Numerical and experimental predictions of formability parameters in tube hydroforming process

ABSTRACT The purpose of this study is to improve the bulging and minimise the thinning ratio so that manufacturing processes will be improved in Industries. Tube hydroforming is an advanced manufacturing technology used for making intricate and complex tubular parts which required less cycle time. This research focusses on hydroforming process, formability and process parameters design for replacing the conventional tube bending, welding and cutting operations. The prediction of parameters is done by applying numerical and experimental approach. During experimentation the pressurised fluid is used to deform the tubes in a plastic deformation. In this study, two types of grade materials are used such as AISI304 and AISI409Lof 57.15 mm external diameter with 1.5 mm thickness in the form of ERW tubes to measure stain path, thinning and bulge height. However, it is observed that the internal pressure and L/D ratio are effective parameters in both numerical analysis and experimentation. In axial feed condition, it is observed that 7.7% thinning in weld region and 24.9% thinning in base metal region, whereas, in fixed feed condition, it is observed that 9.2% thinning in weld region and 26.2% thinning in base metal region for L/D = 1 and L/D = 3, respectively. The numerical analysis with experimental results shows a very good match.


Introduction
The hydroforming (THF) process is an advanced manufacturing process for sheet as well as tube forming with applications in various sectors such as pharmaceutics, chemical, aerospace, and automotive industries with better quality and competitive manufacturing cost of the products. The hydroforming process is an alternative manufacturing process for conventional manufacturing and also propose product can be manufactured in competitive price and time with weight reduction. The AISI316L material characterisation has studied under different flow and friction conditions. The study is focused on stress concentration reduction so that punch life can be enhanced (Colpani, Fiorentino, and Ceretti 2020).
Industries are attracting towards tube hydroforming technology because this technology has ability to manufacture intricate size and shapes of the tubes for high and low weight steel. The research focus was on process and forming parameters estimation (such pressure, yielding, ultimate and calibration points etc.) during copper tube forming under axial loading condition (Fatemi, Biglari, and Morovvati 2010). It is seen that the success of tube hydroforming process depends on feed and pressure parameters in which the reliability of FE model in hydroforming is studied. The reliability of FE model was depending on the accuracy of the material properties and seen that the hydroforming performed by numerical analysis was more accurate and simpler than trial-error method (Lan et al. 2004a). The internal pressure and axial feeding parameters have the major impact over the bulging of tube component (Abdessalem and Hami 2014). The tube hydroforming process has many advantages over the conventional manufacturing process such as improved component quality, reduction in weight and lower manufacturing costs (Alaswad, Benyounis, and Olabi 2012). Many researchers performed comparative study of experimental and numerical study under free bulge and calibration conditions (Abrantes, Szabo-Ponce, and Batalha 2005). (Omar, Tewari, and Narasimhan 2015) studied that the strain path for weld as well as base metal during tube bulging. The hydroforming process has advantages over stamping and welding conventional technology such as parts consolidation, weight reduction through more efficient section design and tailoring of the wall thickness in structural components etc. Also, observed improvement in structural strength and stiffness through optimised section geometry, lower tooling cost due to fewer parts, fewer secondary operations, tight dimensional tolerances, low springback and reduced scrap. Automotive applications observed in exhaust parts, camshafts, radiator frames, front and rear axles, engine cradles, crankshafts, seat frames, and space frames (Ahmetoglu and Altan 2000). The performance of tube hydroforming process is highly dependent on process parameters such as internal pressure, axial feeding, friction, etc. without any type of defects. Therefore, the forming parameters must be determined carefully (Aydemir et al. 2005). Now a day the tube hydroforming process is rapidly implemented in many industrial applications for bulging of tube in desired die cavity. The advantages over the conventional methods are higher strength to weight ratio and lower price. The applications in automotive and aerospace industries such as engine cradle, chassis components, seat frames, exhaust manifolds, structural body and power transmission components, T, X and Y fittings manufacturing (Hartl 2005;Lan et al. 2004b).
The hydroforming process is employed for manufacturing of tubular parts with the objective as vehicle weight reduction (Dohmann and Hartl 1996). The Tube hydroforming was used frequently in automotive and aerospace Industries. The process gives better product quality within less production expenses. The T-shape tubular part is used for tube hydroforming parameters optimisation such as axial feed, counter force and forming pressure by employing ANN (Artificial Neural Network) and Finite element analysis (FEA) (Abbassi et al. 2020). The Goodwin forming limit diagram (FLD) diagram has been widely used for the representation of formability analysis of material for seamless and ERW tube. The parameters such as microstructure, mechanical behaviour is studied for various laser-welded and ERW tube material (Goodwin 1968). FEA was employed for the analysis of formability parameters to study the effect on various heat affect zone (HAZ), weld zone and base metal regions. It was also found necking near weld zone for seamed weld tube (Kim et al. 2004).
The seamed, laser-welded and electric resistancewelded (ERW) tubes have been widely used in automotive vehicles and so on. Also found that laser-welded tube has better formability for diameter to thickness ratio as compared with ERW tube. FEA is commonly used in auto industries for analysis of process and forming parameters to improve product quality as well as to reduce product design and development time. The FEA is also helpful to analyse formability parameters of complex geometries (Kang, Kim, and Kang 2005). The researcher has proposed 0.92 new necking criteria for prediction of necking in sheet and tube deformed components (Kumar, Date, and Narasimhan 1994). An initially FLC was introduced (Keeler and Backofen 1963). Tube hydroforming (THF) is a widespread technique in metal forming process, which can produce lightweight tubes or tube components with complex cross sections (Lang et al. 2004;Lee, Korkolis, and Kim 2015). The researcher has investigated the parameters such as microstructure, deformation behaviour and mechanical properties of the annealed pure copper material for double branched tube component (Chen et al. 2018). In this process, it is possible to manufacture the intricate or complex geometry parts or components. The effect of friction and forming pressures on formability parameters was studied. Also, found that the uniform thickness distribution in both low-and high-pressure hydroforming processes. The friction has more and less sensitive parameter in both high-and low-pressure tube hydroforming respectively (Nikhare, Weiss, and Hodgson 2009). The loading and die geometry input parameters were considered for the formability study for SS304 material and the strain paths were predicted under the free and fixed conditions (Naghibi et al. 2016). The various diameter and thickness geometry parameters were used for the comparative study of formability parameters on seamless and welded tubes. It was also found that the formability increased in both tube geometries (Omar et al. 2016). The effect of corner radius and coefficient of friction on thickness distribution and bulge height was studied by FEA. The numerical and analytical results were observed in good agreement for formability parameters (Reddy et al. 2020a). The necking points of bulged tube were used to construct the forming limit stress diagram (FLSD) based on principle stresses (Kim et al. 2009). THF process is a special manufacturing process used to produce tubular structural components. Many researchers have found optimum parameters of tube hydroforming process to attain the maximum bulge height with distinguish parameters such as internal pressure, axial feed and coefficient of friction conditions. Also, found that the maximum bulge height is possible when the pressure is more and feed rate is less and the bulge height is minimum when the feed rate is more and pressure is less (Memon, Omar, and Narasimhan 2013). The forming pressures were predicted by applying implicit and explicit FEA tool. The explicit tool has better deformation properties by comparing with implicit solver (Thanakijkasem et al. 2015). The researcher has constructed forming limit diagram for QSTE340 seamed tube material. The theoretical and numerical comparative models were developed for the construction of left and right side of the forming limit diagram (FLD), respectively (Chen et al. 2011). The analytical model was employed for the prediction of forming pressure. The analytically predicted results are verified with experimental for free bulging behaviour of tube (Xu et al. 2014). The simple and complex strain paths were constructed by employing Swift's diffused necking and Hill's necking criterions. The experimental strain paths were compared and validated (Yang, Hu, and Liu 2015). The tubular components are manufactured with axial feed and internal pressure in tube hydroforming process. The tube was fed into the die setup and the axial feeds were applied till the bursting of tube so that the effective process parameters can be analysed. The forming limit curve (FLC) has been widely applied for the analysis of hydro formability parameter representations. The researcher has main focus on the study on laser seamed tube. There are three types of test methods such as free bulging and elliptical bulging, hydroforming limit test. These test methods were applied on laserwelded and electric resistance-welded tubes (ERW). The cracking failure defect has been analysed on both seamed and ERW tubes during bulging of tube. The FLC analysis demonstrates that the laser-welded tube exhibits a better hydro-formability than that of the ERW tube under same input conditions (Lan et al. 2004b;Yu et al. 2014;Levy 1996;Naghibi et al. 2016). The sensitivity analysis of thickness variations during tube bulging was studied (Omar, Tewari, and Narasimhan 2020), whereas a novel FLD diagram was developed for nonlinear loading paths under fixed and free conditions (Zhu et al. 2020). The tailor-welded tubes were developed with various thicknesses components for hydroforming experimentation and also concluded that seam weld issues are resolved in tailor weld tube (Han et al. 2019). The wrinkling defects are analysed on magnesium alloy material under the axial feed condition and also predicted the variations in between deformation and axial feed by simulation (Kong, Lu, and Chan 2019). The strain non-uniform index and forming limit diagram are good methods to identify the defect free components by simulation (Pandey, Walunj, and Date 2018). The fracture and necking parameters were analysed numerically and observed that the static pressure was increased which led to shifting the fracture area from P to C type shaped tubes (Shi et al. 2017), whereas the forming limit diagram was drawn at necking points of bulged tube with experimentation and simulation on AL-7020-T6 material grade (Afshar et al. 2017).
Various researchers studied the process and forming parameters during bulging of tube. Day by day fuel consumption in automotive sector is increasing due to heavy weight of materials. Hence, it required to reduce the weight of components or vehicle. The fuel consumption can be minimised by reducing weight of the vehicle or by adopting advanced manufacturing techniques. Also, it is found that the ferrite and austenite grade material is not used for tube hydroforming process. The common bulging tube defects are observed to be wrinkling, buckling, spring-back and fracture or necking. Hence the purpose of this study is to improve the bulging and minimise the thinning ratio so that manufacturing processes will be improved in industries. This research focuses on hydroforming process, formability and process parameters design for replacing the conventional tube bending, welding and cutting operations.

Materials and methodology
The AISI304 grade material is frequently used for manufacturing of domestic equipment, medical instruments, boilers and measuring instruments, whereas AISI409L grade material is used in two and threewheelers exhaust system, catalytic converter and muffler systems. The chemical composition (wt. %) of the material under consideration is shown in Table 1. The tubes were prepared by using plane sheet metal with 1.5 mm thicknesses. Tube procurement parameters are presented in Table 2. The specimen's preparations and the details of the used tube dimensions for tube hydroforming process is shown in Table 3. It is the selection and design of parameters for numerical and experimental study. The tube geometry parameters like tube diameter, length to diameter ratio and the feed type have been used. Therefore, three tubes for similarity check are defined and out of which consistency were checked for at least two experiments, and it is set that it must have same necking for the success of the bulging tube.

Mechanical and material parameters
The mechanical and material properties have important role in tube hydroforming process. The  simulation model was designed in FEA-based Pamstamp software, which is dedicated for metal forming analysis using two types of grades as shown in Table 4. The specimens are prepared as per the ASTM E8 standard for tensile test. The testing was performed on UTM (universal testing machine) computerised control machine along with feedback system. The maximum load capacity of the machine was 250 kN. The load was applied gradually on specimen to find the true stress strain curve. The anisotropy material properties are calculated by using mathematical Equations (1)-(4). The strain hardening exponent value shows the formability and stretchability in tube bulging.

Plastic strain-based Hill criterion
The anisotropic yield function employed to calculate failure strains in plane stress during simulation as shown in following equation. The Hill's yield criterion (Hill 1948) and its coefficients are measured based on anisotropy property along the three different directions such as 0, 45 and 90 in degrees. The Hills equation and its coefficients are given in Equations (5) and (6).
ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi

Thickness gradient necking criterion (TGNC)
Initially this criterion is developed from simulation for forming limit strains findings. In THF process, the critical neck is seen by the nearness of a basic neighbourhood thickness gradient in the tube. Such an impression of the neck is autonomous of the strain path, forming rate and the tube metal (material properties). The critical neighbourhood thickness gradient R critical , exists at the on set of an obvious nearby neck.
After beginning of deformation of the tube, a thickness gradient, 'R thickness gradient ' creates in the deformation tube as presented by Equation (7).
Where, R TG = thickness gradient, t n = necking element thickness, t nÀ 1 = neighbouring element thickness As the tube starts bulging (forming), the thickness gradient continues to reduce from original value of 1.5. The thickness gradient goes on decrease at the on set of localised necking and at a certain stage called diffused necking, it reaches to a critical value. From the work of (Kumar, Date, and Narasimhan 1994;Nandedkar 2002;Reddy et al. 2020b) the R cri is experimentally estimated as 0.92. If R cri is less than or equal to 0.92, the tube specimen is considered as necked.

Numerical analysis
The Finite Element Analysis (FEA) procedure is developed for the simulation of tube bulging in Pamstamp software. Basically, there are three stages of simulation such as Pre-processing-Input, Solver and Post processing-output as shown in Figure 1.
The explicit FEA based Pamstamp software have steps which are followed during simulation. The input parameters are material properties, boundary conditions along the two different directions such as unidirectional and bidirectional. The anisotropy yield base model was solved i.e. Hill criteria. The output or post-processing parameters such as strain  distribution, thinning etc. were measured at necking point and it was done before the fracture of the components.
The simulation model was developed in CAD solid work tool. Then, the CAD files imported in FEA environment. The obtained 3D solid model and tube loading position on lower die are shown in Figure 2. Solid model shows the upper die, lower die, left and right piston as well as coordinate frames. The friction coefficient used in between the contact surfaces of dies and punch is taken as 0.008.

Experimentation procedure
The block diagram of tube hydroforming process is shown in Figure 3. The tube is loaded in between upper and lower dies, and then axial or fixed feed is applied to the both ends of the tube. Here, in hydroforming process an intensifier has an important role to develop required pressure inside the tube so that created inside pressure should be exerted inside the tube and then tube bulged into die set cavity. The strain paths of the bulging tube were sensed in computer system and its further process to analyse the forming parameters. The process parameters such as pressure and axial feeds affect the material behaviour and quality of the components. The pressure and feed ranges from 0 to 0.05 GPa and 0 to 3 mm, respectively.  The micro hardness of tube is measured according to ASTM E-92-82standard. The locations of hardness measurements are also shown in right hand side of the Figure 4. After hardness measurement as shown in Figure 5, it was found that AISI409L furnished higher hardness properties than AISI304. It means that AISI409L difficult to form in desired size and shape as compared to AISI304 grade material.
For experimentation tubes required as shown in Figure 6 are used and prepared as per requirement. The operational and experiementation steps are presented in flowchart as shown in Figure 7. The die set are loaded on machine as per the design of experimentation (DOE) planning and tubes were loaded between the upper and lower dies. After applying all conditions, the tube bulging started. The deformation at neck position recorded with all required parameters.The complete tube hydroforming setup is shown in Figure 7. The left and right pistons are used to apply axial or fixed conditions to both ends of the tubes. The pressure intensifier has major role for bulging of tubes. The experiemntal setup and necking specimens are shown in Figures 8 and 9 along with bulging height and length.
Tube hydroforming experiments with varying L/D ratios were performed. The experimental strain path data was recorded using digital image correlation system. The mechanical properties obtained from the tensile testing of the base and weld metal were incorporated in the finite element simulation. The strain path data obtained from experimental hydroforming was compared to FE simulations. Finally, the systematic finite element-based study was performed to understand the role of material (material inhomogeneity and thickness imperfection) in triggering localisation for different L/D ratio. The hydraulic tube bulge tests were performed on tube hydroforming machine having clamping force capacity of 200 ton and maximum hydraulic pressure of 150 MPa.
In the present work, the tube hydroforming experiments were performed at different L/D ratio of 1, 2 and 3 with axial feed deformation conditions, to generate variety of stress states in the uniaxial drawing region.
The strain measurements were performed with the digital image correlation (DIC) technique utilising 3D ARAMIS system manufactured by a German company GOM (Helfrick et al. 2011).
The non-uniform speckle pattern was applied on the surface of the tube before hydroforming. The speckle pattern was obtained by first spraying surface with the white paint and then spraying with black droplets (McCormick and Lord 2010).
This system takes into account the relative displacements of the speckle patterns painted on the surface of the undeformed and deformed tube, thus calculating the surface strains distribution by continuous analysis of the digital images obtained from DIC camera setup.

Numerical analysis
The simulations were performed on finite element based commercially available PAM-STAMP 2 G software. The simulation methodology adopted was based on the work carried out. The tubes were modelled as two material system, viz: weld zone and the base metal region. The weld width modelled in the finite element simulation is taken as 7.5 mm. The weld zone and base metal properties obtained from tensile test were assigned for the two material regions in the  Sim. For AISI409L along fixed feed Figure 13. Forming limit diagram shows for numerical and experimental results.  simulation. The strain path analysis for different L/D ratios was carried out in 2-Dimensional FE analysis using shell element of size 1.5 mm. The co-efficient of friction for the axial feed simulations was assumed to be 0.04. This was found, from previous studies, to be the most optimal value to simulate the experimentally obtained die and tube surface lubrication conditions (Nikhare and Narasimhan 2008) The FEA tool is helpful to find the approximate forming parameters such as strain path, thinning, etc. of tube metal deformation during tube hydroforming process. In base metal thinning has started from 16.3% to 24.9% under the axial feed condition. The maximum and minimum thinning observed in L/ D = 3 and L/D = 1, respectively. However, in weld metal, it was observed that thinning varies from 7.7 to 10.4% under fixed feed condition. The thinning is directly proportional to L/D ratio in both fixed and axial conditions as shown in Table 5.
In base metal thinning started from 14.2% to 20.3% under the axial feed condition. The maximum and minimum thinning observed in L/D = 3 and L/ D = 1, respectively. The base and weld metal thinning are shown in Figure 10.
However, in weld metal it is observed that thinning varies from 6.8 to 12.8% under fixed feed condition. The thinning is directly proportional to L/D ratio in both fixed and axial conditions as shown in Table 6.

Experimental test
The strain paths for base and weld metal of AISI304 and AISI409L has been recorded as shown in Figures  11 and 12.
The strain paths were measured for weld and base metal as shown in Figures 11 and 12. The engineering and true stress strain curves for base and weld metal of AISI304. The experimental true stress-strain curves  data are used for simulation and further development in metal forming. The true stress-strain curve has more surface area as compared to engineering curve because this area is used for the study of formability parameters of any sheet or tube metal forming. The engineering curves or values are used to calculate true stress-strain curve and following relations (Equation (10)) used.
Whereas, σ True =true stress in MPa, ε True =true strain in %, σ engg =engineering stress, ε engg =engineering strain The experimental results (FLD) have been compared with mathematical FLD model and FEA simulation FLD results. The predictions have made for two grades such as AISI304 and AISI409L materials. The comparisons were made in between austenitic and ferritic stainless steels. The result shows the Austenitic stainless steel has better formability as compared to ferritic stainless steel. The Simulation Hill 98 plasticity law based on hardening curve which was Hollomon law gives the little bit upper boundary for all FLD curves as shown in Figure 13. The simulated results show a closed match with experimental analyses. By comparing the results among the three FLD, it is observed that the sufficient level of accuracy under axial and fixed feed conditions. The strain limits diagram was obtained experimentally. Initially, the tube was kept under the loading position and then loading stopped as bursting occurred. After bursting, the major and minor diameters of the ellipse near the crack were measured and then represented on forming limit diagram (FLD). The major and minor engineering strains were calculated by using Equation (10) and diameters were measured on the profile projector machine.    (10) whereas, e major = major engineering strain, e min or =minor engineering strain, d major =major diameter, d min or =minor diameter, d initial = initial diameter of circle The power hardening law or material model equation was used to model the tube behaviour and the Holloman equation (Pambhar and Narasimhan 2013) as written by Equation (12).
whereas σ Y = effective stress along Y direction, K = strength coefficient, � ε=effective plastic strain, n = strain hardening exponent. The tubes are prepared ( Figure 6) as per requirement with data presented in Table 7.
The conditions ( Figure 14) were applied for experimental work as axial and fixed feed condition. In axial feed condition the feed was given from 0 to 3 mm along the both ends. But in case of fixed feed condition feed was given from 0 to 0.001 mm, respectively. From experimentation tube, bulging was taken place in both dimensions such as length and diameter. Here, F and Pi parameters represents the feed applied in axial direction and internal pressure developed for tube bulging. In fixed condition case both ends were fixed by using fixed plungers and pressure were applied inside through the opening of the left and right plungers.
From Figures 15 and 16, it is observed that maximum bulging was observed when L/D = 3 in both cases. The variation in simulation and experimental results was observed to be 8% to 17%. But in fewer samples it is observed to be more than 17%, which is not shown in these plots. During comparative study between two materials, it was observed that AISI304 grade material has maximum formability strength. The affected formability parameters were studied for both axial and fixed feed condition. The L/D formability strain path was studied and found in L/D = 1 near weld and is greater than one in base metal at necking point. The minimum strain paths were found in base metal during L/D = 2 and 3 and that was away from weld or greater than 90 degree. In axial feed it is found that maximum thinning was 40% and 15% in base and weld metal, respectively, for AISI304 material. Again, in axial feed it is found that maximum thinning was 14.8% and 8.5% in base and weld metal, respectively, for AISI409L material. The bulging has a certain limit up to necking point and at this point formability parameters are measured before fracture. Bulge height is higher than it feeds lesser material to compensate the necking at the bulged portion. So that, the bulging of the tube component decreases with increase in bulge height. The internal pressure developed inside tube with different feed conditions for bulging tube as shown in Figure 17.

Conclusions
As per the objective of this work the simulation model results are compared with an experimental analysis for tubes with varying dimensions. From investigations, it is observed that the mathematical and simulations model shows sufficient level of accuracy for austenitic and ferritic stainless steel in unidirectional conditions. The three types of predictions show better correlation among each other. The influencing or interacting parameters are considered for tube metal part manufacturing through material optimisation, formability and process parameters and alternative material selection for vehicle, weight reduction, product quality improvement and customer satisfaction.
The simulation and experimental analyses show sufficient level of quality with exact curve fitting with maximum variation of 15%. AISI304 grade material shows better formability as compared to AISI409L, lead to highly suitable material for tube hydroforming components. The L/D ratio forming parameter has major impact on the quality of the forming because L/D = 3 ratio has more uniform formability as compared to L/D = 1. The forming parameters such as thinning, FLD, L/D ratio and bulge height are in good agreement obtained numerically and experimentally. From experimental investigation, it is observed that the internal pressure plays significant role to get an optimum quality of the components or products. The bulging can be improved by axial feeding with respect to L/D ratio as compared with fixed feed condition. The maximum thinning was observed in fixed feed condition as compared to axial feeding for both materials. The better formability parameters are found better for AISI304, hence this material is suitable for hydroforming process. Finally, it is concluded that the thinning can be improved by taking care of leakage and process parameters during axial feed condition.