Experimental research on deformation and dimensional accuracy of rectangular-section tubular part during open die hydro-pressing process

Abstract

To solve the problems involving in the open die hydro-pressing process, such as different corner radii and bigger dimensional deviation, an open die hydro-pressing process was proposed and an experiment was conducted on hydro-pressing process of DP590 steel tubular part with rectangular-section. The effects of pressing sequence and supporting pressure on cross-sectional shape and corner filling were discussed. An analysis was conducted to reveal the reason for uneven deformation of the section corners. It is illustrated that the values of corner radii of the tubular part are obviously different under the condition of one pressing step, and the corner nearby the fixed die is larger than that nearby the pressing punch. The reason is that a difference exists in the circumferential force between the four corners due to the existence of the friction, which results in the uneven deformation on the section corner zone. The deviation of the cross-sectional dimension can be effectively improved by multi pressing steps, but too great a number of pressing steps also reduces the forming efficiency. Under the condition of two pressing steps, a rectangular-section tubular part with high dimensional accuracy was obtained by a reasonable pressure loading path. Its relative corner radius is only 2.5, which exceeds the limiting value of that formed by conventional tube hydroforming.

Keywords

Low pressure hydroforming open die corner radius dimensional accuracy

Introduction

Tube hydroforming has been widely used as a lightweight forming technology in automotive industry due to its advantages in manufacturing hollow structures.^1,2 In such forming process, an internal pressure is applied to force the tube to expand and to conform to the die cavity.³ However, besides the function of driving force for the plastic deformation, the internal pressure amplifies the effect of friction simultaneously. Friction force hinders the metal flowing greatly, which makes over thickness thinning and even cracking near the corner zone.^4,5 Accordingly, corner forming is a major difficulty in tube hydroforming. Previous studies illustrated that the minimum relative corner radius was 5 for steel parts achieved by hydroforming, and 7.5 for aluminum alloy parts.⁶ In addition, the required internal pressure increases rapidly as the corner radius decreasing. The forming pressure of a tubular part with small corner is even close to the flow stress of the material.⁷ Excessive high pressure induced several shortcomings, such as heating build-up as compressing and difficulty in pressure control, which leads to demand on the duty-heavy hydraulic press and the large size of die sets. Therefore, to reduce the required internal pressure is a goal pursued by many scholars.

To overcome these problems, a low pressure tube hydro-pressing technology was put forwarded.⁸ Different from the tube hydroforming, the internal pressure only plays a supporting role and a moving punch forces the pressurized tube to conform to the die cavity.⁹ In general, the “closed” structure die is mostly employed in this process. Thus it is also called as closed die hydro-pressing.^10,11 The internal pressure required to hydro-press a 409 stainless steel tubular part with relative corner radius of 12.5 is decreased to 10 MPa, which is only 10% of that necessary in conventional hydroforming.¹² The deformation behaviors of tube under the conditions of linear increasing pressure and constant pressure were compared and analyzed, and the optimal loading path was determined as the latter one.¹³ Some studies focused on the shape accuracy of the formed part. A closed die hydro-pressing process of rectangular cross section was experimentally researched and demonstrated that obvious springback occurred, and also resulted a difficulty in taking the part out of the die cavity.¹⁴ For the closed die hydro-pressing, it was the only way to limit the springback by increasing the internal pressure. In the closed die hydro-pressing process, the tube blank must be put into the die through a preforming process, because the cross section circumference of the tube is unchanged but the shape is changed. The effect of preform on the closed die hydro-pressing in terms of pressure requirement, buckling, and die filling was investigated.^15,16 With higher pressure the buckling reduced but thickening of tube increased. A closed die hydro-pressing process of hollow component with varied cross-section perimeters was researched and the tube wall was subjected to compression deformation.^17,18 The critical supporting pressure was given through the analytical model and it increases gradually as the deformation going on.^19,20 As discussed above, many problems would be introduced if the internal pressure improved greatly. Furthermore for the closed die, springback compensation can only be applied along the die closing direction, which resulted in a poor dimensional accuracy along the direction perpendicular to the die closing movement. A study on the processes of tubes in a trapezoid-sectional die has been carried out.²¹ The result showed that buckling defect was tend to occur for the difficulty in parting surface design due to there is only one relative movement between the tube and the die.²²

As discussed above, the low pressure tube hydro-pressing is a promising alternative for the forming of hollow components, especially for the high strength steel part. Up to now, the die structures used in the hydro-pressing process are all closed. There are still several limitations that would have to be considered, such as buckling defects, poor dimensional accuracy, preform, and difficulty in taking the part out of the closed die. The above disadvantages limit the practical application of the closed die hydro-pressing technology.

To overcome the limitations of the closed die hydro-pressing, an open die hydro-pressing process was proposed by the author. The open die is composed of a semi-closed lower die, a vertical punch, and a horizontal punch. The punches apply the pressing movement independently, which provides the process with greater flexibility. For the die can be opened along two directions, there is no need for preforming, the buckling defect is eliminated and the difficulty in taking the part out of the die cavity is overcome at the same time. However, there is no cavity on the corner zone of the open die to constrain the tube in die contacting and forming, so a variety of problems have been arisen such as different corner radii and bigger dimensional deviation.

To analyze the deformation and dimensions accuracy, an experimental research was conducted on the hydro-pressing process for a DP590 steel tubular part with rectangular cross section. The effects of pressing sequence and supporting pressure on cross-sectional shape and corner deformation were discussed. A tubular part with relative corner radius of 2.5 was formed to validate the effectiveness and feasibility of open die tube hydro-pressing.

Specimen and experimental schemes

Principle of the open die hydro-pressing process

The schematic of the open die hydro-pressing process is illustrated in Figure 1. The whole forming process can be divided into three stages: filling stage, vertical pressing stage, and horizontal pressing stage. In the filling stage, the vertical punch and the horizontal punch are opened. A tube is put into the die, then sealed by sealing punches, and filled with liquid medium. The pressure in the tube is increased to a target value. In the vertical pressing stage, the vertical punch moves toward the die and press the tube into a racetrack shaped cross section, and there is no constraint on both sides of the tube. The displacement of vertical punch is represented by Y. In the horizontal pressing stage, the tube is formed into the desired shape under the movement of the horizontal punch and the constraint of the vertical punch. The displacement of horizontal punch is represented by X.

Figure 1.

Schematic diagram of the open die hydro-pressing processing: (a) filling stage, (b) vertical pressing stage, (c) horizontal pressing stage, (d) dimensions of tube blank, and (e) dimensions of specimen.

Specimen and material

The wider application of high strength steel tubular parts in the automotive industry is limited by the high pressure required during the conventional tube hydroforming. Thus, DP590 steel tube with nominal thickness of 2.6 mm was used in this study and the outer diameter of the initial tube was 65 mm. For hollow components, any section is composed of straight lines and circular arcs. Thus, a rectangular-section part was researched as shown in Figure 1(e). The relative corner radius of the rectangular-section was designed to be 2.5, and the ratio of length to width was a/b = 1.1. According to the principle of constant perimeter, the section length was a = 56 mm, the section width was b = 52 mm, and length of the pressing zone was l = 200 mm. The uniaxial tensile tests were conducted on an Instron-5569 testing machine along the axial direction of the tube and the mechanical properties are listed in Table 1.

Table 1.

Mechanical properties of DP590 tubes along the axial direction.

Ultimate tensile strength (MPa)	Yield strength (MPa)	Total elongation (%)	Strength coefficient K (MPa)	Strain hardening exponent n
748	557	0.21	895	29.7

Experimental schemes

In the process of hydro-pressing, the ultimate supporting pressure p_s is the minimum internal pressure that causes the tube to expand circumferentially, that is, the initial yield pressure of tube blank. However, the tube did not bulge during the whole process of hydro-pressing, its cross-section perimeter was unchanged, and the internal pressure only played a role of supporting the tube wall. Thus, the supporting pressure needs to be smaller than the ultimate supporting pressure. According to the Tresca yield criterion, the ultimate supporting pressure p_s can be derived as

p_{s} = \frac{2 t}{d} σ_{s}

(1)

Where, t is the tube wall thickness, d is the outer diameter of the initial tube, and $σ_{s}$ is the yield stress. According to equation (1) and Table 1, the ultimate supporting pressure is 45 MPa, thus the supporting pressure is set as 0.3p_s = 13.5 MPa. In order to make full use of the advantage of the open die compared with the closed die, the vertical and horizontal pressing punches are independently controllable, a multi-step hydro-pressing method was proposed. The deformation sequence of the tube blank is different under different pressing sequence. Therefore, in the first group of experiments, the number of pressing steps was set to 1, 2, 3, respectively. The effects of the number of pressing steps on cross-sectional shape and corner filling were studied, during which the total pressing displacement and the supporting pressure remained constant. The total vertical pressing displacement is the difference between the outer diameter of the initial tube and the section width of the designed specimen, that is, Y = d−b = 13 mm. The total horizontal pressing displacement is the difference between the outer diameter of the initial tube and the section length of the designed specimen, that is, X = d−a = 9 mm. In the multi-step hydro-pressing process, the deformation behavior of the tube is also affected by the supporting pressure loading path. Therefore, in the second group of experiments, the number of pressing steps was set to 2. The supporting pressure loading path can be divided into four stages, which are respectively set to 0.3p_s-0.3p_s-0-0, 0-0-0.3p_s-0, 0-0-0-0.3p_s.

Two groups of hydro-pressing experiments were performed based on the scheme detailed in Table 2, and the loading paths are shown in Figure 2. For specimen 1 (Figure 2(a)), internal pressure is increased to a target value during the filling stage (t₀−t₁). In the pressing stage (t₁−t₃), the supporting pressure is kept constant and pressing punches are successively pressed down, wherein the displacements of vertical and horizontal punches are Y and X respectively. In the unloading stage (t₃−t₅), the internal pressure decreases to zero and the vertical and horizontal punches move backward. For specimen 2, the pressing process is uniformly divided into two steps, during which the pressing displacement in each step is 1/2 of the total displacement. For specimen 3, the pressing displacement in each step was 1/3 of the total displacement. For specimen 4 (Figure 2(b)), there are two stages in the whole process, one with supporting pressure and the other without supporting pressure, the pressure acts the function of supporting in the first step, and then the tube is formed by pressing punch without pressure in the second step. For specimen 5, the pressing stage with pressure is located in the second vertical pressing step. For specimen 6, the pressing stage with pressure is located in the second horizontal pressing step.

Table 2.

Experimental schemes.

Group	Specimen	Supporting pressure (MPa)	Pressing sequence	Vertical displacement (mm)	Horizontal displacement (mm)
I	1	13.5	Y-X (1 step)	Y=13	X=9
I	2	13.5	1/2Y-1/2X-1/2Y-1/2X (2 steps)	Y=13	X=9
I	3	13.5	1/3Y-1/3X-1/3Y-1/3X-1/3Y-1/3X (3 steps)	Y=13	X=9
II	4	13.5-13.5-0-0	1/2Y-1/2X-1/2Y-1/2X (2 steps)	Y=13	X=9
II	5	0-0-13.5-0	1/2Y-1/2X-1/2Y-1/2X (2 steps)	Y=13	X=9
II	6	0-0-0-13.5	1/2Y-1/2X-1/2Y-1/2X (2 steps)	Y=13	X=9

Figure 2.

Loading paths: (a) specimen 1 of group I and (b) specimen 4 of group II.

Design and manufacturing of novel experimental device

The key to hydro-pressing is how to keep the pressure constant in the pressing process, but the volume of the tube cavity is reduced during the die closing, thereby the pressure in the tube is going up due to the compressed liquid. To keep the pressure constant during the whole pressing process, the liquid inside the tube must be discharged as required. Taking a rectangular-section as an example, the initial volume of the tube cavity can be derived as

V_{0} = \frac{π}{4} d^{2} l

(2)

After pressing, the internal volume of the rectangular-section tubular part can be calculated as

V = l [b (a - 2 r) + 2 r (b - 2 r) + π r^{2}]

(3)

Assuming the ratio of the vertical pressing displacement to the outer diameter of the tube is $α = Y / d = (d - b) / d$ , the volume compression ratio can be expressed as

\begin{matrix} V' = \frac{V_{0} - V}{V_{0}} = \frac{{[2 (a + b) (1 - α) - π b]}^{2}}{π b^{2} (4 - π)} \\ - \frac{4 a}{π b} {(1 - α)}^{2} + 1 \end{matrix}

(4)

According to the formula for liquid volume compression, the relationship between the internal pressure and the pressing displacement can be expressed as

\begin{matrix} p - p_{0} = E_{V} V' = 2000 \\ {\frac{{[2 (a + b) (1 - α) - π b]}^{2}}{π b^{2} (4 - π)} - \frac{4 a}{π b} {(1 - α)}^{2} + 1} \end{matrix}

(5)

Where, p is the internal pressure of the compressed tube, p₀ is the initial pressure inside the tube, E_V is the liquid bulk elastic modulus, that of water is $E_{V} = 2000$ MPa. When the vertical pressing displacement is 13 mm, that is, $α = Y / d = 0.2$ , the volume compression ratio is 12.11%, and the corresponding pressure in the tube is up to 255 MPa. It is known that the initial volume of the tube cavity is 0.66 L. It can be calculated that the internal volume of the tubular part is 0.58 L from equation (4). Therefore, it is necessary to discharge 0.08 L of water through hydraulic system in time to ensure that the pressure in the tube remains constant at 13.5 MPa.

To maintain a constant pressure during the pressing process, the experimental setup for open die hydro-pressing process used in this study was developed based on analysis above, as shown in Figure 3, which is composed of a hydraulic press, an open die set, an oil-water pressure transducer, a hydraulic system, and a computer control system. To keep the internal pressure constant, a pressure relief valve was set in the hydraulic system so that the superfluous compressed liquid can be discharged rapidly. The function of the oil-water pressure transducer is to transfer the oil pressure into the water pressure, so that the tube can be formed by water. The open die set includes a die, a vertical punch, a horizontal punch, and two sealing punches, as shown in Figure 3(b). The vertical punch and horizontal punch were independently controlled by the hydraulic press and the horizontal hydro-cylinder, respectively.

Figure 3.

Experimental setup of low pressure tube hydro-pressing: (a) schematic diagram of experimental setup and (b) actual experimental setup.

Results and discussion

Cross section size under different pressing sequences

Figure 4 shows the shape of the cross section under the condition of one pressing step (specimen 1) under a supporting pressure of 13.5 MPa. In the vertical pressing stage, a racetrack shaped cross section without buckling defect was directly formed from a circular tube blank by the displacement of Y = 13 mm for vertical punch. The diameter of the arcs on both sides of the racetrack section is 52.52 mm, which is equal to the difference between the tube blank diameter d and the vertical pressing displacement Y. The deviation of the cross section dimension along the vertical direction is 0.52 mm due to the springback of the tube along the pressing direction. The racetrack section length of 73.13 mm, can be calculated as the design value of 72.41 mm based on the principle of constant perimeter, which is mainly due to the sharper and smaller radius of the mid-point area of the arc. Such that the horizontal dimension of the arc is larger than the design value. It can be found from Figure 4(c) that the corner radius nearby the fixed die is significantly larger than that nearby the horizontal punch, the former is about 8 mm, and the latter is about 6.5 mm. There is an obvious difference exists in the cross section size under different pressing sequences. Figure 5 is the cross section of specimen 2 under the condition of two pressing steps. Figure 6 is the cross section of specimen 3 under the condition of three pressing steps.

Figure 4.

Cross section shape under the condition of one pressing step (specimen 1): (a) initial cross section, (b) cross section after vertical pressing, and (c) cross section after horizontal pressing.

Figure 5.

Cross section shape under the condition of two pressing steps (specimen 2).

Figure 6.

Cross section shape under the condition of three pressing steps (specimen 3).

The corner radius non-uniformity, $Δ r = (r_{max} - r_{min}) / r$ , was used to evaluate the difference between the cross section corners, where r_max is the maximum corner radius of the cross section, r_min is the minimum one, and r is the design value of the corner radius. Small Δr means high accuracy section shape. Figure 7 shows the effect of pressing sequence on corner radius distribution. Under the condition of one pressing step (specimen 1), the radius of the upper corner (r1) near the pressing punch is the smallest, that is, 6.52 mm, the radius of the lower corner (r2) near the pressing punch is 6.58 mm, the radius of the lower corner (r3) near the die is the largest, that is, 8.45 mm, the radius of the upper corner (r4) near the die is 8.05 mm. The four corner radii above are all larger than the design value of 6.5 mm. The difference between the maximum radius and the minimum radius is 1.93 mm, and the corner radius non-uniformity of specimen 1 is 29.7%. Under the condition of two pressing steps (specimen 2), the difference between the maximum radius and the minimum radius is 0.95 mm, and the corner radius non-uniformity of specimen 2 is 14.6%. Under the condition of three pressing steps (specimen 3), the difference between the maximum radius and the minimum radius is 0.36 mm, and the corner radius non-uniformity of specimen 3 is 5.5%. The degrees of corner uneven deformation of the cross section mentioned above are different, but the corner radius near the die is larger than the design value, and the corner radius near the pressing punch is basically equal to the design value. The corner radius non-uniformity of two-step pressing is 50.8% lower than that of one-step pressing. Compared with one-step pressing, the corner radius non-uniformity of three-step pressing is reduced by 81.5%.

Figure 7.

Effect of pressing sequence on value of the corner radius.

To reveal the mechanism of uneven deformation of the section corners, the force of rectangular cross section is analyzed, as shown in Figure 8, where Fx is horizontal pressing force, Fy is vertical pressing force, and f is friction force between the tube and the die. According to the force equilibrium condition along the horizontal direction, it can be derived as

2 σ_{θ} t + 2 f (a - r_{1} - r_{4}) + p (b - 2 r_{1}) = F_{x}

(6)

Figure 8.

Force of the rectangular cross section: (a) the rectangular cross section and (b) forces and moments acting on the corner of the tube.

From equation (6), it can be seen that $σ_{θ}^{r_{1}} > σ_{θ}^{r_{4}}$ . Assuming that the four corners of the cross section are circular arcs, the forces, and bending moments on the corner of the tube are shown in Figure 9(b). According to the force and moment equilibrium condition, it can be derived as

{\begin{matrix} (T \cdot \sin \frac{π}{4} + F_{y} \cdot \cos \frac{π}{4}) s = 2 M \\ T \cdot \cos \frac{π}{4} + F_{y} \cdot \sin \frac{π}{4} = 0 \end{matrix}

(7)

Figure 9.

Cross section size under different number of pressing steps: (a) length and (b) width.

Where, $T = σ_{θ} tl$ , $s = r (1 - \cos \frac{π}{4})$ , collate equation (7) can be obtained as

σ_{θ} = \frac{2 (\sqrt{2} + 1)}{tl} \cdot \frac{M}{r}

(8)

Because of $σ_{θ}^{r_{1}} > σ_{θ}^{r_{4}}$ , the relationship of corner radius is $r_{1} < r_{4}$ . From equation (8), it can be seen that the circumferential forces on the four corners are different due to the existence of friction, which results in an uneven deformation of the cross section corners. Therefore, the friction is the essential parameter for the uneven deformation. In the process of hydro-pressing a circular-section into a rectangular-section, multi pressing steps can shorten the straight side length and reduce the influence area of friction force accordingly, and as a result the corner radius non-uniformity is improved.

Both the length and width of the cross section were measured for calculating the dimension deviation, as shown in Figure 10. Under the condition of one pressing step (specimen 1), the length deviation of 56.23 mm is 0.41% compared with the design value of 56 mm, and the width deviation of 52.19 mm is 0.37% compared with the design value of 52 mm. The length deviation is 0.26% and the width deviation is 0.18% under the condition of two pressing steps (specimen 2). The section dimension deviation of three-step pressing (specimen 3) is the lowest, that is, the length is 0.12% and the width is 0.11%. Compared with specimen 2, the dimension deviation of specimen 3 decreased 53.85% in length and 38.89% in width. It was demonstrated that multi pressing steps reduces the single step pressing displacement, so that the single step deformation amount is decreased and springback of tube is reduced accordingly. The accuracy of the length and width of the cross section is improved as a result.

Figure 10.

Indentation depth of cross section under different supporting pressure: (a) specimen 4, (b) specimen 5, (c) specimen 6, and (d) depth of dent.

Cross-sectional shape under different pressure loading paths

Three specimens were formed under different supporting pressure loading paths from which buckling defects of varying degrees can be observed, as shown in Figure 9. In order to characterize the degree of dent of the straight side on the section, the dent ratio was defined as the ratio of the dent depth to the length of the side along dent direction. Under the loading path that the first pressing step with a supporting pressure of 13.5 MPa and the second pressing step without pressure (specimen 4), the dent depth in vertical direction was greatest (5.41 mm), with a corresponding dent ratio of 10.4%, and the dent depth in horizontal direction was 2.52 mm, with a dent ratio of 4.5%. Under the loading path that the second vertical pressing step with a supporting pressure of 13.5 MPa and the other steps without pressure (specimen 5), the degree of dent was slight (2.7%) in vertical direction but obvious (9%) in horizontal direction. Under the loading path that the second horizontal pressing step with a supporting pressure of 13.5 MPa and the other steps without pressure (specimen 6), the degree of dent in vertical direction was lowest (1.3%), and the dent ratio in horizontal direction was 3.4%. In contrast with specimen 5, the dent ratios of specimen 6 in the vertical and horizontal directions were reduced by 51.9% and 62.2%, respectively. The dent ratios of specimen 6 in both vertical and horizontal directions were reduced by 87.5% and 24.4% than the values of specimen 4. In the first pressing step, the buckling defect is not easy to occur in the straight side without supporting pressure due to the small pressing displacement. In the second pressing step, as the pressing displacement increased, the straight side is formed under the internal pressure support, and without the supporting pressure, the straight side will be buckling.

Pressure loading path under the condition of two pressing steps

Based on the results of the above analysis, reducing the effect of friction force can effectively enhance the dimensional accuracy of cross section. The effect of friction force depends heavily on both the contact area and supporting pressure. Large contact area with the straight side can lead to different corner radii of the cross section. The contact area can be reduced by multi pressing steps, but too great a number of pressing steps also reduces the forming efficiency. Unreasonable design of the loading path of the supporting pressure can also lead to the appearance of buckling defect. Therefore, a reasonable pressure loading path under the condition of two pressing steps was determined. Under the loading path that the first pressing step without pressure and the second pressing step with a supporting pressure of 13.5 MPa, specimen 7 was obtained as shown in Figure 11. It can be observed that the difference between the maximum and minimum corner radii was 0.5 mm and the corner radius non-uniformity was 7.7%. Table 3 lists the measured lengths, widths, corner radii, and the related deviations of the cross-section. The deviations of length and width were 0.21% and 0.13%, respectively. Under the condition of two pressing steps, the corner radius non-uniformity of specimen 7 was reduced by 47.3% compared with that of specimen 2, while the deviations in length and width were reduced by 19.2% and 27.8%, respectively. The pressure loading path of specimen 2 was that the supporting pressure kept constant (13.5 MPa) during the whole two pressing steps. Under the same condition of pressing displacement and pressing sequence, reasonable change of the supporting pressure reduced the effect of the friction force, and narrowed the differences between the circumferential force and bending moment on corner zones, which thus enhanced the dimensional accuracy of the cross section.

Figure 11.

Cross section size of specimen 7: (a) cross section of specimen 7 and (b) cross section corner radius distribution of specimen 7.

Table 3.

Cross section size of specimen 7.

Length		Width		Corner radius
Measured value (mm)	Deviation (%)	Measured value (mm)	Deviation (%)	No.	Measured value (mm)	Corner radius non-uniformity (%)
56.10	0.21	52.08	0.13	r₁	6.52	7.7
56.14		52.06		r₂	6.53
56.12		52.07		r₃	7.02
				r₄	6.74

Conclusion

An open die hydro-pressing process was proposed and a novel experimental device was firstly manufactured, in which the pressing punches can be operated independently along two directions and the internal pressure can be kept constant with the pressing displacement ongoing.

The values of four corner radii of the cross section are different from each other under the condition of one pressing step, the corner nearby the fixed die is larger than that nearby the pressing punch, and the corner radius non-uniformity is 29.7%. Multi pressing steps can effectively reduce uneven deformation. The non-uniformity is decreased to 14.6% under the condition of two pressing steps, when the condition of three pressing steps was used, the non-uniformity is less than that of one and two steps.

An analysis was performed to reveal the reason for uneven deformation of the cross section corners. There is a difference in the bending moment and circumferential force on the four corner zones due to the influence of friction force on the four straight sides, which results in different values of corner radii of the same cross section. The action of friction can be improved by multi pressing steps, so that the corner radius nonuniformity was decreased.

The section length and width deviations of the part formed by one-step pressing are bigger, which are 0.41% and 0.37%, respectively. The greater the number of pressing steps, the higher the dimensional accuracy of the cross section. The dimension deviations of two-step pressing are reduced by 37% and 51%, which are 0.26% in length and 0.18% in width.

Under the condition of two pressing steps, a rectangular-section tubular part was successfully obtained without internal pressure in the first pressing step and 13.5 MPa pressure in the second pressing step. Its relative corner radius is only 2.5, which exceeds the limiting value of that formed by conventional tube hydroforming. The corners radii of cross section are more uniform and the dimensional accuracy is greatly improved by 19.2% in length and 27.8% in width compared with the specimen under the condition of constant pressure (13.5MPa) during two pressing steps.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1229) and the National Natural Science Foundation of China (grant no. 51775134).

ORCID iD

Shijian Yuan

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