulse width current was applied, as shown in figure 11.The experimental results shown that the sudden change in strain rate caused by the current pulse and the rapid heating rate lead to dynamic strain aging (DSA), as well as the occurrence of cumulative plastic strain and transient high-temperature strain hardening.While DSA could explain numerous observations in EA deformation in the past.However, the decrease inflow stress cannot be explained by material softening caused by thermal effect fully [50].Ross et al [51] conducted a battery of tests in which the current applied in the middle of the test to determine how the electrical effect changes with current.As two representative results shown in figure 12, the current reduced the flow stress of Ti-6Al-4V immediately while the temperature would take longer to achieve this response.Therefore, the effect of the pulse current within the flow stress equation cannot be described by temperature alone, and an independent influence term of pulse current should be added.Salandro et al [52] established a constitutive model involving Joule heating effect and athermal effect and used the electro-plastic interaction coefficient to describe the interaction between current and dislocation, as shown in equation ( 11) [52].The model fitted the experimental values well, but the electro-plastic interaction Where, r 0 , r inst and h ins are initial radius, instantaneous radius and instantaneous height respectively; u  is the die compression rate; ξ is the electro plastic action coefficient; V, I is the input voltage and current.Li et al [53] investigated the mechanism of electro-plastic effect from the micro level based on the classical free electron theory and proposed a method for calculating metal flow stress under electro-plastic effect.The stress-strain relationship is shown in equation (12) [53].Both the exchange energy between free electrons and metal ions under the action of pulse current and the change of Gibbs activation free energy of dislocation were considered in the calculation method.The results showed that the decrease in metal flow stress is associated with the enhanced plastic strain rate.
e e e e g = -+ Where, C is the model constant; e 0  e is the charged strain rate; 0  e is electric strain rate; x is the average number of metal ions in a dislocation; t is the current action time; n is the number of free electrons per unit volume of metal; γ is the metal conductivity; k is Boltzmann constant.The results of formula derivation show the correlation between metal electro-plastic flow stress and micro parameters clearly.The metal flow stress drop decreased with increasing conductivity and free electrons number, electron charge and average free path per unit volume.Furthermore, the flow stress drops of metal increased as the thermal velocity increases, as does the electron mass and the average number of metal ions forming dislocations.However, the electronic state of metal is unobservable.Only qualitative analysis can be conducted.The model is inconvenient to use for containing the micro physical quantities such as x, n and γ.
Wang et al [85] modeled the flow stress under certain conditions to study the controversial mechanism, that is whether the material response function called 'electro plasticity' was needed to define the mechanical behavior of a metal during EAF, or just used the thermal-mechanical constitutive model to characterize the EAF behavior of metal materials under electric current.The flow stress model included strain hardening, rate hardening, thermal softening, solute dislocation interaction, and the influence of electron wind.The model predicted the mechanical behavior of AZ31 under different current densities in the process of EAF effectively.The change in the flow stress of the material is affected by the softening effect because of Joule heating as shown in figure 13.
Most of the previous studies only introduced the Joule heating effect into the corresponding model, which means the temperature change generated by the current was used to describe the deformation behavior of the material in the electroassisted process without considering the influence of athermal effects.Xie et al [86] used AZ31B magnesium alloy sheet to investigate the effect of non-thermal effect of current on this material.Based on the Johnson-Cook model, a flow stress model for uniform pre-necking deformation considering pure EPE is established, as follows:  )is the EPE factor; D is the material parameter; A, B, n, C and m are the same parameters in the above formula; 0  e is the reference strain rate; t r and t m are the room temperature and melting temperature; K is the constant; I ev is the intensity of the pulse current applied to the material.When the parameters (temperature, frequency, and tensile rate) changed, the difference between the predicted result and the experiment became obvious with an increase in strain, as shown in figure 14.The change of flow stress during deformation is related to temperature and strain rate.However, this model can only be applied to pulse current with limited frequency (120 Hz ƒ 480 Hz), and the EPE at pulse current with different frequency and density needs further explored.
The intrinsic model of physical properties can not only capture the changes in the relevant properties of materials under electroplastic conditions, but can also be combined with finite element software to predict the deformation behavior of materials under multiple physical fields.
In contrast to other models, dislocation density models has unique advantages in terms of deformation mechanisms and microstructure evolution.However, single-parameter dislocation density models cannot predict complex mechanical behaviors during pulsed currents, such as current-induced reversion and softening processes.Based on the dislocation density model, researchers have explored the EPE of pulsed currents by different methods, such as by proposing additional state quantities based on the dislocation evolution model and combining the size effect with the EPE at the microscopic scale to investigate the effects of currents on material flow stresses, respectively.Hariharana et al [87] studied the deformation behavior of Al2052 during electrically assisted tension based on a dislocation density model to explain the complexity of pulsed currents in the material deformation process.They used the Kocks-Mecking-Estrin (K-M-E) model [88], which is shown in equation (15):

M Gb
Where, M, G, b and m are the Taylor factor, shear modulus, Burger vector and strain rate index, respectively; r is the dislocation density; 0  e is the material constant corresponding to the strain rate at which the thermal component of the flow stress reaches zero; α is the material constant, related to temperature and current, obtained by fitting the actual stress-strain curve of the experiment, as shown below: As shown in figure 15 from a local point of view, the stress decreases during the application of current, while the stress returns to transient hardening during the non-application of current.On the whole, the model has a good prediction for the deformation behavior of Al 5052 alloy under pulse current.
Although researchers have made significant progress in modeling the electroassisted process of materials, few studies have combined the electroassisted deformation process of materials with finite element software.The model established by Hariharana et al [87] only considers the influence on the overall stress change, and does not consider the proportion of thermal and athermal effects on the reduction of flow stress.To address this limitation, Tiwari et al [89] proposed to changethe dislocation density model to a constitutive model based on thermal density and dislocation density to predict the electroassisted deformation process of AA6063 and applied it to finite element software.The models and results are shown below:  Where, friction s is friction; ss s is solid solution strengthening; p s is precipitation strengthening, M is Taylor factor, G is shear modulus, b is Burgers vector, r is forest dislocation density, p e is true plastic strain, d is average grain size, D is the average precipitation spacing on the slip plane.α is a numerical constant that considers the interaction between dislocation arrangement and slip system, and f represents the inhibition of dislocation recovery by precipitated and solute atoms.After the introduction of current, T J , ( ) a and f T J , ( ) are functions with respect to temperature and current, and parameter s T J , ( )is used to describe the surface effects coupled by deformation temperature and current density.Figure 17 described the comparison between stress-strain curves and predictions for ultrathin alloy plates during room temperature and electrically assisted tensionwith good predictive power at different grain sizes.The RMSD values at different grain sizes and current densities are illustrated in figure 18, which vary from 6 to 28 Mpa, indicating that the multi-scale constitutive model has good predictability.As shown in figure 19, at the same current density, the flow behavior of poly-crystalline high temperature alloys follows the classic Hall-Petch relationship, but the pulsed current limits the grain size effect, as reflected by the slope of the Hall-Petch relationship decreasing with increasing current density.It is shown that the grain size effect in polycrystalline superalloys is inhibited because of the increase in current density.
The multi-scale constitutive model explores the influence of EPE on the size effect, revealed the coupling effect of grain size and pulse current on the mechanical properties of materials, and provided a rationale for the deformation behavior of materials in the EAF.The above models only verify the EPE of a specific material, but do not establish a unified model of multiple materials.Xu et al [92] used three typical materials, Cu, SS304 and Ti-6Al-4V, to conduct uniaxial tensile experiments under current.Through the dislocation accumulation/recovery, solution strengthening, and phase transition behaviors under different conditions, a unified analytical model was established for short-range internal stress and long-range internal stress under different conditions.To capture the influence of thermal effect and athermal effect on flow stress, as shown in the following equation: Where, ⁎ s is the short-range stress and G s is the long-range stress; x ( ) h is the characteristic coefficient and 0 for HCP material; 0 t m is the adiabatic shear stress; J is the current density; J c is the characteristic current strength; erf  e is the reference strain rate; P ē is the plastic strain rate; f b is the activation energy required to overcome the short range barrier and p and q the material constants satisfying 0 p 1 and 0 q 1, respectively.
Figures 20(a) and (b) shown the stress-strain curves of copper under thermal assisted tensile (TAT) and electrical assisted tensile (EAT) conditions.The reduced flow stress of Cu under the action of electric current compared to the TAT experiment shows the electroplasticity effect.Figures 21(a) and (b) show the stress loss coefficients and microstructure factors of three different materials under TAT and EAT.The decrease of 〈111〉 texture volume fraction of copper in the EAT showsthat the non-thermal effect of current promotes the dislocation movement, which agrees with the flow stress reduction results.For SS304, when the current density does not exceed 22.4 A mm -2 , the reduction of martensitic transformation in EAT leads to the reduction of nonthermal stress in SS304.However, at higher current densities, the non-thermal effect is not obvious because no martensitic transformation occurs and solid solution strengthening plays a leading role.The phase transition of Ti-6Al-4V in the electroassisted experimental results contributes to the stress reduction caused by non-thermal effects because the phase transition of Ti-6Al-4V occurs before its EPE.
The model establishes a unified electroplastic model for a variety of materials, and considers the thermal and non-thermal effects of current on the flow stress of materials comprehensively.Through the influence of current on dislocation, solution strengthening, and phase transformation, the microstructure evolution in Cu, SS304 and Ti-6Al-4V is captured to characterize the influence of short and long range stress on the flow stress under different current conditions.The research provides a basis for subsequent material electroassisted forming processes.Most studies only consider the influence of thermal effect or non-thermal effect on materials but do not comprehensively consider and decouple them to explore the changing behavior of materials in the electroassisted process.
Based on the experimental results of thermal and non-thermal effects of pulsed current in the process of electroplastic deformation of superalloys, Gao et al [93] defined the current density as a vector and created an electrothermal coupling crystal plastic model based on non-thermal effects of current and local Joule heating.1.The dislocation density evolution model based on the non-thermal effect of current is shown as follows: Where, D  a+ and D  a-are the rate of dislocation density increase and decrease; k 3 is the coefficient of dislocation density increase; k 4 is the function of the temperature and shear strain rate of the slip system; J a is the current density vector.Effect of current on dislocation slip: reduce deformation activation energy and promote dislocation movement.Dislocation density is balanced mainly through two mechanisms: dislocation proliferation and dislocation annihilation.
2. The temperature evolution model based on the local Joule heating effect considers the correlation between temperature, crystal surface spacing, current direction, dislocation density and resistivity, so that the local Joule heating effect can be characterized, as follows: Where, T D is the temperature rise; m r a is the resistivity of the corresponding region; t D is the time; N is the total number of slip systems; x is the density of the material; c is the specific heat capacity.
The model was established and calibrated at current densities of 10, 20, and 24 A mm -2 , and temperature histories and stress responses were obtained from figures 22(a) and (b).To validate the accuracy of the model, experiments were conducted at current densities of 33 and 45 A mm -2 as shown in figures 22(c) and (d).The predicted temperature histories showed good agreement with experimental results.However, when the strain exceeded 0.15, there was an increase in the difference between the predicted true stress curve and the experimental true stress curve under current density.This discrepancy might be attributed to the temperature difference between the simulation and the experiment.
The influence of the dislocation density evolution model based on the temperature evolution model of local Joule heating effect and the athermal effect of current on the flow stress proposed by Gao et al compared with the flow stress model proposed by Xie et al considering the electronic wind theory, the applicable range of current density is increased, not limited to pulse current of a certain frequency, but with the increase of strain, there is a certain gap between the simulation and the experiment.This may be because of the ideal heat dissipation conditions used in the simulation.Xu and Gao et al explored the influence of EPE generated by current on material properties from short range and long range stress model and electro-thermal coupling crystal plastic model, respectively.Different from previous studies on a single mechanism, the thermal effect and athermal effect of current were decoupled to explore their influence on material properties, thus promoting the development of EAF for different metal materials.
The constitutive model can not only predict the chang behavior of materials under experimental conditions but also predict the influence of current on materials under complex strain paths.Dong et al [94] applied the EPE to the cyclic loading model to study its cyclic deformation behavior at different current densities using 7075-T6 alloy as a research object.In addition, a modified Y-U hardening model is established based on the experimental results and verified by simulation, which shown that the model has the feature of describing the cyclic deformation ability of the material at different current densities.In order to characterize the deformation of the material at high temperature and current density, researchers changedthe original model to get yield functions of equations ( 29) and (30), as follows: Where, S and α are the skewness of Cauchy stress and the skewness of reaction force, respectively; Y are the radius of the yield surface in the skewness space.In the boundary surface function, β is the center of the boundary surface; B and R are the initial size and isotropic hardening value of the boundary surface, respectively.The modified p ē* is the state variable in the deformation process, and its evolution is related to the loading direction, which is easy to determine in the uniaxial stress state.
As shown in figure 23, under different current parameters, predicted results coincide well with the experimental results.The model is applicable to tensile-compressive cyclic load models under the action of electric current.The researchers then verified the EA draw bending process, the results of which are shown in figure 24, indicating that the model can effectively describe the cyclic deformation behavior of 7075-T6.However, it has low pulse current density, which makes deformation temperature low and cannot predict cyclic deformation ability at high temperature.
Some researchers have used finite element simulation to study the field distribution in the EAF process.Bao et al [95] investigated the influence of pulse current on strain distribution during EA micro-scale shear compression of Ti-6Al-4V.The study found that the finite element method is highly applicable in predicting micro-scale shear compression behavior with the assistance of pulsed currents.The representative effective stress, total strain and strain rate distribution of 60% deformed specimen, which are shown in figures 25(b), (c) and (d) respectively.The strain and strain rate were distributed along the semicircular groove of 45°and the width W relatively evenly, which also showedthat the selection of sample size parameters is reasonable.In another study, the high Joule heating temperature resulted in local softening deformation zone of the sample, accelerating the deformation in both severe deformation zone and free deformation zone [96], which is shown in figure 26.
The theoretical method has certain advantages in studying the rules of macro mechanical properties, and the simulation can display the changes of various quantities in the forming process comprehensively and in realtime [97].But there are variousassumptions in the calculation process of the theoretical method.For complicated forming conditions or special products, the theoretical analysis is challenging, and there is a certain  gap between simulation and realistic forming process.Specific experiments are needed to study the relevant performance.

Effect of electric pulse on microstructure of metal
Section 2 of the paper highlights that electrical pulse influences the metal microstructure mainly by modifying dislocation movement.A significant reduction in deformation resistance and an increase in plasticity are  observed when electrical pulses are applied to metals under deformation.The significant decrease in flow stress and deformation resistance is attributed to the interaction between electrons and the dislocation field.No effect of current pulses was noticed in the elastic deformation region, while the unexpected change in flow stress happened onlyin the plastic region, which confirms further the interaction of electrons with dislocations, that is, the drifting electron has an 'electron wind' effect on the dislocation [98,99].On the one hand, under the thermal activation of Joule heating effect, the slip and climbing ability of dislocations are enhanced, the dislocations with different signs balance each other, and the dislocation density is reduced.On the other hand, the movement ability of the dislocation is further enhanced under the action of electronic wind.Xiang et al [8] studied the effect of high current density electrical pulses (103 A mm −2 , 150 μs) on the plastic strain and dislocation evolution of quenched steel by in situ electrical TEM and in situ thermal TEM.The results shown that the remaining stress and the density of dislocations, both of which are intimately associated with plastic strain, are obviously reduced under the action of electrical pulses.In addition, apart from the force that the electron wind exerts on the dislocations, the moving of the thermally activated dislocations is also affected by the drifting electrons.The motion of vacancies and dislocations is enhanced by the action of drifting electrons, and the annihilation of dislocations issped up.In contrast, due to the electronic wind, the Frank-Read source cannot generate a great number of dislocations, thus the multiplication rate of bit errors is concurrently reduced.Eventually, the density of dislocations decreases and the structure of dislocations is aligned with the direction of motion of drifting electrons in parallel.Zhang et al [98] demonstrated the existence of electrical forces during EAF by directly comparing in situ electrical TEM and in situ thermal TEM experiments.The behavior of dislocations was found to be influenced by electronic forces and local Joule heating effects.The electronic forces in the EAF process can promote the movement of dislocations, and that is not easily possible at RT or conventional high temperatures.Therefore, the mechanical properties and microscopic behaviors during EAF differ from those of high temperature deformation.It is important to note that the effect on the metal is different as the current application time and current direction change, so it is a key issue for the future use of EAF to take advantage of the comprehension of local temperature, current direction and dislocation distribution.
Electric pulse has multiple effects on the metal matrix, including: (1) Increasing nucleation rate, decreasing dynamic recrystallization temperature and promoting grain boundary slip; (2) Phase transition; (3) Eliminating the texture formed during previous processing and generating alternative texture; (4) Promotng the micro-crack healing in the matrix; (5) Reduce the geometrically necessary dislocation (GND) caused by additional dislocations during metal's plastic deformation.Microstructural changes in metallic materials induced by pulsed currents can be used to the improvement of the plastic deformation capacity of metals.

Recrystallization
Research has shown that the heating speed caused by pulse current was quitefast, approaching 65-400 °C s -1 , and the recrystallization process caused by pulse current treatment was completed in a short time and the surface temperature of the sample is distributed in gradient during the electric treatment [100], as shown in figure 27.Part of the argument is that a high heating rates inhibit recovery and recrystallisation of materials [101].The others believe that the high heating rates speed upthe recrystallisation process.High heating rate can quickly eliminate statistical storage dislocations [102].However, speculation about the effect of pulse current is not limited to the effect of heating rate.Several researchers have concluded that the dislocation movement, reaction and sub-grain growth in the metal are accelerated due to pulse current [103].The flow of electrons will be generated when the current passes through metal.The collision between electrons and atoms in the lattice transfers energy from the former to the latter [104].
Pulse current contributes to the coalescence of sub-grain boundaries in grains and the formation of distortion free equiaxed grains through recrystallization [102].Pulse current is helpful in improve the nucleation rate, reduce dynamic recrystallization temperature and promote grain boundary slips.The driving force of recrystallization induced by pulse current is the high-density dislocations accumulated because of deformation in the metal matrix.Grain refinement is influenced by the previous processing state and current treatment conditions.For example, the recrystallization starting temperature of NiTi alloy under pulse current was less than 300 °C, which is lower than 500 °C during heat treatment in hot furnace [105].As shown in figure 28, pulse current accelerated the recrystallization and reduced the recrystallization temperature.The recrystallization process eliminated the dislocations caused by work hardening and released the high strain energy in the metal matrix, which resemble something the recovery process.
Mechanical property of the material was improved for recrystallisation [106,107].As shown in figure 29, the current promoted recrystallization of cold rolled commercial pure copper, resulting in grain refinement.It was worth emphasizing that the changes of metal microstructure and properties caused by current were closely related to the pretreatment method.According to the research, recrystallization and considerably refined of microstructure also appeared in 'hot rolled' 2024 Al alloy after electric pulse treatment [108].The mechanical property of Al alloy improved after electric pulse treatment compared with the results of cold rolled Al alloy after current treatment [108].The increase of tensile strength and elongation is because of grain refinement.The effect of current significantly reduced the recrystallization temperature of the material.As shown in figure 30, dynamic recrystallization occured on both sides of the Cu/Al layered metal under the action of current [109].In contrast to the quasi-static tensile specimens at room temperature, the recrystallization rate of the EAT specimens was slightly higher than that of the RT tensile specimens and most of the recrystallization positions of Al layer in EAT sample were distributed in elongated grains.

Texture evolution
Pulse current can also eliminate the texture formed in previous processing and generating a new alternative texture [110].To some extent, pulse current can realize custom structure, that is, the long axis direction of grains can be rearranged along the current direction.Jiang et al [111] found novel recrystallized grains with other crystal orientations in the cold-rolled Mg-9Al-1Zn Mg alloy treated by pulse current.The texture strength of {0001} with stronger strength in the cold rolled sample gradually decreased, and the weaker {1( ) -21( ) -1} pyramid fiber texture and prism texture disappeared.Other research havs shown that the nucleation rate of pulse current induced recrystallization will increase when there is an angle between the current direction and the rolling direction.It was an important finding that pulsed current induced recrystallization grains are randomly  nucleated but have directional growth.Yan et al [103] found that a small amount of cube texture {100} 〈100〉 remained in the uniaxial tensile Al alloy sample without the influence of any electric pulse.However, the intensity of cube texture becomes obvious with the increase of electric pulse intensity.The effect of pulse current on texture evolution can be explained by directional nucleation and directional growth mechanisms.It is conducive to favorable to the growth of cubically oriented sub-grain, but not to the growth of S-oriented subgrain as the increase of current intensity.Therefore, the intensity of the cube texture becomes obvious with the increase of the electric pulse intensity, which is shown in figure 31.

Phase transition
Some studies showed that the phase transformation of the metal matrix can be facilitated and the phase transition temperature can be reduced by pulse current.In general, the conversion temperature of α→β precipitation for Ti-6Al-4 V alloy is about 676 °C [112].Nevertheless, α phase of the Ti alloy is gradually transformed into β phase under the action of pulse current.The rate of phase transition accelerated as the extent of thermal effects increased.The whole phase transition process is completed in an ultrafast process (6s) because of the coupling of thermal and ahermal effects of pulse current, which significantly reduces the phase transition temperature compared with the starting temperature 676 °C of the conventional heating process.The phase transition process is shown in figure 32.The thermodynamic energy barrier of phase transition is reduced due to pulse current treatment, and the process is sped upin a few seconds.For example, in the pulse current treatment for cold deformed ZA27 in the 20 A/150 s, the cyclic continuous phase transformation induced by electric pulse occurs through quenching-upper quenching-quenching [113].The phase transition induced by pulse current can be attributed to the favorable change in phase stability in the system.Electrical pulse can restore mechanical properties at a relatively low temperature and faster speed, that is, the electrical pulse annealing effect.The efficiency of the electric pulse annealing effect is influenced by the number of pulses and current density [114].
The evolution of the second phase in the material is influenced by the pulse current.The second phase in metal alloys can be divided into solid solution phases or intermetallic precipitation [110].As shown in figure 33, γ′ phase was observed in Inconel 718 plate treated with a solid solution after EA tension with a density of 125 A mm -2 [115].It is observed that the deformation temperature is 633K, which is lower than the precipitation temperature 866-1089 K of the phase γ′.It is reported that pulse current can promote thermal vibration, accelerate the migration of atoms through the generation and migration of vacancies, promote solute atoms to leave the matrix and add precipitation, and form a second phase pre precipitation at low temperature finally [27].In addition, local temperature rises and the γ′ phase pre precipitation for the reason of local Joule heating effect induced by electron scattering around defects [116].Research shows that pulse current will lead to lattice strain of intermetallic compound precipitates in metal matrix [117] and subsequent dissolution behavior [26].

Self-healing of microcrack
Microcracks may appear in the metal matrix randomly after plastic deformation.It is more than just difficult to inspect by equipment, and uneven stresses during use may cause crack expansion leading to specimen fracture.An example is that in Ti/Al laminated composites prepared by explosive welding, the stress is not uniformly distributed within each metal matrix layer because of the existence of the wavy interface structure.The area where the stress is concentrated will produce a large plastic deformation [118].The formation of a local melted zone (LMZ) along the wave-shaped interface formed by the explosion, consisting mainly of the IMCs of TiAl 2  and TiAl 3 .With the accumulation of internal stress, cracks are generated at the thinnest Ti layer at the top of the wavy interface, and local layers are formed along the interface.The crack tip extended from Ti layer to Al layer [2].Therefore, autonomous detection and repair of metal internal micro-cracks is a challenge.It is found that the self-healing of damaged metals could be triggered by the use of electrical pulses [119][120][121][122].For instance, Xu et al [123] used short-time high-density eddy current pulse treatment (ECPT) to repair micro-cracks in magnesium alloy pipes.The micro-cracks of pipes have been repaired and the mechanical properties improved significantly after the ECPT.Yu et al [124] healed cracks in SUS304 stainless steel with electric pulses.It was found that the main reasons for crack healing were bypass effect and Joule heating effect.A schematic diagram of the healing mechanism is shown in figure 34.The current cannot pass through when the pulse current flows through the micro-crack surface and accumulates at the crack tip (circuitous effect).The macro performance is that the resistance at the tip of the micro-crack is large.The temperature at the tip rise makes the temperature exceed the melting point of the sample for the reason of Joule heating.Then the local compressive stress will occur because of the large temperature gradient of the material matrix.The expansion of the metal tip will be stalled and form a healing zone and a new crack tip at the same time under the local compressive stress.The circuitous effect and Joule heating effect will occur repeatedly at the new tip and form a new healing zone and crack tips when the next pulse current is applied again.Save as aforesaid mechanisms explained above, dislocation filling and diffusion filling are also possible healing mechanisms [125].This means that the electric pulse heals the crack by promoting the movement of dislocations and the diffusion of atoms into the crack.
Applying pulse current has a certain effect on plastic deformation damage and crack damage of metal materials, and has great potential in regulating the mechanical properties of damaged metal materials.However, the change rules of mechanical properties after pulse current treatment of damaged metal materials have not been deeply explored.The effect will vary with time.In order to analyze the response rules of current parameter changes, as well as the evolution and mechanism of the internal microstructure of the material, a finite element analysis model of the plastic deformation damage process during the pulse current treatment of the material should be established.
In summary, it is clear that the pulse current is able to decrease the flow stress and friction coefficient of metal materials, promote the self-healing of micro-cracks in the matrix of metal materials, and improve the forming properties of metal materials.In addition, changes in the microstructure of metallic materials can be induced by pulsed currents, and the macro performance is also the improvement of the formability of materials.The influences of pulse current on the microstructure of metal materials is mainly primarily by Joule heating effect and athermal effect.

Geometrically necessary dislocation
The configuration and number of dislocations inside a metal significantly affect its plastic deformation ability.Geometrically necessary dislocation (GND) are caused by some additional dislocations in the plastic deformation process of a metal, which is produced in order to coordinate the continuity of the deformation gradient between crystals.When heterogeneous deformation occurs, geometric dislocation adapts to strain analysis across heterogeneous interfaces, resulting in strengthening and hardening.
To investigate whether current changes the GND density during material strain, Yang et al [31] analyzed the change of GND density of Al0.6CoCrFeNiMn through EBSD data in the EA uniaxial tensile process.The kernel average misorientation (KAM) and the corresponding KAM distribution for RT and EAT conditions are shown in figure 35.When the strain was 0, the sample was more evenly distributed on the KAM chart at RT than in the EAT30 and EAT60 samples (figures 35(a), (e), (i)).The KAM value of the specimen after treatment is more than that of the untreated one, and the KAM value in RT is the largest.The experimental results shown that the KAM increment decreases as the current density increases.
KAM is used as an approximate indicator for analyzing the GND density of the plastic deformation process, which in turn is obtained through the strain gradient theory, As shown in equations (31) and (32 Where, , q D m and b are the average value of the local orientation difference in the measurement area, the EBSD step of data acquisition (0.5 μm) and the magnitude of the Burgers vector; i q is the local orientation difference at i point; j sur q is the orientation difference at its neighboring point j; n is the number of points in the test area.Figure 36 shown the GND density versus current density variation curve, and the red dots indicate the increase in GND density at strain from 0 to 6%.It can be seen from the figure that the value of GND accumulation is larger at RT and the increment of GND decreases significantly with the increase of current density.It shown that the applied current can reduce the GND in the material.In summary, the material increases its GND density during deformation in order to coordinate the deformation, leading to an increase in strength and hardness, while its GND density decreases after current treatment.Its plastic deformation capacity is increased.
The pulse current treatment process is controlled by various physical effects produced when acting on metal materials.The analysis of its physical mechanism is mainly theoretical calculation and finite numerical simulation based on the electro-thermal-mechanical coupling theory.Many previous studies only considered the temperature generated by current on material properties.The electroplastic effect and crystal plasticity should be combined to comprehensively consider the impact of the current itself on the overall flow stress.Both thermoplastic effects and electroplastic effects can reduce the flow stress of materials and improve the ductility of materials.However, in order to achieve precise control of electrically assisted forming, it is necessary to face the problem of decoupling electrical effects and thermal effects during plastic deformation.Computer simulation software should be combined with actual experiments to decouple and analyze thermal and non-thermal effects under different temperature conditions.

Summary and future aspects
Overall, the effect of pulsed current on the deformation behavior of metallic materials is mainly studied.The mechanisms of action and the key factors which affect the electroplasticity effect are identified.The EAF-related theoretical models are summarized.The effect of pulsed current on the microstructure and properties of metallic materials is discussed.
As an effective method for improving metal formability, the microstructure change is affected by the pulse current, the deformation resistance of the material is reduced, and the plastic deformation ability of the metal is further improved.The research on the pulse current influence on metal micro forming properties mainly focuses on the Joule heating effect and ahermal effect.In addition, the effect of the magnetic field and dislocation based on the current is also discussed.There are various factors that affect the EPE, such as current frequency, current density, pulse width, etc When the material is different.The law of EPE is also quite different under different influencing factors.This review summarizes the theory model associated with EAF, as well as and the microstructure and properties change of metal materials caused by pulse current.The constitutive model has theoretically the ability to guide the actual electroplastic forming process.For different materials and deformation conditions under different conditions, researchers have established flow stress models that considered Joule heating effect and ahermal effect to estimate the influence of current parameters on metal formability in the forming process, for example, Johnson-cook model, CP Model, dislocation density model, hardening model and other corresponding theoretical models.
Current-assisted forming technology combines electrical energy, thermal energy and deformation energy, and couples the effects of multiple physical fields.The processing process is extremely short, and it is difficult to accurately characterize experimental phenomena using conventional experimental methods.Although electroplasticity has complex material and physical parameter dependencies, both the thermal and electrical effects of electric current affect the overall mechanical properties through the microstructure evolution during plastic deformation.Therefore, the influencing factors of microstructure and constitutive behavior can be studied based on the microforming mechanism, and the mechanical behavior of electroplasticity can be explored.Because it relates stress and strain independently to the evolution of microstructural parameters, which in turn are related to dislocation density.However, a complete theoretical model that can predict EAF has not been proposed because ofthe controversial mechanism of pulse current influence on metal formability.The research on the pulse current influence on metal micro forming properties mainly focuses on the Joule heating effect and ahermal effect.The coupling of thermal energy and kinetic energy caused by pulse current promotes the migration of dislocation in metal matrix, grain refinement and phase transformation process, accelerates metal recovery, recrystallization and grain growth.
As another product with broad application prospects, because of the excellent comprehensive properties of each layer, the formability of metal laminate composites (MLC) has also attracted extensive attention from researchers.It can realize the advantages of weight reduction and lightweight, saving precious metals, high temperature and corrosion resistance and so on.It has broad application prospects in aerospace, new energy and other high-tech fields.However, the forming limit of MLC is limited because of the existence of bonding zones between heterogeneous layers greatly.The EAF is expected to solve the key problems of MLC forming in the future.Currently, there is a lack of relevant investigation on the experiment of electropulsing assisted forming of MLC and the constitutive model describing the deformation of MLC under electropulsing assisted forming, which considers the key current parameters and scale effect at the same time.To some extent, it hinders the application of pulse current assisted forming technology in the field of formability of MLC.

Figure 4 .
Figure 4. Schematic diagram of influence of weak magnetic field on mechanical properties of crystals with paramagnetic central structure defects.Reproduced from [39], with permission from Springer Nature.

Figure 6 .
Figure 6.Dislocation distribution and its angle relationship in Inconel 718 at a current of 200A/1500 Hz : (a) Relationship between dislocation lines W1 and W2 and the direction of magnetic field strength H, and (b) The relationship between the dislocation lines W1 and W2 and the direction of magnetic field strength H when β is equal to 90°.Reprinted from [42], Copyright (2023), with permission from Elsevier.

Figure 7 .
Figure 7.The size distribution of M s under different angles of a and b .Reprinted from [42], Copyright (2023), with permission from Elsevier.

Figure 9 .
Figure 9. (a) Deformation force changes with frequency, (b) deformation force changes with current density, (c) friction coefficient varies with frequency, and (d) friction coefficient varies with current density.Reproduced from [84], with permission from Springer Nature.

Figure 10 .
Figure 10.Prediction of Ti flow stress changes in EA tensile tests by an improved Hollomon and Johnson-Cook model.Republished with permission of ASME, from [49]; permission conveyed through Copyright Clearance Center, Inc.

Figure 12 .
Figure 12.The electrical effect changes with the compression delay current.Republished with permission of ASME, from[51]; permission conveyed through Copyright Clearance Center, Inc.
r and r r represents the forward and reverse dislocation density respectively and other parameters are the same as those in formula 15.Figure16(a) shown the comparison results of the true stress-strain curves obtained from the EA compression experiments and the finite element simulations.The experimental and predicted results are roughly consistent, indicating the accuracy of the model.Figure16(b)shown the dislocation density in relation to true plastic strain for RT deformation and EA deformation.Due to the change of material properties caused by thermal effect, the true stress-strain curve established by the finite element simulation results of Joule heating effect and the deformation results at RT and EA in the electroassisted compression test is shown in figure16(c), showingthe existence of not only Joule heating influence, but also EPE.While the mechanisms of EPE and the modeling of materials during electroassisted deformation have been extensively studied, the combination of size effects and EPE at the microscale has been very limited.Liu et al[90] performed RT and EA uniaxial tensile tests on ultrathin nickel-based superalloy sheets in the grain size range from 27.2 to 79.4 μm.Based on the experimental results, the effects of solid solution atoms, sediments and grain size are introduced into the dislocation density evolution equation and a multi-scale constitutive model is established by considering various strengthening mechanisms, grain size and EPE, as shown below:

Figure 15 .
Figure 15.An explanation of the electroplasticity effect of Al 5052 alloy based on dislocation density model.Reprinted from [87], Copyright (2017), with permission from Elsevier.

Figure 17 .
Figure 17.Comparison between stress-strain curves and model predictions for ultra-thin alloy plates under RT and EA tension.Reprinted from [90], Copyright (2021), with permission from Elsevier.

Figure 16 .=
Figure 16.(a) Comparison curves of EA compression simulation and experiment, (b) Evolution of dislocation density of RT deformation and EA deformation, and (c) Changes in the mechanical behavior of materials by thermal effects under different experimental conditions.Reprinted from [89], Copyright (2022), with permission from Elsevier.

Figure 18 .
Figure 18.Schematic diagram of RMSD distribution for different grain sizes and current flow.Reprinted from [90], Copyright (2021), with permission from Elsevier.

Figure 19 .
Figure 19.Schematic diagram of the effect of pulsed current on grain size.Reprinted from [90], Copyright (2021), with permission from Elsevier.

Figure 24 .
Figure 24.Different hardening model curves for the same temperature conditions.Reprinted from [94], Copyright (2022), with permission from Elsevier.

Figure 25 .
Figure 25.Schematic diagram of distribution obtained by finite element simulation at 20 A mm −2 current density: (a) micro scale shear compression specimen, (b) effective stress, (c) total strain, and (d) strain rate.Reprinted from [95], Copyright (2020), with permission from Elsevier.

Figure 26 .
Figure 26.(a) The temperature distribution of sample under 60% deformation and (b) longitudinal section strain distribution of compressed sample obtained by finite element simulation (OM image on the left), under the condition of 50 A mm −2 with strain rate of 1s −l .Reprinted from [96], Copyright (2021), with permission from Elsevier.

Figure 27 .
Figure 27.(a) Temperature curve of T2 copper in the pulse current treatment.Reproduced from [100], with permission from Springer Nature, and (b) temperature curve of Ni-based superalloy in electrically assisted tension.Reprinted from [27], Copyright (2018), with permission from Elsevier.

Figure 32 .
Figure 32.The α→β transition of Ti-6Al-4V alloy under the action of current: (a)XRD patterns of samples in the original state and under high-energy pulse current treatment, (b)schematic diagram of grain growth and phase transformation: original equiaxed α Grain state, (c) Schematic diagram of the diffusion of Al and V atoms in the phase transition process, (d) Expansion of the interface in the phase transition process, and (e)Growth of continuous α grain boundaries.Reproduced from [112], with permission from Springer Nature.

Figure 33 .
Figure 33.Distribution and size of the second phase of Inconel 718 superalloy at a current density of 125 A mm −2 after solution treatment.Reprinted from [117], Copyright (2019), with permission from Elsevier.