1 Introduction

Nowadays, increasing competition and environmental regulations has forced the transportation manufacturing industry towards producing low-mass vehicles to achieve fuel savings, reduced emissions and safe structures. Hydroforming process has been taken as an effective approach that could enable better structural integrity, high strength-to-weight ratios, tight tolerances, and a better rigidity [1]. Tube hydroforming has become a widespread metal forming processes in the industry. In this process, the internal fluid pressure forces the circular shape of the tube to form into the shape of the die cavity [2]. As yet, vast studies have been carried out to examine tube hydroforming process parameters [3,4,5,6]. The influences of plastic anisotropy [7], strain hardening exponent [8], compressive stress [9] and parameters of material properties [10] were reported in previous studies. In addition, some researchers have focused on microstructural evolution during tube hydroforming process [11, 12]. However, there has not been studies on the deformation behavior of the ultra-fine grained (UFG) material known as a high-strength to weight ratio materials during hydroforming process. As mentioned, interest to use high-strength to weight ratio tube have been increased significantly recently. Severe Plastic Deformation (SPD) processes have been introduced to produce UFG materials as a high strength material [13]. Parallel tubular channel angular pressing (PTCAP) process developed by Faraji et al. is a suitable method to produce high strength UFG tubes [14]. Tube undergoes two half cycles shear deformation in the PTCAP process shown schematically in Fig. 1. Diameter of the tube expands while passing two shear zones (Fig. 1(a)) in the first half cycle. Then, in the second half cycles, the tube returns to its initial dimensions (Fig. 1(b)). The equivalent strain achieved from the N passes of the PTCAP process can be estimated via the following equation [14]:

$$ \overline{\varepsilon }_{PTCAP} = 2N\left\{ {\sum\limits_{i = 1}^{2} {\left[ {\frac{{2\cot {(}\phi_{i} {/ 2 + }\psi_{i} {/ 2) } + \, \psi_{i} \cos ec{(}\phi_{i} {/ 2 + }\psi_{i} {/ 2) }}}{\sqrt 3 }} \right]} + \frac{2}{\sqrt 3 }\ln \frac{{R_{2} }}{{R_{1} }}} \right\} $$
(1)

where the parameters are shown in Fig. 1.

Fig. 1
figure 1

Schematic of (a) the first and (b) the second half cycles of the PTCAP process and (c) the die parameters (mm)

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The main purpose of the present study is to investigate formability behavior of the UFG tubes during square-sectional hydroforming process. In this regard, the UFG Cu-30Zn tubes processed one pass PTCAP process formed under pressurized fluid in a square-sectional die set. The comparison between thickness variation of the annealed and one pass PTCAP processed tubes during the hydroforming process were examined. In addition, FEM simulation was carried out to examine the experimental results.

2 Experimental Procedure

In the current study, the PTCAP die with the die parameters shown in Fig. 1 was used to produce UFG tubes. Drawn brass tubes (Cu-30Zn) were annealed at the temperature of 600 ˚C for a period of 1 h. Tubes with the dimensions of 40 mm in length, 2.5 mm in thickness and 20 mm outer diameter were processed by the PTCAP die through one pass at ram speed of 5 mm/min at room temperature. To reduce the friction during the process, the molybdenum disulfide (MoS2) was used as a lubricant. Mechanical properties of the samples were measured through performing tensile test in both axial and peripheral directions with gage length of 10 mm and width of 1 mm. To investigate the effect of the PTCAP process on the formability of the brass tubes during hydroforming process, annealed and one pass PTCAP processed tubes were machined to a length of 30 mm, and the thickness of the tubes was tried to decrease to about 0.8 mm, however there was a little difference in thickness of the machined tubes since it was difficult to machine them at exact 0.8 mm thickness.

A simple and practical hydroforming die set as shown shematically in Fig. 2. was made to form high-strength UFG brass tubes. Through pressing the punch, high-pressure fluid can be applied to form the tubes in a square-sectional die without requiring expensive equipment. A 300 KN Universal INSTRON single action press at a punch velocity of 2 mm/min was implented to carry out the hydroforming process. Due to the low velocity of the deformation process, the hydroforming process can be considered quasi-static process, and the effect of the strain rate on deformation can be neglected. The tubes were processed at three different pressures, of which the highest applied prussure was the bursting one. The FEM simulation was carried out using commrecial software ABAQUS to investigate the thickness variation and corner radius of the hydroformed tubes and to compare with the experimental datas. The thickness variation of the processed tubes were measured using optical microscopy. The measuremt presicion was 0.01 mm. In addition, fracture surfaces of the bursted tubes were analyzed using scanning electron microscope (SEM).

Fig. 2
figure 2

Schematic of the tooling for the hydroforming process

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3 Results and Discussions

In our previous study, both a microsructure and mechanical properties of the Cu–Zn tubes after PTCAP process were investigated [15]. Optical microstructure of the anealed and one pass PTCAP process tube is shown in the Fig. 3. A coarse grain structure of the annealed brass tube with average grain size of 70 µm was significantly reduced after PTCAP process, and homogenous fine grains achieved as depicted. In fact, severe shear strain applied in the PTCAP process causing this great grain refinement occurred after only one pass [16]. Mechanical properties of the tubes is indicated in Fig. 4. After PTCAP process, the strength of the tube increased remarkably in both axial and peripheral directions. Grain refinement which leads to the considerable enhancement of the dislocation density testifies the incredible rising of the strength in both axial and peripheral directions while reducing the unltimate strain [17]. Tavakkoli et al. reported that the higher increase of the strength in the peripheral direction to the axial direction can be related to the variation in the crystallographic texture of the brass tube after the PTCAP process [18]. In the hydroforming process, the primary stress that drives the deformation of the tubes occurs in the peripheral direction. Therefore, the mechanical properties of the tubes in this direction (Fig. 4(b)) can be viewed as indicative of the material's strength during deformation.

Fig. 3
figure 3

Optical micrographs of (a) annealed tube and (b) one pass PTCAP processed tube [15]

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Fig. 4
figure 4

Stress–Strain curves of the annealed and PTCAPed tubes in (a) axial and (b) peripheral directions

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Three level fluid pressures were considered to evaluate thickness variation of the annealed and the PTCAP processed tubes during square-sectional hydroforming process. These pressures were chosen by trial and error based on the thickness and ultimate strength of the tubes as the highest pressure was the bursting one. Figure 5 shows the annealed tubes after the hydroforming process. In this figure, the fluid pressure magnitude as well as initial thickness for forming the tubes and corner radius achieved in both experimental procedure and FEM simulation are also presented. The minimum corner radius in which the annealed tube burst was 1.9 mm at the pressure of 152 MPa for the initial thickness of 0.78 mm which shows a good formability of the annealed brass tube that through gradually increasing the fluid pressure, material flaw and small corner radius could be achieved. According to the large grain structure (Fig. 3(a)), it can be predicted that the annealed tube has a ductile deformation behavior in which dislocations can easily move, and the material's good formability can be attributed to its high strain-hardening coefficient (Fig. 4(b)), which enables it to undergo plastic deformation and distribute the applied stress more evenly across its structure. As a result, the material can be easily shaped into complex forms during hydroforming. The high strain-hardening exponent indicates the material's excellent ductility, toughness, and ability to absorb energy, which are desirable properties for successful hydroforming operations. For the lower pressures, as expected the corner radius was larger. It was 4.7 mm and 3.55 mm at the pressure of 92 MPa with the initial thickness of 0.95 mm, and 106 MPa with the initial thickness of 0.78 mm, respectively. The corner radiuses predicted by the FEM simulation were almost in good agreement with the experimental results. The average error between FEM and experimental data was about 10%.

Fig. 5
figure 5

Annealed brass tubes during the square-section hydroforming process at the three level fluid pressures

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Figure 6 shows PTCAPed processed tubes after the hydroforming process. As indicated, the minimum corner filling radius for the PTCAPed tube was 6.35 mm at the bursting pressure of 148 MPa with the initial thickness of 0.78 mm. Comparison between two annealed and PTCAPed burst tubes showed that the fluid pressure for both tubes was almost equal however the corner filling radius for the PTCAPed tube was bigger that of the annealed tube. It means that PTCAPed tubes had a higher strength and lower formability which was consistent with the tensile test result. The same result was gained for the FEM simulation. The corner radius for two other pressures were 8.25 mm and 7.2 mm at the pressure of 102 MPa with the initial thickness of 0.78 mm, and 117 MPa with the initial thickness of 0.7 mm, respectively. According to the UFG structure of the PTCAPed tube (Fig. 3(b)), the smaller grain size allows for a higher number of grain boundaries, which act as barriers to the motion of dislocations during plastic deformation which impedes the movement of dislocations. As a result, the tube had a low formability. In addition, the stress–strain curve (Fig. 4(b)) indicates that the tube had an extremely high strength and low ultimate strain which implies that the ultrafine-grained tube had limited ductility or ability to undergo plastic deformation before failure. The low ultimate strain is attributed to the higher dislocation densities and reduced ability of dislocations to move through the fine grains. While the material exhibits high strength, it may have limited ductility and may be more susceptible to premature failure or necking compared to materials with higher ultimate strains. Same as the annealed tubes, the forming pressures were smaller for the larger corner radius. The FEM simulation predicted the corner radius well for the PTCAPed tubes with the average error of about 2%. Considering the corner radius, the forming pressure for the UFG tubes whose strength was enhanced due to the PTCAP process were more than the annealed tubes. Furthermore, increasing the forming pressure leads to the increasing of the friction force which prevent from flowing material [19]. Both the lower formability and the higher friction force caused to reach the larger corner radius in comparison to the annealed tube. Maximum tensile stress exists in the area between corner and the tube contacted with the die wall in which fracture occurred in that region.

Fig. 6
figure 6

PTCAPed processed brass tubes during the square-section hydroforming process at the three level fluid pressures

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Figure 7 shows thickness distribution of the annealed and PTCAPed tubes during hydroforming process in both experimental and FEM procedures. The important measurement points from direction A to F are shown in this figure. As depicted, thickness variation of all the tubes in both experimental and simulation had same trend with a small error. As depicted, the wall thickness was varied from the initial thickness at the center-line of the die to the minimum at the unsupported corner radius which can be related to the lack of material flow due to the high friction force between tube and die wall [6]. There was no significant thickness variation in the corner area since a uniform stress existed in that region (point D in all the tubes) [19]. For the burst annealed tube (Fig. 7 (c)), the thickness reduced to about 0.55 mm at the points C and E in the transition zone from the initial thickness of 0.78 mm (about 30% reduction). The thickness reduction for two other annealed tubes were about 16% and 20% since the forming pressures were lower. The thickness variation became more non-uniform as the fluid pressure increased and the corner radius reduced. On the other hand, due to the lower formability and the larger corner radius, the thickness variation was less non-uniform for the PTCAPed tubes. For the lowest pressure of the PTCAPed hydroformed tube, since the corner radius was large (8.25 mm) and the measurement precision was 0.01, thickness variation was not seen in all regions of the tube (Fig. 7 (d)). Increasing the forming pressure led the material to flow. The thickness reduction for the second level pressure was about 5%, and the largest thickness reduction for the bursting pressure was about 22%. In addition, the reduction of the strain hardening led to unproper distribution of the strain that resulted in fracture happening sooner for fine grained materials [8, 20].

Fig. 7
figure 7

FEM simulation and experimental results of the thickness distribution of the annealed tubes at the pressure of (a) 92 MPa, (b) 106 MPa, (c) 152 MPa and the PTCAPed tubes at the pressure of (d) 102 MPa, (e) 117 MPa, (f) 148 MPa

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Fracture surface of the annealed and PTCAP tubes after bursting in the hydroforming process are shown in Fig. 8. As depicted, there was a ductile fracture for the annealed tube due to the existence of deep and coarse dimples. On the other hand, there were many small and preferred oriented dimples for the PTCAP processed tube which could be the sign of the brittle fracture. The fracture type changed from the necking mode for the annealed tube to the shear mode for the PTCAP processed one. Also, Tavakkoli et al. reported that brass PTCAP processed tube fractured by the shear mode in tensile test [18].These results are completely consistent with the results of the forming tubes during hydroforming process in which the annealed tube reached to the small corner radius because of the better formability in comparison to the PTCAP processed tube.

Fig. 8
figure 8

SEM images showing the fracture surfaces of (a) annealed and (b) PTCAP processed tubes after hydroforming process

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4 Conclusions

The formability of UFG tubes in square-sectional hydroforming were investigated for the first time. Evaluating specific parameters such as corner filling and thickness distribution, comparing the corner radius and thickness variation between UFG and annealed tubes, and analyzing the fracture behavior of hydroformed tubes were the main output of this study. These findings could potentially contribute to the understanding of the deformation behavior of UFG materials and provide valuable insights. The minimum corner radius for the UFG tube was 6.35 mm at the pressure of the 148 MPa, while it was 1.9 mm for the annealed tube at the pressure of the 152 MPa. Lower formability of the UFG tube caused to reach larger corner radius. Thickness variation of the tubes indicated that non-uniform thickness distribution existed for the annealed tube, however it was less non-uniform for the UFG tubes. The fracture study of the hydroformed tubes after bursting showed that the mode of fracture changed from the necking mode for the annealed tube to the shear mode for the UFG tube.