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International Journal of Plasticity xxx (2016) 1e23

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International Journal of Plasticity

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Electric currenteassisted deformation behavior of Al-Mg-Sialloy under uniaxial tension

Moon-Jo Kim a, b, 1, Myoung-Gyu Lee c, 1, Krishnaswamy Hariharan d,Sung-Tae Hong e, **, In-Suk Choi f, Daeyong Kim g, Kyu Hwan Oh a,Heung Nam Han a, *

a Department of Materials Science and Engineering and Research Institute of Advanced Materials, Seoul National University, Seoul,08826, Republic of Koreab Liquid Processing and Casting Technology R&D Group, Korea Institute of Industrial Technology, Incheon, 21999, Republic of Koreac Department of Materials Science and Engineering, Korea University, Seoul, 02841, Republic of Koread Department of Mechanical Engineering, Indian Institute of Technology Delhi, Delhi, 110016, Indiae School of Mechanical Engineering, University of Ulsan, Ulsan, 44610, Republic of Koreaf High Temperature Energy Materials Research Center, Korea Institute of Science and Technology, Seoul, 02456, Republic of Koreag Materials Deformation Group, Korea Institute of Material Science, Changwon, 51508, Republic of Korea

a r t i c l e i n f o

Article history:Received 25 April 2016Received in revised form 31 August 2016Accepted 24 September 2016Available online xxx

Keywords:ElectroplasticityDislocationMicrostructuresMechanical testingConstitutive behavior

** Corresponding author.E-mail addresses: [email protected] (S.-T. Hong

1 Equal contributors: Moon-Jo Kim and Myoung-

http://dx.doi.org/10.1016/j.ijplas.2016.09.0100749-6419/© 2016 Elsevier Ltd. All rights reserved.

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a b s t r a c t

The tensile deformation behavior of Al-Mg-Si alloy under a pulsed electric current has beeninvestigated. Specimens subjected to three types of heat treatment, solution treatment,natural aging, and artificial aging, are prepared. In solution treated specimens, elongation andflow stress increase when pulsed electric current is applied during plastic deformation; also,the PortevineLe Chatelier (PLC) phenomenon, which is observed in the tensile test withoutelectric current, nearly disappears when the pulsed electric current is applied. In naturallyaged specimens, the flow stress decreases and the elongation significantly increases whenpulsed electric current is applied during the tensile test. In artificially aged specimens, bothelongation and flow stress decrease under pulsed electric current. The result of XRD analysisshows that thermal andelectric currenteinducedannealingoccurs in all specimens subjectedto theelectric current. Especially in the solution treated specimen, the formationof early stageprecipitates from a supersaturated state might be accelerated by the electric current, in aneffect distinct from Joule heating; this effect would explain the observed increase in flowstress and the disappearance of the PLC phenomenon. Microstructural observation showsthat electric current accelerates the formation of microvoids around the precipitates at thegrain boundary, resulting in earlier fracture in the artificially aged specimen. A constitutivemodel based on dislocation density model and precipitation hardeningmodel is proposed todescribe the uniaxial tensile behavior for the age hardening alloys. Based on the experimentalfindings, the proposed constitutive model is modified to describe the upper boundary of theratchet shape stress-strain curve under a pulsed electric current. Thermal and electriccurrent-induced annealingwith precipitation hardening is considered simultaneously in themodified constitutive model. Phenomenological descriptions of each parameter aredemonstrated considering the microstructural features observed in experiments. Themodified model is capable of predicting the experimental results very well.

© 2016 Elsevier Ltd. All rights reserved.

* Corresponding author.

), [email protected] (H.N. Han).Gyu Lee.

.-J., et al., Electric currenteassisted deformation behavior of Al-Mg-Si alloy underlasticity (2016), http://dx.doi.org/10.1016/j.ijplas.2016.09.010

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M.-J. Kim et al. / International Journal of Plasticity xxx (2016) 1e232

1. Introduction

In recent years, improvement of fuel efficiency has been an important issue in the automotive industry. Using lightweightmaterials such as aluminum alloys is one way to improve fuel efficiency (Donati et al., 2012; Jobba et al., 2015). However,despite aluminum alloy's high strength-to-weight ratios comparedwith typical ferrous alloys, their commercial application isstill limited due to their poor formability at room temperature (Khan and Liu, 2012; Klusemann et al., 2015; Pogatscher et al.,2013). Forming at elevated temperatures is an effective method to counter the poor formability of aluminum alloys. Warmand hot forming of aluminum alloys has been generally conducted at elevated temperatures (200e350 �C) up to therecrystallization temperature. However, heating strategies to increase the forming temperature may induce inhomogeneoustemperature distribution on the material, surface oxidation, and adhesion between the die and the alloy sheet (Toros et al.,2008; Hirsch, 2013). Hydroforming and incremental forming processes have also been investigated for the forming ofaluminum alloy sheets. However, these forming processes require excessive process time and considerable initial capitalinvestment. Therefore, new forming methods are still desired for increasing the formability of aluminum alloys at relativelylower forming temperatures compared to those of warm and hot forming, without requiring excessive process time or capitalinvestment.

Electricallyeassisted forming is a promising alternative forming technique in which the mechanical properties of a metalalloy are altered by simply applying electricity to the alloy during deformation. The reduced flow stress and increasedductility, which are often called the electroplastic effects, are generally observed in electrically-assisted deformation(Troitskii, 1969; Conrad, 2000; Salandro et al., 2010). Recently, the effect of electric current on mechanical behavior has beenstudied actively to utilize the benefits of electrically assisted deformation in practical applications including bending(Salandro et al., 2011; Jordan and Kinsey, 2012), blanking (Kim et al., 2014c), drawing (Zimniak and Radkiewicz, 2008; Wang,2009), forging (Perkins et al., 2007; Hong et al., 2015) and reduction of springback (Green et al., 2009; Kim et al., 2014b).

Various previous studies have focused on the effect of electric current on mechanical behavior during plastic deformation.The possible influence of electric current on mechanical behavior was suggested for the first time by Machlin in 1959(Machlin, 1959). Recently, Roth et al. (2008) applied a pulsed electric current to aluminum 5754 alloy during tension, therebyachieving increased elongation up to 400% of the gauge length. The effects of pulse duration and current density have beeninvestigated as a mean to reliably achieve optimal specimen elongation (Salandro et al., 2009). Also, Salandro et al. (2010)investigated the effect of pulsed electric current on the tensile behavior of aluminum 5xxx alloys subjected to various heattreatments.

Based on the positive effects of electric current on the plastic deformation, some researchers have carried out micro-structural observations to examine the effect of electric current on the mechanical behavior. Heigel et al. (2005) found thatelectric current affects the number and size of precipitates in aluminum 6061 alloy. The relationships between the grain sizeand the reduction of flow stress under an electric current also have been investigated (Siopis and Kinsey, 2010; Fan et al.,2013). In addition, the authors observed the annihilation of dislocation by applying a pulsed electric current during uniax-ial tension of 5052 aluminum alloy (2014a). The electric currenteinduced annealing occurs due to the annihilation ofdislocation with a distinct role from Joule heating (Kim et al., 2014a).

The mechanism of electroplasticity has been explained from a few different points of views. For example, the mechanicalbehavior of metals under an electric current could be described satisfactorily in terms of the thermal effects of resistiveheating, without consideration of electroplasticity theory (Goldman et al., 1981; Klimov and Novikov, 1984; Magargee et al.,2013). On the contrary, it also has been reported that the mechanical behavior under an electric current may not be clearlyexplained without considering the athermal electroplastic effect. A popular hypothesis to explain the athermal effect ofelectroplasticity is the electron wind effect (Sprecher et al., 1986; Conrad, 2000b; Antolovich and Conrad, 2004). In the hy-pothesis of the electron wind effect, electric current densities greater than 104e106 A/mm2 may cause atoms to move,resulting in interactions between electrons and dislocations. Also, an empirical expression (Roh et al., 2014) and a numericalmodelling approach (Hariharan et al., 2015) have been suggested to quantify the effect of electric current on mechanicalbehavior. Hariharan et al. (2015) conducted an electro-thermo-mechanical finite element study to decouple the thermal effectfrom the tensile behavior under a pulsed electric current, and thereby numerically quantified the athermal effect of electriccurrent on the mechanical behavior. However, the underlying mechanism of electroplasticity still remains controversial.

Even though quite a few studies have been conducted on the effect of electric current on deformation, the amount ofexperimental data available is not yet sufficient to clearly understand the phenomenon of electroplasticity. For example, theelectroplasticity of age-hardening nonferrous metal alloys has not yet been studied well. Also, a constitutive model is stillneeded to describe the tensile behavior of the age-hardening alloys under a pulsed electric current.

The objective of the present study is to investigate the effect of electric current on the mechanical behavior of Al-Mg-Sialloy, a representative age-hardening alloy system. First, microstructural observations of specimens subjected to tensiledeformation, either with or without the effect of pulsed electric current (hereafter “electric current assisted (EA) tensile test”and “non-electric current assisted (Non-EA) tensile test”, respectively), were carried out by X-ray diffraction (XRD), scanningelectron microscopy (SEM) and transmission electron microscopy (TEM). The deformation behavior associated with elec-troplasticity was then discussed based on the microstructural changes of the deformed specimens. Second, based on theexperimental results, a constitutive model is proposed to describe the uniaxial Non-EA tensile behavior of the age-hardeningalloys. A flow stress model based on dislocation-dislocation interactions (Kocks andMecking, 2003; Krausz and Krausz,1996),which is often named as ‘K-Mmodel’, was used for the basis of the proposed model. The K-Mmodel was further extended by

Please cite this article in press as: Kim, M.-J., et al., Electric currenteassisted deformation behavior of Al-Mg-Si alloy underuniaxial tension, International Journal of Plasticity (2016), http://dx.doi.org/10.1016/j.ijplas.2016.09.010

M.-J. Kim et al. / International Journal of Plasticity xxx (2016) 1e23 3

Estrin et al. (1998) to consider the effect of precipitation hardening. The constitutive model for the uniaxial Non-EA tensilebehavior is thenmodified to estimate the flow stress responses during the tensile tests with pulsed electric current. Annealingwith precipitation hardening due to Joule heating and a distinct effect of pulsed electric current is considered simultaneouslyin the modified constitutive model. Also, a phenomenological description of parameters in the modified constitutive model isproposed considering the microstructural features observed in the experimental result. Finally, the flow stress curvescalculated by the modified constitutive model are compared with the experimental results.

2. Experimental procedure

2.1. Specimen preparation

A commercial Al-Mg-Si alloy (Al-0.87Mg-0.66Si-0.23Cu in wt.%) sheet with a thickness of 2 mm in artificially aged state(T6 temper, as-received) was used. Tensile specimens of gauge width 12.5 mm and gauge length 50 mmwere prepared alongthe rolling direction of the sheet according to ASTM E8 (ASTM, 2010). Three different heat treatments were considered in thepresent study: solid solution treatment (or simply, solution treatment), natural aging, and artificial aging (Fig. 1). For thesolution treatment, artificially aged (as-received) tensile specimens were placed in a furnace at the temperature of 530 �C for1 h and then quenched in water. To avoid aging effects in the solution treated specimens even at room temperature, tensiletests of these specimens were conducted within a few minutes after quenching. Naturally aged (T4 temper) specimens wereprepared by holding the solution treated specimens at room temperature for 4 days after quenching according to ASTM B918(ASTM, 2001). As-received specimens were directly used as artificially aged specimens without additional heat treatment.

2.2. Experimental set-up

Quasi-static uniaxial tensile test was conducted using the experimental setup illustrated in Fig. 2a, operated at the con-stant crosshead speed of 2.5 mm/min (corresponding to the nominal strain rate of 0.05/min) at room temperature.Displacement of each specimenwas measured using ARAMIS Digital Image Correlation (DIC) system (GOM, Germany), whichprovides non-contact measurements based on the principle of digital image correlation. The DIC systemwas calibrated usingan extensometer during a tensile test without application of electric current. Tensile specimens were prepared for DICanalysis by applying a stochastic pattern of black spots on a white background on one side of each specimen.

To carry out tensile tests with pulsed electric current, the tensile test machine (INSTRON, USA) was insulated by insertinginsulation made of bakelite between the grips, thereby ensuring that electric current would be applied only to the specimenduring the test. Electric current was generated by a Vadal SP-1000U DC power supply (Hyosung, South Korea), and wasperiodically applied to the specimen with a duration (td) of 0.5 s and a period (tp) of 30 s until fracture (Fig. 2b). For all threeheat treatment conditions selected in the present work, the first pulse of electric current was applied after yielding. Theamplitude of the electric current was then kept constant through thewhole tensile test with pulsed electric current, to inducea constant nominal electric current density of 90 A/mm2, based on the initial cross-sectional area of the specimen. Note that asa specimen is continuously deformed by tension, the cross-sectional area of the gauge continuously decreases. Therefore,under an electric current of constant amplitude, the true electric current density during the tension test continuously in-creases and is always higher than the constant nominal electric current density.

Specimen temperature during tensile test under pulsed electric current was measured using a FLIR-E40 infrared (IR)thermal imaging camera (FLIR, Sweden). The spatial resolution is ~0.3mm/pixel. Temperature resolutionwas less than 0.07 �C

Al-Mg-Si alloycommercial sheet (T6 temper)

530oC, 1hour in furnace thenquenched in cold water

Artificially aged(as-received)

Aging at room temperature for 4 days

Solution treated(super-saturated)

Naturally aged(T4 temper)

Fig. 1. Three types of specimens based on different heat treatments.


Fig. 2. (a) Illustration of the instrumental setup and (b) schematic illustration of the pulse pattern applied during testing. Uniaxial tensile machine is modified toinsulate it from the applied electric current. A selective pulsing pattern (r0 ¼ 90 A/mm2, td ¼ 0.5 s, tp ¼ 30 s) was applied to the specimen during plasticdeformation after yielding. A constant amplitude of electric current was applied during the deformation.


with the observation range of �20 to 650 �C. The back side of the specimenwas sprayed with black thermal paint to stabilizeits emissivity and thus to improve the accuracy of the temperature measurement. The emissivity was calibrated by separateexperiments using a K-type thermocouple.

2.3. Microstructural observation

In order to compare the grain size among different types of specimens, microstructures were acquired by FE-SEMequipped with EBSD system (FE-SEM: SU70, Hitachi, Japan and EBSD: Hikari EBSD detector with TSL OIM 6.1 software,EDAX/TSL, USA). Specimens were prepared by a standard metallographic grinding technique. After grinding and polishing,they were electropolished with 10% perchloric acid and 90% ethanol at a temperature of about �20 �C and a voltage of 20 V.For EBSD observation, the accelerating voltage was 15 kV and the working distance was 15 mm. The mapping grid was aregular square in 1 mm, and critical misorientation angle was set to 15� for grain identification.

Thin-foil specimens for TEMwere prepared bymechanical grinding followed by electropolishing in a Tenupol-3 double jetthinner (Struers, Denmark) with an electrolyte consisting of 30% nitric acid and 70% methanol at the temperature of ~20 �Cand the voltage of 6 V. Nova Nanolab 200 focused ion beam (FIB) micromachining (FEI, USA) was used to prepare the specificregion. TEM investigation was carried out in a JEM-2100F (JEOL, USA) operated at 200 kV. The chemical composition ofprecipitates was investigated by energy dispersive spectrometer (EDS, Oxford instrument, UK) in TEM.

The topography of the fracture surface was examined by using a SU 70 FE-SEM (Hitachi, Japan) operated at 15 kV. Toinvestigate the effect of electric current on aging, Vickers hardness measurements (430 SVD, Wolpert group, USA) wereconducted under 1 kg load; each specimenwasmeasured at least 10 times. Also, to measure the change of dislocation densityduring the electricallyeassisted deformation, the full width at half maximum (FWHM) of the diffraction peak was observedfrom D8-advance XRD (Bruker Miller Co., USA) using CuKa radiation source (l ¼ 0.15406 nm) operating at 40 kV. Diffractionlines were recorded in the region of 30��2q� 130� under the scan rate of 3�/min. The measured diffraction peaks were fittedwith Pearson VII function.



3. Results and discussion

3.1. Basic properties: mechanical behavior and microstructure

As expected, the engineering stressestrain curve of Non-EA tensile test shows significantly different yield stress andelongation depending on the heat treatment conditions (solution treated, naturally aged, and artificially aged) as shownin Fig. 3. The solution treated specimen showed the greatest elongation (about 20%) with a minimal yield stress amongthe three types of specimens tested. One interesting phenomenon is that, the serrations in the stressestrain curves,which are attributed to the PortevineLe Chatelier (PLC) phenomenon, were clearly observed until fracture in the solutiontreated specimen only. The yield stress of the naturally aged specimen was greater than that of the solution treatedspecimen, whereas its elongation was slightly lower than that of the solution treated specimen. The artificially agedspecimen showed the highest yield stress as well as the lowest elongation, of less than 10%, among the three types ofspecimens studied.

The grain sizes of the solution treated, naturally aged and artificially aged specimens were quite similar: 44 ± 16 mm,39 ± 14 mm, and 42 ± 15 mm, respectively, as shown in Fig. 4. Thus, the grain size appeared to have a negligible effect on thedissimilar mechanical behaviors shown in Fig. 3. It is clear that the different mechanical behaviors shown in Fig. 3 are mainlydue to the different precipitation states of the specimens caused by the three different heat treatments.

It is well known that Al-Mg-Si alloys can be strengthened by precipitation hardening during aging (Edwards et al., 1998). Ithas been reported that there is no evidence for specific precipitation immediately after solution treatment followed byquenching (Gracio et al., 2004). The dissolved solute atoms by solution treatment exist as a supersaturated state rather thanforming precipitates immediately after quenching. Through natural aging at room temperature (T4 temper) after solutiontreatment, supersaturated Mg and Si solutes form atomic clusters or GuinierePreston (GP) zones as an early stage of pre-cipitates (Murayama et al., 1998; Banhart et al., 2010).

Upon artificial aging (T6 temper), the early stage precipitates begin to develop into needle/lath-like precipitates (b00) andfinally form stable precipitates (b, Mg2Si) (Murayama and Hono, 1999). A high density of short needle-shaped b00 pre-cipitates having the <001>Al direction was observed in the artificially aged specimen (Fig. 5a). These precipitates with thelength of 30e100 nm existed inside the grain, thereby affecting hardening properties. Also, the grain boundaries weredecorated by intermetallic compounds (Fig. 5b). These intermetallic phases, having a size distribution of about150e300 nm, were coarser than the b00 precipitates. EDS analysis confirmed that its composition type was Al-Si-Cu,different from the composition of Mg2Si as a hardening phase in Al-Mg-Si alloy (Fig. 5c). It is important to note that theintermetallic phase containing Si and Cu was segregated at the grain boundary and thus, unlike the b00 precipitates, does notsignificantly affect the hardening properties of the alloy. This intermetallic compound was not observed in the solutiontreated and naturally aged specimens.

These microstructural features of Al-Mg-Si alloy suggest that the observation of the lowest yield stress in the solutiontreated specimen arose from its absence of a hardening phase. Also, the PLC phenomenon was clearly observed only in thesolution treated specimen, arising from the interaction between supersaturated solute atoms and dislocations. In thenaturally aged specimen, the increased yield stress compared to that of the solution treated specimen arose from the for-mation of the early stage of precipitates, such as atomic clusters or GP zones during the natural aging. In the case of theartificially aged specimen, tens of nanometer sized b00 precipitates (Fig. 5a) are believed to act as obstacles to dislocationmovement. As a result, the artificially aged specimen showed the highest yield stress among the three types of specimensstudied here.

0 5 10 15 20 250

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600 Artificially aged Naturally aged Solution treated

Eng.

stre

ss (M

Pa)

Eng. strain (%)Fig. 3. Engineering stressestrain curves of Al-Mg-Si alloy for artificially aged, naturally aged, and solution treated specimens.


Fig. 4. Inverse pole figure maps of (a) solution treated, (b) naturally aged, (c) artificially aged specimens for grain size determination. The grain sizes of solutiontreated, naturally aged and artificially aged specimens are 44 mm, 39 mm, and 42 mm, respectively.


3.2. Effect of electric current on uniaxial quasi-static tensile behavior

Fig. 6 presents engineering stress-strain curve with pulsed electric current (in red) compared to that without pulsedelectric current (in black). When electric current was applied to each specimen for the duration of 0.5 s during plasticdeformation, the flow stress decreased nearly instantly in all tested specimens (Fig. 6). After each pulse of electric current, theflow stress showed strain hardening until the next pulse of electric current (so called local stressestrain curve) (Roh et al.,2014). The sharp drop in stress by the application of each individual pulse of electric current has been explained as a com-bined effect of instantaneous annealing of the material by the electric current and, thermal expansion and softening due toJoule heating (Roth et al., 2008; Salandro et al., 2009; Kim et al., 2014a; Roh et al., 2014).

Since the electric current parameters of duration, period, and electric current density were fixed throughout the tensiletest, the measured temperature histories were almost the same for each specimen subjected to different heat treatmentconditions, as expected (Fig. 6, blue traces). Themeasured temperature histories in Fig. 6 shows themaximum temperature ofthe specimen in the gauge section. In each pulse period, the temperature increased instantly by Joule heating and then rapidlydecreased by air cooling until the next pulse of electric current. For all specimens, the peak temperature showed a steadyincrease due to the continuous decrease in cross-sectional area during deformation.

The electric current parameters selected in the present study led to different tensile behaviors depending on the heattreatment conditions (Fig. 6). For the solution treated specimen, the elongation under the pulsed electric current was about1.2 times greater than the elongation from Non-EA tensile test (Fig. 6a). As electric current was applied to the specimenrepeatedly during deformation, the local stressestrain curve started to deviate from the stressestrain curve from Non-EAtensile test. The peak stress of the local stressestrain curve was higher than that of the stressestrain curve from Non-EA


Fig. 5. Bright-field TEM images of precipitate dispersions in artificially aged specimen before uniaxial tension: (a) in the grain interior (needle-shaped b00 phase),including [001]Al selected area diffraction pattern; (b) at the grain boundary (coarse intermetallic compound). (c) EDS spectra of the intermetallic compound atthe grain boundary.



0 5 10 15 20 25

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Fig. 6. Engineering stressestrain curves (left axis) without (Non-EA, in black) and with (EA, in red) application of electric current to (a) solution treated, (b)naturally aged, and (c) artificially aged specimens. The temperature due to Joule heating versus engineering strain is shown below the stressestrain curve (inblue, right axis). Magnified versions of regions 1 and 2 in (a) are included to facilitate observation of the serrated flow of solution treated specimen. (Forinterpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


tensile test and the differences of peak stress between the local stress-strain curve and stressestrain curve from Non-EAtensile test increased as plastic deformation proceeded. The PLC phenomenon, which was clearly observed in Non-EA ten-sile test, became weaker and finally disappeared in the solution treated specimen at the engineering strain above 8% underthe given pulsed electric current. Magnified views of these serrations in the stressestrain curve (regions 1 and 2) are shown inthe right side of Fig. 6a.

For the naturally aged specimen, the elongation increased significantly under the pulsed electric current, by about 1.4times in comparison with the Non-EA tensile test (Fig. 6b). The local stressestrain curve also began to deviate from thestressestrain curve from Non-EA tensile test and the differences in peak stress between the local stress-strain curve andstressestrain curve from Non-EA tensile test increased. However, the peak stress of the local stressestrain curve was lowerthan that of the stressestrain curve from Non-EA tensile test, contrary to the result observed in the solution treated specimen(Fig. 6a). Also, serration in flow stress was not observed for the naturally aged specimens in both Non-EA and EA tensile tests.

It is interesting to note that the solution treated and naturally aged specimens showed similar deformation behavior at theengineering strain above 15%, when electric current was applied during plastic deformation, even though the stressestraincurves from Non-EA tensile test of solution treated and naturally aged specimens showed different mechanical behaviors inflow stress and elongation. The flow stress at the engineering strain of 15.4%, 16.7%, and 18.0% were 228 MPa, 233 MPa, and236 MPa, respectively, when electric current was applied to the solution treated specimen. In comparison for naturally agedspecimen, the values of flow stress at the same strain were 241 MPa, 242 MPa, and 243 MPa, respectively, when electriccurrent was applied. The difference of flow stress at the engineering strain above 15% between the solution treated andnaturally aged specimens was less than 5% in EA tensile test. Also, the fracture elongation during EA tensile test was alsosimilar: 23% for the solution treated specimen and 24% for the naturally aged specimen. These results indicate that the tensilebehavior of the solution treated specimen becomes gradually similar to that of the naturally aged specimen under the givenpulsing pattern.

As mentioned above, the PLC phenomenon, which was not observed in the naturally aged specimen, disappeared from thesolution treated specimenwhen it was subjected to the pulsed electric current. This disappearance of PLC represents another



aspect of the similarity in mechanical behavior between solution treated and naturally aged specimens subjected to thepulsed electric current. If supersaturated solute atoms are not present in sufficient quantity to interrupt the movement ofdislocation by the formation of precipitates, the PLC phenomenon may become weaker. Therefore, in solution treatedspecimens, the increase of flow stress compared to the Non-EA tensile test and the disappearance of the PLC phenomenonunder the pulsed electric current may be caused by the formation of early stage precipitates from supersaturated solute atomsunder the applied electric current. Note that the formation of early stage precipitates naturally decreases the quantity ofsupersaturated atoms. In other words, the solution treated specimen undergoes aging by formation of early stage precipitatesfrom supersaturated solute atoms under the given electric current applied during deformation.

Hardness test is well known method to reflect the existence of early stage of precipitation in the whole region of thespecimen statistically (Gracio et al., 2004; Banhart et al., 2010; Ozturk et al., 2010). To investigate the effect of the electriccurrent on aging, Vickers hardness test was also conducted. The Vickers hardness of the solution treated specimen beforetension was 50.5 ± 1.7 HV. At the engineering strain of 17%, owing to the accumulation of plastic deformation, the hardnessincreased to 82.8 ± 2.3 HV in the Non-EA tensile test. The hardness of a specimen strained to 17% under EA tension was97.5 ± 3.2 HV, clearly higher than that observed under Non-EA tension. This indicates that aging took place during defor-mation when the electric current was applied.

To classify the distinct effect of electric current on aging, apart from the effect of Joule heating, Vickers hardness mea-surements were performed for solution treated specimen, which had undergone the engineering strain of 17% under Non-EAtension followed by the application of one of a few different heat treatment conditions. Heat treatments were conductedusing either a furnace or a dilatometerwhich is able to control the temperature of the specimen rapidly by an induction heaterin a vacuum. The total time over 100 �C before the engineering strain of 17%was reached was about 250 s in the EA tensile test(Fig. 7a, red line); accordingly, the holding time for the furnace heat treatment of the specimen strained to 17% was set to250 s. The temperatures for heat treatment were chosen as 100 �C, 150 �C, and 200 �C (Fig. 7a, green lines). In the case of heattreatment using the dilatometer, the same temperature history in the EA tension test was applied (Fig. 7a, blue line).

No increase in hardness was observed after the heat treatment at 100 �C for 250 s, compared to the results of hardness testconducted before the heat treatment. This suggests that the heat treatment condition, 100 �C for 250 s, was insufficient toobtain an aging effect. However, it can be seen that the hardness increased when the treatment temperature was elevated to150 �C or 200 �C. Especially, the hardness of the specimen subjected to the heat treatment at 200 �C (97.4 ± 2.7 HV) wasalmost the same as that of the specimen strained to 17% in the EA tension test (97.5 ± 3.2 HV). Note that this heat treatmentwas conducted at much higher temperature compared to the temperature history of the specimen during the EA tension test.The hardness of the induction heat treated specimen by dilatometer was 88.5 ± 4.2 HV, much lower than that of the specimenstrained to 17% under the pulsed electric current, even though the temperature history during the induction heat treatmentwas quite similar to that during the EA tension test. It is noted here that, in the hardness test, the heat treatments wereconducted after specimens were pre-strain to 17%, while in the specimen subject to the electric current, the joule heatingeffect takes place at the same time as the deformation occurs. Based on these results of the heat treatments imposed on thespecimens strained to 17% in the Non-EA tension test, it is suggested that aging is likely accelerated under the applied electriccurrent with a distinct effect of Joule heating.

In artificially aged specimen, the flow stress under the electric current decreased compared to the Non-EA tensile test, atrend similar to that observed in naturally aged specimens (Fig. 6c). However, in contrast to the two other heat treatments(solution treatment and natural aging), the fracture elongation of 7.9% under the electric current decreased compared to thatof 9.3% from Non-EA tensile test. The reason for the earlier fracture of the artificially aged specimen in the EA tension test willbe discussed in detail in Section 3.4.

3.3. Annealing during EA tension

In author's previous study, it was reported that Al-Mg alloy was annealed due to the annihilation of dislocations when apulsed electric current was applied during deformation; two different effects, a Joule heating effect and a distinct electriccurrent effect (i.e., an electric currenteinduced annealing effect), were suggested to explain this annealing (Kim et al., 2014a).In the present study on Al-Mg-Si alloy, the flow stress under electric current decreased compared to the Non-EA tensile test inboth naturally aged and artificially aged specimens (Fig. 6b and c). It is reasonable to expect that, like the result observedpreviously in the Al-Mg alloy, annealing should also occur in the Al-Mg-Si alloy under the pulsed electric current duringdeformation. The annealingmight also occur in the solution treated specimen under the applied electric current, even thoughthe flow stress under the electric current increased compared to the baseline due to the formation of early stage of pre-cipitation. Therefore, it should be checked whether the annealing would take place in these three types of specimens.

It is known that the X-ray diffraction peaks broadenwhen lattice defects such as dislocations are present in large amountsin the crystal (Wilkens,1970; Ung�ar, 2001). The increased FWHM (i.e., FullWidth at Half Maximum) indicates microstructuralbroadening due to lattice defects under the same instrumental condition and finite crystallite size. In the present study, sincethe instrumental effect could be assumed to be the same for every measurement due to the identical operational conditions,and since the finite crystallite size was also quite similar under the Non-EA or EA tensile tests conducted at the same strain,the FWHMwas closely related to the density of lattice defect including dislocation in the specimen. The FWHMwasmeasuredfor specimens subjected to Non-EA and EA tensile tests under the engineering strains of 6% and 14% (Fig. 8).


0 100 200 300 400 5000

100

200

300

400

200oC150oC

Joule heating in EA tension Furnace heat treatment Induction heat treatment

Tem

pera

ture

(o C)

Time (sec)

100oC

Solution treated

70

80

90

100

110

90-227oCNon-EAtension

EA tension 200oC

150oC

HV

1

100oC

Solution treated *Before tension : 50.5 HV1

Eng. strain=17% Eng. strain=17%(Non-EA tension)

+ Furnace

Eng. strain=17%(Non-EA tension)

+ Induction

(a)

(b)

Fig. 7. (a) Temperature histories by Joule heating during EA tension (in red), furnace heat treatment (in green) and induction heat treatment (in blue); (b) Vickershardness (HV) of solution treated specimens under the engineering strain of 17% from Non-EA and EA tension and after each heat treatment using specimenstrained to 17% from Non-EA tension. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


Line broadening was observed (i.e. FWHM increased) in all deformed specimens after both Non-EA and EA tensile tests.This is explained by the accumulation of plastic deformation in the specimens. Note that the FWHMs of the specimenssubjected to the EA tensile test were always lower than those of specimens subjected to the Non-EA tensile test. The dif-ference in FWHM between specimens subjected to the Non-EA and EA tensile test was significantly increased in the region oflarger deformation (Fig. 8aed). This suggests that the specimens were annealed due to the annihilation of dislocations whenthe pulsed electric current was applied during deformation. Note that the annealing was still observed in the solution treatedspecimen (Fig. 8a and b), even though the flow stress under the pulsed electric current (Fig. 6a) was higher than that from theNon-EA tensile test. The difference in FWHM between the Non-EA and EA tension of the selected alloy is smaller than thatobtained from previous work in Al-Mg alloy (Kim et al., 2014a). This can be explained by that the FWHM is also affected by theprecipitation as well as the dislocation density during EA tension.

3.4. Effect of electric current on fracture behavior

Fractographs were obtained for all specimens subjected to both the Non-EA and EA tensile tests (Fig. 9). The entire fracturesurfaces of solution treated and naturally aged specimens were covered with dimples after the Non-EA and EA tests(Fig. 9aed). However, in artificially aged specimens, brittle intergranular separation was observed after fracture in both theNon-EA and EA tensile tests (Fig. 9e and f). The feature of intergranular separation in the artificially aged specimens wascaused by the formation of voids around preexisting intermetallic compounds along the grain boundaries (Fig. 5b). Note thatintergranular separation with river line patterns in grain was clearly observed in the EA tensile specimen (Fig. 9f). Theseresults suggest that the formation of microvoids around precipitates at the grain boundary is accelerated by the electriccurrent during deformation. These microvoids may considerably reduce the bonding force between particles and the matrix,


Fig. 8. FWHM profiles of (a,b) solution treated; (c, d) naturally aged and (e) artificially aged specimens under the engineering strains of 6% and 14%.


consequently allowing the formation of river line patterns throughout the grain interior as crack paths. This may induceearlier fracture in the artificially aged specimen subjected to the pulsed electric current.

To observe the microvoids around precipitates, additional microstructural observations of the artificially aged specimensafter the EA tensile test were performed using SEM and TEM. Themicrovoids were observed to exist along the grain boundaryand around precipitates near the fracture surface. In the region right below the fracture surface shown in Fig. 9f, the formationof microvoids around precipitates was clearly observed (Fig. 10c).

3.5. Dislocation density based constitutive model: Non-EA loading

Constitutive models based on crystal plasticity to describe the plastic deformation of metallic materials have gained lots ofattention in the past few decades (Kocks and Mecking, 2003). The work hardening of aluminum alloys was successfullydescribed by Kocks (1976), (2001); Kocks andMecking (2003) andMecking and Kocks (1981); Mecking et al., (1986), (1996) byusing an average dislocation density approach. The average dislocation density r is a structure dependent variable and itsevolutionwith strain, temperature and strain rate describes the complete work hardening of metals, at least in average sense.One of the advantages of the approach compared to other phenomenological strain hardening models is that the stress-strain


Fig. 9. Fracture surfaces after Non-EA and EA tensile test of solution treated, naturally aged and artificially aged specimens.


curve is related to the physical deformationmechanisms. Therefore, the rate controllingmechanisms such as dislocation glideand twinning can be superposed for complete description of the macroscopic mechanical behavior. In the present work, thegeneralized Kocks-Mecking model following Estrin and Mecking (1984); Estrin and Kubin (1991); Estrin et al. (1998); Krauszand Krausz (1996) is used to describe the Non-EA stress-strain curve of solution treated, naturally and artificially agedspecimens. In the later section, this model will be extended to include the electrical pulse effect.


Fig. 10. Microstructure near the fracture surface of artificially aged specimen after EA tension. (a,b) SEM images showing microvoids (a) along the grain boundaryand (b) around precipitates. (c) Bright-field TEM image of microvoids (marked with red arrow) around precipitates right below the fracture surface. Magnifiedversions of regions 1 and 2 in (c) indicate the formation of microvoids (red arrow) around precipitates. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)


The simplest form of the hardening model assumes that the strain hardening is primarily due to the dislocation-dislocation interactions (Estrin et al., 1998; Kocks and Mecking, 2003; Krausz and Krausz, 1996), which is usually valid inthe case of coarse grainedmaterials withmean-free path for dislocationmovement. For plastic deformation of polycrystal andsingle crystal, the stage II work hardening exhibits highest rate of hardening due to immobilization of mobile dislocations byobstacles. As the plastic deformation continues, recovery of dislocations occurs during stage III, which softens the material.The flow stress, s and the evolution of dislocation density, r describing stage II and stage III hardening are given as

s ¼ bs � _ε

_ε0

�1=m

(1)

in which bs ¼ M a G bffiffiffir

pis the microstructure parameter. And, its evolution is expressed as

drdε

¼ MðK1ffiffiffir

p � K2 rÞ (2)

where s, G, b, r, and _ε refer to the flow stress, shear modulus, the magnitude of burgers vector, dislocation density and strainrate, respectively. a, _ε0, and m are material parameters.

The Taylor factor M relates the polycrystal and single crystal deformation. The factor M is texture-dependent and variesduring deformation (Estrin et al., 1998; Mecking et al., 1996). However, the variation is small and is usually assumed to be aconstant for the simplicity of modelling (Krausz and Krausz, 1996). The constants K1 and K2 are used to describe dislocationgeneration and recovery, respectively. It is known that the constant K2 is dependent on both strain rate and temperature(Estrin et al., 1998; Kocks and Mecking, 2003).

The stress-strain relation using Eqns. (1) and (2) is best suited for single phase coarse grained materials without pre-cipitates. The principal advantage of the above framework is the superposition of concurrent deformation mechanisms usingappropriate mathematical models (Fazeli et al., 2008). Following this principle, superposition of precipitation hardeningmodels due to coherent and non-coherent precipitates have been successfully developed for precipitation hardened



aluminium alloys (Estrin, 1996; Fazeli et al., 2008; Myhr et al., 2010; Simar et al., 2007; Zolotorevsky et al., 2009). Estrin et al.(1998) extended the above dislocation density model for precipitation hardening by Orowanmechanism inwhich the mobiledislocations bow around the hard precipitates dispersed at a mean spacing between precipitates D along the glide plane(Krausz and Krausz, 1996). The above equations can be further modified as follows

s ¼ ðbs þM G c b=DÞ�

_ε

_ε0

�1=m

(3)

The evolution of dislocation density is given by

drdε

¼ MðKD þ K1ffiffiffir

p � f K2 rÞ (4)

where KD ¼ 1/bD and c is a material constant. In this model, the mean spacing between precipitates, D, is assumed to beconstant during the plastic deformation, indicating that the mean distance between the precipitates are less affected bystrain. The flow stress is further increased due to the storage of dislocations at the particle interface. The storage of dislo-cations reduces the recovery during stage III hardening. As a result, the material constant, K2 will decrease during precipitatehardening. An additional coefficient f is defined to scale down the value of K2 in the presence of precipitates (Krausz andKrausz, 1996). The maximum value of f is 1.0.

It is surmised that the Non-EA tensile behavior of the solution treated specimen can be described using Eqns. (1) and (2)assuming only dislocation-dislocation interactionwithout any precipitate hardening, as confirmed in the experiments. In thecase of the solution treated specimen, however, there exists additional hardening effect due to supersaturated solute atoms,which can offer resistance to deformation. Similarly, in the naturally aged specimen, there could be shearable precipitates,which cannot be modelled using the Orowan bowing mechanism for non-shearable particles described by Eqns. (3) and (4).The artificially aged specimen is characterized with intermetallic Al-Si-Cu compounds, thus the role of which in resisting thedislocation motion will be different from that of the b'' precipitates. Moreover, the dispersion of high density precipitates cancontribute further to the stress concentration. While each effect mentioned above may need separate description ofconstitutive behavior, it is preferable to combine all these effects into a single equation. Following modification is thereforeproposed, in which an additional stress term sSP is incorporated phenomenologically to the microstructure parameter suchthat bs ¼ M a G b

ffiffiffir

p þ sSP . Note that sSP can account for the effects of solute, shearable particle, intermetallic compounds, andstress concentration rather implicitly due to excessive precipitates. A net effect of all of these is attributed to increase in flowstress. The flow stress can then be given as

s ¼ ðbs þ sSP þM G c b=DÞ�

_ε

_ε0

�1=m

(5)

The material constants c ¼ KD ¼ 0 in the solution treated specimen under Non-EA tension, which is assumed to be freefrom precipitates. The parameters of sSP, D, f, and K2 vary with temperature and the application of electric current, which willbe discussed in the ensuing section (Table 1).

The uniaxial Non-EA tensile test for solution treated, naturally aged, and artificially aged specimens are described usingEqns. (4) and (5). The engineering stress-strain curve shown in Fig. 3 is converted to true stress-true strain curve and theelastic region is ignored for comparison. The material constants in the Non-EA tensile test are identified by fitting theexperimental data using the commercially available MATLAB software and listed in Tables 2 and 3. The parameter identifi-cation procedure is similar to that adopted in other similar work using dislocation density based models (Babu and Lindgren,2013; Estrin, 1996; Lindgren et al., 2008). The true stress-true plastic strain curve of the Non-EA tension predicted using themodel in Eqns. (4) and (5) correlates very well with the experimental data as shown in Fig. 11.

As mentioned earlier, the solution treated specimen is assumed to be free from precipitates and hence the materialconstants c ¼ 0 and f ¼ 1 in Table 3. The constant D indicating mean spacing between precipitates is comparatively lower forartificially aged specimen than naturally aged specimen. As a consequence of precipitate concentration, the storage rate ofdislocation density increases and the recovery rate decreases. The scaling constant for the recovery term, f in Eqn. (4) is lessthan unity for both the naturally and artificially aged specimens, with the least value for the naturally aged specimen. Thematerial parameters fitted to the experimental curves validate that the proposed constitutive model can explain the phys-ically driven nature of deformation mechanism in the existence of precipitates and their interactionwith mobile dislocations.

3.6. Dislocation density based constitutive model: extension to EA uniaxial loading

A hypothetical ‘global stressestrain curve’ describing the upper boundary of the ratchet shape stressestrain curve in EAtension up to the point of necking can be defined by connecting the peak stress of local stressestrain curves (Roh et al., 2014).In the present study, a modified constitutive model for the global stress-strain curve is suggested to describe the EA tensilebehavior using the proposed model in the previous Section 3.5. The pulsing condition including electric current density,


Table 1Material parameters used in the constitutive model.

Parameter Description

s Flow stressbs Microstructural parameter related to the long range internal stresssSP Flow stress component due to the shearable particles. The source of these arise from different mechanisms and depends upon the prior heat

treatment._ε Strain rater Average dislocation densityM Taylor factora, _ε0 Material constants of work hardeningm Exponent describing the strain rate dependenceG Shear modulusb Burgers vectorc Material constant to account for the work hardening offered by precipitatesD Mean spacing between the precipitateK1 and K2 Material constants to describe stage II and stage III work hardeningK20 and n Coefficient and exponent to describe the temperature dependence of ‘K2’ with strain rate and temperatureKD Material constant to account for the influence of precipitates in the evolution of dislocation densityf Scale factor to account the effect of precipitates in recovery of dislocation. 0 < f < 1. f ¼ 1 for solution treated condition without precipitatesa0 Athermal stress coefficient of the constant, ‘a’s Temperature and strain rate dependent scaling factor of ‘a’l1, and l2 Coefficient and exponent of the mathematical function assumed to describe the temperature dependence of the scaling factor, ‘s’.

Can be estimated from the variation of yield strength with temperature.x1 and x2 Coefficient and exponent of the mathematical function assumed to describe ‘n’. The constants can be estimated from the strain hardening

rates of stress-strain curves at different temperatures.G Material constant correlating the density of shearable particles in the matrix. This is dependent upon the prior heat treatment.j and C Material constants to describe the temperature effect of work hardening contributed by shearable particles. The constant ‘C’ can be calculated

by extrapolating the temperature dependent ‘sSP’ to the minimum value of temperature range.Dc, Ds Intercept and slope of the assumed linear evolution equation of precipitates with temperaturefc, fs Intercept and slope of the assumed linear evolution equation of precipitates with temperature


duration and period is set to identical to the solution treated, naturally aged, and artificially aged specimens. Therefore, thetemperature profile as a function of strain extracted at each peak stress of local stress-strain curve is used as an input forpredicting the mechanical behavior. Note that the effect of electric current may be indirectly incorporated in each materialparameter through temperature effect. Experimental results in titanium (Magargee et al., 2013) and magnesium alloys (Liuet al., 2016) indicate that the stress strain behavior under uniaxial tensile test subjected to constant electric current issimilar to that at elevated temperature Therefore, the material parameters in the proposed model combines the effect of boththe temperature and electrical current. Further work is however needed to separate the contribution of each materialparameter for electrical effect in the mechanical behavior.

The flow stress and the hardening rate are influenced by both temperature and strain rate. Kocks and Mecking (2003),showed that the constant, a is temperature and rate dependent as given by

a ¼ a0:s ð _ε; TÞ (6)

where a0 is an athermal material constant and s is a scaling factor, which is a function of both temperature and strain rate. At aconstant strain rate, s may also be affected by application of electric current with temperature effect indicating softening. Inthe present work, pulsing condition is identical for the solution treated, naturally aged and artificially aged specimens.Therefore, s is approximated so as to yield the following dependence with temperature at a given strain rate and pulsingpattern,

ðaÞ _ε ¼ a0:l1Tl2 (7)

where s ¼ l1Tl2 , l1, and l2 are material constants, which can be identified by calibrating the initial yield strength at differenttemperature. However, the temperature dependence of parameter may include a distinct electric current effect indirectly.

As discussed in Section 3.5, the stage III hardening characterized by K2 is also influenced by strain rate and temperature(Krausz and Krausz, 1996)

K2 ¼ K20:

_ε

_ε*0

!�1=n(8)

where K20, _ε*0, and n are material constants. As discussed in Section 3.3, annealing takes place by both thermal and electric
current effect. Therefore, parameter K2 incorporates a distinct electric current effect with the thermal effect. In the presentwork, the strain rate and pulsing pattern are set to identical to three types of specimens, so the parameter n is assumed to be afunction of temperature at low temperature region (typically T<0.5 Tm). Similar to a, it is proposed to model n as

Table 2Material constants of Al-Mg-Si alloy obtained by optimizing the experimental data.

Condition M a G (MPa) b (mm) m _ε0ðs�1Þ r0

All cases 2.71 0.488 27,000 2.86E-07 40.98 3.24E-06 3.77Eþ07

0.00 0.05 0.10 0.15 0.200

100

200

300

400

Artificially aged Naturally aged Solution treatedTr

ue st

ress

(MPa

)

True strain

Symbol: experimental dataLine: fitting result

Fig. 11. Comparison of experimental stress-strain curve (symbol) and predicted stress-strain curve (line) based on constitutive model for solution treated,naturally aged and artificially aged specimens under Non-EA tension.


n ¼ x1:nTx2o

(9)

The constants x1 and x2 can be optimized based on the complete stress-strain curve at different temperatures. Thehardening rate or the slope of the stress-strain curve could be used to estimate x1 and x2.

In EA tensile test, the dynamic recovery increases leading to higher value of the material constant K2 compared to Non-EAtensile test due to a Joule heating effect and a distinct electric current effect for each type of specimen. Also, the shearresistance offered by the coherent and shearable precipitates in the matrix may be affected under a pulsed electric current byboth thermal and a distinct electric current effect. Therefore, the stress term sSP in Eqn. (5) will decreasewith the temperaturerise and application of electric current. Since sSP represents multiple mechanisms such as solute hardening, shearable pre-cipitates, and stress concentration rather implicitly due to excessive precipitates, sSP was obtained at different temperaturesby curve fitting and an empirical equation was used for modelling. From the results described in subsequent sections, thefollowing relation is found to be suitable for all the three types of specimens, namely, solution treated, naturally and arti-ficially aged specimens,

sSP ¼ G sinðT :jþ CÞ (10)

in which G, j and C are the optimized constants.From the experimental data, it was inferred that precipitates are formed in the solution treated specimen during the EA

tension test. A similar effect contributing to increase in the precipitate density is also expected in the naturally aged specimen.This will decrease the mean spacing between precipitates, D, thereby reducing the mean free path available for dislocationmobility. The dislocations stored at the interface increase with precipitate density leading to reduction in the recovery rate,accounted by the scaling factor f. Both the electric current and the temperature increase are responsible for this precipitationformation. In the identical pulsing condition for the three types of specimens, the evolution of precipitates under the pulsedelectric current is modelled as a function of temperature like other parameters of s and n. For a given range of temperature, D,and f are approximated to vary linearly as

D ¼ Dc þ DsT and f ¼ fc þ fsT (11)

where the subscript ‘c’ and ‘s’ in Eqn. (11) respectively refer to the intercept and slope of the linear fit.Since both Ds and fs decrease with temperature rise and application of electric current, the slope Dc and fc would be

negative. The material constants, Dc, Ds, fc, and fs are identified iteratively. Note that there are no constraints applied for thedetermination of these material parameters, but rather their final values will be obtained from the nature of physically drivenconstitutive models. Future investigations on the contribution of electrical effect to individual mechanism will howeverenable accurate prediction of these constants. The parameters for the three types of specimens are listed in Table 4. In Fig. 12,


Table 3Parameters for three types of specimens in uniaxial Non-EA tensile behavior obtained by optimizing the experimental data.

Condition K1 K2 c sSP (MPa) D f

Solution treated 1.78Eþ05 8.18 1.8 14.97 N.A N.ANaturally aged 10.13 62.72 9.91E�03 0.86Artificially aged 26.75 192.89 6.60E�03 0.75


D and f are plotted for each specimen in the range of observed temperature under a EA tension. As observed in Fig.12, the leastvalues of ‘D’ and ‘f’ for a given temperature (and hence electric current) is for the aged condition and the maximumvalues arefor solutionized condition. While identifying the material parameters, the aged condition was first identified by curve fittingas ‘D0 and ‘f’ remain invariant with temperature. Later the constants for solutionized case were identified by correlating thestress at different temperatures and ensuring that the values of ‘D’ and ‘f’ are not less than the aged condition. The naturallyaged condition was identified finally by varying the parameters between the range of solutionized and age hardenedcondition.

As discussed in Sections 3.2 and 3.3, the flow stress and hardening behavior in EA tension are simultaneously influenced byboth a Joule heating effect and a distinct electric current effect, which results in varying three components; i.e., the dislocationdensity (parameters, K2 and a), solute hardening, shearable precipitates, and stress concentration rather implicitly due toexcessive precipitates (sSP) and the non-shearable precipitates (D and f). The resultantmechanical behavior depends upon therelative contribution from each of the above phenomena.

It was mentioned in Section 3.1 that artificial aging forms stable precipitates. It is therefore assumed that the averagetemperature rise from room temperature to around 80 �C will not further contribute to the precipitate density; D and f areassumed to be constant (Ds ¼ fs ¼ 0) in the EA tension for the artificially aged specimen. The material constants of K2 (x1 andx2) and sSP (G, j and C) are iteratively determined. Among these constants, G would vary for the solution treated, naturallyaged and artificially aged specimens whereas the constants x1 , x2, j and Cwouldn't. The constants, x1 and x2 accounts for thetemperature dependent strain hardening due to dislocation density. Since the dislocation mechanism is common to all theheat treatment cases, the constants remain invariant. At a given temperature, the resistance offered by the shearable particlesdepend only upon the their initial population (Fazeli et al., 2008; Guo and Sha, 2002; Khan et al., 2008; Wu and Ferguson,2009; Zolotorevsky et al., 2009). As temperature rises, their resistance decreases. The population of shearable particles isbelieved to arise from multiple mechanisms that are dependent upon the thermomechanical history (Myhr et al., 2010).Therefore, the constant, Gwhich controls the initial population is dependent on the prior heat treatment. The constants j andC on the other hand represent the loss of resistance offered by shearable particles with temperature. The trend is expected tobe same irrespective of prior heat treatment and hence remain constant. The above assumption is supported by priorexperimental studies in Al-Mg-Si studies indicating that the work hardening contribution by shearable particles does notchange between the as-quenched and naturally aged conditions (Myhr et al., 2010). The stress-strain behavior of the arti-ficially aged specimen is predicted using these constants, which is well described in Fig. 13.

In the solution treated specimen, it was pointed out in Section 3.2 that the mechanical behavior after around 15% engi-neering strain is similar to that of the naturally aged specimen suggesting gradual formation of precipitates under the EAtension. The stress-strain curve predicted by ignoring the precipitate formation is shown in Fig. 14a. Appreciable differencebetween the experimental and predicted results is noted. The predicted data begins deviating from the experimental ob-servations at the engineering strain above 8% in Fig. 14a, which corresponds to approximately 65 �C. The difference increasedsteadily with strain suggesting continuous formation of precipitates which harden the specimen. Therefore, the solutiontreated specimen is furthermodified for precipitate formation once the temperature reached 65 �C. Unlike the artificially agedspecimen with stable precipitates, the precipitate density continues to increase which reduces D and f by applying electriccurrent. The rate of formation of early stage precipitates is expected to be high in solution treated specimen due to the ex-istence of supersaturated solute atoms. This is well described by the value of Ds and fs in the solution treated specimen, whichis the steepest among the three types of specimen, as shown in Fig. 12. The thermal and electric current-induced softeningdue to annihilation of dislocation is opposed by the thermal and electric current-induced hardening due to precipitate for-mation. Also, the precipitate hardening increases with strain due to formation of new precipitates in EA tension. Byconsidering both annealing and precipitation hardening due to Joule heating and distinct electric current effect, the predicteddata is found to correlate very well with the experimental data as shown in Fig. 14b.

Table 4Parameters for three types of specimens in uniaxial EA tensile behavior obtained by optimizing the experimental data.

Condition a K2 sSP D f

a0 l1 l2 K20 x1 x2 G j C Dc Ds fc fs

Solution treated 0.562 1 �1.25E�02 13.8 0.15 0.75 15 8.15E�03 18.1 6.14E�02 �1.34E�04 1.72 �2.29E�03Naturally aged 17 63 1.30E�02 �1.04E�05 0.93 �2.29E�04Artificially aged 45 193.5 6.60E�03 0 0.75 0


0 25 50 75 100 125 1500.005

0.010

0.015

0.020

0.025

Solution treated Naturally aged Artificially aged

Mea

n sp

acin

g be

twee

n pr

ecip

itate

s, D

Temperature (oC)

EA tension

0 25 50 75 100 125 1500.7

0.8

0.9

1.0

1.1

Solution treated Naturally aged Artificially aged

Coe

ffic

ient

, f

Temperture (oC)

EA tension

(a)

(b)

Fig. 12. Parameters of (a) mean spacing between precipitates, D and (b) coefficient, f for solution treated, naturally aged and artificially aged specimens in EAtension.


The thermal and electric current-induced annealing due to annihilation of dislocation and hardening due to precipitateformation are also observed in the naturally aged specimen. However, by the prior existence of precipitates, the formation ofnew precipitates in the naturally aged specimen is not as rapid as that in the solution treated specimen. This is evident from

0.000 0.025 0.050 0.075 0.1000

100

200

300

400

500

600

Non-EA tension (Exp.) EA tension (Exp.) EA tesnsion (Predicted)

True

stre

ss (M

Pa)

True strain

Artificially aged

Fig. 13. Comparison of experimental stress-strain curve (in red) and predicted stress-strain curve (in blue) based on modified constitutive model for the arti-ficially aged specimen under EA tension. Non-EA stress-strain curve is shown in dotted line. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)



the value of Ds and fs which gradually reduced from the solution treated specimen to the artificially aged specimen, as shownin Fig. 12. Therefore, the contribution of additional hardening by the formation of precipitation under the pulsed electriccurrent is lower than that of the solution treated specimen, resulting in an overall softening. When comparing the Non-EAand EA tensile behavior, the temperature remains almost constant in the Non-EA tensile test whereas the temperaturevaries in the EA tensile test. The parameters of D and f are plotted with true strain for the naturally age specimen, as shown inFig.15. The parameters ofD and f in the EA tension decrease continuously with strain and these are always lower than those inthe Non-EA tension. It is evident that precipitates are formed during the EA tensionwhich induces the reduced value of D andf compared to the Non-EA tension. The predicted result for the naturally aged specimen in comparisonwith the experimentaldata is shown in Fig. 16.

The constitutive model developed in the present work is flexible to accommodate a wide range of precipitation hardeningmaterials subjected to pulsed electric current. The proposed model can be integrated with the generalized plasticity modelsused in finite element method. In general, many classical models use the Swift or Voce hardening laws to describe theeffective stress-strain curve. The use of dislocation density models have been demonstrated in literature (Barlat et al., 2011),and the present model can be used to extend the application to electroplasticity. The model can also be used for the crystalplasticity based simulations of representative volume element which are increasingly adopted to predict the macroscopicbehavior from single crystal plasticity calculations (Ghorbani Moghaddam et al., 2016; Kim et al., 2013, 2012; Mareau andDaymond, 2016). The anisotropy induced by crystallographic texture in sheet metals can be incorporated by combiningthe model with a suitable anisotropic yield criterion, as demonstrated elsewhere (Barlat et al., 2011; Lee et al., 2013).

A further quantitative analysis to distinguish the distinct electric current effect form Joule heating effect in annealing andprecipitate formation for age hardening alloy under the EA tensile test is beyond the scope of the present study and will bereported as results of a separate study.

0.00 0.05 0.10 0.15 0.20 0.250

100

200

300

400

500

Non-EA tension (Exp.) EA tension (Exp.) EA tesnsion (Predicted:

with considering aging)

True

stre

ss (M

Pa)

True strain

Solution treated

0.00 0.05 0.10 0.15 0.20 0.250

100

200

300

400

500

Non-EA tension (Exp.) EA tension (Exp.) EA tesnsion(Predicted:

without considering aging)

True

stre

ss (M

Pa)

True strain

Solution treated(a)

(b)

Fig. 14. Comparison of experimental stress-strain curve (in red) and predicted stress-strain curve (in blue) based on modified constitutive model for the solutiontreated specimen under EA tension; (a) ignoring early stage precipitation, (b) incorporating early stage precipitation. Non-EA stress-strain curve is shown indotted line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)



4. Conclusions

The electric currenteinduced deformation behavior of Al-Mg-Si alloy was investigated by uniaxial tension combined withsubsequent microstructural observation using SEM, XRD, and TEM. Three heat treatment conditions were considered: so-lution treatment, natural aging, and artificial aging. In the solution treated specimen, elongation and flow stress increasedwhen pulsed electric current was applied during plastic deformation; also, the PortevineLe Chatelier (PLC) phenomenon,which was clearly observed in the tensile test without electric current, nearly disappeared when the pulsed electric currentwas applied during deformation. In the naturally aged specimen, the elongation increased drastically and the flow stressdecreasedwhen the pulsed electric current was applied during deformation. In the artificially aged specimen, both elongationand flow stress decreased under the pulsed electric current. From XRD analysis, it was observed that thermal and electriccurrenteinduced annealing occurred in all specimens subjected to the pulsed electric current during deformation. Also, theresult of hardness analysis suggests that in a manner distinct from the effect of Joule heating, the pulsed electric currentaccelerated the formation of early stage of precipitation from a supersaturated state, thereby causing increased flow stressand disappearance of the PLC phenomenon in the solution treated specimen. In addition, the pulsed electric current mayaccelerate the formation of microvoids around the precipitates. It may induce earlier fracture in the artificially aged specimen,even though the current also causes thermal and electric currenteinduced annealing. These experimental observationsmightbe related to the hypothesis that electric current enhances atomic diffusion (Bertolino et al., 2001; Samuel and Bhowmik,2010; Kim et al., 2014a).

A constitutive model based on dislocation density model and precipitation hardening model is proposed to describe theuniaxial tensile behavior for the age hardening alloys. Based on experimental findings in the EA tensile test, the proposedconstitutive model in uniaxial tensile test is modified to describe the upper boundary of the ratchet shape stress-strain curveunder a pulsed electric current. Thermal and electric current-induced annealing with precipitation hardening is consideredsimultaneously in the modified constitutive model. Phenomenological descriptions of each parameter are demonstratedconsidering the microstructural features observed in experimental data. The modified model is capable of predicting theexperimental results very well.

0.00 0.05 0.10 0.15 0.20 0.250.0085

0.0090

0.0095

0.0100

0.0105

0.0110

Non-EA EA

Mea

n sp

acin

g be

twee

n pr

ecip

itate

s, D

True strain

Naturally aged

0.00 0.05 0.10 0.15 0.20 0.250.83

0.84

0.85

0.86

0.87

0.88

Non-pulsed Pulsed

Coe

ffic

ient

, f

True strain

Naturally aged

(a)

(b)

Non-EAEA

Non-EAEA

Fig. 15. Parameters of (a) mean spacing between precipitates, D and (b) coefficient, f for naturally aged specimen under Non-EA and EA tension.


0.00 0.05 0.10 0.15 0.20 0.250

100

200

300

400

500

Non-EA tension (Exp.) EA tension (Exp.) EA tesnsion (Predicted)

True

stre

ss (M

Pa)

True strain

Naturally aged

Fig. 16. Comparison of experimental stress-strain curve (in red) and predicted stress-strain curve (in blue) based on modified constitutive model for the naturallyaged specimen under EA tension. Non-EA stress-strain curve is shown in dotted line. (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)


The present study provides important insights into electric currenteassisted forming. A positive aspect of applying electriccurrent is that it induces recovery by both thermal and electric currenteinduced annealing. This can enlarge the capacity fordeformation. Also, electric currenteassisted aging occurs during deformation more rapidly and at lower temperaturescompared to conventional aging. However, electric current can accelerate the formation of microvoid around particles,resulting in earlier fracture as a negativeway in formability. Therefore, to obtain enhanced formability without degradation ofmechanical properties, electrical pulsing parameters should be carefully designed to include consideration of the micro-structural features.

Acknowledgement

HNH and MJK were supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Sci-ence, ICT and Future Planning (MSIP) (NO. NRF-2015R1A5A1037627) and Technology Innovation Industrial Program fundedby the Ministry of Trade, Industry and Energy, Republic of Korea (Grant no. 10052779, Development of Car Body Modulari-zation Technology using Advanced Cold Forming and Welding Technologies of Low Density GIGA Grade Light Steel Sheets).STH was supported by the IT R&D program of MOTIE/KEIT (10044807) and the National Research Foundation of Korea Grantfunded by the Korean Government (NRF-2013R1A1A2010145). KH would like to acknowledge the support from IIT Delhi'sinitial faculty grant. . MGL appreciates the supports by the National Research Foundation of Korea (NRF) Grant funded by theKorea government (MSIP) (Nos. 2012R1A5A1048294) and (NRF-2014R1A2A1A11052889).

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