Research on hydroforming of 5A06 aluminum alloy semi-ellipsoid shell with differential thickness

For the purpose of eliminating the annular welding seams in welding structures with differential thickness, a hydroforming method using a circular 5A06 aluminum alloy plate with a radial differential thickness in coupling with a flexible polyurethane auxiliary plate was proposed to form an integrated semi-ellipsoid shell. The circular 5A06 aluminum alloy plate had a smaller in the middle and a larger thickness in the periphery. In the forming process of such aluminum alloy plates, concentrated deformation and fracture might have occurred in the thin zone. According to the size of the target specimen, the testing plates with two types of thickness ratios were obtained by mechanical processing. Furthermore, the thickness and strain of the drawn specimens with different thickness ratios were analyzed under different hydraulic pressure by means of deep drawing experiments. Compared to the conventional deep drawing, the formability of 5A06 aluminum alloy plates with differential thickness could be effectively improved by hydroforming. The integrated semi-ellipsoid shells with the thickness ratios of 2/3 and 1/2 were obtained under the hydraulic pressure of 10 MPa with maximum thinning ratios of 8.5% and 10.9%, respectively. In a word, the increase in hydraulic pressure could effectively reduce the maximum thinning ratio in the thin zone, and improve the thickness distribution uniformity.


Introduction
To meet the demands for the new-generation carrier rockets, the thin-walled curved surface components have been gradually designed to be lightweight, large, and integrated [1]. However, the safety and reliability of such components have become a huge challenge in processing. For example, the dome of the propellant tank is a typical thin-walled curved component, which suffers from complex loads and extreme service conditions. Generally, limited by the size of aluminum alloy blanks and the capacity of equipment, a dome is manufactured with a welding structure constituted of several petal parts [2]. But this kind of structure has the problems of low-dimensional accuracy, high rejection rate, and low reliability. The welding seams between the petal parts can be eliminated via hydroforming of the integrated dome without wrinkling defects [3]. However, even though this enables one to improve the reliability of the propellant tank and to greatly reduce the manufacturing cycle, the annular welding seam between the dome and the fork ring is still unavoidable. To address the above issues, NASA has adopted the technical route of spinning and CNC milling to manufacture the dome and the fork ring with an integrated structure [4]. However, this technique is complicated by the long manufacturing cycle and serious material waste.
As an important part of the propellant tank, the fork ring is used to connect the dome, tank section, and short shell, and this structure is widely used in the carrier rockets in current service [5]. In the manufacturing of the aluminum alloy fork rings, the multi-pass ring rolling and heat treatment are coupled to obtain the ring blanks with large diameter and thickness [6], and the component is then obtained by numerical control machining. Meanwhile, the material is wasted seriously via this forming method, and it is difficult to control its microstructure and properties. Both the fork ring and the dome belong to the components with large size and high precision, but the welding technology between two parts has been a challenge for a long time because of the risk of fracture, and the welding quality can thus be hardly guaranteed, in which the fracture easily occurs. During the service of such components, the strength and service life of the welding seams are lower than those of the base metal, and the distribution of mechanical properties tends to be uneven, which makes the welding seam a main danger zone for the whole components. The most important thing is that the dome and the fork ring are required to be connected by a forced assembly, which results in the large welding residual stress and low reliability for the welding seam.
For the components with such kind of structural characteristics, an integral deep drawing process of plates with radial differential thickness seems to be the most optimal processing route. Assisted with machining, this type of plates can be obtained with a thin zone in the middle and a thick zone in the periphery, and the transition zone between two zones is further designed in a reasonable way. The thin and thick zones are used to form the dome and the fork ring of a propellant tank, respectively, which can realize the integrated manufacturing of these two components. This allows one not only to eliminate the annular welding seam between the dome and the fork ring but also to increase the reliability of the integrated component. Moreover, the machining volume in the later period as well as the springback can also be reduced, which fundamentally enhances the production efficiency.
At present, studies on plates with differential thickness mainly focus on tailor-welded (TWB) and tailor-rolled (TRB) blanks. These types of blanks are mainly used in automobile industry to produce lightweight pieces [7]. The welding seam or the rolled thickness transition zone has basically the straight line shape, and most studies mainly focus on the movement defects of the transition zone, as well as the mechanical properties and forming limits of the blanks. In that regard, various methods, e.g., uniaxial tensile testing [8,9], bulging testing [10][11][12], bending experiments [13], U-channel forming [14,15], and deep drawing [16,17], have been employed to assess the formability and mechanical properties of such blanks. The strain distribution and movement defects in the thickness transition zone are usually monitored by stamping experiments and finite element simulation [18], in which the movement defects are considered to be structure-dependent [19]. A finite element model was proposed for the non-uniform thickness TRB top-hat structure component, and it was validated through the bending experiments, so that the bending characteristics of this blank were improved by optimizing the TRB parameters [20]. Based on the analysis of the major strain rate via the discrete Gaussian convolution, a forming curve was proposed to predict the forming limit of a high strength steel TWB [21]. Nevertheless, eliminating the non-uniform deformation between different zones of the blanks with differential thickness is still a challenge.
The transition zone of the plates with radial differential thickness is ring-shaped, and the main deformation mode of the plates is deep drawing instead of bending. Because of the thickness difference between the thick and thin zone, the radial tensile stress in the thin zone during deep drawing is dramatically increased, which results in an excessive thinning or fracture defect. As an advanced metal forming method, hydroforming can effectively improve the forming limits of aluminum alloys, achieving a more uniform thickness distribution within the deep-drawn components, and improving the quality of products [22]. Meanwhile, setting an auxiliary plate upon deep drawing and adopting the multilayer plate hydroforming method [23] can also reduce the thinning ratio of the drawn components.
In view of the above, the semi-ellipsoid shells with differential thickness were taken as the research subjects in this work, and the hydroforming method using an auxiliary polyurethane plate was proposed. The formability of the 5A06 aluminum alloy plates with different thickness ratios was analyzed by deep drawing experiments under various hydraulic pressures. The results are expected to provide the experimental basis for the forming of complex thin-walled curved components with differential thickness, opening up new prospects for the development of components with this type of structure.

Materials and specimens
The annealed 5A06 aluminum alloy sheet with a 3-mm thickness was selected for the deep drawing experiments, and the mechanical properties of the material were determined by uniaxial tensile testing, as shown in Table 1.
The target specimen was a semi-ellipsoid shell with a thick zone in the periphery and thin zone in the middle (see Fig. 1a). The semi-major axis a, the semi-minor axis b, and the axial length ratio m of the shell are 112 mm, 80 mm, and 1.4, respectively. Figure 1b displays the testing plate with a differential thickness used in the experiments. The thin zone, transition zone, and thick zone were arranged from the middle to the periphery, with a transition angle of 5°. The measuring points were marked along the radial direction every 10 mm on the 5A06 aluminum alloy plates to analyze the deformation behavior of the experimentally drawn specimens. The thickness ratio λ is defined as the thickness of a thin zone (t A ) to that of a thick zone (t B ) as follows: The thickness in the thin zone was designed as 2 mm and 1.5 mm, and the corresponding thickness ratios λ were 2/3 and 1/2, respectively. To ensure that the height of the thick zone in the target specimen is at least 15 mm in the vertical direction, the diameters of the thick zone D 0 and the thin zone D 1 were set at 330 mm and 250 mm, respectively. The circular 5A06 aluminum alloy plates with the diameters of 330 mm were obtained by wire-electrode cutting, and the thin zones of the plates were reduced to 2 mm and 1.5 mm.
The thicknesses of polyurethane auxiliary plates (t PU ) were 3 mm, and their diameters were 330 mm, corresponding to the 5A06 aluminum alloy plates. The shore hardness of the polyurethane plate was HA85. Figure 2 demonstrates the schematic diagram of hydroforming of the plate with a radial differential thickness. A flexible plate is placed between the aluminum alloy plate and the die as a process auxiliary plate. The hydraulic pressure applied to the lower surface of the polyurethane plate is provided by the fluid medium of the pressurization system. Figure 3 depicts the experimental setup for hydroforming. Figure 3a displays the 2000 kN double-action hydraulic

Experimental setup and procedure
press, in which the movements of the drawing slide and blank holder slide are controlled by a servo hydraulic system. Figure 3b shows the pressurization system, which provides a hydraulic pressure for hydroforming. Figure 3c demonstrates the drawing tool, including the blank holder, the punch, and the die.
A preset blank holder force was applied by the blank holder slide, and the punch was driven by the drawing slide. The initial blank holder force was set at 6 tons, and as the hydraulic pressure increased, the blank holder force was correspondingly adjusted to allow a slight overflow between the plate and the die. Three types of hydraulic pressure loading paths were designed to meet the punch stroke, as shown in Fig. 4, under the maximum hydraulic pressures of 5 MPa, 7.5 MPa, and 10 MPa, respectively.

The effect of thickness ratio on the limit drawing depth
Besides the hydroforming method, the conventional deep drawing experiments (p = 0, t PU = 0) were also carried out on the plates with differential thickness need to be carried out. First, a 5A06 aluminum alloy plate with a differential thickness and a thickness ratio of 2/3 was selected for the deep drawing experiment without hydraulic pressure. Figure 5a shows the related semi-ellipsoid shell with the drawing stroke of 90 mm. Figure 5b demonstrates the section diagram of the drawn specimen and the thinnest position corresponds to a radius of 73 mm.
To study the effect of the thickness ratio on the deep drawing behavior, a 5A06 aluminum alloy plate with a differential thickness and a thickness ratio of 1/2 was chosen for the experiment. Figure 5c shows the drawn specimen with the thickness ratio of 1/2 without hydraulic pressure. Once the drawing stroke reaches 72 mm, the fracture defect occurs, evolving into a crack in the thin zone with a radius of 95 mm. Therefore, when the thickness ratio is 1/2, it becomes more difficult to form the 5A06 aluminum alloy plate by the conventional deep drawing.

3.1.2
The effect of thickness ratio on the thinning ratio of a thin zone Figure 6 shows the thinning ratio distributions within the thin zone with the thickness ratios of 2/3 and 1/2. Compared with the case of the thickness ratio of 2/3, the overall thinning ratio of a thin zone with the thickness ratio The maximum thinning ratio of the specimen with the thickness ratio of 2/3 is 11.9%, while that close to the fracture of the specimen with λ = 1/2 is up to 22%. As the thickness ratio decreases, the forming difficulty of the plates with differential thickness increases and gradually reaches the forming limit, which means that a more advanced forming method needs to be adopted to form this type of plates. During deep drawing, the thin zone in the middle of the plate bears the much greater radial tensile stress than that of the plate of the same thickness, which is due to a thick flange. The hanging zone and the contact zone of the aluminum alloy plate are subjected to the radial tensile stress. Figure 7 displays the stress state of the transition zone along the radial direction under the condition of conventional deep drawing (p = 0). The radial tensile stress at points A and B is σ φA and σ φB , respectively. The thicknesses in the thin and thick zones are t A and t B , respectively. Besides, σ φA can be understood as the tensile stress required to produce the plastic yield of the material in the thick zone. It can be considered that σ φA is inversely proportional to t A , and the smaller t A is, the larger σ φA is. This means that the thin zone of the part is more prone to cracking and the deep drawing of plates with differential thickness is thus more laborious.

Strain distributions within the thin zone with different thickness ratios
According to the thickness distribution of the drawn specimens and the initial thickness i the thin zone, the normal strain of the measuring points can be expressed as follows: where t and t 0 represent the thicknesses of the initial plates and the drawn specimens, respectively.
(2) t = In(t∕t0) Determining the radii of the measuring points on the drawn specimen and comparing them with the initial radii allows one to calculate, the circumferential strain of the measuring points: where r and r 0 donate the radii of the measuring points before and after the drawing experiments, respectively.
On the basis of the volume invariance principle, the radial strain of the measuring points can be obtained as follows: Figure 8 displays the calculated normal strain, circumferential strain and radial strain of the drawn specimens with different thickness ratios after the conventional deep drawing. The overall normal strain of the plate with the thickness ratio of 2/3 is larger than that of the specimen with λ = 1/2, while the overall radial strain is smaller. For the specimen with the thickness ratio of 2/3 and the punch stroke of 90 mm, the minimum normal strain and the maximum radial strain in the thin zone are − 0.127 and 0.154, respectively. In turn, for the sample with λ = 1/2 and the drawing stroke of 72 mm only, the normal strain and the radial strain close to the fracture reach the values of − 0.249 and 0.253, respectively. The maximum circumferential strains of the two thickness ratios are both located at the poles of the drawn specimens with the values of 0.039 and 0.053, respectively. Thus, with the decrease in the thickness ratio, the deformation in the thin zone becomes more severe, making it more difficult to form the plates with differential thickness, and increasing the risk of fracture.

Limit drawing depth in hydroforming
To improve the formability of the 5A06 aluminum alloy plate with a differential thickness, a hydroforming method using a polyurethane auxiliary plate was further adopted. A 5A06 aluminum alloy plate with a diameter of 330 mm and a thickness ratio of 1/2 was used in the experiment. Figure 9a displays a semi-ellipsoid shell obtained by hydroforming (hydraulic loading path 1, maximum pressure of 5 MPa). Figure 9b shows the section diagram of the drawn specimen. The thick zone, thin zone, and transition zone can be clearly distinguished between each other, and the thinnest position of the drawn specimen is marked with a radius of 76 mm. Figure 9c depicts the thickness distribution within the drawn specimen and the maximum thinning ratio is found to be 12.9%. Therefore, hydroforming with an auxiliary plate can effectively improve the formability of 5A06 aluminum alloy plates with differential thickness, and specific complex thin-walled curved components can be manufactured. Figure 10 shows the stress state of the transition zone along the radial direction during hydroforming (p > 0). The normal contact stress between the aluminum alloy plate and the punch is increased due to the hydraulic pressure, and the interface friction τ P also shows an increasing trend. Meanwhile, the flexible auxiliary plate is in close contact with the aluminum alloy plate under the action of hydraulic pressure, and the interface friction τ PU between them is opposite to the relative sliding direction of the aluminum alloy plate. In turn, σ φA is lower under the action Because of the existence of interface friction between the upper and lower surfaces of the aluminum alloy plate, the relative sliding between the aluminum alloy plate and the punch becomes more difficult, which hinders the deformation of the contact zone to some extent and inhibits the excessive thinning in the thin zone.

The effect of hydraulic pressure on the thickness distribution
To elucidate the effect of hydraulic pressure on the thickness distribution within the drawn specimens with differential thickness, hydraulic loading path 2 (maximum pressure of 7.5 MPa) and loading path 3 (maximum pressure of 10 MPa) were designed to conduct the hydroforming experiments. 5A06 aluminum alloy plates with the diameters of 330 mm and two thickness ratios of 2/3 and 1/2 were used in the tests. Figure 11 depicts the thickness distributions across the drawn specimens with different thickness ratios obtained through various hydraulic loading paths. For the plates with λ = 2/3, the maximum thinning ratios of the drawn specimens are 11.9%, 10.8%, 9.8%, and 8.5% under the hydraulic pressure of 0, 5 MPa, 7.5 MPa, and 10 MPa, respectively. And for the plates with λ = 1/2, the maximum thinning ratio of the drawn specimens are 22.0% (close to the fracture), 12.9%, 12.2%, and 10.9% under the hydraulic pressure of 0, 5 MPa, 7.5 MPa, and 10 MPa, respectively. It can be seen from the thickness distribution curves that as the hydraulic pressure increases, the maximum thinning ratio of the drawn specimens gets decreases, and the overall thickness distribution becomes more uniform. This is mainly due to the fact that the aluminum alloy plate is attached to the punch by the fluid medium, and the interface friction between them is proportional to the hydraulic pressure. The direction of their interface friction is opposite to the direction of the radial tensile stress in the thin zone, which can reduce the radial tensile stress, thereby inhibiting the excessive thinning in the thin zone and improving the uniformity of the thickness distribution within the drawn specimen.
Therefore, during the hydroforming with a polyurethane auxiliary plate, the elevated hydraulic pressure can be helpful to improve the thickness distribution, reduce the maximum thinning ratio, and restrain the fracture defect of the drawn specimens. Figure 12 displays the normal strain calculated using formula (2) within the thin zone under different hydraulic pressures, and a smaller normal strain is corresponding to  Figure 13 shows the circumferential strain calculated using formula (3) within the thin zone under different hydraulic pressures. The maximum circumferential strain is located at the pole of the drawn specimen with a strain state of biaxial tension. With the increase of hydraulic pressure, the overall circumferential strain across the thin zone gets decreased, and the radius of the strain boundary (corresponding to a zero circumferential strain) decreases. Figure 14 demonstrates the radial strain calculated using formula (4) within the thin zone under different hydraulic pressures. As the hydraulic pressure gradually increases, the radial strain within the thin zone shows an overall downward trend. For the drawn plates with λ = 2/3, the maximum radial strains of the drawn specimens are 0.154, 0.l43, 0.139, and 0.132 under the hydraulic pressures of 0, 5 MPa, 7.5 MPa, and 10 MPa, respectively. And for those with λ = 1/2, the maximum radial strains are 0.253 (close to the fracture), 0.155, 0.150, and 0.144 under the hydraulic pressures of 0, 5 MPa, 7.5 MPa, and 10 MPa, respectively.

The effect of hydraulic pressure on the strain distribution
According to the above strain calculation results, the increase in hydraulic pressure can decrease the overall deformation and inhibit excessive thinning throughout the thin zone, which is beneficial to the forming of semi-ellipsoid shells with differential thickness.

Conclusions
In this paper, hydroforming of 5A06 aluminum alloy plates with differential thickness was studied based on the deep drawing experiments. By comparing the deformation behavior of plates under different thickness ratios and hydraulic pressures, the thickness and strain distributions were analyzed. Based on the finding, the conclusions can be drawn as follows.
(1) The hydroforming method using a polyurethane auxiliary plate could significantly improve the formability of 5A06 aluminum alloy plates with differential thickness. The maximum thinning ratio of the drawn specimens decreased a lot, and the strain distribution became more homogeneous. For the aluminum alloy plate with a thickness ratio of 1/2, a qualified semi-ellipsoid shell with the maximum thinning ratio of 10.9% could be successfully obtained via hydroforming under the hydraulic pressure of 10 MPa. (2) The smaller the thickness ratio λ of the 5A06 aluminum alloy plate was, the larger were the thinning ratio and radial strain within the thin zone, which directly led to a worse formability. A drawn specimen with a thickness ratio of 2/3 with the maximum thinning ratio of 11.9% was successfully fabricated via the conventional deep drawing, while the fracture defect occurred at the thickness ratio of 1/2, being smaller than the critical thickness ratio in the conventional deep drawing process. (3) The increase in hydraulic pressure was shown to be beneficial not only to improve the uniformity of the thickness distribution within the drawn specimens with differential thickness but also to effectively reduce the overall thinning ratio within the thin zone. For the thickness ratios of 2/3 and 1/2, as the hydraulic pressure increased to 10 MPa, the maximum thinning ratio in the thin zone gradually decreased, and the strain distribution could be improved as well.