Tube Bulging Test Research Articles

Analytical Model and Testing Method for Equivalent Stress-Strain Relation of Anisotropic Thin-Walled Steel Tube

Abstract The deformation behavior of sheet metal is currently presented by the stress-strain curve, which gives the variation of flow stress as strain increases. The correlation between stress and strain is also used to characterize the material hardening under different stress states. For anisotropic materials, the deformation behavior depends on stress state, and it is important to realize similar deformation conditions to obtain the stress-strain relationship. In this article, the profile of the free bulging zone was described by a tangent circle model during tube bulging test with fixed ends. In conjunction with the newly suggested linear-model for instantaneous thickness at the middle point, an analytical model and testing method is developed to establish the equivalent stress–equivalent strain relation of tubes. Experiments of STKM11A steel tube have been carried out, and different yield criteria are adopted to define the equivalent stress and equivalent strain. The effect of the anisotropic parameters on the mechanical property is analyzed. Results show that the profile of the free bulging zone can be well reproduced by the tangent circle model for practical application, and the analytical model and data measuring method for the bulging test can be simplified. The equivalent stress–equivalent strain curve by bulging test is rather different from that by uniaxial tension test, with a lower equivalent stress in the initial yielding stage and a greater rate of the equivalent stress increasing with the increase of the equivalent strain. In addition, the shorter the bulging zone length is, the greater the maximum equivalent strain is, because equal-biaxial stress state is approached. As the axial stress is significantly smaller than the hoop stress in bulging test, the anisotropic parameter along the hoop direction has a stronger effect on the determined curve and should be determined precisely.

Mechanism on increased sheet formability induced by tangential adhesive stress in sheet flexible forming process employing viscoplastic pressure-carrying medium

Abstract In flexible die forming processes employing semi-solid or elastic materials as pressure-carrying medium, there exist tangential adhesive stress or friction at medium/blank interface, which may improve sheet formability and has been experimentally verified. However, the mechanism behind this phenomenon has not been clarified yet. In order to fill this gap, analytical investigations were implemented in this paper based on previous studies involving through-thickness shear stress. Concretely, the analytical model of axisymmetric shell bulging process considering tangential adhesive stress and the extended M-K model under non-planar stress state were established at first. Accordingly, the relationship between tangential adhesive stress and through-thickness shear strain was deduced together with the relationship between through-thickness shear stress (strain) and sheet forming limit. On the basis of that, the viscous pressure forming (VPF) process was taken as an example to exhibit the characteristic that forming limit changes with tangential viscous adhesive stress and through-thickness shear stress (strain). It is shown that the tangential viscous adhesive stress has positive correlation with through-thickness shear strain which results in increased sheet formability. Tube bulging tests employing viscous medium with different molecular weight as pressure-carrying medium were conducted to give an experimental evidence of the proposed analytical results.

Formability Prediction for Tube Hydroforming of Stainless Steel 304 Using Damage Mechanics Model

Tube hydroforming (THF) is an important manufacturing technology for producing tube components by means of fluid pressure. In comparison to other basic forming processes like deep drawing, forming steps can be reduced and more complex shape is allowed. In this work, it was aimed to establish the forming limit curve (FLC) of stainless steel tube grade 304 for the THF process by using finite element (FE) simulations coupled with the Gurson–Tvergaard–Needleman (GTN) damage model as failure criterion. The parameters of the GTN model were obtained by metallography analysis, tensile test, plane strain test of the examined steel in combination with the direct current potential drop (DCPD) and digital image correlation (DIC) techniques. These parameters were well verified by comparing the predicted FLC of steel sheet with the experimental FLC gathered from the Nakazima test. Then, the FLC of steel tube 304 was established by FE simulations coupled with the damage model of tube bulging tests. During the bulge tests, pressure and axial feed were properly controlled in order to generate the left-hand FLC, while pressure and external force needed to be simultaneously incorporated for the right-hand FLC. Finally, the FLC was applied to evaluate material formability in an industrial THF process of the steel tube.

Evaluation of models for tube material characterization with the tube bulging test in an industrial setting

It is now well recognized that the material data obtained from a tensile test is less appropriate than those from a Tube Bulging Test (TBT) for a finite element simulation of tube hydroforming. However, the manufacturers still use classical data (often tensile test data) for designing metal operations due to the lack of standard for the TBT and a more complex post processing analysis of experimental measures. Getting the hardening curve from the tube bulging test requires the use of an analytical or numerical model. In this paper, three models for post-processing measures obtained from the TBT are compared based on the same experimental procedure. Thanks to a preliminary step, consisting of the validation of the analytical models through the use of finite element simulations of the TBT, it highlights that the results obtained for the local (stress and strain) and global components (the thickness distribution along the tube and the deformed tube profile) are very close, whatever the models. The test configuration (die radius and free length) seems to have no significant impact on the resulting stress-strain curve for the three models. The three models are used for post processing tube bulging tests performed on AISI304, INCONEL and Copper tubes validating their capacity for tube characterization on different materials. Finally, this study demonstrates that the Boudeau-Malecot Model can be used to obtain hardening curve from TBT without a loss of accuracy compared to more complex post-processing models and with an important gain of quality compared to tensile test.

Flow stress identification of tubular materials using the progressive inverse identification method

Purpose – The purpose of this paper is to propose a progressive inverse identification algorithm to characterize flow stress of tubular materials from the material response, independent of choosing an a priori hardening constitutive model. Design/methodology/approach – In contrast to the conventional forward flow stress identification methods, the flow stress is characterized by a multi-linear curve rather than a limited number of hardening model parameters. The proposed algorithm optimizes the slopes and lengths of the curve increments simultaneously. The objective of the optimization is that the finite element (FE) simulation response of the test estimates the material response within a predefined accuracy. Findings – The authors employ the algorithm to identify flow stress of a 304 stainless steel tube in a tube bulge test as an example to illustrate application of the algorithm. Comparing response of the FE simulation using the obtained flow stress with the material response shows that the method can accurately determine the flow stress of the tube. Practical implications – The obtained flow stress can be employed for more accurate FE simulation of the metal forming processes as the material behaviour can be characterized in a similar state of stress as the target metal forming process. Moreover, since there is no need for a priori choosing the hardening model, there is no risk for choosing an improper hardening model, which in turn facilitates solving the inverse problem. Originality/value – The proposed algorithm is more efficient than the conventional inverse flow stress identification methods. In the latter, each attempt to select a more accurate hardening model, if it is available, result in constructing an entirely new inverse problem. However, this problem is avoided in the proposed algorithm.

A Comparative Study of the Identification Methods for Tube Hydroforming Process

The present paper aims to assess the accuracy of identification methods used in the evaluation of the flow stress relationship of tubular materials for hydroforming applications. Based on experimental data acquired from home designed and manufactured experimental tool and results collected from literature, flow stress parameters are determined using both analytical and inverse identification methods. The obtained results are coped to experimental measurements to validate the proposed approaches. It is shown from the analysis based on the comparative assessment of flow stress inferred from tube bulge test that, inverse parameter identification method is the appropriate methodology that contribute to a more accurate tube hydroforming characterization.

Tube free bulging experiment with force-end and material properties testing

Compared with uniaxial tension,the material property parameters obtained by tube bulging test(TBT) can accurately reflect the plastic forming properties of materials under high-pressure fluid condition.Different end-conditions will seriously affect the experiment results of TBT. According to the defects of existed experimental method and equipment internationally,a special TBT system,with accurate boundary conditions and loading units,was successfully designed and developed. The axial force,axial displacement,and the internal pressure are the key points of the system which could be accurately controlled in real-time bycontrol strategy of displacement under dynamic active loading state and proportional servo valves. The free sliding of fixed tube ends was implemented by a special designed fixture. During the experimental process,the real-time thickness and bulging height in the pole,and the real-time internal pressure were monitored by the ultrasonic thickness gauge,the magnetostrictive displacement sensor and the ultra-high pressure sensor. The stress-strain curve and material properties were derived by the Swift material constitutive model and the monitor data. The experimental data demonstrate that the two load balance conditions,which are the balance of two axial forces with internal pressure and the balance of two axial contractive displacements,are always satisfied during all the test process. The test data processing results show that the monitor data have good repeatability and can be used to get the material properties.

Formability Determination of Titanium Alloy Tube for High Pressure Pneumatic Forming at Elevated Temperature

High pressure pneumatic forming is a forming technology at elevated temperature, whose ultimate goal is to form a tube blank of usually uniform cross-section into a die cavity of complex shape with variable cross-sections by applying internal pressure and axial feeding. In this paper, the mechanical property and formability of Ti-3Al-2.5V were evaluated by tube bulging tests at 800°C. The limit expansion ratios of Ti-alloy tube were 56.1%, 43.3% and 34.2% with constant internal pressure of 7.5, 12 and 14M Pa, respectively. The outline of the bulging zone was considered as a parabolic model. The relationship between thickness at the highest position and bulging height was considered as a linear model. The Fields–Backofen constitutive model was used to describe the flow stress of Ti-3Al-2.5V under biaxial stress states.

Mechanical and metallurgical analyses of longitudinally friction stir welded tubes: the effect of process parameters

Friction stir welding (FSW) is a welding technology used to join materials considered difficult to be welded. Mechanical properties of FSW joints are generally evaluated by means of tensile tests that might provide insufficient information because maximum strain obtained before necking is small and that cannot be used when the joint path is not linear or when the welds are executed on curved surfaces. The present work investigates the mechanical properties of FSW tubes by means of tube bulge tests. An experimental campaign was performed on tubular specimens (thickness equal to 3 mm, external diameter equal to 40 mm). In particular, bent plates in AA6060 alloy were longitudinally friction stir welded by means of a CNC machine tools varying the welding parameters. The burst pressure, the stress state and the wall thickness were measured for each tested tube. Finally, macro and micro analyses were carried out on the joints.

Mechanical properties and formability of TA2 extruded tube for hot metal gas forming at elevated temperature

The mechanical properties of TA2 extruded tube were tested by uniaxial tensile test at high temperatures ranging from 700 °C to 850 °C and different strain rates changing from 4×10−4s−1 to 4×10−1s−1. The tube bulging test was carried out at elevated temperatures up to 950 °C to evaluate the formability of TA2 extruded tube for hot metal gas forming (HMGF). The total elongation and the maximum expansion ratio of the tube were obtained. The bursting pressure and fracturing manner were analyzed. The results show that the tensile strength of TA2 tube decreases practically with temperature increasing and strain rate decreasing. Meanwhile, the total elongation is between 142% and 331%. In tube bulging test, special experimental setup was established by the way of induction heating. The bursting pressure decreases from 6.5 MPa to 1.2 MPa as temperature increases. The maximum expansion ratio increases firstly and reaches the maximum value of about 70% at 890 °C, and then decreases. Fracture occurs along hoop direction, axial direction and random direction at different temperatures. The ideal temperature range for TA2 tube forming is from 860 °C to 920 °C in HMGF process.

A simplified analytical model for post-processing experimental results from tube bulging test: Theory, experimentations, simulations

A complete analytical model combined with a very simple experimental procedure is proposed. It permits the post-processing of experimental measures to obtain the stress–strain curve for tubes very quickly and well adapted for industrial use. The quality of the results is proved by comparison with experimental measures and finite element results. Anisotropy in tube is revealed by plotting the (ρ,α) curve where ρ and α stand for strain and stress path respectively. Two quadratic criteria (Hill 1948 and Hill 1993) are studied and it is found that the Hill 1993 criterion seems the best to represent tube anisotropy for 316L stainless steel tube studied in the present paper.

Study of True Stress-Strain Curve after Necking for Application in Ductile Fracture Criteria in Tube Hydroforming of Aerospace Material

Tube hydroforming (THF) is an advanced metal forming process that is used widely in automotive industry, but the application of the THF process in aerospace field is comparatively new with many challenges due to high strength and limited formability of aerospace materials. The success of THF process largely depends on many factors, such as mechanical properties of the material, loading path during the process, tool geometry and friction condition. Due to complexity of this process, finite element modeling (FEM) can largely reduce the production cost. One of the important input in FEM is the material behavior during hydroforming process. The true stress-strain curve before necking can be easily determined, using either tensile testing or bulge testing, but for an accurate failure prediction in a large deformation, such as hydroforming, the study of true stress-strain curve after necking is important because it improves the quality of the analysis due to utilizing a real extended stress-strain curve. Hence, the objective of this research was to establish a methodology to determine the true stress-strain curve after necking in order to predict burst pressure in the THF of aerospace materials. Uniaxial tensile tests were performed on standard tensile samples (ASME E8M-04) to determine the true stress-strain before and after necking, using an analytical method presented in this study. To validate the approach, burst pressure in the THF process was predicted using the extended stress-strain curve in conjunction with Brozzo's decoupled fracture model. The approach was evaluated using data obtained from the free expansion (tube bulging) tests performed on stainless steel 321 tubes with 2 inches diameter and two different thicknesses, 0.9 mm and 1.2 mm. The comparison of the predicted and measured burst pressures was promising, indicating that the approach has the potential to be extended to predict formability limits in THF of complex shapes.

New Developments of Hydroforming in China

This paper reviews the recent developments of hydroforming technology in China. Limited corner radius, ring hoop tension test and tube bulging test were introduced on fundamentals of hydroforming. New hydroforming and hydro-bending process of ultra-thin tubes were investigated. Ultra-thin Y-shaped parts and complex section components were manufactured and applied in aerospace and aviation industry. Applications of tube hydroforming in automotive industry in China are also presented, including the hydroforming machines and production lines, typical automotive parts and potential market. New sheet hydroforming process with controllable radial pressure was proposed to increase the formability of sheets metals. Warm tube and sheet hydroforming were analyzed and discussed. [doi:10.2320/matertrans.MF201122]

Study on the Formability and its Geometric Factors of Seamed Tube Hydroforming

Forming limit curve (FLC) is an important tool for assessing formability of steel metal. It is commonly obtained from experiment, theoretical calculation and finite element method (FEM) simulation. In this study, the FLC of a seamed tube hydroforming is established by combining the failure criterion of strain increment ratio and FEM simulation. The numerical method is verified by tube bulge tests. Then the sensitivity studies are carried out to evaluate the effect of the geometrical features of seamed tube on its formability by numerical approach. Results show that the changes of the formability with the geometrical features of a seamed tube.

Error evaluation on experimental stress–strain curve obtained from tube bulging test

To get precise material data for advanced numerical modelling of tube hydroforming process, the tube bulging test is recommended. Stresses and strains in the tube cannot be evaluated easily and several approaches have been proposed. A review is proposed and points out their advantages and drawbacks. A semi-analytical model is presented and experimental measures done on an original tube show the thickness scattering along a generating line of the tube. These observations justify the processing of a linear sensitivity analysis which reveals the most influencing parameters on the accuracy of the hardening curve and gives information to perform relevant experiments.

Formability determination of AZ31B tube for IHPF process at elevated temperature

Ring hoop tension test and tube bulging test were carried out at elevated temperatures up to 480 °C to evaluate the formability of AZ31B extruded tube for internal high pressure forming (IHPF) process. The total elongation along hoop direction and the maximum expansion ratio (MER) of the tube were obtained. The fracture surface after bursting was also analyzed. The results show that the total elongation along hoop direction and the MER value have a similar changing tendency as the testing temperature increases, which is quite different from the total elongation along axial direction. Both the total elongation along hoop direction and the MER value increase to a peak value at about 160 °C. After that, they begin to decrease quickly until a certain rebounding temperature is reached. From the rebounding temperature, they begin to increase rapidly again. Burnt structure appears on the fracture surface when tested at temperatures higher than 420 °C. Therefore, the forming temperature of the tested tube should be lower than 420 °C, even though bigger formability can be achieved at higher temperature.

Inverse method for flow stress parameters identification of tube bulge hydroforming considering anisotropy

The objective of this paper is to determine the behaviour parameters of hydroformed tubular materials of annealed 25CrMo4 steel seamless tubes. An inverse identification procedure has been developed to determine the flow stress parameters from experimental free bulge and simple tensile tests. Two inverse identification strategies are proposed. In the first one, the tubular material behaviour is assumed isotropic, and then the parameters of the effective stress-strain relationship are derived from experimental bulge height versus the forming pressure. In the second one, the planar anisotropy of Hill'48 yield criterion is considered. Firstly, the simple tensile test is used to fit the isotropic strain hardening law. Secondly, the anisotropic parameter is identified by inverse technique from the experimental bulge test. The obtained results are compared with experimental measurements to validate the proposed strategies. It is proven that inverse identification methods could be a better alternative to analytical methods for flow stress parameters determination. Moreover, the anisotropy parameter has shown a large effect on the hydroformed tube responses, particularly on the wall thickness. Consequently, this material anisotropy should be considered within the flow stress identification of tube bulge tests.

Study on the Formability and Deformation Behavior of AZ31B Tube at Elevated Temperature by Tube Bulging Test

Internal high pressure forming of tube is widely used to form complex tubular part with different cross sections and curved axis. The ability of tube to undergo expansion deformation is crucial for the forming process. To evaluate the formability of AZ31B extruded tube, bulging test was carried out at different temperatures from RT up to 480 °C. Bursting pressure and maximum expansion ratio (MER) of the tube were obtained. The fracture surface after bursting was analyzed and compared with that obtained by tensile test along axial direction. Hardness changes in different positions along axial direction were also measured. Results show that the MER value remain almost unchanged from RT to 100 °C. In the temperature interval between 100 and 480 °C, an oblique N model can be used to describe the variation of MER value. The first peak and the bottom MER value occurred at 160 and 330 °C, respectively, and about 30.3% expansion ratio was reached at 480 °C. The bursting pressure decreased almost linearly as testing temperature increased. The fracture mode also changed from intercrystalline fracture to gliding fracture. However, burnt structure happened when the forming temperature was about 480 °C. The hardness value of the tube decreased significantly after the bulging test.

THE FACTORS AFFECTING THE PROFILE OF MIDDLE BULGE REGION DURING TUBE BULGE TEST

Tube bulge test is one novel method of determining the stress-strain relations of tubular materials, compared with the traditional tension test, which can give better description of the mechanical properties of tube. Based on the ellipstical surface assumption of the middle free bulge region during hydrobulging, the tube hydrobulge process is analyzed first. The main factors that affect the shape of the tube were determined and analyzed. Results show that the length of tube bulge region and the entrance radius of the die are two key factors that determine the profile of the middle free bulge region. When other conditions are fixed, the ratio of the two semi-radii will decrease as the decrease of the initial length of tube bulge region or the increase of the die radius. It means that the profile of the middle free bulge region after hydrobulging will change from long ellipsoid to sphere and then to flat ellipsoid. The stress-strain curves determined by tube bulge test differ for different length of tube bulge region and the entrance radius of the die, but are all lower than that of traditional tension test along axial direction. The smaller the length of tube or the bigger the entrance radii of the die, the bigger is the difference.

Error evaluation on experimental stress-strain curve obtained from tube bulging test

The paper is focused on a sensitivity analysis developed to study the relevance of experimental hardening curves obtained from tube bulging test to quantify the influence and the contribution of experimental uncertainties on the response variability. The experiments are based on “online” measurements of the internal pressure and the bulge height. A semi analytical model developed from a geometrical representation of the bulged tube and equilibrium of infinitesimal volumes (slab method) permits to evaluate the stress-strain curve. The differentiation of all the equations of the model and the evaluation of all the input parameters allow to get the total uncertainty on the resulting hardening curve and to identify the critical experimental parameters. Hence the results of this sensitivity analysis open up ways of improvements for conducting experimental tube bulging test.