Takuma Kishimoto,Peihua Du,Tsuyoshi Furushima

Department of Mechanical and Biofunctional Systems,Institute of Industrial Science,The University of Tokyo,4-6-1 Komaba,Meguro,Tokyo 153-8505,Japan

Abstract The crystal orientation and outer surface roughening of magnesium alloy tubes were evaluated to clarify the effect of the mandrel on the microstructure and outer surface roughness in die-less mandrel drawing.Locally heated ZM21 tubes with an outer diameter of 6.0 mm and an inner diameter of 3.8 mm were drawn with and without a mandrel.The outer surface roughness and crystal orientation were evaluated in the same measurement area.The results indicated that the outer surface becomes rougher in the die-less mandrel drawing than in die-less drawing for a given outer circumferential strain.The outer surface roughness developed when there was large difference in the pyramidal slip system Schmid factor.Therefore,the slip deformation of the pyramidal slip system seems to be mainly responsible for the outer surface roughening in the die-less mandrel drawing.Furthermore,the crystal grain with the{20}crystal plane vertical to the normal direction of outer surface had a larger Schmid factor than the other crystal grains.The large number of crystal grains with the{20}crystal plane in the die-less mandrel drawing is one of the reasons that the outer surface roughness develops more in the die-less mandrel drawing than in die-less drawing for a given outer circumferential strain.These results will contribute significantly to the development of fabrication process of the microtube with high surface quality,which prevents rapid corrosion of biomedical applications.

Keywords:Tube forming;Die-less drawing;Surface roughness;Crystal plasticity;Magnesium alloy;Electron backscatter diffraction.?Corresponding author.

1.Introduction

Magnesium(Mg)alloys have been recognized as biomaterials owing to their biodegradable and bioabsorbable mechanical properties.For example,Mg-based composites provide great strength-to-weight ratio as well as bio-compatibility and bio-degradability to be used as orthopedic implants[1].Furthermore,Mg alloys are often used as implants[2–5]and bioresorbable electronic platforms[6].Mg alloy microtubes,which easily corrode in the human body,are often used as bioabsorbable materials in devices such as stents and implants,which have thin walls and high surface quality[7–9].Sajjad et al.reported that the larger surface roughness led to higher corrosion speed of Mg alloys[10].Uppal et al.reported that Mg alloy implants face a major challenge of rapid corrosion in body fluids that degrades before the bone tissue has completely healed[11].Low surface roughness is required to prevent rapid corrosion of stents and implants during healing period.Therefore,a thin wall and low surface roughness should be achieved in the Mg alloy microtube fabrication process.Usually,an inner tool reduces the wall thickness of a tube during plug or mandrel die drawing[12,13].Furthermore,the wall thickness decreases during the new hollow sinking process,which controls the drawing speed on both the die entrance and exit sides[14–16].However,fabricating Mg alloy microtubes is usually difficult in cold die drawing because of the low plasticity of a hexagonal close-packed(HCP)structure.Usually,Mg alloy tubes break when the reduction in the cross-sectional area is large in a single pass.The maximum reduction in the cross section of the Mg alloy tube is below 10 % in cold die drawing[17,18]and 15 %in warm die drawing[19].Therefore,fabricating microtubes by die drawing is inefficient because the tube must be drawn many times.

Weiss et al.first developed a die-less drawing process in 1969,which reduced the cross-sectional area of the material by pulling with localized heating[20].Hashmi obtained an outer diameter reduction of 15 % by die-less drawing of a copper tube[21].A die-less drawing process can achieve a large reduction in cross-sectional area even for a Mg alloy tube in a single pass,because the elongation is improved by localized heating during drawing.Furushima and Manabe reported that a reduction in the cross-sectional area of 50%was obtained in a single pass of die-less drawing[22].However,active thinning of the wall thickness is generally difficult in die-less drawing because the ratio of the wall thickness to the outer diameter is constant[23].Recently,a die-less mandrel drawing,which can achieve active thinning of the wall thickness by suppressing the decrease in the inner diameter due to the mandrel,has been developed.In this study,the dieless drawing with a mandrel is called as the die-less mandrel drawing.Furushima and Manabe reported that a substantial thinning of the wall thickness of 54 % was accomplished through multiple rounds of die-less mandrel drawing of a Mg alloy tube[24].Therefore,die-less mandrel drawing is more suitable for fabricating thin-walled microtubes than die-less drawing.However,the outer surface roughness of the tube generally increases during die-less mandrel drawing.Blood clots caused by outer surface roughness reduce the performance of stents.Suppressing outer surface roughening in dieless mandrel drawing enable fabricating a high-performance stent with a thin wall and high surface quality.Therefore,the outer surface roughening should be suppressed in the die-less mandrel drawing.However,the mechanism causing the outer surface roughening has not been clarified.

Several studies have shown that inhomogeneous plastic deformation among the crystal grains caused the development of the free surface roughness in a simple model,such as uniaxial tensile deformation of sheet metals[25–33].For example,Wouters et al.reported that the free surface roughness developed when there was a large difference in the Schmid factor among the crystal grains[31,32].Kishimoto et al.reported that the crystal grains with a{102}crystal plane parallel to the inner surface suppressed the increase in the unevenness of the surrounding grains,and themselves,in the hollow sinking of stainless-steel tubes[33].Therefore,the relationship between crystal deformation and surface roughening should be investigated to suppress outer surface roughening in die-less mandrel drawing.

Several studies have investigated crystal deformation such as slip deformation of basal,pyramidal,and prismatic slip systems and twin deformation of HCP metals[34–38].Galiyev et al.reported that twinning,basal slip,and(a+c)dislocation slip were dominant in the plastic deformation at temperatures below 200 °C[34].Furthermore,during high strain deformation at high temperatures(300–450 °C),dynamic recrystallization(DRX)occurs via nucleation in the slip band,and the moving dislocations are trapped by the low-angle grain boundary.At room temperature,the critical resolved shear stress(CRSS)of the basal slip system is much smaller than that of the non-basal slip systems such as pyramidal slip system.The CRSS of the basal slip system did not change much but decreased in the non-basal slip systems such as pyramidal slip system as the temperature increased at temperatures below 500 °C[37,38].

Crystal deformation and surface roughness in die-less drawing also have been investigated as follows.Du et al.reported the effect of the microstructure on mechanical properties such as corrosion properties in a die-less mandrel drawing[39].Furthermore,microstructural changes of the Mg alloy tubes related to twinning and DRX during die-less mandrel drawing have been reported[40].Surface quality of die-less drawn wires and tubes have been investigated[41,42].However,the crystal orientation of the crystal grain,which constitutes the outer surface roughness in die-less mandrel drawing,has not been evaluated because it is difficult to mirror-polish the outer surface so that the polished depth is within the grain size.Kishimoto et al.achieved the mirror polishing so that a polishing depth was less than the grain size of the hollow sank microtube in a previous study[33].This mirror polishing technique makes it possible to clarify the effect of the mandrel on the microstructure and outer surface roughening in die-less mandrel drawing.Investigating the relationship between the crystal orientation and the surface roughness directly is the novelty of this paper,which had not been conducted in the previous study of the die-less mandrel drawing.

Based on the above discussion,the objective of this study was to clarify the effect of the mandrel on the microstructure and outer surface roughening in die-less mandrel drawing.We performed die-less drawings both with and without the mandrel to investigate its effect on the microstructure and outer surface roughness of Mg alloy tubes.The crystal plasticity finite element method(CPFEM)is often used to investigate the crystal plasticity behavior.However,a CPFEM usually cannot analyze recrystallization that occurs due to local heating in die-less mandrel drawing.Therefore,the CPFEM was not performed in this study.This study focused on the experimental validation of the crystal plastic behavior causing outer surface roughening in die-less mandrel drawing,which has never been investigated.

2.Experimental procedures

2.1.Materials

Mg alloy(ZM21)tubes with an outer diameterD0of 6.0 mm and inner diameterd0of 3.8 mm were used as the starting materials.They were manufactured by the die drawing after extrusion by Macrw Co.Ltd.(Shizuoka,Japan).

2.2.Tube drawing

The starting materials were drawn using a die-less mandrel drawing machine of our own making.A stainless steel(SUS304)rod with a diameter of 3.8 mm was used forthe mandrel.A schematic illustration of the die-less mandrel drawing machine used in this study is shown in Fig.1.

Fig.1.Schematic illustration of the die-less mandrel drawing machine used in this study.The parameters V0 and V1 are the feeding speed and drawing speed,respectively.

The distance between the heating and cooling coils was 10 mm.The tube was chucked on both the entrance side of heating coil and exit side of cooling coil.A graphite spray(Fine Chemical Japan Co.LTD.,FC-169,Tokyo,Japan)was applied on the inner surface of starting material as a lubricant before chucking.The mandrel was chucked on a fixed chuck and inserted into the starting material to the exit of the cooling coil.The chucks were mounted on a ball screw connected to a servo motor.The rotational speed of the servo motors on the heating coil entrance and cooling coil exit sides controlled the feeding speedV0and drawing speedV1,respectively.The feeding speedV0was set to 5.0 mm/s.The starting material was drawn for a single pass with drawing speedsV1of 6.0,7.0,8.0,and 10.0 mm/s to give tubes drawn with various speed ratiosV1/V0of 1.2,1.4,1.6,and 2.0.A high-frequency induction heating device(Ameritherm Inc.,114060–11030294,New York,USA)with a power of 10 kW and a frequency in the range of 150–400 kHz controlled the temperature inside the heating coil to 400 °C.The temperature around the heating coil was measured using infrared thermography(Optris GmbH,X1400,Berlin,Germany).The tube that passed through the heating coil was water-cooled inside the cooling coil during drawing.The starting material was also drawn without the mandrel under the above conditions to investigate the effect of the mandrel on outer surface roughness and microstructure in the die-less mandrel drawing.Contact between the tube and the mandrel during the die-less mandrel drawing process was verified by stopping in the middle of the process.

Square-shaped marking-lines were placed on the outer surface of the starting material using a height gage(Mitutoyo,192–106,Kanagawa,Japan).The starting material with the square-shaped marking-lines was drawn for a single pass at a speed ratioV1/V0of 2.0 to evaluate strain and outer surface roughness distributions of the drawn tube in the longitudinal direction.The measurement method of the strain and surface roughness distribution are described in Sections 2.3.2 and 2.3.3.

2.3.Measurement methods

2.3.1.Dimension measurement

The cross sections of the starting material and the drawn tubes were mechanically polished after resin embedding.The polished cross sections were observed using a threedimensional microscope(VR-5000,Keyence,Osaka,Japan).Approximate circles of the outer and inner circumferences were drawn based on three arbitrary pixels of the tube crosssectional image.The outerD1and innerd1diameters of the drawn tubes were measured as the approximate circle diameters of the outer and inner circumferences,respectively.The wall thickness of the drawn tubet1was calculated using the formula(D1-d1)/2.The dimensions were evaluated at four points in the drawing direction.The average values were calculated,and the standard deviations were obtained.

The longitudinal section of the tube drawn with the mandrel but stopped midway through the drawing process was mechanically polished after resin embedding.The polished longitudinal section of the area between the heating and cooling coils was observed using a three-dimensional microscope.Furthermore,the outer diameters of the tubes corresponding to around the heating and cooling coils were measured.

2.3.2.Strain measurement

Fig.2 shows a schematic illustration of the square-shaped marking-lines drawn on the outer surface of the Mg alloy tubes.The longitudinalland circumferentialnlengths of each square-shaped marking-line on the outer surface of drawn tube were measured using a three-dimensional microscope.The longitudinalεland circumferential strainεθin the longitudi-nal direction around the heating and cooling coils were measured using the formulas ln(l1/l0)and ln(n1/n0),respectively.The subscripts 0 and 1 indicate before and after drawing,respectively.The longitudinall0and circumferentialn0lengths before drawing were 2.0 and 2.4 mm,respectively.

Fig.2.Schematic illustration of the square-shaped marking-lines before and after drawing.The parameters l and n indicate the length of the square-shaped marking-lines for the longitudinal and the circumferential directions,respectively.The subscripts 0 and 1 indicate before and after drawing,respectively.

Fig.3.Process of evaluating the outer surface roughness and the crystal orientation of the tubes in the same measurement area.The symbols DD,CD,and ND represent the drawing direction,circumferential direction,and normal direction to outer surface,respectively.

2.3.3.Surface quality and crystal orientation

Fig.3 shows the process for evaluating the outer surface roughness and crystal orientation of the tubes in the same measurement area.Here,DD,CD,and ND represent the drawing direction,circumferential direction,and normal direction to the outer surface,respectively.The tubes were pasted onto metal plate.Cross-shaped marking-lines were made on the outer surface of the tubes using a height gage(Mitutoyo,192–106,Kanagawa,Japan).These marking-lines are the positioning marks for measuring the surface roughness and crystal orientation in the same measurement area.Marking-lines were also used to evaluate the polished depth.

The outer surface roughness of the tube was evaluated using a confocal laser microscope(VK-100,Keyence,Osaka,Japan)over 1 mm away from the edge of the marking-lines in the drawing direction to avoid the area deformed by the marking-lines.The heightHwas measured from an arbitrary position of the outer surface of the tube,excluding an abnormally high or low value.The average heightHavewas calculated from an arbitrary position.The height of the outer surface of the tubehwas calculated as the difference between the height from the arbitrary positionHand the average heightHaveusing the formula(H-Have).In this study,the arithmetic average roughness of areaSais defined as the surface roughness.Eq.(1)defines the arithmetic average roughness ofSa.ParameterSrepresents the area of the evaluation region.The parameterh(x,y)is the height at position(x,y)on the evaluation surface.The position axesxandycorrespond to the DD and CD,respectively.

The outer surface was mirror-polished at a polishing depth below the grain size to evaluate the crystal orientation of the crystal grain which constituted the outer surface roughness.After mirror polishing,the outer surface was etched using a picric acid solution.After etching,the outer surface was examined using a confocal laser microscope to measurethe polished depth.The marking-line depth was defined as the difference between the maximum and minimum heights of the roughness profile of the marking-line.The polished depth was defined as the difference between the markingline depths before and after mirror polishing.Kikuchi patterns of the outer surface of tubes were obtained in the same area as the surface roughness using a field-emission scanning electron microscope(JSM-7100F,JEOL,Tokyo,Japan)with electron backscatter diffraction(OIM8,TSL Solutions,Kanagawa,Japan).The inverse pole figure(IPF)map was drawn based on the measured Euler angle using a proprietary programming language,MATLABTM(R2021a,MathWorks,Massachusetts,USA).The weighted mean of the grain area was calculated using OIM AnalysisTM(TSL Solutions,ver.8,Kanagawa,Japan),and the average diameter of the crystal grains was calculated as the grain sizeg.The kernel average misorientation(KAM)of the drawn tube was also calculated using OIM AnalysisTM.

Fig.4.Cross sections of the tubes.Cross-sectional images of(a)the starting material and(b)the drawn tubes.The symbols DD,CD,and ND represent the drawing direction,circumferential direction,and normal direction to outer surface,respectively.

Fig.5.Final dimensions of the drawn tube.(a)Final outer diameter D1,inner diameter d1,and wall thickness t1 of the die-less and the die-less mandrel drawn tubes.(b)Wall thickness t1/outer diameter d1 against the speed ratio of the die-less and the die-less mandrel drawn tubes.The parameters V0 and V1 are the feeding speed and the drawing speed,respectively.The gray and black dotted lines in Fig.5(a)are the eye guide and the theoretical line derived from the constant volume law,respectively.The dotted lines in Fig.5(b)are the eye guide.The error bars in Fig.5(a)and(b)indicate the standard deviations.

3.Results

3.1.Dimension of drawn tubes

Fig.4 shows the cross-sectional images of the starting material and drawn tubes.The equivalent plastic strainεeqof the die-less and die-less mandrel drawn tubes was calculated using Eqs.(2)and(3)[24].The parameterRrepresents the reduction in the cross-sectional area of the tube.The parameterAindicates the cross-sectional area.The subscripts 0 and 1 indicate before and after drawing,respectively.

Fig.6.Longitudinal section images of the die-less mandrel drawn tube with the inserted mandrel at the speed ratio V1/V0 of 2.0.(a)The entire image of the drawn tube and the magnified view at(b)the heating coil side,(c)the deformation area,and(d)the cooling coil side.The symbols DD,CD,and ND represent the drawing direction,circumferential direction,and normal direction to outer surface,respectively.The white dotted circles were the positions where the mandrel began to contact the inner surface of the tube.

Fig.7.Deformation behavior of the tubes drawn at a speed ratio V1/V0 of 2.0.Strain distributions of(a)die-less drawn and(b)die-less mandrel drawn tubes.

The cross-sectional size decreased as the speed ratio increased in both the die-less and die-less mandrel drawings.The wall thickness of the die-less mandrel drawn tube was thinner than that of the die-less drawn tube for each speed ratio.Fig.5.shows the measurement results for the final dimensions of the drawn tubes.The outer diameter and wall thickness decreased as the speed ratio increased in both the die-less and die-less mandrel drawings.The outer diameter of the die-less mandrel drawn tube was larger than that of the die-less drawn tube for each speed ratio.The inner diameter of the die-less drawn tube decreased as the speed ratio increased.In contrast,the inner diameter did not decrease significantly in the die-less mandrel drawing.For example,the inner diameterd1of the die-less mandrel drawn tube decreased by only 0.04 mm from the initial inner diameterd0of 3.8 mm at the speed ratioV1/V0of 2.0.The wall thickness of the die-less mandrel drawn tube was smaller than that of the die-less drawn tube for each speed ratio.The ratio of the wall thickness to the outer diametert1/D1of the die-less mandrel drawn tube was smaller than that of the die-less drawn tube,as shown in Fig.5(b).Therefore,it was confirmed that the die-less mandrel drawing had a larger thinning of the wall thickness than the die-less drawing.Eqs.(4)and(5)show the theoretical formula of the outer diameter and the wall thickness change in the die-less mandrel drawing derived from the constant volume law[24].Parameterdmrepresents the mandrel diameter of 3.8 mm.The outer diameter and the wall thickness of the die-less mandrel drawn tube generally agree with Eqs.(4)and(5),respectively.

Fig.8.Outer surface roughness and temperature distributions for the longitudinal direction of(a)the die-less drawn tube and(b)the die-less mandrel drawn tube at the speed ratio V1/V0 of 2.0.The dotted gray lines show the approximate line based on the least squares method.The dotted black lines show the eye guides.

Fig.9.Measurement results of the outer surface roughness.The height maps of the(a)starting material and the(b)drawn tubes.The symbols DD,CD,and ND represent the drawing direction,circumferential direction,and normal direction to outer surface,respectively.

Fig.6 shows the longitudinal section of the die-less mandrel drawn tube for which the drawing process at a speed ratioV1/V0of 2.0 was interrupted.The outer diameter of the tube on the heating coil side almost agreed with that of the starting material of 6.00 mm.Furthermore,the outer diameter of the drawn tube at the cooling coil side agreed with the measurement value of 4.96 mm obtained by the image analysis,as shown in Fig.5.Therefore,it was confirmed that the longitudinal section of the drawn tube was polished in the central region of the drawn tube.The mandrel did not contact to the inner surface of the tube on the heating coil side.However,the mandrel came on contact with the inner surface between the heating and cooling coils.After entering the cooling coil,the mandrel was still in contact with theinner surface.Therefore,it was confirmed that the mandrel suppressed the decrease in the inner diameter of the Mg alloy tube between the heating and cooling coils by contacting the inner surface of the tube.

Fig.10.The surface roughness against the outer circumferential strain εθ at the speed ratio V1/V0 of 2.0.The circumferential strain corresponds to Fig.7.The dotted lines indicate eye guides.

Fig.11.Measurement results of the grain size of the die-less and the die-less mandrel drawn tubes.The dotted lines indicate the eye guide.

Fig.12.Evaluation results of the polishing depth of the drawn tubes at the speed ratio V1/V0 of 2.0.(a-1)Height map and surface roughness profile of the die-less drawn tube at the line segment A-B before mirror polishing and(a-2)after mirror polishing.(b-1)Height map and surface roughness profile of the die-less mandrel drawn tube at the line segment C-D before mirror polishing and(b-2)after mirror polishing.The symbols DD,CD,and ND indicate the drawing direction,circumferential direction,and normal direction to the outer surface,respectively.

Fig.13.Comparison of the height maps and IPF maps in the same observation area of the outer surface.(a)Staring material and(b)tubes drawn at the speed ratio V1/V0 of 2.0.The symbols DD,CD,and ND represent the drawing direction,circumferential direction,and normal direction to the outer surface,respectively.

3.2.Strain distribution around heating and cooling coils during drawing

Fig.7 shows the strain distribution of the drawn tube in the longitudinal direction around the heating coil at a speed ratioV1/V0of 2.0.The longitudinal strainεlincreased and circumferential strainεθdecreased slightly before passing through the heating coil exit.After entering the heating coil,the longitudinal strainεlincreased to the strain calculated from the speed ratio(ln(l1/l0)=ln((V1-V0)/V0)=0.69).The outer circumferential strainsεθof the die-less and dieless mandrel drawn tubes decreased to the strains calculated from the measured values of the final outer diameters(ln(D1/D0)=-0.26 and-0.19,respectively).

3.3.Outer surface roughness of starting material and drawn tubes

Fig.8 shows the outer surface roughness and temperature distributions during the die-less and die-less mandrel drawings.As shown in Fig.8(a-1)and(b-1),thermography could not measure the temperature of the tube outer surface directly under the heating coil.Therefore,the temperature at thexpositions from-22 to-12 mm and from-10 to 0 mm could not be measured,as shown in Fig.8(a-2)and(b-2).An approximate line is drawn for the temperature distribution based on the least-squares method.The temperature was greatest at a position of approximately-5 mm during both die-less and die-less mandrel drawings.The outer surface roughness increased slightly before exiting the heating coil.The outer surface roughness increased significantly after exiting the heating coil,especially in the temperature range of 200–300 °C.

Fig.9 shows the height maps of the outer surfaces of the drawn tubes measured using a confocal laser microscope.The area of the convex(red)and concave(blue)parts increased as the equivalent plastic strain increased in both the die-less and die-less mandrel drawings.Fig.10 shows the outer surface roughness of the drawn tubes against the outer circumferential strain,which is shown in Fig.7.The outer surface roughness increased as the outer circumferential strain increased in both the die-less and die-less mandrel drawings.The outer surface roughness of the die-less mandrel drawn tube was larger than that of the die-less drawn tube for a given outer circumferential strain.Therefore,the outer surface roughnessdeveloped in the die-less mandrel drawing more than in the die-less drawing.

Fig.14.Comparison of the IPF map,KAM map,and height map in the same measurement area of the die-less drawn tube at a speed ratio V1/V0 of 2.0.The white line in the IPF map indicate the low-angle grain boundary.The symbols DD,CD,and ND indicate the drawing direction,circumferential direction,and normal direction to the outer surface,respectively.

Fig.15.Schmid factor maps considering each individual slip system and all slip systems of the drawn tubes.(a)Die-less and(b)die-less mandrel drawn tubes.The evaluation area corresponds to the IPF map of the drawn tubes in Fig.13.The symbols DD,CD,and ND indicate the drawing direction,circumferential direction,and normal direction to the outer surface,respectively.

3.4.Outer surface roughness and IPF maps in the same observation area

Fig.11 shows the grain size of the cross section of the die-less and die-less mandrel drawn tubes.The grain size increased slightly as the equivalent plastic strain increased.Furthermore,the grain sizes of the die-less mandrel and die-less drawn tubes were almost the same.

Fig.12 shows the marking-lines on the outer surface of the die-less and die-less mandrel drawn tubes before and after mirror polishing.It was evaluated that the polished depth was within the grain size to confirm that the crystal orientation of the crystal grain which constituted the outer surface roughness could be measured.The polished depths on the outer surface of the die-less and the die-less mandrel drawn tubes were 25 μm,10 μm,respectively,which were sufficiently smaller than the grain size.Therefore,the crystal orientation was evaluated in almost the same layer as the outer surface roughness layer.

Fig.13 shows a comparison of the height maps and IPF maps in the same observation area of the outer surface of the starting material and the drawn tubes at a speed ratioV1/V0of 2.0.The concave and convex outer surfaces are composed of multiple crystal grains.The concave and convex parts,which were expressed as red or blue parts in the height map,were observed around the crystal grains with the{20}plane vertical to the ND.Twinning was observed on the outer surface of the starting material,but not on the outer surfaces of the drawn tubes.

4.Discussion

4.1.Active slip system causing outer surface roughening in die-less mandrel drawing

The outer surface roughness increased significantly after exiting the heating coil,especially in the temperature range of 200–300 °C,as shown in Fig.8.Galiyev et al.reported that DRX occurs in the temperature range of 200–300 °C via nucleation in the slip band,trapping the moving dislocations by the low-angle grain boundary[34].Fig.14 shows a comparison of the IPF map and the KAM map of the die-less drawn tube at the speed ratioV1/V0of 2.0 for the same measurement area.The white line in the IPF map is a lowangle boundary within 5°,which corresponds to a high KAM value.Therefore,the dislocation activity during die-less mandrel drawing was confirmed.It is considered that the outer surface developed by the dislocation activity such as slip deformation.The outer surface roughness did not develop at the low-angle grain boundary,where the dislocation piled up,as shown in Fig.14.Therefore,the piled-up dislocation caused by DRX does not seem to be a dominant factor in outer surface roughening.Williams et al.reported that twinning deformation is an important factor in the plastic deformation of HCP metals[35].However,twinning was not observed on the outer surface of the drawn tubes,as shown in Fig.13(b).Therefore,dislocation activity,such as slip deformation but excluding twin deformation,seems to be a dominant factor that causes outer surface roughening during both die-less mandrel drawing and the die-less drawings.

The effect of the Schmid factor on the outer surface roughness in both die-less and die-less mandrel drawings was in-vestigated as follows.The Schmid factor in each slip system was calculated using Mtex,which is a MATLABTMtoolbox.Fig.15 shows the Schmid factor map considering each individual slip system(basal,prismatic,and pyramidal)and all slip systems of the outer surface of the drawn tubes.The maximum Schmid factor in each slip system and all slip systems is plotted in the grain map.Fig.16 shows the line profiles of the Schmid factor in Fig.15 and the outer surface roughnesson the same measurement line of the die-less and die-less mandrel drawn tubes.Some grains in the grain map are numbered in Fig.16(a-1)and(b-1)to compare the Schmid factor and the outer surface roughness.The line profiles of the dieless mandrel and die-less drawn tubes were obtained in line segments A-B and C-D,respectively.

Fig.16.Comparison of the Schmid factor and surface roughness in the same line profile.(a-1)Grain map;line profile of the Schmid factor at the line segment A-B considering only the(a-2)basal slip,(a-3)prismatic,(a-4)pyramidal,and(a-5)all slip systems;and(a-6)surface roughness profile of the die-less mandrel drawn tube at a speed ratio of 2.0.(b-1)Grain map;line profile of the Schmid factor at the line segment C-D considering only the(b-2)basal slip,(b-3)prismatic,(b-4)pyramidal,and(b-5)all slip systems;and(b-6)the surface roughness profile of the die-less drawn tube at a speed ratio of 2.0.The symbols DD,CD,and ND represent the drawing direction,circumferential direction,and normal direction to the outer surface,respectively.

Fig.17.Inverse pole figures of the drawn tubes.(a)Die-less mandrel and(b)die-less drawn tubes.

On line segment A-B of the die-less mandrel drawing,grains-1 and-2 were convex and flat,respectively,as shown in Fig 16(a-6).Wouters et al.reported that surface roughness developed when there was a large difference in the Schmid factor among the crystal grains[31,32].However,the Schmid factors of grains-1 and-2 considering only the basal slip system were almost the same even though grain-1 was convex,as shown in Fig.16(a-2).Furthermore,the Schmid factor considering only the prismatic slip system of grain-2 was larger than that of grain-1 even though the crystal deformation of grain-2 was so small that it was flat in the surface roughness profile,as shown in Fig.16(a-3).Thus,the slip deformation of the basal and prismatic slip systems did not cause the outer surface roughening in the die-less mandrel drawing.The same result was obtained for the die-less drawn tube.

On the other hand,the outer surface roughness developed with a large difference in the Schmid factor when only the pyramidal slip system was considered.For example,grains-1 and-3 developed convexly and concavely,respectively,and had larger Schmid factors than grain-2,as shown in Fig.16(a-4).Furthermore,the Schmid factor difference considering all the slip systems between grains-2 and-3 was small even though concavity developed in grain-3,as shown in Fig.16(a-5).The same result was obtained for the die-less drawn tube.For example,convex and concave areas developed around grain-5(flat part),where the Schmid factor was smaller than that of grains-4 and-6,as shown in Fig.16(b-4).Therefore,it is considered that the outer surface roughening was mainly caused by the slip deformation of the pyramidal slip system during both the die-less and die-less mandrel drawings.

Several studies have reported the relationship between the CRSS and the temperature for each slip system of HCP metal as follows:At room temperature,the CRSS of the basal slip system is much smaller than that of the pyramidal and prismatic slip systems.The CRSS of the basal slip system did not change much but decreased in the pyramidal and prismatic slip systems as the temperature increased at temperatures below 500 °C.Therefore,the difference in the CRSS between the basal and non-basal slip systems decreased as the temperature increased[37,38].The CRSS difference between the basal and non-basal(pyramidal and prismatic)slip systems was small when the outer surface roughness developed at temperatures of 200–300 °C.Therefore,the non-basal slip systems seem to be active during outer surface roughening in this study.

4.2.Difference in microstructure between die-less and die-less mandrel drawn tubes

The crystal grains with the{20}plane vertical to the ND had a large Schmid factor,as shown in Figs.13 and 15.For example,the white grain in Fig.15 corresponds to the green grain shown in Fig.13.It is considered that the crystal grain with the{20}plane vertical to the ND was mainly responsible for outer surface roughening because the large Schmid factor difference between the grain and the surrounding grains caused inhomogeneous plastic deformation.For example,grain-1,in which the{20}plane was vertical to the ND,was convex,as shown in Fig.16(a-6).

Fig.17 shows the IPF for the ND of the outer surface of the drawn tubes.The{20}crystal plane of the die-less mandrel drawn tube was more oriented in the ND than the die-less drawn tube.Therefore,the large number of crystal grains with the{20}plane vertical to the ND in the dieless mandrel drawing was one of the reasons why the outer surface roughness was more developed in the die-less mandrel drawing than in the die-less drawing.Fig.18 shows the relationship between the equivalent plastic strain and final outer surface roughness.Osakada et al.reported empirically that the free surface roughness developed linearly with the equivalent plastic strain[43].Eq.(6)shows the empirical relationship between the equivalent plastic strainεeqand the final surface roughness.

The theoretical line is illustrated in Fig.18.The surface roughness of the starting materialS0was 0.48 μm.The parametergis the average grain size,which is the average value in Fig.11.The parametercis a coefficient,which is set to0.16 so that the theoretical line agrees with the plots.The final outer surface roughness increased linearly with the equivalent plastic strain in both the die-less mandrel and die-less drawings.The final outer surface roughness of the die-less and die-less mandrel drawn tubes were almost the same for a given equivalent plastic strain,even though the outer circumferential strain was larger in the die-less drawing than in the die-less mandrel drawing,as shown in Fig.7.This phenomenon may have been caused by the large number of crystal grains with the{20}plane vertical to the ND in the die-less mandrel drawing.

Fig.18.Final outer surface roughness against the equivalent strain of the die-less and the die-less mandrel drawn tubes.The dotted line indicates the empirical formula of the free surface roughening.

4.3.Summary of the effect of the mandrel on the outer surface roughening and microstructure

Fig.19 shows a schematic illustration of the outer surface roughening behavior during the die-less mandrel drawing of the Mg alloy tube.The outer surface roughness slightly increased in the heating coil.The outer surface roughness mainly develops between the heating and cooling coils,when the material is at the DRX temperature.The slip deformation of the pyramidal slip system mainly causes the roughening of the outer surface.Furthermore,the crystal grains with the{20}plane vertical to the ND had a larger Schmid factor than the other crystal grains.Therefore,it is considered that the outer surface roughness developed most around crystal grains with the{20}plane vertical to the ND because the large Schmid factor difference between the grain and the surrounding grains caused inhomogeneous plastic deformation.The{20}plane is strongly oriented toward the ND owing to the contact between the mandrel and the inner surface of the tube.The large number of crystal grains with the{20}plane vertical to the ND in the die-less mandrel drawing is one of the reasons why the outer surface roughness was more developed in the die-less mandrel drawing than in the die-less drawing for a given outer circumferential strain.The inner circumferential strain in the die-less mandrel drawing was almost zero because the inner diameter did not change due to the mandrel,as shown in Fig.5.On the other hand,the outer circumferential strain was less than zero because the outer diameter decreased during drawing,as shown in Figs.5 and 7.The circumferential strain gradient in the wall thickness direction was one of the reasons why the{20}plane was strongly oriented in the ND in the die-less mandrel drawing.This study focused on the experimental validation of the relationship between the crystal orientation and the outer surface roughness in die-less mandrel drawing,which has never been investigated.Therefore,a detailed investigation of the orientation process of the{20}plane vertical in the ND in die-less mandrel drawing remains for future studies.

Fig.19.Schematic illustration of the outer surface roughening behavior in the die-less mandrel drawing.The symbols DD,CD,and ND indicate the drawing direction,circumferential direction,and normal direction to the outer surface,respectively.

Usually,the CRSS of the basal slip system is much smaller than that of the pyramidal and prismatic slip systems at room temperature.In this study,we took the CRSS difference between the basal and non-basal(pyramidal and prismatic)slip systems to be small when the outer surface roughness developed at temperatures of 200–300 °C,in accordance with previous studies[37,38].However,the actual CRSS of each slip system was not evaluated in this study.Therefore,the reason that the pyramidal slip system seems to be more active than the prismatic slip system was not clarified.Investigating the effect of CRSS on outer surface roughening remains a topic for future work.

We performed the die-less mandrel drawing only under the heating temperature of 400 °C to stably obtain the drawn tubes according to previous study[24],which reported that the highest reduction in area was obtained at 400 °C in dieless mandrel drawing of Mg alloy tubes.Galiyev et al.reported that the Low-temperature DRX occurred under the temperature below 200 °C[34].Therefore,outer surface roughening behavior below 200°C seems to be different from that in this study.Investigating the effect on the temperature other than 400 °C on the outer surface roughness during drawing with non-uniform deformation,as shown in Fig.19,remains as a future work.

Consequently,this study clarified that although a large amount of thinning of the wall thickness can be achieved in die-less mandrel drawing,as shown in Fig.5(b),the contact between the mandrel and the inner surface of the tube further develops the outer surface roughness.Therefore,future research should investigate a process that significantly suppresses the development of outer surface roughness in the manufacturing process of microtubes by die-less mandrel drawing.

5.Conclusions

In this study,the outer surface roughness and crystal orientation of die-less and die-less mandrel drawn Mg alloy tubes were evaluated in the same measurement area.As a result,the effects of the mandrel on the outer surface roughening and the microstructure in the die-less mandreldrawing were clarified as follows.

(1)The surface roughness increases as the equivalent plastic strain increases.The outer surface becomes rougher in the die-less mandrel drawing than in the die-less drawing for a given outer circumferential strain.

(2)It is considered that the slip deformation of the pyramidal slip system is mainly responsible for the outer surface roughening after the tube exits the heating coil.

(3)The crystal grain with the{20}crystal plane vertical to the ND has a larger Schmid factor than the other crystal grains.Inhomogeneous plastic deformation owing to large Schmid factor difference between{20}grain and the surrounding grains seems to cause large outer surface roughening.

This study clarified that contact between the mandrel and inner surface of tube increases the outer surface roughness.Future research should investigate processes that suppress outer surface roughening in manufacturing process of microtubes by die-less mandrel drawing.

Acknowledgments

This study was supported by JSPS KAKENHI Grant Nos.19H02476 and 20KK0321,and by the Amada Foundation Grant No.AF-2021035-C2.T.K.performed this study as a project researcher under financial support from the Institute of Industrial Science of the University of Tokyo.