Bulge Test Research Articles

Inverse Identification of a Constitutive Model for High-Speed Forming Simulation: An Application to Electromagnetic Metal Forming

Forming simulation requires a constitutive model whose parameters are typically determined with tensile tests assumed static. However, this conventional approach is impractical for high-speed forming simulation characterized by high strain rates inducing transient effects. To identify constitutive parameters in relation to high-speed forming simulation, we formulated the problem of constitutive modeling as inverse parameter estimation addressed by regularized nonlinear least squares. Regarding the proposed inverse constitutive modeling, we adopted the L-curve method for proper regularization and model order reduction for rapid simulation. For demonstration, we corroborated the proposed strategy by identifying the modified Johnson–Cook model in the context of a free bulge test with electromagnetic metal forming simulation. The L-curve method allowed us to systematically choose a regularization parameter, and model order reduction brought enormous computational savings. After identifying constitutive parameters, we successfully verified and validated the reduced and original simulation models, respectively, with a manufactured workpiece. In addition, we validated the numerically identified constitutive model with a dynamic material test using a split Hopkinson pressure bar. Overall, we showed that inverse constitutive modeling for high-speed forming simulation can be effectively tackled by regularized nonlinear least squares with the help of an L-curve and a reduced-order model.

On the identification of material hardening for anisotropic sheets via bulge tests

The hydraulic bulge test provides a useful tool to characterize the mechanical behavior of sheet metal under nearly equibiaxial loading, such as the material hardening response. However, the kinematic relationships during bulge tests of anisotropic sheets are still less understood and need further clarification. To this end, extensive numerical simulations of bulge tests are first performed, covering different die geometries and materials that exhibit distinct hardening features and Hill48 anisotropy. Based on the general scaling laws of the kinematic relationships, the numerical results are then used to establish an analytical model that explicitly relates the dome height, apex strain, and radii of curvatures in terms of the die ratio, material hardening parameter, and anisotropy. In addition, the general extraction procedure, which incorporates the analytical model to obtain the hardening responses of anisotropic sheets, is also provided. Finally, the effectiveness of the analytical model is confirmed based on representative results of AA6061 and DP600 sheet experiments and supplementary numerical simulations. The proposed model is expected to help facilitate the application of bulge tests in characterizing the plasticity and forming behavior of anisotropic sheet materials.

Analysis of texture evolution and slip activity of a near-α titanium alloy sheet under different biaxial-tension strain paths

Understanding of the texture evolution and slip activity of titanium alloys during hot forming is crucial for designing reasonable strain path and improving formability of materials. To this goal, a hot gas bulging test was developed to investigate the texture evolution and slip activity of a near-α TA32 titanium alloy sheet under different biaxial-tension strain paths at elevated temperature. Four elliptical through-hole dies with different minor–major axis ratios and two dies with different suddenly-changed cavities were designed to realize various strain paths. The deformation texture was characterized by electron backscatter diffraction (EBSD) technique. The global Schmid factor (GSF) was adopted to analyze the dominant slip systems under different strain paths and their effects on texture evolution. Results showed that when the strain path changed from equi-biaxial tension to plane strain, the formability of the material decreased due to the decrease of the prismatic slip activity of the initial transverse texture. Meanwhile, the deformation texture changed from a band with (0001) orientation perpendicular to RD to TD-split basal bimodal texture. Furthermore, nonlinear strain paths at elevated temperature can be effectively realized by bulging with cavities suddenly-changed dies. When the first principal stress direction was converted from TD to RD during continuous deformation, the activity of pyramidal-2 slip obviously increased, and the preference of (0001) orientation transformed from perpendicular to RD into rotation towards RD. The formability of titanium alloy sheets during hot deformation can be improved by controlling texture based on the relationship between strain paths, texture evolution and slip activity.

Evaluation of the Mechanical Properties of Nanometer-Thick Graphite Film and Graphene Using the Bulge Test

The mechanical properties of nanometer-thick graphite film (NGF) and graphene were characterized using a bulge test. Young’s modulus, fracture stress, residual strain and stress of the NGF were measured. The NGF was synthesized on a Ni/SiO2/Si substrate using a chemical vapor deposition system. Large-area freestanding NGF was prepared via camphor transfer. Young’s modulus, fracture stress and fracture strain of the NGF were 106 GPa, 462 MPa, and 0.3%, respectively, confirming that the bulge test is a very useful technique for evaluating the mechanical properties of NGF. A bulge test was performed to evaluate the mechanical properties of graphene with a free-standing poly (bisphenol A carbonate) (PC)/graphene layer. Large-area freestanding PC/2D material layers were prepared by peeling-off and stamping. The PC layer was used as the supporting layer in this study. Young’s modulus of graphene was calculated from Young’s modulus of the PC/2D material layers and PC layers using the rule of mixtures. Young’s modulus of the graphene was 260 GPa. The results of this study confirm the efficacy of the bulge test for determining the mechanical properties of nanometer-thick films and 2D materials, including graphene.

Microstructure evolution of transformation induced plasticity seamless steel tube in hydraulic free bulge test

AbstractIn this study the hydraulic free bulge test with an internal pressure boosting velocities of 0.5 MPa/s and punch feeding speed of 0.2 mm/s was carried out to study the microstructure evolution of the transformation induced plasticity seamless steel tube in the hydroforming process. The microstructure of the selected parts of the tube after the hydraulic free bulge test were investigated with the optical microscope and transmission electron microscope. The transformation rate of the retained austenite to martensite of the selected parts were determined by the x‐ray diffraction. To study the deformation behavior and obtain the stress‐strain state of the tube, the finite element simulation of the hydraulic free bulge test was also carried out. The results show that the retained austenite in the microstructure of all the selected parts transformed to martensite after the hydraulic free bulge test. In the center part of the tube, the highest transformation rate of 82.84 % was obtained. The retained austenites distribute inside of the ferrite grains transform to martensite firstly under the compressive stress and strain state. The retained austenites distribute at the ferrite grain boundaries start to transforme into martensite when the tube is subjected to the tensile stress and strain.

Forming limit of 6061 aluminum alloy tube at cryogenic temperatures

Cryogenic medium pressure forming has been proposed to fabricate aluminum alloy complex tubular components. It is urgently needed to evaluate and predict the cryogenic forming limit of aluminum alloy tubes for the novel process. Cryogenic bulging test using different length-diameter ratios was proposed to test the forming limit in the tension-tension zone. A modified M-K model was established to rapidly predict the cryogenic forming limit, based on the dynamic hardening with deformation. Theoretical analysis and fracture characterization were implemented to reveal the improvement mechanism of cryogenic forming limit from the macroscopic and microscopic perspectives, respectively. The forming limit of AA6061 tube at −196 °C is approximately double that at room temperature, especially in the tension-tension zone, which contributes significantly to the forming of complex features under biaxial tension. The cryogenic limiting deformation ability increases gradually as the strain state changes from plane strain to biaxial tension. Under the biaxial tension condition of λ=1.2, the limiting strain can reach 0.52 at −196 °C. The cryogenic forming limit can be successfully predicted by the modified M-K model with a prediction deviation of only 4.35% at −196 °C. The enhanced cryogenic hardening ability promotes the improvement of deformation uniformity and delays the occurrence of uncoordinated deformation. Ductile fracture is main fracture mechanism at cryogenic temperature. The significantly increased ductile fracture characteristics contribute to the improved cryogenic forming limit. This research can provide important guidance for the cryogenic forming of aluminum alloy tubular components.

Determination of the Plastic Stress–Strain Relationship of a Rupture Disc Material with Quasi-Static and Dynamic Pneumatic Bulge Processes

Rupture discs, manufactured using a hydraulic or pneumatic bulge process, are widely used to protect vessels from over-pressuring. The stress–strain relationship of the material in the bulge process plays a major role in understanding the performance of rupture discs. Moreover, both the theoretical analyses and numerical simulations of rupture discs demand a reliable stress–strain relationship of the material in a real bulge process. In this paper, an approach for determining the plastic stress–strain relationship of a rupture disc material in the bulge process is proposed based on plastic membrane theory and force equilibrium equations. Pressures of compressed air and methane/air mixture explosions were used for the bulge pressure to accomplish the quasi-static and dynamic bulge processes of tested discs. Experimental apparatus for the quasi-static bulge test and the dynamic bulge test were built. The stress–strain relations of 316L material during bulge tests were obtained, compared, and discussed. The results indicated that the bulge height at the top of the domed disc increased linearly with an increase in bulge pressure in the quasi-static and dynamic bulge processes, and the effective strain increased exponentially. The rate of pressure rise during the bulge process has a significant effect on the deformation behavior of disc material and hence the stress–strain relationship. At the same bulge pressure, a disc tested with a larger pressure rise rate had smaller bulge height and effective strain. At the same effective stress at the top of the domed disc, discs subjected to a higher pressure rise rate had smaller effective strain, and hence they are more difficult to rupture. Hollomon’s equation is used to represent the relationship between the effective stress and strain during bulge process. For pressure rise rates in the following range of 0 (equivalent to quasi-static condition), 2–10 MPa/s, 10–50 MPa/s, and 50–100 MPa/s, the relation of stress and strain is σe = 1259.4·εe0.4487, σe = 1192.4·εe0.3261, σe = 1381.2·εe0.2910, and σe = 1368.4·εe0.1701, respectively.

Evaluation of the Rheological Behaviour of Magnetorheological Fluids Combining Bulge Tests and Inverse Analysis

Magnetorheological Fluids (MRFs) are included in the so called “smart materials”: they are suspensions of magnetically responsive particles in a liquid carrier, whose rheological behaviour (e.g., its viscosity) can be changed quickly and reversibly if subjected to a magnetic field. Their application as forming medium in sheet metal forming processes is gaining interests in the recent years since the thickness and the strain distribution on the formed part can be affected by properly changing the properties of the MRF. In order to widely adopt MRFs in such processes, the evaluation of their rheological behaviour according to the applied magnetic field plays a key role. But there are still few works in the literature about the most effective way to characterise the MRFs to be used in sheet metal forming applications.In this work, the rheological behaviour of a MRF is carried out by means of an inverse analysis approach using data from bulge tests performed using an MRF as forming medium. Bulge tests were conducted on sheets having known properties using an equipment with a solenoid to generate the magnetic field, which was specifically designed and manufactured. Pressure rate and magnetic flux density were varied according to a Design of Experiments (DoE) while the strain experienced by the sheet material was acquired by means of a Digital Image Correlation (DIC) system in order to compare it with the numerical one. In particular, the fitting between numerical and experimental data was obtained by changing the MRF’s rheological properties using an inverse analysis technique. The proposed methodology allows to evaluate the MRF behaviour at different levels of both magnetic field and pressure rate, which are determinant for the FE simulation of sheet metal forming processes.

On the Anisotropic Mechanical Response of Ti6Al4V Sheet at High Strain Rates

In traditional sheet metal forming processes, a thin sheet metal is deformed at relatively low speeds. However, more and more the speed of production processes is increased, very often to take advantage of the beneficial implications that high strain rates can have on the formability of certain metals. In this work, the effect of strain rate on the anisotropic behavior of Ti6Al4V is investigated performing tensile tests in different orientations, namely 0o, 45o and 90o, with respect to the rolling direction (RD), and in-plane shear experiments along RD. Three nominal strain rates, i.e., , 0.5 and 1000, are considered. A novel high-speed bulge (HSB) test developed at Ghent University, designed to deform sheet metals in nearly equibiaxial loading conditions at high strain rates, is used for the dynamic bulge test. The experimental results, presented in this paper, clearly show the need of including the effect of strain rate, and eventually temperature, into the formulation of the yield function in order to correctly model and predict deformation processes performed at high speed.

Bulging of Isotropic Materials

There is a large body of literature on both the techniques for bulge testing and experimental results for various metallic materials (see the book of Banabic [1]). Generally, the experimental data for isotropic materials are interpreted using the von Mises yield criterion [2]. In this paper, we investigate the role played by the third invariant of the stress deviator, on the response under bulging of isotropic materials that have the same mechanical response in tension and compression. To this end, we use the yield criterion developed by Cazacu [3] and our implementation of this model in the F.E. code Abaqus [4]. For isotropic materials, this yield criterion involves a unique parameter, denoted ; in the case when it reduces to the von Mises yield criterion while for it involves dependence on . The results of F.E. simulations of bulge tests for isotropic materials characterized by various values of the parameterput into evidence new aspects concerning the stress states experienced by the respective materials under bulging.

Determination of Forming Limit Curves - Strain Path and Failure Analysis

With the goal to define a cost-effective and efficient process to identify adequate materials for sheet metal forming processes, it is crucial to evaluate the formability of materials. Forming limit curves (FLC) are used to analyze the forming and failure limits of sheet metals and dependence of the major (φ1) and minor strain (φ2) from the uniaxial stress-strain area through the plane-strain point to the biaxial strain area. According to ISO 12004-2, the FLC is performed by Nakajima or Marciniak tests. Due to the experimental setup and the preconditions, pre-stretching occurs in the specimens and bending and friction effect are the result. The determination of the onset of necking (FLC) results mathematically from a “best-fit inverse parabola” on section lines. In addition, the failure point, i.e. the maximum strain value one frame before failure, is also analyzed. In contrast, tensile, notched tensile and hydraulic bulge tests, which together have a potential to map an alternative FLC, exhibits a linear strain path evolution. The behavior of the various strain paths of Nakajima and the alternative methods are examined for necking and cracking. Furthermore, the fracture surfaces are investigated by confocal laser scanning microscopy to identify influences of the different FLC methods on the fracture mechanics. FLCs were conducted with the Nakajima and the alternative FLC characterization method for a ductile steel (DX54D). To ensure transferability, the tensile tests are also performed with a high-strength steel (DP800). The FLC of the ductile steel, generated through the alternative method, exhibits a similar shape to the Nakajima generated FLC with the advantage of a constant strain rate leading to linear strain paths and a lower number of tests. The same results are achieved for the uniaxial strain tests with DP800.

Constitutive modeling of commercial pure titanium sheet based on non-associated flow rule and differential hardening

The commercial-pure titanium (CP-Ti) sheet has attracted a great interest from biomedical and aerospace industries because of its strong mechanical advantages such as lightweight, high strength, good formability, and corrosion-resistance. However, strong anisotropic features, such as evolutionary yield surface and strength difference in tension and compression, of the CP-Ti require advanced constitutive modeling compared to standard advanced high strength steel sheets. This study took into account the differential hardening behavior and the changing R-value of CP-Ti sheet observed during the uniaxial tensile and bulge tests in developing a material model. The observed behaviors are modeled by Hill48 quadratic function based on non-associated flow rule with equivalent plastic work dependent evolutionary parameters. The developed material model was then implemented into a user material subroutine (VUMAT) for ABAQUS/EXPLICIT and used to simulate a circular deep drawing to verify the developed model. Simulation results are compared with those of a material model coupling Yld2000–2d yield function with associated flow rule. The comparison shows that the developed material model provides not only a good agreement with the experiment for yield and potential surfaces but also accurate predictions in forming simulations.

Analytical, numerical and experimental study of the finite inflation of circular membranes

In the present work we derive an analytical expression for the pressure–deflection curve of circular membranes subjected to inflation. This problem has been studied mostly from a numerical point of view and there is still a lack of accurate closed-form solutions in nonlinear elasticity. The analytical formulation is developed with a semi-inverse method by setting a priori the kinematics of deformation of the membrane. A compressible Mooney–Rivlin material model is considered and a pressure–deflection relation is derived from the equilibrium. The kinematics is approximated and therefore the obtained solution is not exact. Consequently, the formulation is adjusted by introducing an additional polynomial function in the pressure–deflection equation. The polynomial is calibrated by fitting numerical solutions of the exact system of differential equilibrium equations. The calibration is done over a wide range of constitutive parameters that covers the response of all rubber materials for technological applications. As a result, a definitive and accurate expression of the applied pressure as a function of the deflection of the membrane is obtained. The formula is validated with finite element (FE) simulations and compared with other solutions available in the literature. The comparison shows that the present model is more accurate. In addition, unlike the other models, it can be applied to compressible materials. Experimental uniaxial and bulge tests are carried out on rubber materials and the model proposed is used to characterize the Mooney–Rivlin constitutive parameters. Since the pressure–deflection formula is accurate and easy-to-use, it is an innovative tool in engineering applications of inflated membranes.

Effect of structural relaxation at bellow crystallization temperature on internal stress of Ni–Nb–Zr thin film amorphous alloys diaphragm for micro electromechanical systems sensors

In this paper, the effect of structural relaxation at temperatures below crystallization on internal stress of Ni–Nb–Zr thin film amorphous alloy (including thin film metallic glass: TFMG) diaphragms was investigated. We fabiricated the Ni–Nb–Zr diaphragm samples with four compositions. Before fabrication of diaphragm structure by etching, Ni–Nb–Zr thin films on Si substrate were annealed at a temperature below crystallization (473, 523, and 573 K) for structural relaxation. By performing bulge tests on annealed Ni–Nb–Zr diaphragms, we were able to determine their mechanical properties. As the result, Young’s modulus of all samples increased slightly with increasing annealing temperature because of the decrease of the free volumes during structural relaxation. Based on the results of internal stress, structural relaxation of all samples occurred below 473 K. Moreover, the effects of annealing temperature on internal stress differed by compositions. They were thought to be caused by the rate of structural relaxation.

On the use of elliptical bulge tests in material characterization through inverse methodologies

The hydraulic bulge test is an experimental technique that can be used to identify the properties of sheet metals up to large strain. The hydraulic bulge test, usually, is a free expansion of a sheet blank through a circular hole, driven by the pressure of a fluid, where the ends of the blank are blocked using a suitable die. The state of stress during the bulge test is mainly equi-biaxial, however, using elliptical holes with different aspect ratios, it is possible to produce heterogeneous stress-strain fields that can be used to identify the properties of the material through an inverse method; in this case, the non-linear Virtual Fields Method (VFM) was adopted. With respect to the traditional tests employed with the VFM in plasticity, i.e. double notched specimens or specimens with holes subjected to tensile tension, elliptical bulge tests allow to investigate a different zone in the stress-strain space, with a higher triaxiality. The capability of this type of test to calibrate the parameters of advanced anisotropic models is here assessed using simulated experiments.

New approach for the identification of anisotropy material parameters using hydraulic bulge tests

This paper put forwards a new method for the identification of the flow curves of anisotropic sheet metals using hydraulic bulge tests throughout circular and elliptical dies. This method is based on the membrane equilibrium equation, numerical simulation to derive the pole thickness and experimental data involving the measurement of only the polar deflection versus the applied hydraulic pressure curves. The experimental curves of four hydraulic bulge tests were obtained: one bulge test through circular die, and three bulge tests through elliptical dies, where the major axe of the elliptical die was oriented in three directions with respect the rolling direction of the sheet metal. These results were used in the identification of flow parameters and anisotropy coefficients of Hill48’ yield criterion. Then, FEA was utilized to perform sensitivity analysis of material parameters on the different hydraulic bulge test responses. The case study was a sheet metal of low carbon steel DC04. The identified material parameters were used in the numerical simulation of hydraulic bulge tests for the accuracy verification of the proposed method. It was shown a good agreement between model’s prediction and experimental results.

Hot tensile and expansion tests of Ductibor®1000 steel

The boron steels present high mechanical properties which are of great interest for lightening the vehicle parts. But these steels, as the Ductibor®1000, need to be hot formed. The hot stamping process consists of a heating/austenization step leading to an increase of the formability, followed by simultaneous forming and quenching steps. In order to understand the thermomechanical and metallurgical cycles occurring during this process, this study focuses on two different test devices at high temperatures using direct resistance heating: a Gleeble 3500 machine for tensile tests and a new bulge test device. The two different tests were performed on the Ductibor®1000 steel for a temperature of 900°C (with temperature holding during deformation) after an austenization step, which consists of heating up to 900°C and a temperature holding stage. The stress-strain curves of the tensile tests obtained using Digital Image Correlation (DIC) are compared to the stress-strain curves of the bulge tests obtained using a laser profilometer and the membrane theory.

Evaluation of testing methods for the characterization of material properties under plane strain

With the first numerically calculated forming simulations of a complex component by Hora in 1987, a renewed need emerged for a large number of stress-based material parameters for the yield locus modelling. Material characterization and modelling under plane strain is an important step towards an improved mapping accuracy in numerical calculated sheet metal forming processes. There are numerous of different testing methods, which can be used for this purpose. It is crucial to choose the right experiment depending on which material properties or characteristic values are needed. The aim of this investigation is to analyze the suitability of the currently mostly used testing methods that induce a plane strain in the material, the notched tensile test, the biaxial tensile test and the hydraulic bulge test with an elliptical die. For this purpose, the stress-based material properties of DC06 in all three tests are determined and compared. Subsequently, recommendations for material characterization are derived depending on the application.

Development of a high-temperature double-layer bulge test for failure prediction in gas-based hot forming of a high-strength aluminium alloy

In order to meet the continuously increasing environmental concerns, automotive lightweight concepts of replacing steels with high strength aluminium alloys are one promising solution. Therefore, complex automotive structural components manufactured with new processes like rapid gas-based hot sheet metal forming can become a key factor from a forming technology point of view. A product and process development phase, which is mainly assisted by numerical simulations, mandates knowledge of the material forming limits under the process conditions. The aim of this work is to determine the FLD of a 6xxx precipitation-hardening aluminium alloy within the solution heat treatment temperature range under gas-based hot forming process conditions. For this purpose, a hydraulic double-layered bulge test, as introduced by Banabic, is used as the basis and a high-temperature test setup as well as a characterization methodology are established. FE simulations are utilized to optimize the specimen geometries aiming at specific strain paths. Experiments are conducted with the optimized specimen geometries and the high-temperature FLD is extracted. The FLD is further used in simulations for process parameter identification for failure-free gas-based hot forming of a laboratory scale benchmark component. Experimental validations showed the reliability of the methodology and the determined FLD for failure prediction in the novel forming process.

Experimental Bulging and Buckling of Bi-segmented Cylinders

This paper studies the experimental free bulging and buckling of bi-segmented cylinders. Two cylindrical shells are manufactured using argon-arc welding and analyzed for manufacturing errors. Next, free bulging tests and hydrostatic pressure tests are conducted to verify the feasibility of the free bulging technique and to confirm the destruction form of the bulged bi-segmented barrel. At the same time, the reasonableness of the circular thick plate is examined, which is determined according to the deformation consistency. The results show that the bi-segmented cylindrical preforms exhibit good welding quality by TIG welding technology. It has the same critical pressure load as a single cylindrical preform. Nevertheless, the bi-segmented cylindrical preforms have larger internal volume and better buoyancy capability than the single cylindrical preform. The free bulging bi-segmented shell has good symmetry along the axial direction. It has larger internal volume and higher critical buckle capacities than the non-bulging one.