Improvement of AA5052 Sheet Properties by Electromagnetic Twin-Roll Casting

Int J Adv Manuf Technol DOI 10.1007/s00170-015-7963-8

ORIGINAL ARTICLE

Improvement of AA5052 sheet properties by electromagnetic twin-roll casting

J. T. Li1,2 & G. M. Xu1 & H. L. Yu2 & G. Chen1 & H. J. Li2 & C. Lu2 & J. Y. Guo3

Received: 6 April 2015 /Accepted: 11 October 2015 # Springer-Verlag London 2015

Abstract Electromagnetic fields were used in twin-roll cast- 1 Introduction ing (TRC) of aluminum alloy 5052 (AA5052) for improvement of the microstructure and mechanical properties. A static Twin-roll casting (TRC) is proposed as an alternative to con- magnetic field induces an inhibiting effect on the melt in the ventional direct chill (DC) casting followed by hot rolling, a cast-rolling area and reduces diffusion of the solutes. It also proven technology for economical production of thin alumi- results in more nucleating opportunities and less segregation, num sheets directly from the melt [1–3]. TRC is a shorter thus enhancing the mechanical properties. However, the static process route that combines casting and dynamic hot defor- magnetic field does not change the orientation of crystal mation in a single step and is suitable for the production of thin growth and columnar crystals still exist in microstructure. sheets (mm gauge). The method involves pouring the melt On the other hand, an oscillating magnetic field can refine into the gap between two rotating and water-cooled cylindrical the suspended particles and induce strong convection. This rollers. The metal solidifies just before reaching the bite of the leads to more uniform distribution of temperature and solute rollers and is then rolled as it passes through the rollers. Com- elements, simultaneously increasing nucleating opportunities pared with conventional DC casting, the TRC technique can and decreasing segregation, thereby enhancing the mechanical lead to reduced capital and operating costs, less energy con- properties. An oscillating magnetic field also inhibits the ori- sumption, and reduced scrap rate. entation of crystal growth and makes finer and equiaxed In the TRC process, several methods have been used for grains. controlling the microstructure and thus the mechanical properties. Berg et al. [4] accomplished gauge reduction from 5 to 1.9 mm. The thicker 5-mm strip did indeed show the typical Keywords AA5052 . Twin-roll casting . Segregation . dual-grain microstructure expected of TRC material in the as- Inhibiting effect . Oscillating effect cast state. However, the 1.9-mm strip exhibited purely equiaxed grains finer in size as compared to the 5-mm strip. No cell structure region was seen within the grains, and solid- * G. M. Xu ification was apparently completed by equiaxed grain growth [email protected] in the mushy zone. Haga et al. [5] combined low superheat * H. L. Yu casting and semisolid casting with an unequal diameter twin [email protected] roll caster with a long solidification length. The macrostructure of the as-cast strip was equiaxed and spherical, not columnar. Haga et al. [6] also carried out semisolid strip casting 1 Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, Shenyang 110819, with a twin roll caster equipped with a cooling slope, leading China to improvement in sheet elongation. Das et al. [7]compared 2 School of Mechanical, Materials and Mechatronic Engineering, the microstructure resulting from TRC with that produced by University of Wollongong, Wollongong, NSW 2500, Australia melt-conditioned TRC (MC-TRC). A uniform, fine, and 3 Hongyanhe Project Department, China Guangdong Nuclear Power equiaxed grain structure was observed in as-cast MC-TRC Engineering Co. Ltd, Dalian 116319, China samples. However, coarse columnar grains with centerline Int J Adv Manuf Technol segregation were observed in the as-cast TRC samples. Kim field. The application of a pulsed electromagnetic field led to et al. [8] investigated the feasibility of producing high-strength an increase in the dendrite fragmentation rate. Yu et al. [20] Al sheets with high solute content using a twin roll strip caster directly applied alternative current (AC) to the melt in the equipped with an asymmetric nozzle. The centerline segrega- mold through the launder during electromagnetic continuous tion and hot tear of the sheets could be reduced, thereby in- casting (EMCC) of copper billets. The imposition of the AC creasing the casting speed. Cheon et al. [9]successfullyfab- current on the melt during EMCC significantly increased the ricated Al alloy sheets using a combination of twin roll strip convection and vibration in the melt, which are very beneficial casting and asymmetric rolling. The Al sheets exhibited ex- for the solidification of the alloy. cellent formability and mechanical properties, far exceeding Electromagnetic fields obviously have an effect on grain those in commercially available Al sheets. Sun et al. [10] refinement and microstructure improvement during melt so- homogenized the AA3105 alloy prior to cold rolling and an- lidification. However, there have been few studies of the effect nealing and found that homogenization reduced the supersat- of an electromagnetic field on TRC. The AA5052 alloy has uration and coarsened the constituent particles, thus reducing been attracting increasing attention in recent years because of the total number of particles. Homogenization also resulted in its desirable attributes for processing, machining, and welding a marked reduction in the recrystallized grain size and faster [21–24], making it suitable for use in the automobile, ship- recrystallization kinetics after cold rolling and annealing. ping, machinery manufacturing, and other industries [25–27]. Birol [11] also investigated the effect of homogenization on However, in the forming process of AA5052 sheets, segrega- TRC-processed thin Al-Mn strips and obtained similar results. tion has always been a critical hindrance to improvement of Imposition of an electromagnetic field can provide more the microstructure and mechanical properties [28, 29]. In the possibilities to control the development of the microstructure. present study, static and oscillating magnetic fields were im- Hicher et al. [12] designed a new mirror furnace crystal posed on the AA5052 melt with a view to abating segregation growth device using a static external electric field. They found and improving the microstructure and mechanical properties. a significant change in the melting temperature and a strong The effects of the electromagnetic field on the microstructure, change in the separation between the liquid and solid states segregation, and mechanical properties such as tensile during growth upon application of an electric field. Ma et al. strength are examined. [13] analyzed the thermal and fluid effects caused by applying alternating electric fields during BiMn/Bi eutectic directional solidification. They found that the microstructure formation depends on the frequency of the applied alternating current 2 Experimental investigation and that it changes spontaneously as the alternating electric field is applied. Li et al. [14, 15] investigated semi-continuous AA5052 sheets were produced by twin-roll casting, both with casting of Al alloy with the application of a static magnetic and without an electromagnetic field. The twin-roll caster has field. They found that the static magnetic field changes the two counter-rotating rollers, which are water-cooled from the microstructure from regular columnar grains to twinned la- inside. The roller shell is made of heat-resistant alloy steel. mellas. Jie et al. [16] used a rotating magnetic field (RMF) The roller gap is adjusted by hydraulic pressure. The twin- during solidification of hypereutectic Al-Si alloy and found roll caster dimensions are listed in Table 1.AnAA5052alloy that it resulted in efficient congregation of the primary Si (composed of 2.8 % Mg, 0.40 % Mn, 0.50 % Cr, 0.25 % Si, phase near the inner wall of the crucible and formation of a 0.10 % Cu, 0.40 % Fe, and 95.5 % Al) was used in the TRC Si-rich layer. This suggested that a forced intense melt flow experiments. An Al ingot was completely melted in an elec- combined with proper cooling conditions can greatly change trical resistance furnace. After the furnace temperature the solidification structure of alloys, which could be beneficial reached 700 °C, Mg, Mn, and Cr were added to the melt. for microstructure control. Zhang et al. [17, 18] studied the The well-stirred melt was then heated up to 800 °C. This influence of a low-frequency electromagnetic field on the mi- was followed by standing and filtration in the temperature crostructure and macrosegregation in continuous casting. In range 720–740 °C. When the temperature reduced to the presence of an electromagnetic field, a substantial reduc- 690 °C, the TRC experiment commenced. Figure 1 presents tion of grain size and macrosegregation of the alloy elements the flow chart of the melting process of AA5052. was achieved. The frequency of the applied electromagnetic The melt was poured into a sodium silicate thermal insula- field was found to play a significant role in grain refinement tion nozzle which was pre-heated to 400 °C. The twin-roll and macrosegregation inhibition. Liotti et al. [19] developed caster with copper coil excitation apparatus on the upper roller an in situ technique for studying the effect of a pulsed electro- was prepared for the AA5052 sheet production and is sche- magnetic field on dendrite fragmentation. They used synchro- matically illustrated in Fig. 2. The experimental rolling speed tron X-ray imaging, involving the passage of an oscillating was 1.4 m/min. The cross section of the AA5052 sheets was current through a foil specimen placed in a static magnetic 5×400 mm. Int J Adv Manuf Technol

Table 1 Dimensions of twin-roll caster Diameter of upper roller Diameter of lower roller Minimum rolling speed Maximum rolling speed

500 mm 500 mm 0.5 m/min 7 m/min

A static magnetic field was applied to cast-rolling area with 3Results a nominal strength of 0.3 T. Three sheets were produced under different conditions: (1) without the applied field (B=0 Tand 3.1 Structure I=0 A), (2) with a static magnetic field (B=0.3 T), and (3) with a combination of three-phase AC (I=200 A) and static The macrostructures of the AA5052 sheets produced using no magnetic field (B=0.3 T). field, a static magnetic field, and an oscillating magnetic field, After the TRC process, the sheet macrostructure was respectively, are shown in Fig. 3. In all three cases, the macro- inspected visually by etching using an etchant (5 % nitric acid structure at the edges consists of fine grains. However, the core and 17 % hydrofluoric (HF) acid) for about 15 s prior to grains are comparatively larger for all three conditions. The “no rinsing by water. Specimens measuring 5×15×20 mm select- field” core macrostructure (Fig. 3a) is coarse and unevenly ed from a quarter of the thickness or width were prepared by distributed. The core macrostructure with the static magnetic standard metallographic polishing with MgO paste followed field (Fig. 3b) is relatively refined but shows grain growth along by etching with 4 % HF acid reagent for about 20 s to observe certain orientations. The macrostructure induced by the oscil- the microstructures in the vertical cross section, using a Leica lating magnetic field (Fig. 3c) is obviously refined, and the DMI5000M optical microscope (OM). In addition, the distri- grain size is uniform with no clear orientation preference. bution of Mg was investigated using a Hitachi S-3400N scan- Figure 4 shows the microstructures of the rolled AA5052 ning electron microscope (SEM). Specimens were also select- sheets: (a) no field, (b) with a static magnetic field, and (c) ed from the sample cores (half thickness or width) to analyze with an oscillating magnetic field. The no field microstructure the macrosegregation. (Fig. 4a) has coarse columnar crystals which are a clear pref- Three 200 mm long pieces were cut out from the cast-rolled erence for growth direction. The grain size was measured sheets and processed sequentially: 5 mm→annealing at using a mean linear intercept method and the value is 360°Cfor3h→cold rolling to 2 mm→annealing at 360 °C ∼24 μm. The “static magnetic field” microstructure (Fig. 4b) for 3 h→cold rolling to 1 mm→annealing at 360 °C for 3 h. is significantly refined compared to the no field microstructure Tensile tests were conducted to evaluate the mechanical prop- (Fig. 4a), with restrained secondary dendrites and thinner pri- erties of the AA5052 sheets. Tensile testing at room tempera- mary dendrites. The dendrites become more uniform and ture in the longitudinal direction was carried out using a denser, but the growth of dendrites is perpendicular to the computer-controlled electronic universal testing machine roller surface. The grain size is ∼18 μm. The “oscillating mag- CMT5105 at a constant deformation speed of 1 mm/min. netic field” microstructure (Fig. 4c) shows the maximum refinement. The dendrites become extremely small with no pre- ferred orientation and very few rod-like crystals. In some areas, the dendrites have degenerated into spherical crystals Adding the Al ingot and some secondary dendrites are suppressed completely. The grain size is ∼15 μm. For comparison, grain sizes of AA 5052 obtained using other methods are also listed. The microstructure produced by homogenization at 550 °C for 30 min Adding the Mg , the Mn, and the Cr followed by air cooling has coarse grains (∼95 μm) [30]. The microstructure of an AA5052 produced by rheo-squeeze casting with a solid fraction of 0.17 solidified under 100 MPa ∼ μ Stirring consists of the relatively large grains ( 75 m) and fine grains (∼32 μm) [31]. In the l.6-mm thick cold rolled sheet of a continuous-cast AA 5052, the average length and average thickness of the elongated grains in the near-surface region Standing are 18 and 1.5 μm, respectively, whereas the corresponding values in the core region are 20 and 2.0 μm, respectively [29]. The microstructure resulting from four-pass differential speed Filtration rolling is characterized by nearly equiaxed nanostructured grains of size ∼0.7 μm[30]. The grain size resulting from Fig. 1 Flow chart of melting process of AA5052 alloy equal channel angular extrusion (ECAE) changed from 0.3 Int J Adv Manuf Technol

Fig. 2 Schematic diagram of electromagnetic TRC of AA5052. 1 nozzle, 2 electrode, 3 metallic melts, 4 casting roller, 5 roll casting sheet, 6 pinch roll (electrode), 7 coiler, 8 coil, 9 DC power supply, 10 AC power supply

to 2.0 μm following an increase in the extrusion temperature microstructure at a quarter of the thickness in the no field sheet, from 50 to 300 °C [32]. The microstructure of the sheets after and the Mg content revealed by linear scanning. The maximum 3 cycles of accumulative roll bonding (ARB) consists of near- Mg content was measured to be 5.0 % by weight at the grain ly equiaxed grains whose diameters range from 0.2 to 0.5 μm boundary and 1.1 % by weight in the grain interior. It can be [33]. Cryogenic deformation with 80 % reduction leads to the shown that the segregation ratio (SR)isgivenby formation of parallel bands of elongated substructures, 0.05– ωmax 0.15 μminwidthand0.4–0.8 μminlength[34]. SR ¼ ð1Þ ωmin ω ω 3.2 Segregation where max is the maximum solute content and min is the minimum solute content. This yields SR=4.5 in the case above. Solidification proceeds from the outside to the inside as the With the static magnetic field (Fig. 6b), the maximum Mg heat is dissipated during the TRC process, so that the melt in content by weight at the grain boundary is 4.0 % and the the core solidifies last and segregates readily. Figure 5a shows minimum Mg content is 1.5 %, giving a segregation ratio of the severe segregation following the no field TRC process. 2.7. Similarly, under the oscillating magnetic field (Fig. 6c), Various precipitates with different physical properties, such the maximum and minimum Mg contents are 4.4 and 2.1 %, giving a segregation ratio of 2.1. as Mg2Si and Al3Fe [35], are formed by the added elements. This is accompanied by the packing of massive dendrites in The influence of the electromagnetic field on the Mg seg- the microstructure of the AA5052 sheet, which can be seen regation ratio is shown in Fig. 7. It can be seen from the chart using an optical microscope. Following application of the that the Mg content inside and outside of the grains tends static magnetic field, the microstructure of the second sheet towards equilibrium and that the Mg segregation ratio for is mostly composed of thinner, denser, and more uniform pri- the no field AA5052 sheet is much higher than those for the mary dendrites, as shown in Fig. 5b. Segregation is obviously sheets with the fields applied. In other words, the application reduced, compared with the no field case. Figure 5c shows the of the static and oscillating magnetic fields contributes to an refinement in the microstructure due to the oscillating mag- increase in the solute solubility. netic field. A few precipitates can be spotted, and they are almost completely replaced by equiaxed grains. 3.3 Mechanical properties Apart from the severe centerline segregation in the core of the AA5052 sheet, intergranular segregation also occurs due to se- In general, the AA5052 sheets produced by the TRC process quential crystallization. Figure 6a shows the cross-sectional using the static and oscillating magnetic fields are much Int J Adv Manuf Technol

a also increased to 25.7 %. The improvement in the properties due to the effect of static magnetic field is smaller than that due to the oscillating magnetic field.

4Discussion

The sheet macrostructure at the edge is distinctly different from that in the core for all three conditions, as shown in Fig. 3. The fine crystal zone at the edge is formed due to rapid cooling (cooling rate 100–1000 °C/s), causing the generation b of numerous nuclei and restricting the available space for the individual nuclei. The grains in the core are comparatively large because of the lesser heat dissipation there. The no field macrostructure (Fig. 3a)islargerthanthe“with field” macrostructure (Fig. 3b, c). That indicates that this is unfavorable for nucleation and that every nucleus has sufficient space to grow if no field is applied. However, application of electromagnetic field improves the nucleating environment. The no field microstructure (Fig. 4a) at quarter thickness is formed at regions of comparatively high temperature gradient, generating columnar crystals and causing the grains to grow along certain orientations. The orientation of grain growth induces the ex- c pulsion of alloy element particles, leading to segregation. Core segregation (Fig. 5a) is the result of delayed solidification of the melt with a high content of alloy element particles. Inter- granular segregation (Fig. 6a) occurs because the expelled alloy element particles solidify in the intergranular regions. The large rolling deformation during the TRC process also contributes to the segregation because dislocation and deformation-induced vacancies enhance the mobility of the Mg atoms [38]. Rolling stress also induces grain boundary migration and grain rotation. However, second-phase particles and solute atoms segregated at the grain boundaries slow down grain boundary migration and grain rotation [39]. Both Fig. 3 Macrostructures of cast-rolling area of AA5052: a no field, b with astaticmagneticfield,andc with an oscillating magnetic field solidification and deformation conditions result in the formation of non-uniform microstructure, affecting the mechanical stronger. Figure 8 shows the engineering stress vs engineering properties (Fig. 8). The microstructure resulting from the ap- strain curves for the samples after cold rolling in the longitu- plication of the electromagnetic field (Fig. 4b, c)ischaracter- dinal direction for three different TRC conditions during ten- ized by finer grains and slightly reduced orientation. These sile processing. In the tensile processing, the serrated defor- result in the abatement of centerline segregation (Fig. 5b, c) mation called “Lüders strain” occurs. This is an inherent fea- and intergranular segregation (Fig. 6b, c) and, furthermore, ture of Al-Mg alloys [36, 37]. As seen in the figure, the TRC influence the mechanical properties as shown in Fig. 8. sheets produced with the fields imposed have improved prop- In the TRC process, the region most influenced by the erties. Without the magnetic field, the tensile strength is electromagnetic field should be the cast-rolling region, where 200 MPa and the elongation is 21.9 %. With the static mag- the solidification and deformation of the metal occur. Appli- netic field, although the tensile strength increases only slightly cation of a static magnetic field to the TRC process amounts to compared with that in the no field case, the elongation shows a inducing flow in the melt. Atoms lose their valence electrons substantial increase to 23.8 %. The maximum tensile strength and become ions in the metal. If no field is applied, every ion undergoes random thermal motion characterized by a velocity of 241 MPa is obtained in the longitudinal direction under an ! oscillating magnetic field, an increase of 20.5 % over the “no v ,asshowninFig.9a. When a static magnetic field is ap- ! ! ! ! field” specimen. In addition, the elongation of the samples plied, a Lorentz force f ¼ qv⊥ Â B is generated. Here, v⊥ is Int J Adv Manuf Technol

Fig. 4 Microstructures of a b AA5052 sheets: a no field, b with a static magnetic field, and c with an oscillating magnetic field

the velocity component perpendicular to the applied magnetic qB,wherem is the particle mass. The frequency of gyration is ! qB/m. Compared with random motion, spiral motion inhibits field, q is the particle charge, and B is the magnetic field particle diffusion, especially the diffusion of solute particles in intensity. The ion rotates round the magnetic field line under ! the solid phase. Considering the melt flow perpendicular to the action of the Lorentz force f . The velocity component ! the magnetic field at a rolling speed of 1.4 m/min in the TRC v== parallel to the magnetic field causes the ion to move along process, v⊥ is considerably greater than v//, resulting in a very the magnetic field line, as shown in Fig. 9b. The radius of the strong inhibiting effect. This inhibiting effect is equivalent to orbit in the plane perpendicular to the magnetic field is mv⊥/ an effective increase in the fluid viscosity. The effectiveness of

Fig. 5 Macrosegregation of a b AA5052 sheets: a no field, b with a static magnetic field, and c with an oscillating magnetic field

c Int J Adv Manuf Technol

a 1.1% 1 5.0% 2

1 2

keV keV b 1.5% 3 4.0% 4

4 3

keV keV

c 2.1% 5 4.4% 6

6 5

keV keV

Fig. 6 Scanning of AA5052 in different TRC processes. a no field, b static magnetic field, and c oscillating magnetic field the magnetic field in increasingpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the viscosity varies with the equiaxed grains, as shown in Fig. 4b. Moreover, the segrega- Hartmann number H ¼ σB2r2=μc2, where σ is the electri- tion is abated due to the reduction in heat and mass transfer cal conductivity, r the radius of the crystal, μ the ordinary capacity (Figs. 5b and 6b). Additionally, since a local current viscosity (in the absence of the magnetic field), and c the density occurs in the dendrite network, due to thermoelectric velocity of light [40]. Based on this theory, convection in the (TE) effect, a thermoelectric magnetic force (TEMF) is creat- melt is reduced. Reduced convection results in reduction in ed [41, 42]. This also makes the particles follow a spiral path, the diffusion of the solute element. So, evenly distributed high inducing an inhibiting effect in the mushy zone and reducing melting particles can be core of crystal nucleus. This increases the diffusion of the solute element. This force becomes espe- the nucleation rate. However, the heat transfer to the rollers cially important when the magnetic field is applied during also reduces, thereby reducing the undercooling of the bulk solidification under a high-temperature gradient, like in liquid. The arrangement of the primary trunks with the high the TRC process. The inhibiting effect improves the concentration of added elements in the rolling direction forms mechanical properties of the AA5052 sheet to a certain the intermediate morphology between the dendrites and the extent (Fig. 8). Int J Adv Manuf Technol

Fig. 7 Statistical histogram of Mg element segregation ratio displays the reduction of Mg element content according to the no field and static and oscillating magnetic fields

! Simultaneous imposition of a static magnetic field B and electromagnetic force. Compared with the oscillating force ! mentioned previously, the latter force is small. When electro- an alternating electric field with current density J on the non- magnetic oscillation is imposed upon the molten metal, cyclic solid area results in an oscillating electromagnetic body force ! ! ! forces are induced which act as periodic compressive/tensile F ¼ J Â B , with a frequency equal to that of the applied forces, causing oscillations in the liquid. Consequently, forces electric field and a direction perpendicular to the plane of the of tension and compression are alternately developed on the two fields (Fig. 10). This force acts on the particles of the non- surface of suspended particles. This can result in the formation solid area and cause oscillation and convection. On the other of cavities. These cavities may grow in size as vacuum bub- hand, the alternating electric current induces an alternating bles and, partly, by absorbing gas from the melt during the magnetic field with the same frequency, which interacts with tension period of the cyclic force and releasing a part of it the electric current itself and induces an alternating during the compression period (rectified diffusion).

Fig. 8 Engineering stress vs engineering strain curves of AA5052 sheets under various treatments Int J Adv Manuf Technol

Fig. 9 a The relationship of ion velocity and magnetic direction and (b) motion trace of ion

Eventually, the bubbles collapse to produce powerful shock magnetic field. For the no field case, the tensile strength waves by involution and jetting [43]. The shock waves in the was 200 MPa and the elongation 21.9 %. With the static liquid can crush the suspended particles and smash them into magnetic field, the tensile strength increases slightly to each other, causing further refinement. Strong convection can 204 MPa and the elongation to 23.8 %. With an oscillating promote heat transfer and enhance the fluidity of melt, which magnetic field, both the tensile strength and elongation were will lead to the temperature and solute concentration distribu- greatly improved to 241 MPa and 25.7 %, respectively. tion. Uniform distribution of nucleation particles and temper- & A static magnetic field induces an inhibiting effect on the ature is very beneficial for increasing the nucleation rate. This melt, reduces diffusion of the solute elements, and results results in grain refinement as shown in Figs. 3c and 4c. Strong in more nucleating opportunities and less segregation, thus convection is unfavorable for gathering solute particles to enhancing the mechanical properties. However, the cause segregation, so oscillating effect can obviously reduce inhibiting effect cannot change the orientation of crystal the centerline segregation (Fig. 5c) and intergranular segrega- growth and columnar crystals still exist in the tion (Fig. 6c). All of these influences of the oscillating field microstructure. cause the mechanical properties to improve (Fig. 8). & An oscillating magnetic field can “crush” the suspended particles and cause strong convection, leading to more uniform distribution of temperature and solute elements, 5Conclusions simultaneously increasing nucleating opportunities and decreasing segregation, thus enhancing the mechanical & AA5052 alloy sheets were manufactured using the TRC properties. An oscillating field basically eliminates the technique under three conditions: (1) no field applied, (2) orientation of crystal growth and makes the grains finer with a static magnetic field, and (3) with an oscillating and rounder.

Fig. 10 Oscillating force developed by interaction of alternating electric and static magnetic fields Int J Adv Manuf Technol

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