**About the Editors**

### **Yeong-Maw Hwang**

Yeong-Maw Hwang is currently a distinguished professor at National Sun Yat-sen University. He earned his Doctor's degree (1990) in industrial mechanical engineering from Tokyo University in Japan. He was a visiting professor at Ohio State University (1999–2000 and 2005–2006). He has been a professor in the Department of Mechanical and Electro-Mechanical Engineering (MEME), National Sun Yat-Sen University (NSYSU), Kaohsiung, Taiwan, since 1996. He has served as the department chair (2002 –2005 and 2017–2020) of MEME. His research interests have been in the areas of metal forming, design and analysis of micro-generators, machine design and mechanics analysis. He won the Best Paper Award (1992) and Outstanding Engineering Professor Award (2007) from Chinese Society of Mechanical Engineers in Taiwan. He earned the Fellow title from Japan Society for Technology of Plasticity (JSTP), Japan (2012) and Distinguished Professor of NSYSU (2012). He was elected as the president of Taiwan Society for Technology of Plasticity (TSTP) for two terms, equating to four years 2017–2020.

### **Ken-ichi Manabe**

Ken-ichi MANABE has been an Emeritus Professor since 2017 and was awarded his Ph.D. in mechanical engineering in April 1985 form the Tokyo Metropolitan University (TMU), Japan. He had been a Professor at the TMU since 2002. Prof. Manabe has undertaken extensive research on the theory and modelling of tube/sheet metal forming processes and the intellectualization of their forming processes for over 45 years. Recently, his research interests extend toward tube microforming technology and deformation mechanics at the micro/meso scale. He has gained academic recognition from the Japan Society for Technology of Plasticity (JSTP), the Japan Society of Mechanical Engineers (JSME) and so on. He was a Conference chair (1993, 2011) and Co-chair (1995, 1997, 1999, 2017), and Honorary chair (2019) of the International Conference on Tube Hydroforming (TUBEHYDRO). He received the Best Paper Award in 1989, 2009 and 2012 from the JSTP. He received the JSTP Medal in 2010 and attained the grade of Fellow in 2009 from the JSTP. He was the President of the JSTP in 2015–2016.

**Yeong-Maw Hwang 1,\* and Ken-Ichi Manabe <sup>2</sup>**


### **1. Introduction and Scope**

Hydroforming processes of metal tubes and sheets are being widely applied in manufacturing because of the increasing demand for lightweight parts in sectors such as the automobile, aerospace, and ship-building industries. This technology is relatively new compared with rolling, forging, or stamping, so that there is limited knowledge available for the product or process designers. Compared to conventional manufacturing via stamping and welding in particular, tube hydroforming offers several advantages, such as (1) a decrease in workpiece cost, tool cost, and product weight, (2) an improvement of structural stability and an increase of the strength and stiffness of the formed parts, (3) a more uniform thickness distribution, (4) fewer secondary operations, etc. However, this technology suffers some disadvantages, such as slow cycle time, expensive equipment, and the lack of an effective database for tooling and process design.

Compound forming, which involves hydroforming and other forming processes such as crushing or preforming, is implemented to achieve a lower clamping force and forming pressure, as well as to ensure a uniformly distributed thickness of the formed product. Other tube hydroforming related effects like hydro-piercing, hydro-joining, hydro-flanging and hydro-inlaying are also important topics.

The aim of this Special Issue is to present the latest achievements in various tube and sheet hydroforming processes together with other tube processing technology and innovation. Through this Special Issue, a comprehensive understanding of the present status and future trends of tube/sheet hydroforming technology are to be expected. Thus, all researchers in this field were invited to contribute their research works to this special issue.

This special issue consists of some extended papers presented at The 9th International Conference on Tube Hydroforming (TUBEHYDRO 2019) held in Kaohsiung, Taiwan in 2019, and some papers newly submitted from authors with and without attending the conference.

### **2. Contributions to the Special Issue**

The contributions are generally divided into three basic groups according to the workpiece geometry and forming methods. The first group is tube hydroforming (THF) [1–9], in which a hydraulic media and dies are used to deform a tube workpiece. The second group is tube forming [10–14], in which only dies are used to deform a tube workpiece. The third group is sheet hydroforming [15,16], in which dies and/or hydraulic media are used to deform a sheet workpiece.

In the first group, many different forming technologies and methodologies related to tube hydroforming were used to overcome the forming difficulty to successfully obtain the desired product dimensions and material properties. For example, Yasui et al. [1] developed a warm hydroforming system and used this system to examine experimentally and numerically the influence of internal pressure and axial compressive displacement

**Citation:** Hwang, Y.-M.; Manabe, K.-I. Latest Hydroforming Technology of Metallic Tubes and Sheets. *Metals* **2021**, *11*, 1360. https:// doi.org/10.3390/met11091360

Received: 2 August 2021 Accepted: 25 August 2021 Published: 30 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

on the formability of small-diameter ZM21 magnesium alloy tubes in warm tube hydroforming. Supriadi et al. [2] proposed a vision-based fuzzy control algorithm and an image processing technology to manufacture bellows with a semi-dieless forming process. Morishima and Manabe [3] used finite element analysis combined with a fuzzy control model to carry out optimization of symmetrical temperature distributions and process loading paths for the warm T-shape forming of magnesium alloy AZ31B tube. Hwang and Tsai [4] developed a tube hydroforming process using a novel movable die design for decreasing the internal pressure to manufacture irregular bellows with small corner radii and sharp angles. Hwang et al. [5] proposed a new hydro-flanging process combining hydro-piercing and hydro-flanging to investigate the effects of punch shape and loading path in the hydro-flanging processes of aluminum alloy tubes. Bach et al. [6] used the functionality of the tools and the heating strategy for a curved component as well as a measurement technology to investigate the heat distribution in a component during hot metal gas forming (HMGF). Yoshimura et al. [7] proposed a local one-sided rubber bulging method of metal tubes to evaluate various strain paths at an aimed portion and measured the forming limit strains of metal tubes at the place of the occurrence of necking under biaxial deformation. Han and Feng [8] investigated the circumferential material flow using overlapping blanks with axial constraints in tube hydroforming of a variable-diameter part. Alexandrov et al. [9] proposed a simple analytical solution for describing the expansion of a two-layer tube under plane-strain conditions with an arbitrary pressure-independent yield criterion and a hardening law. The results can be applied to the preliminary design of hydro-expansion processes.

The second group consists of manuscripts related to tube forming with dies without hydraulic media inside the tube. Kajikawa et al. [10] proposed a tube expansion drawing method to effectively produce a thin-wall and large-diameter tube. Hirama et al. [11] proposed a new ball spin forming equipment, which can form a reduced diameter section on the halfway point of a tube. The effects of forming process parameters on the surface integrity and deformation characteristics of the product were investigated. Arai and Gondo [12] proposed a method of forming a tube into an oblique/curved shape by synchronous multipass spinning, in which the roller moves back and forth along the workpiece in the axial direction to gradually deform a blank tube into a target shape. Nakajima et al. [13] investigated the deformation properties and suppression characteristics of an ultra-thin-walled rectangular tube in rotary draw bending with a laminated mandrel. Tomizawa et al. [14] investigated the crash characteristics of partially quenched curved products by three-dimensional hot bending and direct quench. The results can be used as fundamental research of the design for improving energy absorption.

The third group includes only two articles, one is related to sheet hydroforming and the other is related to sheet friction tests. Hong et al. [15] developed a pneumatic experimental apparatus to evaluate strain rate sensitive forming limits of 7075 aluminum alloy sheets under biaxial stretching modes at elevated temperature. Hwang and Chen [16] investigated the frictional behaviors of sheets at variant speeds using a self-developed sheet friction reversible test machine. The effects of various parameters, including sliding speeds, contact angles, sheet materials, and lubrication conditions on friction coefficients at the sheet–die interface were discussed.

### *2.1. Tube Hydroforming Processes*

Magnesium and its alloys have been widely applied in the automotive, aircraft and telecommunication industries for their excellent characteristics, such as light weight and high strength. In addition, magnesium alloy has been expected to be employed as a material in medical devices, owing to its outstanding biocompatibility. Yasui et al. [1] developed a warm hydroforming system and used this system to examine the effects of internal pressure and axial compressive displacement on the formability of small-diameter ZM21 magnesium alloy tubes in warm tube hydroforming. The deformation behavior of ZM21 tubes, with a 2.0 mm outer diameter and 0.2 mm wall thickness, was evaluated

in taper-cavity and cylinder-cavity dies. The simulation code used was the dynamic explicit finite element code, LS-DYNA 3D. The experiments were conducted at 250 ◦C. The deformation characteristics, forming defects, and forming limit of ZM21 tubes were investigated. Their deformation behavior in the taper-cavity die was affected by the axial compressive direction. Additionally, the occurrence of tube buckling could be inferred by changes of the axial compression force, which were measured by the load cell during the processing. In addition, grain with twin boundaries and refined grain were observed at the bended areas of tapered tubes. The hydroformed samples could have a high strength. Moreover, wrinkles, which are caused under a lower internal pressure condition, were employed to avoid tube fractures during the axial feeding. The tube with wrinkles was expanded by a straightening process after the axial feed. It was found that the process of warm THF of the tubes in the cylinder-cavity die was successful.

Metal bellows consist of convoluted metal tube that provides high flexibility in various directions. They have been widely applied in the flexible joining of piping systems for water, oil, and gas provisions. Metal bellows are usually produced through a hydroforming or a gas-forming process. Supriadi et al. [2] proposed earlier a novel semi-dieless bellows forming process with a local heating technique and axial compression. However, with this technique it is extremely difficult to maintain the output quality due to its sensitivity to the processing conditions. The product quality mainly depends on not only the temperature distribution in the radial and axial direction but also the compression ratio during the semidieless bellows process. A finite element model clarified that a variety of temperatures produced by unstable heating or cooling will promote an unstable bellows formation. An adjustment to the compression speed is adequate to compensate for the effect of the variety of temperatures in the bellows formation. Therefore, it is necessary to apply a real-time process for this process to obtain accurate and precise bellows. In this paper, they proposed a vision-based fuzzy control to control bellows formation. Since semi-dieless bellows forming is an unsteady and complex deformation process, the application of image processing technology is suitable for sensing the process because of the possible wide analysis area afforded by applying multi-sectional measuring. A vision sensing algorithm was developed to monitor the bellows height from the captured images. An adaptive fuzzy was verified to control bellows formation from 5 mm stainless steel tube in a bellows profile up to 7 mm bellows height and a processing speed up to 0.66 mm/s. Appropriate compression speed paths guide the bellows formation following deformation references. The results show that the bellows shape accuracy between the target and experiment increase becomes 99.5% under the given processing ranges.

The warm tube hydroforming (WTHF) process of lightweight materials such as magnesium alloy contributes to a remarkable weight reduction. The success of the WTHF process strongly depends on the loading path with internal pressure and axial feeding and other process variables including temperature distribution. Optimization of these process parameters in this special forming technique is an important issue to be resolved. Morishima and Manabe [3] used finite element analysis combined with a fuzzy control model to carry out the optimization of symmetrical temperature distributions and process loading paths for the warm T-shape forming of magnesium alloy AZ31B tube. The results show that a satisfactory good agreement of the wall thickness distribution of the samples formed under the optimum loading path condition can be obtained between the finite element analyses and the experimental results. Based on the validity of the finite element model, the proposed optimization method was applied to other material (AZ61) and forming shape (cross-shape), while the applicability was also discussed.

Nowadays, tube hydroforming technologies have been widely applied in automotive and aerospace industries for manufacturing stronger and lighter products. However, higher pressures and complicated loading paths are required in the manufacturing of complex shape products. If the loading path or the relationship between the internal pressure and axial feeding is not controlled appropriately, various defects such as bursting and wrinkling, etc., would probably occur. Metal bellows have been widely applied in various

industries, such as chemical plants, power systems, heat exchangers, automotive vehicle parts, etc., for absorbing the irregular expansions of the pipes and damping vibration of the circumference and mechanical movements. Conventional regular metal bellows with multiple convolutions are usually manufactured by hydraulic bulging and die folding. However, for irregular bellows, in which the outer diameter of the bellows is not much larger than its inner diameter, the conventional manufacturing method combining hydraulic bulging and die folding cannot be applied to this kind of irregular bellows. This kind of irregular bellows can only be made by hydraulically bulging the tube into the desired shape under an irregular closed die set. Hwang and Tsai [4] developed a tube hydroforming process using a novel movable die design for decreasing the internal pressure to manufacture irregular bellows with small corner radii and sharp angles. A finite element simulation software "DEFORM 3D" was used to analyze the plastic deformation of the tube within the die cavity using the proposed movable die design. Forming windows for sound products using different feeding types were also investigated. Finally, tube hydroforming experiments of irregular bellows were conducted and experimental thickness distributions of the products compared with the simulation results to validate the analytical modeling with the proposed movable die concept.

Recently, tube hydroforming processes sometimes incorporate piercing, flanging, or joining processes to become hydro-piercing, hydroflanging, or hydro-joining, which are more efficient compared with a single process and can reduce the total weight of the final product. Hwang et al. [5] proposed a new hydro-flanging process combining hydropiercing and hydro-flanging to investigate the effects of punch shape and loading path in hydro-flanging processes of aluminum alloy tubes. Three kinds of punch head shapes were designed to explore the thickness distribution of the flanged tube and the fluid leakage effects between the punch head and the flanged tube in the hydro-flanging process. A finite element code DEFORM 3D was used to simulate the tube material deformation behavior and to investigate the formability of the hydro-flanging processes of aluminum alloy tubes. The effects of various forming parameters, such as punch shapes, internal pressure, die hole diameter, etc., on the hydro-flanged tube thickness distributions were discussed. Hydro-flanging experiments were also carried out. The die hole radius was designed to make the maximum internal forming pressure needed smaller than 70 MPa, so that a general hydraulic power unit could be used to implement the proposed hole flanging experiments. The flanged thickness distributions were compared with simulation results to verify the validity of the proposed models and the designed punch head shapes.

Climate targets set by the EU, including the reduction of CO2, are leading to the increased use of lightweight materials for mass production such as press hardening steels. Besides sheet metal forming for high-strength components, tubular or profile forming (hot metal gas forming—HMGF) allows for designs that are more complex in combination with a lower weight. Bach et al. [6] used the functionality of the tools and the heating strategy for the curved component as well as the measurement technology to investigate the heat distribution in the component during hot metal gas forming. This paper particularly examined the application of conductive heating of the component for the combined press hardening process. The previous finite-element-method (FEM)-supported design of an industry-oriented, curved component geometry allowed the development of forming tools and process peripherals with a high degree of reliability. This work comprised a description regarding the functionality of the tools and the heating strategy for the curved component as well as the measurement technology used to investigate the heat distribution in the component during the conduction process. Subsequently, forming tests were carried out, material characterization was performed by hardness measurements in relevant areas of the component, and the FEM simulation was validated by comparing the tube thickness distributions to the experimental values.

During tube forming, tube materials are subjected to complex and severe deformation and, thus, some forming defects such as cracking and buckling often occur. To avoid such forming defects, the formability of the tube materials should be evaluated appropriately. Yoshimura et al. [7] proposed a local one-sided rubber bulging method of metal tubes to evaluate various strain paths at an aimed portion and measured the forming limit strains of metal tubes at the place of the occurrence of necking under biaxial deformation. Using this method, since rubber was used to give pressure from the inner side of the tube, no sealing mechanisms were necessary unlike during hydraulic pressure bulging. An opening was prepared in front of the die to locally bulge a tube at only the evaluation portion. To change the restriction conditions of the bulged region for biaxial deformation at the opening, a round or square cutout, or a slit was introduced. The test was conducted using a universal compression test machine and simple dies rather than a dedicated machine. On considering the experimental results, it was confirmed that the strain path was varied by changing the position and size of the slits and cutouts. Using either a cutout or a slit, the strain path in the side of the metal tubes can be either equi-biaxial tension or simple tension, respectively.

Tube hydroforming of overlapping blanks is a forming process where overlapping tubular blanks instead of regular tubes are used to enhance the forming limits and improve the thickness distributions. A distinguishing characteristic of hydroforming of overlapping blanks is that the tube material can flow along the circumferential direction easily. Han and Feng [8] investigated circumferential material flow using overlapping blanks with axial constraints in tube hydroforming of a variable-diameter part. AISI 304 stainless steel blanks were selected for numerical simulation and experimental research. The circumferential material flow distribution was obtained from the profile at the edge of the overlap. The peak value was located at the middle of the cross-section. In addition, the circumferential material flow could also be reflected in the variation of the overlap angle. The variation of the overlap angle kept increasing as the initial overlap angle increased. There was an optimal initial overlap angle to minimize the thinning ratio.

Alexandrov et al. [9] proposed a simple analytical solution for describing the expansion of a two-layer tube under plane-strain conditions. Each layer's constitutive equations consist of an arbitrary pressure-independent yield criterion, its associated plastic flow rule, and an arbitrary hardening law. The elastic portion of strain was neglected. The method of solution was based on two transformations of space variables. First, a Lagrangian coordinate was introduced instead of the Eulerian radial coordinate. Then, the Lagrangian coordinate was replaced with the equivalent strain. The solution reduced to ordinary integrals that, in general, should be evaluated numerically. However, for two hardening laws of practical importance, these integrals were expressed in terms of special functions. Three geometric parameters for the initial configuration, a constitutive parameter, and two arbitrary functions classified the boundary value problems. The illustrative example demonstrated the effect of the outer layer's thickness on the pressure applied to the inner radius of the tube.

### *2.2. Tube Forming Processes*

Kajikawa et al. [10] proposed a tube expansion drawing method to effectively produce a thin-wall and large-diameter tube. In the proposed method, the tube end is flared by pushing a plug into the tube, and the tube is then expanded by drawing the plug in the axial direction while the flared end is chucked. The forming characteristics and effectiveness of the proposed method were investigated through a series of finite element analyses and experiments. The finite element simulation results show that the expansion drawing effectively reduced the tube thickness with a smaller axial load when compared with the conventional method. According to the experimental results, the thin-walled tube was produced successfully by the expansion drawing. The maximum thickness reduction ratios for a carbon steel (STKM13C) and an aluminum alloy (AA1070) were 0.15 and 0.29 when the maximum expansion ratios were 0.23 and 0.31, respectively. The above results suggest that the proposed expansion drawing method is effective for producing thin-walled tubes.

Tubes with variable diameters in the axial direction are in demand but it is costly to manufacture them. For instance, changing the tube diameter is achieved by connecting

different diameter tubes using joints. It takes time and effort to connect, and in some cases, the connection often causes low airtightness. Therefore, the demand for different diameter continuous tubes (DDC tubes) and the process for DDC tubes without joining processes is high. Hirama et al. [11] proposed a new ball spin forming equipment, which can form a reduced diameter section on the halfway point of a tube. The effects of forming process parameters on the surface integrity and deformation characteristics of the product were investigated. The proposed method can reduce the diameter in the middle portion of the tube, and the maximum diameter reduction ratio was over 10% in one pass. When the feed pitch of the ball die was more than 2.0 mm/rev, spiral marks remained on the surface of the tube. Torsional deformation, axial elongation, and an increase in thickness appeared in the tube during the forming process. All of them were affected by the feed pitch and feed direction of the ball die, while they were not affected by the rotation speed of the tube. When the tube was pressed perpendicularly to the axis without axial feed, a diameter reduction ratio of 21.1% was achieved without defects using a ball diameter of 15.9 mm. The polygonization of the tube was suppressed by reducing the pushing pitch. The ball spin forming has a big advantage in flexible diameter reduction processing on the halfway point of the tube for producing different diameter tubes.

Arai and Gondo [12] proposed a method of forming a tube into an oblique/curved shape by synchronous multipass spinning, in which the roller moves back and forth along the workpiece in the axial direction to gradually deform a blank tube into a target shape. The target oblique/curved shape is expressed as a series of inclined circular cross sections. The contact position of the roller and the workpiece is calculated from the inclination angle, center coordinates, and diameter of the cross sections, considering the geometrical shape of the roller. The blank shape and the target shape are interpolated along normalized tool paths to generate the numerical control command of the roller. Aluminum tubes were formed experimentally into curved shapes with various radii of curvature, and the forming accuracy, thickness distributions, and strain distributions were examined.

Nakajima et al. [13] investigated the deformation properties and suppression characteristics of an ultra-thin-walled rectangular tube in rotary draw bending with a laminated mandrel. Aluminum alloy rectangular tubes with a height of 20 mm, width of 10 mm, and wall thickness of 0.5 mm were used. The deformation properties after rotary draw bending were investigated. The results show that deformation in the height direction of the tube was suppressed on applying the laminated mandrel, whereas a pear-shaped deformation peculiar to the ultra-thin wall tube occurred. Because axial tensions and lateral constraints were applied and the widthwise clearance of the mandrel was adjusted appropriately, the pear-shaped deformation was suppressed and a more accurate cross-section was obtained.

Recently, improvement of hybrid and electric vehicle technologies, equipped with batteries, continues to contribute to solving energy and environmental problems. Lighter weight and crash safety are required in these vehicle bodies. In order to meet these requirements, three-dimensional hot bending and direct quench (3DQ) technology, which enables hollow tubular automotive parts to be formed with a tensile strength of 1470 MPa or over, has been developed. Tomizawa et al. [14] investigated the crash characteristics of partially quenched curved products by three-dimensional hot bending and direct quench. The main results are as follows: (1) for partially quenched straight products in the axial crash test, buckling that occurs at the non-quenched portion could be controlled; (2) for the nonquenched conventional and overall-quenched curved products, buckling occurred at the bent portion at the initial stage in axial crash tests, and its energy absorption was low; (3) by partially optimizing quench conditions, buckling occurrence could be controlled; and (4) in this study, the largest energy absorption was obtained from the partially quenched curved product, which was 84.6% larger than the energy absorption of the conventional nonquenched bent product in the crash test.

### *2.3. Sheet Forming Processes*

Hong et al. [15] developed a pneumatic experimental apparatus to evaluate the strain rate sensitive forming limits of 7075 aluminum alloy sheets under biaxial stretching modes at elevated temperature. For optimization of the die shape design, the ratio of minor to major die radius (k) and profile radius (R) were parametrically studied. The final shape of the die was determined by whether the history of the targeted deformation mode was well maintained and if the fracture was induced at the pole (specimen center), to prevent unexpected failure at other locations. As a result, a circular die with k = 1.0 and an elliptic die with k = 0.25 were selected for the balanced biaxial mode and near plane strain mode, respectively. Lastly, the pressure inducing fracture at the targeted strain rate was studied as the process design. An analytical model previously developed to maintain the optimized strain rate was modified for this designed model. The results of the integrated design were compared with the experimental results. The shape and thickness distributions of numerical simulation results show good agreement with those of the experiments.

Friction at the interface between sheet and dies is an important factor influencing the formability of strip or sheet forming. Hwang and Chen [16] investigated the frictional behaviors of sheets at variant speeds using a self-developed sheet friction reversible test machine. This friction test machine, stretching a strip around a cylindrical friction wheel, was used to investigate the effects of various parameters, including sliding speeds, contact angles, strip materials, and lubrication conditions on friction coefficients at the sheet–die interface. The friction coefficients at the sheet–die interface were calculated from the drawing forces at the sheet on both ends and the contact angle between the sheet and die. A series of friction tests using carbon steel, aluminum alloy, and brass sheets as the test piece were conducted. From the friction test results, it became known that the friction coefficients could be reduced greatly with lubricants on the friction wheel surface while the friction coefficients were influenced by the sheet roughness, contact area, relative speeds between the sheet and die, etc. The friction coefficients obtained under various friction conditions can be applied to servo deep drawing or servo draw-bending processes with variant speeds and directions.

### **3. Conclusions**

This Special Issue and Book "Latest Hydroforming Technology of Metallic Tubes and Sheets" includes 16 papers, which cover the state of the art of forming technologies in the relevant topics in the field. The technologies and methodologies presented in these papers will be very helpful for scientists, engineers, and technicians in product development or forming technology innovation related to tube hydroforming processes.

**Funding:** This research received no external funding.

**Acknowledgments:** The Guest Editors would like to thank all who contributed to the development of this Special Issue. Thanks to the authors who submitted manuscripts to share results of their research activity, and to the reviewers who agreed to read them and gave constructive suggestions to improve the final quality of the papers. The Guest Editors would also like to send the warmest gratitude to the *Metals* editorial team and, particularly, to Sunny He for their assistance and support during the preparation of this special issue.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


## *Article* **Warm Hydroforming Process under Non-Uniform Temperature Field for Magnesium Alloy Tubes**

**Toshiji Morishima and Ken-Ichi Manabe \***

Department of Mechanical Systems Engineering, Tokyo Metropolitan University, 1-1 Minamiosawa, Hachioji, Tokyo 192-0397, Japan; toshiji.morishima@gmail.com

**\*** Correspondence: manabe@tmu.ac.jp; Tel.: +81-42-675-3059

**Abstract:** The warm tube hydroforming (WTHF) process of lightweight materials such as magnesium alloy contributes to a remarkable weight reduction. The success of the WTHF process strongly depends on the loading path with internal pressure and axial feeding and other process variables including temperature distribution. Optimization of these process parameters in this special forming technique is a great issue to be resolved. In this study, the optimization of the symmetrical temperature distribution and process loading path for the warm T-shape forming of magnesium alloy AZ31B tube was carried out by finite element (FE) analysis using a fuzzy model. As a result, a satisfactory good agreement of the wall thickness distribution of the samples formed under the optimum loading path condition can be obtained between the FE analysis result and the experimental result. Based on the validity validation of FE analysis model, the optimization method was applied to other materials and forming shapes, and applicability was discussed.

**Keywords:** magnesium alloy tube; warm hydroforming; non-uniform temperature field; protrusion type forming; wall thickness distribution; coupled thermal-structural analysis; optimization

In recent years, the world has begun to move toward carbon neutrality as one of the solutions to prevent global warming. In response to the trend, along with the acceleration toward electric vehicles, the weight of the entire vehicle including the vehicle body is being further reduced. Tube hydroforming (THF), which uses a tubular material with a hollow cross section for high rigidity, is considered to be promising for reducing the weight of vehicles, in addition to material replacement with lightweight materials and high-strength materials, and is actually applied in the automotive industry.

Aluminum, magnesium, and fiber-reinforced polymers have been taken up as typical lightweight materials. Among these, magnesium is the lightest of all practical metals and is attracting attention as one of the important metals for realizing a low-carbon society due to its unique physical and mechanical properties. However, magnesium alloys have been treated as one of the hard-to-form metals at room temperature. So far, several metal forming processes for magnesium alloys using a heat-assisted approach have been introduced in order to enhance the formability and reduce the environmental load.

Most of the research on forming processes for magnesium alloy tubes has been conducted using heat-assisted processing since the mid-2000s, and started with hot spin forming. Yoshihara et al. [1] examined the dome-shape forming characteristics of the tube end while locally heating the formed part with a gas burner for hot spin forming of an AZ31 tube, and Murata et al. [2] investigated the compression spinning process of an AZ31 tube using the heated roller. For the high temperature bulge forming, Okamoto et al. [3] succeeded in warm T-shape forming of an AZ31B tube at 400 ◦C using nitrogen gas. Manabe et al. [4,5] performed T-shape forming (WTHF) at 250 ◦C using silicone oil as a pressure medium for AZ31 tube and compared the forming characteristics by experiment and FE analysis. Hwang and Wang [6] have succeeded in a Y-shape forming experiment

**Citation:** Morishima, T.; Manabe, K.-I. Warm Hydroforming Process under Non-Uniform Temperature Field for Magnesium Alloy Tubes. *Metals* **2021**, *11*, 901. https://doi.org/ 10.3390/met11060901

Academic Editor: Badis Haddag

Received: 5 April 2021 Accepted: 21 May 2021 Published: 31 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of AZ61 tube at 250 ◦C, and it was shown that Y molding can be performed even at 150 ◦C. He et al. [7] investigated and evaluated the formability in a basic formability test of the AZ31B tube at high temperature. For the drawing process of magnesium alloy tube, Furushima et al. developed a high-frequency induction heating device system to locally heat and cool the AZ31 tube, and it was examined to improve the processing time of dieless drawing and the drawability [8,9]. An in vitro corrosion test [10] of the dieless drawn tube of AZ31B and the dieless drawing process by a laser heating device [11] were also performed.

Other heat-assisted processing technologies applied to hard-to-form metals other than magnesium alloy tubes include warm and hot hydroforming [12,13] for aluminum alloy tubes. Hot gas bulge forming was performed on aluminum alloy tubes [14,15] and high-strength steel tubes [16,17] using a direct resistance heating technique. In addition, profile forming [18], utilizing a bulge deformation under axial compression by local heating using a high-frequency induction device for a double-layer metal tube was performed. As a new heat-assisted forming technology, a novel dieless bellows forming that continuously creates a convolution at the heating portion with a difference in axial feeding speed on both tube sides while locally heating with a high-frequency induction device was developed for the stainless steel SUS304 tubes [19,20]. Additionally, the dieless bending process of tubes [21] is a typical heat-assisted processing technology that applies the local heating and cooling technique, and it has been introduced into practical use since the latter half of the 1960s and is the most widely used processing technology in the industry. Recently, a three-dimensional hot bending and direct quench (3DQ) technology [22] was developed as the latest technology that can be applied to high-strength steel tubes of 1470 MPa class or higher, based on basically a push bending process with a local heating and cooling system using a high-frequency induction device.

The various forming processes described above are classified in the heat-assisted forming technology from the viewpoints of "steady deformation", "unsteady deformation", "continuous/sequential processes", "intermittent process", and "dieless process" without die for forming objects. The above-mentioned dieless drawing, dieless bellows forming, and dieless bending process belong to sequential/continuous deformation process at the local heating portion, respectively.

The heat-assisted forming technology is classified according to whether or not the heating temperature is uniform over the entire forming portion. If the temperature field is uniform, the main difference in the forming characteristics is only the variation in the physical characteristics of the material.

Meanwhile, in the case of the non-uniform temperature field, there are two types of non-uniform temperature fields. (1) The first is the case where the temperature distribution is formed on the coordinates fixed on the metal blank, and (2) the second is the case where the temperature distribution is formed on the coordinates fixed on the space such as tooling. In sheet metal forming, the former (1) is used in stretch forming and bending, and in the latter (2), the local heating/cooling deep drawing method has been performed since the 1950s.

However, so far, there are very few studies on WTHF for non-uniform temperature fields. The above-mentioned study on the non-uniform temperature field in (1) was reported by Liu et al. [23]. This is an investigation on a warm axisymmetric bulge forming process with die in the non-uniform temperature field. The effectiveness of the non-uniform temperature distribution was confirmed for the AZ31 tube.

On the other hand, the branch protrusion type THF is an asymmetric deformation process and shows more complicated deformation behavior than the axisymmetric bulge forming. It is a similar deformation mode as the deep drawing process in sheet metal forming. Thus, it can be said that the branch protrusion type THF in this non-uniform temperature field has the same forming principle as the local heating/cooling deep drawing method.

The main deformation domain reduces drawing resistance by heating and softening, while the other load-carrying domain is cooled to prevent failure defects including fracture, improving the forming limit and the quality and accuracy of the product. More importantly, the blank material flows through the heating and cooling domains.

Yoshihara et al. [24] adopted the local heating/cooling deep drawing method to improve the deep drawability of AZ31 sheet and achieved a large drawing limit of *LDR* > 5.

In general, for the warm T-shape THF in the uniform temperature field [4,5], the wall thickness of the blank tube is locally thickened at the place of contact with an axial feeding punch and the bottom on the opposite of protruded branch part. To make the wall thickness distribution of the formed product uniform at the same time, instead of processing under a uniform temperature field, the forming temperature should be kept low at the part where deformation should be suppressed, wall thickness should be suppressed, and the material flow at the other part should be promoted.

Manabe et al. [25,26] investigated the effect of enhancing the hydroforming limit and improving the wall thickness distribution under a non-uniform temperature field by locally heating/cooling warm T-shape forming of an AZ31 magnesium alloy. However, even for the non-uniform temperature field in the previous report [25,26], the above technological issues were not solved enough yet and remain.

The objective of this study is to elucidate the optimum temperature distribution for further improving the formability and wall thickness distribution uniform of magnesium alloy tubes with low hydroformability at room temperature. Therefore, focusing on the non-uniform temperature field in WTHF process, the effect of the temperature distribution in the tooling on the wall thickness distribution of the formed sample is investigated in detail, and the optimum non-uniform temperature field and the optimum loading path for different magnesium materials (AZ31B and AZ61) and forming shapes (T-shape and cross-shape) are examined.

### **2. Experiments**

### *2.1. Materials*

The tubes used in this study were made of AZ31B and AZ61 magnesium alloy with an outer diameter of 42.7 mm and a wall thickness of 1.0 mm, and the test piece for the hydroforming test was 200 mm in length. Table 1 shows the chemical composition of these magnesium alloy tubes. A uniaxial tensile test was carried out using an arc-shaped test piece made by cutting out the tubular material in the longitudinal direction. The tensile test piece used was half the size of JIS 13B. In the tensile test, the test temperature was 20 ◦C, 100 ◦C, 150 ◦C, 200 ◦C, 250 ◦C, and 300 ◦C under 6 conditions, and the tensile speed was 1.5 mm/min, 15 mm/min, and 150 mm/min under 3 conditions (initial strain rate was 0.001 s−<sup>1</sup> , 0.01 s−<sup>1</sup> , and 0.1 s−<sup>1</sup> , respectively). Figure 1 shows the typical stress-strain curves at different temperatures and tensile speeds for AZ31B and AZ61. From these results, the elongation of both materials increases as the temperature rises, and the tensile strength decreases. In addition, although the strain rate dependence is slightly observed as the temperature rises from room temperature, no significant strain rate dependence is observed in the test range, and the temperature dependence is large. Comparing AZ31B and AZ61, AZ61 has a slightly higher strength (deformation resistance) up to about 150 ◦C, and there is no big difference in elongation.

**Table 1.** Chemical composition of AZ31B and AZ61 magnesium alloy tubes (mass %).


− − − **Figure 1.** Stress-strain curves of AZ31 and AZ61 at different temperatures and initial strain rates. (**a**) AZ31B initial strain rate: 0.001 s−<sup>1</sup> ; (**b**) AZ31B, 0.1 s−<sup>1</sup> ; (**c**) AZ61, 0.01 s−<sup>1</sup> . − − −

### *2.2. Experimental Setup and Procedure*

Figures 2 and 3 show the schematic illustration of the T-shape forming tooling used in this study and the configuration of the hydraulic circuit and the closed loop control system for the T-shape WTHF process, respectively [2–4]. To conduct this experimental work, a new T-shape warm forming machine with a local heating/cooling apparatus for the die was developed. This machine is an improved version of the previously developed equipment [3,4], and it enables controlling the temperature distribution of the die as well. In this testing machine, each cylinder and pressure booster is operated by a command from a computer, and closed-loop control can be performed by sending the measured values of the axial punch displacement and internal pressure from moment to moment to the computer.

≦ ≦ ≦ ≦

≦ ≦ ≦ ≦

**Figure 2.** Outline of the tooling for T-shape forming (Unit: mm).

**Figure 3.** Configuration of a hydraulic circuit and its closed loop control system in WTHF.

**Thermocouple**

> **Spray nozzles for cooling**

**Water**

**Compressed air** 

**Cartridge heaters**

**Cooling device**

Figure 4 shows the appearance of the heating and cooling device. For heating and cooling the die, six through holes are opened for inserting cartridge heaters into the upper and lower dies, and heating for uniform temperature field (Figure 4a) can be performed with a total of 12 cartridge heaters with maximum total output of 11 kW. The forming die was fully covered with the insulator boards.

**Figure 4.** Heating and cooling system for the warm T-shape die. (**a**) For uniform warm temperature field, the entire circumference of the die is surrounded by heat insulator material; (**b**) for non-uniform temperature field; (**c**) cooling device with spray nozzle.

As the cooling method, we adopted a method of passing compressed air through the four through holes at the upper and lower ends of the heater and a method of cooling by using the heat of vaporization of water mist (Figure 4b). In the case of the water mist cooling, compressed air of about 70 kPa was provided through a larger pipe from a compressor, and a small amount of water was flowed from a tip of a smaller pipe to spray it into a mist for cooling the die (Figure 4c). In addition, there were six other holes on the side of the die for temperature measurement (Figure 4b). A sheath-type K thermocouple was inserted into each hole, and they measured a variation in the temperature distribution during the forming process.

To create a non-uniform temperature field, after heating to 270 ◦C with all 12 heaters, only the total of eight heaters in the middle continued to be heated, and in the meantime, the cooling devices were attached to the four holes at both ends of the die. After about 30 min, the temperature field became stable. Since the die temperature uniformly shifted down about around 15 ◦C during the total forming time of about 5 min, the forming experiment started when the temperature at the center reached at around 260 ◦C to realize the set temperature distribution in the middle of forming process.

The temperature of upper and lower dies was controlled independently using temperature controllers. To confirm uniform temperature distribution over the tubular blank, thermocouples with 0.1 mm diameter are fixed into a groove made on the tube.

Figure 5 shows the typical temperature distributions of the die for T-shape forming realized by using a local heating and cooling system.

*ρ*

**Figure 5.** Temperature distributions used in WTHF experiment.

Blank tube

Counter punch

T-joint die

Axial punch

*ν α* <sup>−</sup>

The pressure medium was methylphenyl silicone liquid KF-54 (Shin-Etsu Chemical Co., Ltd., Tokyo, Japan), and a dry fluorine lubricant (spray type) was used for the lubrication between the tube and the die. **X coordinate /mm**

**spray nozzle Branch cavity** 

**Uniform heating**

**Cooling with air Cooling with mist effect using** 

### **3. Finite Element Modeling**


**part**

100

150

200

**Temperature /**

℃

250

300

Finite element (FE) analysis is performed by a thermal-structural coupled dynamic explicit FE commercial code, LS-DYNA ver. 971. (Ansys Inc., Canonsburg, PA, USA). Using a quarter-symmetrical model for T-shape and a one-eighth model for the crossshape, the tubular blank was divided into two in the wall thickness direction, 60 in the circumferential direction, and 100 in the axial direction. Figure 6 shows the FE model for warm T-shape hydroforming. The material properties obtained from the tensile test in Section 2.1 were employed in the FE analysis. Other input values are the density *ρ* = 1.78 g/cm<sup>3</sup> , Poisson's ratio *<sup>ν</sup>* = 0.35, linear expansion coefficient *<sup>α</sup>* = 26.5 <sup>×</sup> <sup>10</sup>−6/K, and specific heat *c* = 1.05 kJ/kgK. *ρ ν α* <sup>−</sup>

**Figure 6.** FE model for warm T-shape hydroforming.

In the material model considering the temperature dependence, the equivalent stressequivalent plastic strain relationship was defined by inputting the deformation resistance curve for each temperature, and at the intermediate temperature, the deformation resistance was determined by interpolating each curve. In general, magnesium alloy has a strain rate dependence in the high temperature range. The processing time of this forming experiment, however, was 5 min, and the forming process was performed slowly. In the previously reported FE analysis [2], it was possible to sufficiently predict the detail forming characteristics in the same T-shape forming experiment with a material model that does not consider the strain-rate dependence. Moreover, from the material test results shown in Section 2.2 above, no large strain-rate dependence was observed when the forming temperature conditions and processing time were taken into consideration. Furthermore, under the non-uniform temperature field of 250 ◦C or less in this study, the region of the formed part where the strain-rate dependence appears changes with time, the temperature conditions there were also different, and the strain-rate dependence was considered to become small. Therefore, we used a material model that did not consider the strain-rate dependence in this study.

The coefficient of friction between the tool and the blank was static friction coefficient *µ*<sup>s</sup> = 0.02, the kinetic friction coefficient was *µ*<sup>d</sup> = 0.01, and the heat transfer coefficient was 1400 W/m2K.

### **4. Results and Discussion**

### *4.1. Process Window in Proportional Loading Path under Uniform Temperature Field and Validation of the FE Modeling*

In order to clarify the process window in warm T-shape forming of AZ31B magnesium alloy and the FE modeling validation, WTHF experiments and FE analysis were performed in a proportional loading path under a uniform temperature field. Figure 7 shows the process window for T-shape forming for AZ31B under 250 ◦C obtained by the experiment and FE analysis. The onset point of "bursting" in the FE analysis was determined as when the wall thickness reduction began to increase rapidly without using any fracture criterion, or when the analysis was stopped. On the other hand, the occurrence of buckling was visually evaluated by visually displaying the deformed shape of the blank tube using the graphic processing of the post processor. It is confirmed that the bursting is predominant under higher internal pressure loading, the buckling is dominant when the axial penetration is predominant, and the successful region between both becomes narrow as the process proceeds.

*μ μ*

① ② ③ ④ **Figure 7.** Process window and forming limits of T-shape forming for AZ31B tube in a proportional loading under 250 ◦C. The 1 , 2 , 3 , and 4 in the figure indicate different loading paths (experiment).

Figure 8 shows the comparisons of final bulged heights and their shapes at the forming limit between experimental results and FE simulation results in Figure 7. The failure modes in Figure 8a,b are both bursting, as shown in Figure 7, and their formed shapes and bulged heights are in good agreement. Figure 8c,d show different buckling modes, both of which are in good agreement with the experimental and FE analysis results in a uniform temperature field at 250 ◦C. The results confirmed the validity of this FE model and demonstrated the importance of loading path design using FE analysis.

At the same time, it was confirmed that the loading path has a strong influence on the forming limit. When investigating the effects of temperature fields, the need to determine the appropriate loading paths to avoid bursting and buckling can be understood.

### *4.2. Effects of Temperature Distribution on Wall Thickness Distribution in Proportional Loading Path under Non-Uniform Temperature Field*

The effectiveness of non-uniform temperature distribution for the uniform wall thickness of formed products in the warm T-shape forming process for the AZ31B magnesium alloy tube was reported by a comparison of the FE analysis result by a material model obeying a linear hardening law [4]. In this section, aiming for a more accurate analysis, the effect of the temperature distribution on the wall thickness distribution of formed products is examined by FEM analysis based on the strain hardening characteristics of the material obtained in the tensile test, as described in the previous chapter.

① ② ③ ④ **Figure 8.** Comparisons of final bulged shape between experimental and simulated results at T-shape forming limit for AZ31B tube in a proportional loading under 250 ◦C. (**a**) Path 1 in Figure 7; (**b**) Path 2 ; (**c**) Path 3 ; (**d**) Path 4 .

Figure 9 shows the outline of temperature distributions for the die applied for that purpose, one is a uniform temperature field of 250 ◦C and another is a non-uniform temperature distribution of 250 ◦C to 150 ◦C in Figure 5. Figure 10 shows the comparison of experiments and FE analysis results on the wall thickness distribution along the bulged branch side and the bottom side in the T-shape forming under the two different temperature fields shown in Figure 9. Firstly, Figure 10a shows the wall thickness distributions along the bulging branch side of the T-shaped product. The FE analysis results in a uniform temperature field (red solid line) of 250 ◦C are quantitatively very consistent with the experimental results (red dotted line) except for the seal portions at both ends of the blank tube. As shown in the FE model of Figure 6 above, the shape of the axial punch used in the experiment is stepped to insert into the tube end and seal the internal pressure applied. Therefore, at the ends of the tube where the punch inserts, the deformation shape is constrained. In the non-uniform temperature field (blue line), since this part is a low temperature part at 150 ◦C, the deformation resistance is larger and the deformation is suppressed and smaller, and it is considered that this region is deformed in the same way as the FE analysis result. On the other hand, in a uniform warm temperature field (red line), both tube-end portions are also easily deformed, so it is considered that a local irregular large deformation occurred near the stepped portion where the punch is inserted. On the other hand, on the bottom side shown in Figure 10b, the experiment and FE analysis results show qualitatively good agreement in a uniform temperature field of 250 ◦C (red line). In the non-uniform field, both show a good quantitative agreement except for the central part. The T-shape forming process is an asymmetric deformation that shows a complicated deformation behavior and is a difficult deformation target as compared with an axisymmetric bulge deformation. Due to the asymmetry, the tube material also can flow significantly in the circumferential direction even at the bottom, as shown in Figure 10b during the forming process, and the other parts also flow in the circumferential direction accordingly. The difference between the analysis of the wall thickness distribution in Figure 10b and the experiment is considered to be due to this difference in material flow

in the circumferential direction. There are various possible reasons for this difference, such as processing conditions and material-side factors, but the major problem is that the stress-strain relationship in the large strain range has not been experimentally obtained for the material properties. Additionally, in the result of this experiment in Figure 10b, the wall thickness strain in the central part reached about 1.0 in true strain. However, its relationship over a large strain range cannot currently be determined by material testing, and it is presumed that extrapolation to this large strain range is also one of the major reasons.

**Figure 9.** Temperature distribution conditions in warm T-shape forming process for AZ31B. (**a**) Uniform temperature field at 250 ◦C; (**b**) Non-uniform temperature field.

**Figure 10.** Comparison of wall thickness distribution between uniform temperature and non-uniform temperature fields. (**a**) Bulged side; (**b**) bottom side. Solid line: FE analysis result; dashed line: experimental result; red color: 250 ◦C; blue color: non-uniform temperature.

Consequently, the FE analysis is in good agreement with the experimental results. From this, it can be said that the analysis accuracy is improved by approximating the material model to multiple points according to the actual work hardening characteristics. The validity of this FE model for the evaluation of the wall thickness distribution is confirmed.

### *4.3. Determination and Its Validation of Optimum Loading Path for Improving Formability and Bulged Shape in Warm T-shape Forming Process under Uniform Temperature Field*

In THF, the loading path has a great influence on hydro-formability, forming shape, wall thickness distribution, and so on. In the actual forming process, so far the optimum loading path of the internal pressure and axial feeding is empirically determined. In our previous study [27], the optimum loading path using a fuzzy model was predicted and confirmed. Here, firstly the optimum loading path for improving bulged shape and bulged height is investigated, and the obtained loading path is used to clarify the optimum temperature conditions for the non-uniform temperature field.

The final internal pressure *p*<sup>f</sup> in the T-shape forming process is given from the following empirical formula [28]. 2 0

$$P\_f = k \frac{2t\_0 \sigma\_y}{D\_0} \tag{1}$$

Here, *t*<sup>0</sup> is the wall thickness, *σ<sup>y</sup>* is the yield stress, *D*<sup>0</sup> is the outer diameter of the bulging part, *k* is the experimental constant, and 4.7 is used for T-shape forming. By substituting the dimensions and material properties of the magnesium alloy tube at 250 ◦C into the above equation, *p<sup>f</sup>* = 10 MPa was determined. *σ*

The axial penetration and the counter punch displacements during the forming process were determined every moment by the same fuzzy inference model in the previous report [27]. Basically, the following typical evaluation functions were employed for evaluating the wavy buckling and the contact length with the counter punch with increasing the internal pressure during the process.

Figure 11 shows the evaluation functions used in the fuzzy inference model for T-shape forming. Figure 11a shows an evaluation function *Φ* defined as an index for evaluating the risk of wavy buckling in order to suppress the occurrence of the buckling deformation near the die inlet shoulder part during free bulge deformation at the initial forming stage. *R*max on the right side of the equation of the evaluation function *Φ* in the figure is the maximum bulged height near the die inlet shoulder part, and *R*min is the minimum bulged height near there. *Φ Φ*

*Φ Ψ* **Figure 11.** Evaluation functions for T-shape forming. (**a**) Evaluation function *Φ* for the risk of wavy buckling; (**b**) Evaluation function Ψ for the contact length with counter punch*. R*max*:* maximum bulged height (radius) near the die inlet shoulder part; *R*min: minimum bulged height (radius) near there; *C<sup>l</sup>* : contact length with a counter punch; *Cref*: assumed reference contact length. A red rectangle indicates a maximum bulged part region near the die inlet.

Since the decrease in wall thickness of the bulged part can be suppressed by aggressively feeding the axial punch from the contact of the material with the counter punch to the latter stage of the forming process, the evaluation function Ψ of the contact length with the counter punch is defined as an index for evaluating the risk of the forming failure.

*C<sup>l</sup>* on the right side of the equation of the evaluation function Ψ in Figure 11b is the contact length with counter punch, and *Cref* is the assumed reference contact length in which the contact length with counter punch increases in proportion to the bulge height.

Input and output variables for fuzzy rules were fuzzified so that the input variables *Φ*, *Φ*' (differential value of *Φ*), and Ψ, Ψ' (differential value of Ψ) are "Small" and "Large", and the output variables were ruled for the axial punch displacement increment ∆*APS* and the counter punch displacement increment ∆*CPS*.

As an example of the membership functions that determines the output variables, Figure 12 shows the membership functions for the evaluation function *Φ* that represents the risk of wavy buckling at the initial stage of forming process. The input and output membership functions (∆*APS* and ∆*CPS*) at the main forming stage are similarly ruled.

*Φ Φ Φ Ψ Ψ Ψ*

∆ ∆

∆ ∆

∆

*Φ Δ* **Figure 12.** Membership functions for the early stage. (**a**) Input membership function for *Φ*; (**b**) output membership function for axial penetration increment ∆*APS*.

Fuzzy inference was performed based on the membership functions for each forming stage, and the output value for each forming stage by defuzzification was determined by the centroid method.

*Ψ*

*Ψ*

*Φ*

∆

∆ ∆ The two output variables, ∆*APS* and ∆*CPS*, are sequentially determined during the process to maintain an appropriate contact state.

∆ ∆ ∆ Figure 13 shows a comparison between the loading path at 250 ◦C assumed from the authors' past experience and the loading path obtained by the fuzzy inference model. From the comparison of the two, the *p* of the fuzzy inference result in the loading path is larger than the *p* of the assumed path after the point A. As a result, in the ∆*H*-∆*L* curve for the counter punch, the fuzzy inference model early reaches the maximum setting bulge height of ∆*H* = 30 mm (point B). Therefore, in the assumed loading path, an axial feeding displacement of ∆*L* = about 50 mm was required to obtain the final shape, but in the loading path obtained by the fuzzy inference model, the final shape can be obtained by feeding the axial punch to ∆*L* = about 45 mm (point C). It can be said that efficient forming process can be performed by deriving the loading path using a fuzzy model system.

∆ ∆ **Figure 13.** Comparison of loading path between the manual set from experience and the fuzzy inference model (250 ◦C), *p:* internal pressure, ∆*H*: counterpunch displacement, ∆*L*: axial penetration.

A T-shape forming experiment was conducted to verify the validity. Figure 14 shows a comparison of the final shape and dimensions with the FE analysis results. Quantitatively good agreements are found on the shape, bulge height, and axial length, demonstrating the effectiveness of the loading path determination by this system.

0

4

**A**

Intern

al pressure / M

P

a

8

**Fuzzy inference Δ**

12

0 10 20 30 40 50

**Assumed path Δ Δ**

**Fuzzy inference Δ Δ**

Axial penetration *Δ* **/** mm

**Figure 14.** Comparison between the final shape and dimensions of T-shape formed products. (**a**) Experiment; (**b**) FE analysis.

*4.4. Optimum Temperature Distribution for Improving Wall Thicknes Distribution in Warm T-Shape Forming Process Using the Optimum Loading Path under Non-Uniform Temperature Field*

Since the loading path affecting hydro-formability was optimized in the previous section, the optimum temperature distribution under the no-uniform temperature field will be examined in that loading path condition.

∆ ∆

0

C

o

u

nterp

u

*Δ*

/ m

m

n

c

h displa

c

e

m

e

nt

6

12

**Assumed path Δ**

**B**

**C**

18

24

30

36

4.4.1. Effect of Temperature of Counter Punch on Thinning Behavior of the Bulged Part under Non-Uniform Temperature Field

In the bulging part including a bulge head, wall thinning occurs due to the internal pressure applied, but it is thought that this can be suppressed by cooling the counter punch and increasing the deformation resistance. Figure 15 shows the effect of the temperature *T*CP at the center of the counter punch on the wall thinning rate of the bulging part. It can be seen that the wall thinning of the bulging part can be suppressed by reducing *T*CP. However, since buckling/wrinkling in Figure 15b occurred near the die side and die shoulder part at a temperature of 160 ◦C or less, it is considered that there is an appropriate temperature range that suppresses wall thinning without causing forming defects, and *T*CP in T-shape forming of AZ31B. It is suggested that the optimum temperature of the counter punch is 170 ◦C.

**Figure 15.** Effect of counter punch temperature *TCP* on wall thickness reduction at the center of counter punch. (**a**) Effect of TCP; (**b**) buckling occurred near the die shoulder.

 1

1

2

4.4.2. Effect of Temperature of Die Bottom on Wall Thickness Distribution under Non-Uniform Temperature Field

In order to make the wall thickness distribution on the bulging side and its bottom side uniform at the same time, the authors will consider the case of further cooling to the bottom center. For the purpose, the temperature on the straight tube ends side is set to 150 ◦C, and also the central part on the bottom side is locally cooled to provide a temperature distribution to the central part of the die in the circumferential direction. In this case, in order to quantitatively evaluate the uniformity of the wall thickness distribution and determine the optimum temperature conditions, the root mean square of the bottom wall thickness distribution in each *T*bottom, *tRMS*, was calculated by the following formula,

$$t\_{RMS} = \sqrt{1/N \sum\_{i=1}^{N} t\_i^2} \tag{2}$$

Figure 16 shows the effect of the bottom center temperature *T*bottom on the uniformity of the wall thickness distribution. In this figure, a comparison based on the *tRMS* is performed. It can be seen that the uniformity of the wall thickness distribution is improved by decreasing the *T*bottom. On the other hand, the buckling shown in Figure 16b was confirmed in the bulging part when the temperature of *T*bottom was 120 ◦C or less, so it is possible that there is an appropriate temperature condition for *T*bottom to make the wall thickness distribution uniform without causing forming defects. It is suggested that the optimum temperature of *T*bottom in T-shape forming of AZ31B is 130 ◦C. By the way, the difference in the *tRMS* between the "250 uniform" and the *T*bottom "250" in Figure 16 is caused by the temperature distribution of the die. When *T*bottom = 250 ◦C, there is still a temperature distribution of the die in the axial direction of the tube, and the part where the temperature on the tube end side remains low. Due to the influence of the non-uniform temperature field, there is a difference in *tRMS* from the "250 uniform" for the uniform temperature field.

**Figure 16.** Effect of *T*bottom on RMS of wall thickness distribution along the bottom part. (**a**) The *tRMS*; (**b**) wrinkles occurred at bulging head.

From the above results, by creating a complex non-uniform temperature field lowering not only the die temperature in the direction of the tube axis but also to 130 ◦C to the opposite bottom of the bulge branch, it is found that the wall thickness distribution of the entire T-shaped product is further improved compared to under the uniform temperature field. For the T-shape forming of AZ31B, the optimized temperature conditions for the uniformity of the wall thickness of the formed product may be as shown in Figure 17.

**Figure 17.** Optimum temperature conditions in T-shape forming for AZ31B magnesium alloy.

### *4.5. Wall Distribuntion in the Optimum Loading Path under Optimum Temperature Distribution*

Figure 18 shows a comparison of the wall thickness distribution of the obtained formed product between the results of the conventional manual loading path and the optimum loading path. From these figures, it can be seen that a formed product having a more uniform wall thickness distribution is obtained on both the bulging side and the bottom side. It is shown that it is possible to determine appropriate processing conditions for making the formed product uniform by performing the optimum process path in the hydroforming of the T-shaped sample of the AZ31B magnesium alloy tube.

**Figure 18.** Comparison of wall thickness distribution between manual control and optimum process control (FE analysis). (**a**) Bulge side; (**b**) bottom side.

### *4.6. Application of the Optimization Methods to AZ61 Alloy Tube and Cross-Shape Forming*

Up to the previous section, the authors optimized the temperature distribution and loading path in a non-uniform temperature field and demonstrated numerically the possibility of uniform wall thickness distribution and improvement of formed shape and accuracy. Thereby, in this section, the authors will investigate and compare the case where this method is applied to the AZ61 tube of higher strength magnesium alloy and the case where it is applied to cross-shape forming as a forming shape other than T-shape forming. For cross-shape forming, the forming shape is different from T-shape forming; a new fuzzy model for cross-shape forming was created, and the various fuzzy parameters were modified accordingly.

### 4.6.1. Optimum Loading Path for Different Materials and Formed Shapes

∆

Figure 19 shows the comparison of optimum loading path for T-shape forming and cross-shape forming of AZ31B and AZ61 at 250 ◦C. Figure 19a shows the effect of the different strength between AZ31B and AZ61 on the optimum loading path in T-shape forming. At the initial stage of the *p*-∆*L* curve, the axial punch is feeding at the same

∆ ∆

∆ ∆

∆ ∆

time, while the *p* is applied in order to suppress the thinning of the bulge apex during free bulge deformation, and the *p*-∆*L* curve increases almost linearly. On the other hand, in the ∆*H*-∆*L* curve for the counter punch, the punch keeps stopping at the initial position of ∆*ho* = 10 mm until the blank tube contacts the counter punch. After that, the counter punch starts to move behind the feeding of the axial punch. The counter punch moves almost proportionally as the bulge deformation progresses and stops when it reaches the set maximum bulge height (point B), and in that state, the axial punch feeding is further progressing to the point C in order to attain more uniform wall thickness and improvement of the die filling rate and the dimension accuracy of the product. ∆ ∆ ∆ ∆ ∆

∆ ∆ **Figure 19.** Comparison of optimum loading path for T-shape forming and cross-shape forming of AZ31B and AZ61 at 250 ◦C. (**a**) T-shape forming; (**b**) cross-shape forming; (**c**) comparison between T-shape forming and cross-shape forming. *p*: internal pressure, ∆*H*: counterpunch displacement, ∆*L*: axial penetration.

Regarding the effect of the material on the *p*-∆*L* curve, the strength of AZ61 is higher than that of AZ31B, so the *p* at point A increases corresponding to the increase in strength. The required *p* is high while being maintained even after the point A. On the other hand, in the ∆*H*-∆*L* curve, the effect of the difference in material strength is that the position of the axial punch at which the counter punch starts to move is slightly delayed in AZ61, and then it is almost the same as in AZ31B.

Figure 19b shows the effect of the difference between AZ31B and AZ61 on the optimum loading path in cross-shape forming. The *p*-∆*L* curve of the cross-shape forming is significantly different in shape from the T-shape forming in Figure 19a. For T-shape forming, it is represented by two straight lines at point A, but for cross-shape forming, the latter half forming region is dominant except for the initial stage of forming, and the *p* increases in an upwardly convex quadratic curve. The effects of AZ31B and AZ61 on this quadratic *p*-∆*L* curve are similar to those in Figure 19a at the early stage of the process. In the dominant latter half, the effect of the strength difference expands as the forming progresses. It can be seen that the high-strength AZ61 requires about 1.5 times higher internal pressure. On the other hand, in cross-shape forming, the ∆*H*-∆*L* curve shows almost no difference between AZ31B and AZ61.

By the way, the effects of T-shape forming and cross-forming on the *p*-∆*L* curves, which have different forming shapes, can be clearly seen from the result of AZ61 in Figure 19c, which expresses the vertical axis on the same scale. At the early stage of forming process, there is a slight difference in the *p*-∆*L* curve between the two, but there is a slight difference in the *p* value at point A. It can be seen that the increase in the *p* is large for the crossshape forming, and it requires nearly 1.8 as much as in the latter half of T-shape forming. Meanwhile, the ∆*H*-∆*L* curve does not differ depending on the forming shape.

Until now, the loading path has been determined by experience and trial and error, but it is expected that this method will be applied to the optimization of processing conditions and the process control.

### 4.6.2. Optimum Temperature Distribution for Different Forming Shapes

By applying the optimization method for T-shape forming of AZ31B described above, optimization of the non-uniform temperature field was performed for AZ61 tube and cross-shape forming by the same FE analysis. In T-shape forming for AZ61 tube, buckling occurred at the bulged head area when the temperature of *T*bottom was 140 ◦C or lower. The difference in deformation behavior between AZ31B and AZ61 is considered to be due to the deformation resistance of both. The difference in deformation resistance between the two is not large in the high temperature range of 200 ◦C or higher, but the difference is large in the temperature range of 150 ◦C or lower. Therefore, in the WTHF of AZ61, it is considered that it becomes difficult to form the bulging part by reducing the temperature *T*bottom at the center of the bottom. From these results, it can be said that the optimum temperature of *T*bottom, which makes the bottom wall thickness distribution uniform in T-shape forming of AZ61 magnesium alloy, is 150 ◦C.

In cross-shape forming, the wall thinning of the bulging part can be suppressed by lowering the temperature *T*CP at the center of the counter punch, but wrinkles occur near the die shoulder by reducing the temperature. The temperature condition at which wrinkles began to occur was *T*CP < 200 ◦C for both AZ31B and AZ61. By setting *T*CP = 200 ◦C, it is possible to suppress the wall thinning of the bulging part by about 50% compared to the case of uniform temperature field, and the effect of suppressing the wall thinning by cooling the counter punch was confirmed in cross-shape forming for AZ61 as well as for AZ31B.

Figure 20 shows the optimum temperature distribution for T-shape forming of AZ61 and for cross-shape forming of both magnesium alloy tubes. For T-shape forming of AZ61 in Figure 20a, the optimum temperature distribution is different from that of AZ31B in Figure 18. The bottom temperature for AZ61 is 150 ◦C and 20 ◦C higher than that of AZ31B. On the other hand, for cross-shape forming shown in Figure 20b, in the cross-shape forming of AZ31B and AZ61, the optimum temperature distribution was the same. It was shown that the die was 250 ◦C and the counter punch was 200 ◦C, and for the temperature distribution cooling, only the bulge head was sufficient.

**Figure 20.** Optimum temperature conditions to make the wall thickness distribution more uniform. (**a**) T-shape forming for AZ61; (**b**) cross-shape forming for AZ31B and AZ61.

### **5. Conclusions**

In this study, local heating/cooling in the warm T-shape and cross-shape forming processes was carried out for the AZ31B and AZ61 magnesium alloy tube, which is a hard-to-form material at room temperature, to improve the formability, wall thickness distribution, and formed shape accuracy. For this purpose, a new local heating and cooling apparatus was developed and adopted to achieve a high wall-thickness quality of the hydroformed T-shape and cross-shape products. Under experimental constraints with a forming time of 5 min at 250 ◦C or below, optimization of temperature distribution and loading path during process using fuzzy inference model previously developed by the authors was attempted. As a result, firstly, it was verified that the local heating/cooling

approach to creating a non-uniform temperature field is more effective in the hydroforming process for the hard-to-form materials and enhancing the formability and making wall thickness uniform than that under a uniform temperature field. In addition, optimum symmetric and asymmetric temperature distributions for the T-shape and cross-shape forming of tubes were shown. Its effectiveness is considered to be confirmed under other conditions from the verification results obtained by the experiment and FE simulation for the T-shape forming of AZ31B.

It was suggested that the loading path and temperature distribution have important effects on the WTHF process and that these optimizations are necessary to achieve optimum process design and process control.

The influence of the loading path and the temperature condition on each other is not large, and both the optimizations can be realized independently.

**Author Contributions:** Conceptualization, K.-I.M.; formal analysis, T.M.; investigation, T.M.; validation, T.M.; writing—original draft preparation, T.M.; writing—review and editing, K.-I.M.; supervision, K.-I.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors sincerely express our thanks to Tsutomu Murai and Humiyuki Nakagawa of Sankyo Tateyama Aluminum Ltd. For providing the test materials, Ryouden Kasei Ltd. for providing the thermal insulation boards, and Tetsuya Yagami and Masamitsu Suetake for their invaluable advice.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

