CN204710875U - A kind of crimp processing mold preparing Ultra-fine Grained beta-titanium alloy - Google Patents

Abstract

The utility model discloses an extrusion deformation processing mold for preparing ultrafine-grained β-titanium alloy, which includes an upper mold and a lower mold, a vertical mold cavity is arranged in the upper mold, a horizontal mold cavity is arranged in the lower mold, and a horizontal mold cavity is arranged in the vertical mold cavity. Set the extrusion rod, and the graphite pad set at the end of the extrusion rod, the bullnose lower die includes the lower die clamp and the lower die movable part set in the middle; the lower half of the bullnose horizontal die cavity is set on the lower die movable part Upper: There is an insert between the bullnose upper mold and the lower mold movable part; the lower end of the bullnose lower mold is provided with a mold positioning seat; the upper end of the bullnose lower mold movable part is provided with a back pressure block to close the end of the horizontal cavity ; The size and shape of the channel section of the vertical mold cavity of the bullnose and the horizontal mold cavity are the same; the intersection of the vertical mold cavity of the bullnose and the horizontal mold cavity is provided with an inner fillet and a bullnose; the bullnose is arranged at the end of the insert. The mold can be used to prepare ultra-fine-grained β-titanium alloy, and has a long service life, can increase the fluidity of the material, and improve the uniformity of the strain distribution of the material.

Description

An Extrusion Deformation Die for Preparation of Ultrafine Grain β Titanium Alloy

technical field

The utility model relates to the technical field of research and development of alloy materials, in particular to an extrusion deformation processing die for preparing ultra-fine grain beta titanium alloy.

Background technique

β-type titanium alloy has the advantages of good cold formability, high aging strength and fracture toughness, large hardening depth, and good corrosion resistance. It is widely used in star bomb connecting belts, aviation rivets and fasteners, ultracentrifuge rotors head, elastic elements, etc. Obtaining an ultrafine-grained β-titanium alloy with a submicron grain structure can effectively improve the strength of the material, and at the same time improve the plasticity and toughness of the material and expand its application range.

In recent years, the new process of preparing ultra-fine-grained materials by plastic deformation—equal channel angle extrusion technology has received special attention. Equal channel angle extrusion is to press polycrystalline samples into a specially designed Compared with the methods of preparing ultra-fine-grained materials such as evaporation condensation-in-situ cold pressing forming method, high-energy ball milling method, and amorphous crystallization method, the shear deformation process in the mold to achieve large deformation, equal channel angle extrusion It avoids the impurities that may be brought in during grinding and the large number of microvoids in the ultrafine crystal material prepared by the ultrafine powder cold pressing synthesis method. The obtained material has the advantages of no holes, good compactness, and pure material. The effective process of large-scale dense ultra-fine grain bulk materials has great potential for industrial application; compared with the traditional plastic processing of metal materials, since the cross-sectional area and cross-sectional shape of the material are not changed during the deformation process, only Low working pressure is required to achieve repeated orientation and uniform shear deformation of the material, and the material can obtain a uniform and significantly refined grain structure under a particularly large amount of deformation.

The equal channel angle extrusion die model originally proposed by Segal is shown in Figure 1, and the die only considers one internal angle Φ; Iwahashi et al. improved Segal's model and proposed the die model in Figure 2, compared with the previous Segal model There is an extra exterior angle ψ. For these two mold structures, there is a sharp corner transition in the inner corner, and the outer corner is not tangent to the inner wall of the mold. Therefore, in the actual equal channel angle extrusion process, the sharp corner is prone to rapid wear and damage The surface of the workpiece, in addition, because the Ψ inner angle is not tangent to the inner wall of the mold, it will cause uneven flow when the material is deformed.

Therefore, designing a new type of equal-channel angle extrusion die that can prolong the service life of the die, increase the fluidity of the material, reduce the inhomogeneity of the strain distribution of the material, and be used to prepare ultra-fine-grained β-titanium alloy is an advanced titanium alloy component manufacturing enterprise. inevitable needs.

Through patent search, there are the following known prior art solutions:

Patent 1:

Application number: 200710092779.4, application date: 2007.9.28, authorized announcement date: 2008.04.09, the utility model discloses a magnesium alloy extrusion deformation processing method and mold, which are formed by unidirectional extrusion radial flow Extrusion die, the extrusion ratio is 4~60, after heating the die, evenly apply lubricant in the extrusion channel cavity of the die, and then heat the homogenized magnesium alloy billet and put it into the heated die for extrusion In the cavity, the punch moving downward through the extrusion die is extruded at the same speed from the upper end of the magnesium alloy billet at the extrusion speed of 0.5m/min~3m/min and the extrusion force of 3MPa~35MPa, so that The magnesium alloy billet is flowed and deformed from the upper part to the variable-diameter cavity channel in the radial direction of the extrusion cavity of the die. The utility model adopts unidirectional extrusion radial variable diameter angular flow extrusion deformation, which can not only greatly improve the refinement effect of magnesium alloy grains, improve the comprehensive mechanical properties of magnesium alloy materials, but also realize extrusion at low temperature. In this state, the extrusion speed is not reduced, and the quality of the formed sample is not reduced, thereby improving the production efficiency of the magnesium alloy extrusion deformation process.

Patent 2:

Application number: 201310379830.5, application date: 2013.08.27, authorization announcement date: 2013.12.18, the utility model discloses an equal-channel extrusion die for powder superalloy billet making, which is a kind of powder superalloy blank microstructure improvement The characteristic equal-channel extrusion die, after the forging blank enters the die, its cross-section is twisted from a circular cross-section to an elliptical cross-section to a circular cross-section. This deformation is a combination of torsional shear deformation and extrusion deformation, realizing a single extrusion process. Combination of multiple deformation modes in . In the deformation torsion transition section, due to the torsional deformation of the elliptical torsion surface, under the action of shear stress, the billet undergoes rotation and shear strain, which realizes the shearing and breaking of grains and achieves the effect of refining grains. At the same time, because the blank is limited by the cavity, the intergranular deformation of the blank under compressive stress is difficult, which can inhibit the development of various microscopic defects that originally existed in the deformed body. Due to the obvious grain refinement effect during the extrusion process and the complete elimination of the original grain boundaries, the comprehensive mechanical properties of the powder superalloy billet are significantly improved.

Patent 3:

Application number: 03132471.1, application date: 2003.06.30, authorized announcement date: 2005.01.19, the utility model proposes a preparation method of magnesium alloy unequal-diameter bend extrusion-shear induction isothermal treatment spheroidized semi-solid billet. The magnesium alloy billet is extruded through unequal bends to induce large shear deformation, and then heated to the semi-solid temperature zone for isothermal treatment. By controlling the time and temperature of isothermal treatment, a semi-solid billet with fine and spherulite structure can be obtained. The utility model is the popularization and application of the semi-solid forming technology in the field of magnesium alloy processing, and will produce positive effects.

Through the above search, it is found that the above technical solutions cannot affect the novelty of the utility model; and the mutual combination of the above patent documents cannot destroy the creativity of the utility model.

Utility model content

In view of the above problems, the utility model provides an extrusion deformation processing die for preparing ultra-fine-grained β-titanium alloys. Uniformity of material strain distribution.

In order to achieve the above purpose, the technical solution adopted by the utility model is: it includes a kind of extrusion deformation processing mold for preparing ultra-fine-grained β titanium alloy, which includes the right half of the vertical mold cavity (11) in the middle, and the right half of the lower part. The upper mold (5) on the upper part of the horizontal mold cavity (3) and the lower mold with the lower half of the horizontal mold cavity (3) on the upper part and matched with the upper mold (5), and the upper mold provided in the vertical mold cavity (11) The extruding rod (9) that can be withdrawn automatically, and the extruding rod fixing plate (6) set on the upper end of the extruding rod (9) and the matching pad (7) and the small bolt (8) that fix it, And the graphite pad (12) provided at the end of the extrusion rod (9), the lower die includes a lower die clamp (16) and the lower die movable part (2) arranged in the middle; the horizontal die cavity (3) The lower half is arranged on the movable part (2) of the lower mold; an insert (14) is arranged between the upper mold (5) and the movable part (2) of the lower mold; the lower end of the lower mold is provided with a mold positioning seat (1 ); the upper end of the lower mold movable part (2) is provided with a back pressure block (21) to close the end of the horizontal mold cavity (3); the channel cross-sectional size of the vertical mold cavity (11) and the horizontal mold cavity (3) and The shape is the same; the intersection of the vertical mold cavity (11) and the horizontal mold cavity (3) is provided with an inner fillet (51) and an outer fillet (141); the outer fillet (141) is arranged on the insert (14 ) end.

Further, the size of the inner fillet (51) is 3-6mm; the size of the outer fillet (141) is 2-5mm.

Further, the size of the inner fillet (51) is 5mm; the size of the outer fillet (141) is 4mm.

Further, the side of the back pressure block (21) in the horizontal mold cavity (3) is provided with a graphite sub-pad (4).

Further, the thickness of the graphite sub-pad (4) is 2mm.

Further, the insert (14) and the upper mold (5) are connected and fixed by bolts (14) and nuts (10); the upper mold (5) and the lower mold clamp (16) are connected and fixed by bolts ( 14) It is connected and fixed with the nut (10), and a positioning pin (15) is arranged between them.

Further, a chute (101) is arranged in the middle of the mold positioning seat (1); the movable part (2) of the lower mold is arranged in the chute (101).

The beneficial effects of the utility model:

1. There is an insert with outer fillet between the upper and lower dies. The outer fillet arc surface of the insert bears the maximum extrusion force during the extrusion molding of β titanium alloy. The insert can be easily replaced. This setting reduces the The frequency of mold maintenance improves the service life of the mold and improves production efficiency.

2. The lower mold is equipped with a back pressure structure, and the lower half of the horizontal mold cavity is set in the movable part of the lower mold. The movable part of the lower mold can slide in the chute of the mold positioning seat, which can reduce the extrusion movement of the titanium alloy material in the channel The friction force generated on the channel wall can reduce the plastic deformation of the titanium alloy material, increase the rate of ultra-fine grain of the titanium alloy material, improve the uniformity of the ultra-fine grain structure of the titanium alloy material, and increase the service life of the mold at the same time.

3. There are inner fillets and outer fillets at the junction of the vertical cavity and the horizontal cavity, and the radius of the inner fillet is 3-6mm, and the radius of the outer fillet is 2-5mm. This setting can make the titanium alloy material in the mold Repeated extrusion without breaking. When the radius of the inner fillet is 5mm and the radius of the outer fillet is 4mm, the ultra-fine grain acquisition rate of titanium alloy can be maximized, the microstructure uniformity can be the best, and the mold can be improved. service life.

4. The mold has long service life, convenient maintenance, low maintenance cost and strong practicability.

Description of drawings

The numbers shown in the figure are marked as: 1. Mold positioning seat, 2. Movable parts of the lower die, 3. Horizontal cavity, 4. Graphite auxiliary pad, 5. Upper die, 6. Extrusion rod fixing plate, 7. Pad Block, 8, small bolt, 9, extrusion rod, 10, nut, 11, vertical cavity, 12, graphite spacer, 13, bolt, 14, insert, 15, positioning pin, 16, lower die clamp , 21, back pressure block, 51, fillet, 101, chute, 141, fillet.

Figure 1 shows the equal channel angle extrusion model of Segal.

Figure 2 is the Iwahashi Equal Channel Angular Extrusion model.

Fig. 3 is a schematic diagram of the overall structure of the utility model.

Fig. 4 is a cross-sectional view of B-B in Fig. 3 .

Fig. 5 is a left view of Fig. 3 .

FIG. 6 is an enlarged view of part A in FIG. 3 .

Fig. 7 is a D-D sectional view in Fig. 3 .

Fig. 8 shows the microstructure of β-titanium alloy before equal channel angle extrusion through a die with an inner fillet of 5 mm and an outer fillet of 4 mm.

Figure 9 shows the microstructure of the longitudinal cross-section of the β-titanium alloy after equal-channel angle extrusion through a mold with an inner fillet of 5 mm and an outer fillet of 4 mm.

Detailed ways

In order to enable those skilled in the art to better understand the technical solution of the utility model, the utility model will be described in detail below in conjunction with the accompanying drawings. The description of this part is only exemplary and explanatory, and should not have any influence on the protection scope of the utility model. restrictive effect.

As shown in Fig. 1-7, the structural connection relation of the present utility model is: it comprises middle part to have vertical die cavity 11 right half part, lower part has upper die 5 of upper half of horizontal die cavity 3 and upper part has horizontal die The bottom half of the cavity 3 and the lower mold that cooperates with the upper mold 5, and the extrusion rod 9 that can automatically withdraw from the vertical cavity 11, and the extrusion rod fixing plate 6 that is arranged on the upper end of the extrusion rod 9 and cooperates with it The cushion block 7 and the small bolt 8 that fix it, and the graphite cushion block 12 provided at the end of the extruding rod 9, the lower mold includes the lower mold clamping part 16 and the lower mold movable part 2 arranged in the middle; the horizontal The lower half of the mold cavity 3 is arranged on the movable part 2 of the lower mold; an insert 14 is arranged between the upper mold 5 and the movable part 2 of the lower mold; a mold positioning seat 1 is arranged at the lower end of the lower mold; the movable part of the lower mold The upper end of the part 2 is provided with a back pressure block 21 to close the end of the horizontal cavity 3; the vertical cavity 11 and the horizontal cavity 3 have the same channel cross-section size and shape; the intersection of the vertical cavity 11 and the horizontal cavity 3 is set There are inner rounded corners 51 and outer rounded corners 141 ; the outer rounded corners 141 are arranged at the end of the insert 14 .

Preferably, the size of the inner fillet 51 is 3-6 mm; the size of the outer fillet 141 is 2-5 mm.

Preferably, the size of the inner fillet 51 is 5mm; the size of the outer fillet 141 is 4mm.

Preferably, the side of the back pressure block 21 inside the horizontal cavity 3 is provided with a graphite sub-pad 4 .

Preferably, the graphite sub-pad 4 has a thickness of 2mm.

Preferably, the insert 14 and the upper mold 5 are connected and fixed by the bolt 14 and the nut 10; the upper mold 5 and the lower mold clamp 16 are connected and fixed by the bolt 14 and the nut 10, and there is also a Locating pins 15 are provided.

Preferably, a chute 101 is arranged in the middle of the mold positioning seat 1 ; and the movable part 2 of the lower mold is arranged in the chute 101 .

When the utility model is specifically used, the β titanium alloy sample is extruded into the vertical cavity 11 by the extrusion rod 9, and the extrusion is continued. When the corner moves, shear deformation occurs, which makes the β-titanium alloy material form a refined crystal structure; when the β-titanium alloy material enters the horizontal cavity 3, a back pressure block 21 is provided at the horizontal cavity 3, and the back pressure block 21 A reverse force is applied to the β-titanium alloy material to improve the extrusion effect and its refined crystallization effect; since the lower half of the horizontal cavity 3 is set on the movable part 2 of the lower die, when the extrusion force generated by the extrusion rod After reaching the critical value, when the thrust generated by the β titanium alloy material on the back pressure block 21 exceeds the friction force between the lower mold movable part 2 and the chute 101, the lower mold movable part 2 moves forward together with the β titanium alloy material, and the lower mold moves When the piece 2 slides to the end of the chute 101, the extrusion ends; at this time, the β titanium alloy material can be taken out, rotated 90° or 180°, and then put into the mold again for repeated extrusion, thereby forming ultra-fine grain β Titanium alloy material.

The mold of the utility model is provided with inserts, and the outer fillet at the end of the inserts is the transition part of equal-channel bending angle extrusion. When extruded, the force is large and it is easy to wear. When the wear is excessive, only the inserts can be replaced. There is no need to completely replace the upper mold and the lower mold, thereby reducing the maintenance cost of the mold and increasing the economic benefits of the product.

The lower mold in the utility model is designed as a base sliding back pressure structure. During the extrusion process of equal channel corners, if there is no friction between the sample and the channel, the sample will undergo simple shear deformation at the plane where the channels meet, and the material will be everywhere. The deformation is uniform; when there is friction, the material will produce a fan-shaped area near the plane where the channels meet, and no deformation will occur at the top corner, and only plastic deformation will occur in the fan-shaped area, resulting in uneven deformation of the material in the mold, resulting in uneven microscopic organize. In the actual equal channel angular extrusion process, there is always a large friction force between the mold and the sample, which directly affects the extrusion effect. The lower mold of the sliding base structure in this mold is designed as the lower mold movable part 2 and the lower mold clamping part 16. Since the lower mold movable part 2 can move together with the sample, the friction force on the sample can be maximized during extrusion. It is also equivalent to giving the sample a reverse thrust, which can well improve the processing performance of the material in the equal channel angular extrusion, and make the deformation of the material more uniform during the deformation process.

In the utility model, the mold is designed with inner and outer rounded corners, the outer rounded corners R=2-5mm, and the inner rounded corners r=3-6mm. It is proved by experiments that this setting can make the uniformity of the extruded structure reach the best.

Experimental data: channel section: 9mm × 9mm, mold corner: Ф = 90°, entrance channel length: L _in = 120mm, outlet channel length: L _out = 120mm.

Set the rint values of the inner fillet to 1, 3, 5, 7, 9mm respectively, and the Rext values of the outer fillet to 2, 3, 4, 5mm respectively, and use the finite element software to calculate different combinations of rint and Rext values. The distribution of the equivalent strain field of the alloy billet after equal channel angle extrusion. The analysis results show that when the rint value is fixed, as the Rext value increases, the maximum equivalent strain value of the titanium alloy after equal channel angle extrusion decrease; when the Rext value is fixed, with the increase of the rint value, the equivalent strain of the lower part of the billet is gradually increasing and expanding to the upper part; the strain value near the inner corner, that is, the upper part of the billet, is higher than that near the outer corner, that is, the strain value of the lower part of the billet . Comparing the simulation results of different rint and Rext combinations, when rint=5mm and Rext=4mm, the overall strain of the billet after extrusion is the most uniform, and the maximum strain value reaches 1.0.

In order to further confirm the appropriate values of rint and Rext, the distribution of the overall equivalent strain field was compared when rint was 5mm and Rext were 3, 4, and 5mm respectively. With the increase of Rext, the maximum equivalent strain value decreased from 1.33 to 1.0, the overall strain distribution of the billet is still the most uniform when rint=5mm, and Rext=4mm. When R=3mm, the equivalent strain value gradually decreases from the bottom to the upper part of the billet; when R=5mm, the equivalent strain value from the bottom to the upper part of the billet On the contrary, the variable value increases gradually; when R=4mm, the section can obtain a uniform distribution of strain value.

Therefore, based on the above analysis results, the mold design with an inner angle of 5 mm and an outer angle of 4 mm is suitable for channel angle extrusion of β-titanium alloy, and deformed parts with better overall strain uniformity can be obtained.

In order to confirm the analysis results and verify it through actual experiments, we use the existing β-Ti alloy for verification. The selected β-Ti alloy composition is Ti-5Mo-5V-8Cr-3Al, and conduct experimental analysis on it to obtain the inner angle of the mold. Equivalent strain field distribution when the angle is 5mm and the outer angle is 4mm, and then the equal-channel angle extrusion experiment is carried out at 600°C and 1.0mm/s using a mold with an inner angle of 5mm and an outer angle of 4mm, and the extruded sample Cut along the length direction, observe its microstructure after metallographic sample preparation, and conduct a longitudinal section hardness distribution test to measure the uniformity of its deformation, and compare it with the finite element simulation results.

After observing the appearance of the billet of β-titanium alloy after equal-channel angle extrusion, it was found that some material folding phenomenon occurred at the front end of the billet in the actual experiment, resulting in a sharper front end of the billet, and the distribution of macro streamlines in the longitudinal section was concentrated and dense. The optical microstructure before and after angular extrusion, the original billet is β titanium forged rod, with obvious processed structure, the matrix is a single β matrix, which is elongated and deformed along the length direction of the billet, and there are granular particles inside the β grains The α phase precipitates out; the structure of β titanium alloy is obviously refined after equal channel angle extrusion, and the average grain size is about 30um, as shown in Figure 8-9; the structure of β titanium alloy after multiple times of equal channel angle extrusion Obtained ultra-fine grains, the average grain size is below the micron level, reaching the nano-ultra-fine grain size, according to the microhardness test results, the hardness of the near two ends of the sample length direction after equal channel angle extrusion The value is low, because the equivalent strain value at both ends of the sample is small, and the microhardness uniformity in the middle part of the sample is better, but there are some fluctuations in the hardness test value, and the fluctuation range is about 30, which is considered normal Measurement margin of error. Calculate the average value of microhardness at all measurement points, the average value of microhardness near the upper part of the sample is 390.5, the average value of microhardness in the middle of the sample is 396.6, and the average value of microhardness near the bottom of the sample is 399.1, which is the same as The trend in the finite element simulation results is the same, and they are all higher than the average microhardness of the original billet of 302.4.

Comparing the numerical simulation results and the actual experimental results, it can be considered that the β-titanium alloy adopts a mold with an inner angle of 5 mm and an outer angle of 4 mm. It is good, that is, the correctness of the finite element simulation prediction of the equal channel angle extrusion process is verified by the equal channel angle extrusion experiment of β titanium alloy.

After finite element analysis and actual experimental analysis, we added a back pressure structure at the end of the horizontal cavity in the mold of the utility model, which can effectively improve the equivalent strain value at both ends of the titanium alloy material and improve its uniformity.

It should be noted that, in this document, the term "comprising", "comprising" or any other variation thereof is intended to cover a non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements, It also includes other elements not expressly listed, or elements inherent in the process, method, article, or apparatus.

In this paper, specific examples are used to illustrate the principle and implementation of the present invention. The description of the above examples is only used to help understand the method and core idea of the present invention. The above is only a preferred embodiment of the utility model, it should be pointed out that due to the limitation of literal expression, objectively there are infinite specific structures, for those of ordinary skill in the art, without departing from the principle of the utility model Under the premise of the invention, some improvements, modifications or changes can also be made, and the above technical features can also be combined in an appropriate way; these improvements, modifications, or combinations, or the ideas and technical solutions of the utility model can be directly applied without improvement In other occasions, all should be regarded as the protection scope of the present utility model.

Claims (7)

1. prepare the crimp processing mold of Ultra-fine Grained beta-titanium alloy for one kind, it comprises middle part and has vertical die cavity (11) right half part, bottom has the patrix (5) of horizontal die cavity (3) the first half and top has horizontal die cavity (3) the latter half and the counterdie coordinated with patrix (5), and the pressure ram (9) that can automatically exit arranged in vertical die cavity (11), and the pressure ram fixed head (6) that arranges of pressure ram (9) upper end and the cushion block (7) coordinated with it and by it fixing stove bolt (8), and the graphite cushion block (12) that pressure ram (9) end is arranged, it is characterized in that, described counterdie comprises counterdie folder (16) and the middle counterdie movable part (2) arranged thereof, described horizontal die cavity (3) the latter half is arranged on counterdie movable part (2), insert (14) is provided with between described patrix (5) and counterdie movable part (2), described counterdie lower end is provided with mold positioning seat (1), described counterdie movable part (2) upper end is provided with back pressure block (21) by horizontal die cavity (3) endcapped, channel cross-section size and the shape of described vertical die cavity (11) and horizontal die cavity (3) are identical, described vertical die cavity (11) and horizontal die cavity (3) intersection are provided with filleted corner (51) and bull nose (141), described bull nose (141) is arranged on insert (14) end.

2. a kind of crimp processing mold preparing Ultra-fine Grained beta-titanium alloy according to claim 1, it is characterized in that, described filleted corner (51) size is 3-6mm; Described bull nose (141) size is 2-5mm.

3. a kind of crimp processing mold preparing Ultra-fine Grained beta-titanium alloy according to claim 2, it is characterized in that, described filleted corner (51) size is 5mm; Described bull nose (141) size is 4mm.

4. a kind of crimp processing mold preparing Ultra-fine Grained beta-titanium alloy according to claim 1, is characterized in that, described back pressure block (21) one side be in horizontal die cavity (3) is provided with graphite pair pad (4).

5. a kind of crimp processing mold preparing Ultra-fine Grained beta-titanium alloy according to claim 4, is characterized in that, described graphite pair pad (4) thickness is 2mm.

6. a kind of crimp processing mold preparing Ultra-fine Grained beta-titanium alloy according to claim 1, is characterized in that, described insert (14) is connected and fixed by bolt (14) and nut (10) with patrix (5); Be connected and fixed by bolt (14) and nut (10) between described patrix (5) and counterdie folder (16), and between it, be also provided with alignment pin (15).

7. a kind of crimp processing mold preparing Ultra-fine Grained beta-titanium alloy according to claim 1, is characterized in that, is provided with chute (101) in the middle of described mold positioning seat (1); Described counterdie movable part (2) is arranged in chute (101).