Bulge Test Results Research Articles

A bulge-test based viscoplastic model for superplastic deformation behaviour of a magnesium alloy

In this work, a new approach is proposed for modelling the superplastic deformation of AZ31B magnesium alloy sheets. Gas bulge tests were performed at 450 ℃ under three constant gas pressure levels of 0.4, 0.7, and 1.0 MPa. The dome height evolutions according to time were recorded in experiments and then translated into stress–strain curves using a new analytical approach. In order to predict the superplastic behaviour of the material, the Variable m-value Viscoplastic (VmV) model was considered in this study, whose constants were directly assessed from the bulge test results. The bulge forming of the magnesium alloy sheet was simulated with ABAQUS/Standard using the VmV model. The predicted dome height-time profiles and thickness distributions along the specimens were compared with the experimental results. Finally, a real case study (a resorbable cheekbone prosthesis) was simulated implementing the VmV model for validation purposes. The results from the simulation of both the bulge tests and the case study manufacturing revealed that the proposed model is able to effectively reproduce the superplastic behaviour of the AZ31B magnesium alloy.

Poking and bulging of suspended thin sheets: Slippage, instabilities, and metrology

Measurement of in-plane elasticity of thin sheets often leverages out-of-plane poking or bulging, also known as indentation or bulge tests. For linear elastic sheets, a load-cubic deflection relation has been frequently assumed so that the stiffness of the sheet could be readily extracted. However, we find that recent results of indentation and bulge tests on 2D materials do not support the assumption, which can be attributed to the slippage of 2D materials against their supporting substrates. Besides, the interfacial slippage could cause instabilities in the sheet such as radial wrinkles in suspended region, with finite lengths. To gain a quantitative understanding, we assume constant interfacial shear traction and study the wrinkling extent and the effective stiffness of thin sheets upon poking and bulging. We identify a single dimensionless parameter governing these mechanical responses—the sliding number—defined by comparing the sheet tension (that drives the slippage) with the interfacial traction (that resists the slippage). We discuss several useful asymptotic behaviors emerging at small and large sliding numbers. These understandings inspire when the effect of the interfacial slippage (as well as other substrate-associated subtleties) can be neglected in these tests. For instance, traditional bulge and indentation tests suffer from complexities caused by the slippage, pretension, Poisson's ratio, substrate roughness, and various interfacial traction-separation laws. Based on such understandings, we propose a simple poking/bulging methodology immune to all of these complexities, enabling an alternative way to measure the sheet stiffness.

Formability of aluminum 1050A at high temperatures: Numerical modeling and experimental validation

Abstract The sheet metals are prone to large plastic deformation during forming processes. The study purpose is to investigate 1050A aluminum sheets thermomechanical behavior with ductile damage. A modified Swift model coupled to isotropic ductile damage and thermal effects was used. The forming parameters are introduced using Swift model coefficients and Erichsen index. An inverse identification procedure is applied to non-homogeneous Erichsen test results. Bulge test is then used to validate the identified parameters. Erichsen test (Punch force vs displacement) results were obtained by experimental testing and simulation to build the objective function. Aluminum 1050A plasticity flow parameters and ductile damage variables were identified using a part of Erichsen test results. The remaining part of Erichsen test and bulge test results were used for validation. The numerical approach allowed the detection of failure zones with respect to thermal gradient induced by heat exchange. Within the isothermal condition, equivalent stresses and strains for 1050A Aluminum were obtained by simulations and experimental data.

A general and unified theory of the kinematic relationships in bulge tests

The hydraulic circular and elliptical bulge tests have been widely used in extracting mechanical properties of sheet materials. Theoretical analysis of bulge tests usually requires the kinematic relationships between the apex strains, radii of curvatures and dome heights to be established. Most of the available analytical solutions are derived on a case-by-case basis and are often limited to circular bulge tests of isotropic materials, and thus cannot be applied to materials with more complicated constitutive behaviors or non-circular bulge tests. Based on the variable-separable assumption and proportional kinematic conditions at the apex, this study develops a set of power-law relationships between the apex strains, radii of curvatures and dome heights that hold for both circular and elliptical bulge tests, irrespective of material properties. Numerical simulations of a set of circular and elliptical bulge tests with different material models are performed and the scaling laws between the apex strains, radii of curvatures and dome heights are verified. An extensive set of experimental results of circular and elliptical bulge tests from the literature are compared with the theoretical predictions and the power-law kinematic relationships are again validated. This general and unified theory contributes to the fundamental understanding of the intrinsic kinematic constraints in circular and elliptical bulge tests and is expected to facilitate the application of bulge tests to a broader class of sheet materials.

Characterization of human female breast and abdominal skin elasticity using a bulge test.

Characterization of material properties of human skin is required to develop a physics-based biomechanical model that can predict deformation of female breast after cosmetic and reconstructive surgery. In this paper, we have adopted an experimental approach to characterize the biaxial response of human skin using bulge tests. Skin specimens were harvested from breast and abdominal skin of female subjects who underwent mastectomy and/or reconstruction at The University of Texas MD Anderson Cancer Center and who provided informed consent. The specimens were tested within 2 h of harvest, and after freezing for different time periods but not exceeding 6 months. Our experimental results show that storage in a freezer at −20 °C for up to about 40 days does not lead to changes in the mechanical response of the skin beyond statistical variation. Moreover, displacement at the apex of the bulged specimen versus applied pressure varies significantly between different specimens from the same subject and from different subjects. The bulge test results were used in an inverse optimization procedure in order to calibrate two different constitutive material models – the angular integration model proposed by Lanir (1983) and the generalized structure tensor formulation of Gasser et al. (2006). The material parameters were estimated through a cost function that penalized deviations of the displacement and principal curvatures at the apex. Generally, acceptable fits were obtained with both models, although the angular integration model was able to fit the curvatures slightly better than the Gasser et al. model. The range of the model parameters has been extracted for use in physics-based biomechanical models of the breast.

Formability of Ultrasonically Additive Manufactured Ti-Al Thin Foil Laminates.

This study investigates the effect of strain rates and temperatures on the mechanical behavior of ultrasonically consolidated Titanium–Aluminum thin foils to understand and characterize their formability. To this goal, laminated composite samples with a distinct number of layers were bonded using ultrasonic consolidation. Then, tensile and biaxial hydraulic bulge tests at different strain rates and temperature conditions were conducted. The effect of the sample orientation on the mechanical response was also examined. Tensile and hydraulic bulge tests results were compared to observe differences in ultimate tensile strength and strain levels under uniaxial and biaxial loading conditions. The effects of loading condition, strain rate, and temperature on the material response were analyzed and discussed on the basis of test results. In general, it was concluded that the maximum elongation values attained were higher for the samples subtracted along the sonotrode movement direction compared to those obtained from the normal to sonotrode movement direction. The elongation was obtained as high as 46% for seven bi-layered samples at high-temperature ranges of 200–300 °C. Hydraulic bulge test results showed that elongation improved as the number of bi-layers increased, yet the ultimate strength values did not change significantly indicating an expansion of the formability window.

Improving the optical and mechanical characteristics of aluminum thin-film filters by adding thin cap layers

In this paper we investigated the influence of thin nanometer cap layers of aluminum nitride (AlN) and molybdenum disilicide (MoSi2) on the temporal stability of transmission and the ultimate strength of aluminum (Al) film filters. An increase in the stability of the optical characteristics and in the mechanical strength of Al films both with AlN and MoSi2 cap layers are shown in comparison with a monolayer Al film. The greatest efficiency was demonstrated in the case of Al with MoSi2 cap layers. The obtained results show that the presence of MoSi2 cap layers 2.5 nm thick on each side of an Al film significantly reduces (for example, by >4 times at the wavelength of 30.4 nm) the rate of film transmission loss in the extreme ultraviolet (EUV) range. In addition, the presence of cap layers can lead to a significant increase in the film's strength: the results of pressure bulge tests show that the Al with MoSi2 cap layers film can withstand an ultimate load 1.5 times greater than an Al monolayer film of comparable thickness. The carried-out bulge tests indicate that an increase in the strength of the Al thin film in the presence of MoSi2 cap layers may be due to the cap layers hindering crack initiation, which allows Al film to be plastically deformed. Acoustic tests of Al with MoSi2 cap layers filters indicate the possibility of their use as entrance filters on a supporting mesh with a mesh size up to 10 mm in solar telescopes.

Experimental and analytical evaluation of the stress-strain curves of AA5754-T4 and AA6061-T6 by hydraulic bulge test

The hydraulic bulge test can be used as a means to achieve large uniform plastic strains under biaxial stress conditions, applied to hardening curve determination of sheet metal materials. The larger information on hardening behaviour is the reason why a mechanical characterization system has been developed to determine stress-strain curve by reading bulge test variables: bulge pressure (p), radius of curvature (ρ) and pole thickness (t). The determination of stress-strain curve may be based on continuous data acquisition from bulge test results (p, ρ, t) or from the use of analytical equations relating these variables with dome height. In this paper it is presented a study comparing different methodologies to obtain stress-strain curve by means of analytical methodologies relating “dome height with pole thickness” evolution. It is shown that these existent methodologies to determine pole thickness don’t apply when compared with experimental values and they show an evident dispersion among them. Therefore a better analytical methodology is proposed and tested. The study and corresponding material characterization is applied to two aluminium alloys, AA5754-T4 and AA6061-T6, currently used in automotive industry.

Mechanical properties determination of dual-phase steels using uniaxial tensile and hydraulic bulge test

Numerical simulations of sheet metal forming processes need the establishment of highly reliable results, which in turn need the accurate identification of mechanical properties. In this paper a study is presented on the choice of the characterization function of flow stress-strain curve of sheet metal materials, as well as the selection of the best yield locus, based on experimental uniaxial tensile and biaxial hydraulic bulge tests performed on dual-phase steels of industrial interest. To obtain a better characterization of the hardening curve, a combination is made using the uniaxial tensile test data with biaxial hydraulic bulge test results, since bulge test covers a larger range of plastic strain when compared to tensile test. Since the two flow curves have different strain paths, they can’t be directly compared or combined. Therefore, it is necessary a transformation of flow stress-strain curve provided from biaxial bulge test into equivalent stress-strain curve. Different methodologies were applied to transform biaxial stress-strain curve to an equivalent one and the different results are compared and evaluated.

Determination of Material Strengths by Hydraulic Bulge Test.

The hydraulic bulge test (HBT) method is proposed to determine material tensile strengths. The basic idea of HBT is similar to the small punch test (SPT), but inspired by the manufacturing process of rupture discs—high-pressure hydraulic oil is used instead of punch to cause specimen deformation. Compared with SPT method, the HBT method can avoid some of influence factors, such as punch dimension, punch material, and the friction between punch and specimen. A calculation procedure that is entirely based on theoretical derivation is proposed for estimate yield strength and ultimate tensile strength. Both conventional tensile tests and hydraulic bulge tests were carried out for several ferrous alloys, and the results showed that hydraulic bulge test results are reliable and accurate.

Influence of Servo Motion on Forming Limit of Thin Metallic Foils Using Micro Bulge Test

The demand of microforming is increasing as one of the economical production methods for small metallic parts. However, the formability of metallic foils decreases with decreasing ratio of thickness to grain size. In the present study, a process combining step motion and ultrasonic vibration is proposed to enhance the formability by stress relaxation. To investigate the effect of stress relaxation on forming limit of metallic foils in different stress states, micro bulge tests were carried out. The material used was brass foils with a thickness of 0.03, 0.05 and 0.08 mm. For calculating the strains of the deformed specimens, a pattern of dots with a diameter and a pitch of 50 and 60 μm was fabricated on the surface of the specimens by photolithography. The results of micro bulge tests showed that the forming limit increases by the stress relaxation regardless of stress states, except for the foil with a thickness of 0.03 mm. The possibility of enhancing the formability of metallic foils by stress relaxation was experimentally demonstrated.

Hetero-Epitaxial Single Crystal 3C-SiC Opto-Mechanical Pressure Sensor

The design, fabrication, early testing and material property assessment work related to the development of an opto-mechanical pressure sensor implemented with hetero-epitaxial 3C-SiC on silicon is described. The sensor is constituted by a single-crystal 3C-SiC membrane whose deflection upon pressure application is measured using a fiber-optic interferometric readout. The fabrication of sensor prototypes and micromachined 3C-SiC membranes for test purposes is described and the results of bulge tests on the membranes are reported. Functional characterization of the sensor prototypes in the pressure range 0-3 bar is also presented, showing good linearity and reproducibility of the sensor response, sensitivity of roughly 2 mV/bar and estimated pressure resolution around 0.5 bar on a 0-200 bar dynamic range.

Influence of Heat Treatment on Hydroformability of TRIP Seamless Steel Tube

A low-carbon TRIP seamless steel tube, which is expected to be used in the hydroforming process, was successfully fabricated using piercing, cold-drawing and two-stage heat treatment process. The two-stage heat treatment is one crucial step because it significantly affects the microstructure and mechanical properties of TRIP seamless steel tube. In order to obtain the TRIP seamless steel tube with high hydroformability, several different heat treatment processes were conducted. The effects of heat treatment conditions (intercritical annealing (IA) and isothermal bainite treatment (IBT)) on the TRIP seamless steel tube hydroformability which was determined by free hydraulic bulge test were analyzed. Two different internal pressure boosting velocities of 0.2 and 0.5 MPa/s of free hydraulic bulge tests were adopted to determine the effective stress vs. effective strain curve of TRIP seamless steel tube. The results showed that for the predetermined IA condition, the maximum bulge height increased, but the maximum burst internal pressure decreased, with the increase of IBT holding time from 4 to 6 min. For the predetermined IBT condition, the maximum bulge height decreased, but the maximum burst internal pressure increased, with the increase of IA holding time from 5 to 10 min. By analyzing the free hydraulic bulge test results, it was found that the maximum bulge heights of TRIP seamless steel tubes with the internal pressure boosting velocity of 0.5 MPa/s were higher than those when the internal pressure boosting velocity was 0.2 MPa/s. This means that an appropriate deformation rate should be chosen to obtain the optimal hydroformability of TRIP seamless steel tube. In addition, the effective stress vs. effective strain curves of TRIP seamless steel tubes were obtained with free hydraulic bulge test.

Experimental Thermomechanical Analysis of Elastomers Under Uni- and Biaxial Tensile Stress State

The objective of the present work is to demonstrate an experimental methodology to determine the viscoelastic material behavior of elastomers independent of the mechanical loading conditions. For this purpose two model materials (elastic and damper formulation) were investigated. The experimental effort ranged from classical uniaxial dynamic thermomechanical analysis (DTMA) and monotonic loading to monotonic biaxial testing. The performed monotonic experiments were loading rate and temperature dependent. Before applying the experimental methodology, some fundamental presumptions had to be verified. First, the applicability of the well-known time-temperature superposition principle to the elastomers, and second the separation of thermomechanical loadings, in which the temperature effects on the mechanical behavior of the materials could be characterized by an appropriate shift factor function; if this function is fundamental, then it should be independent of the mechanical loading condition. The shift factor functions were determined for the investigated elastomers from the DTMA results and were applied for the monotonic uni- and biaxial loading. Two biaxial tests (bulge test and planar biaxial tension test) were performed to show a direct calculation method for the stresses from planar biaxial tests by utilizing FEA with a material model, whose parameters were defined by the bulge test results.

Preparation of highly uniform self‐standing submicrometer polyimide films and an investigation of their antibulging capabilities

ABSTRACTAiming for X‐ray astronomy applications, we prepared large‐area submicrometer polyimide (PI) films [diameter (Φ) = 8 cm] with great thickness uniformity via the spin‐coating technique by using a PI precursor, poly(amic acid) (PAA) derived from 3,3′,4,4′‐biphenyltetracarboxylic dianhydride, and p‐phenylenediamine as the starting materials. The effects of the spinning speed, apparent viscosity of the PAA solution (η), and spinning time on the PI film thickness and its uniformity, as characterized by the measurement of the film thickness every 0.5 cm along the diameter direction, were investigated. By optimizing the spin‐coating conditions, we prepared final submicrometer PI films with average thicknesses in the range of 200–850 nm and with film thickness fluctuations of less than 1.3%. The pressure bulge test results indicate that at a thickness of 805 nm and an inside test aperture diameter of 2.64 cm, the prepared PI films reached a final burst pressure of 20.2 KPa; this suggested excellent mechanical performances in the self‐standing submicrometer PI film. This study makes a contribution by providing a typical example and opening the way for the preparation of robust self‐standing submicrometer PI films with great thickness uniformities for X‐ray astronomy applications. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2014, 131, 39977.

Experimental characterization and inverse constitutive parameters identification of tubular materials for tube hydroforming process

This paper deals with an inverse approach strategy to determine the constitutive parameters of tubular materials made of low carbon steel S235 and aluminum alloy AA6063-O. For this purpose, a new self-designed bulge forming machine is manufactured to perform tubular bulge tests. Additionally, tensile tests are carried out on specimens cut from the tube to measure the Lankford anisotropy coefficients. The proposed inverse identification method is developed to identify efficiently the flow stress parameters considering material anisotropy effects. This method is made up of an optimization algorithm that connects experimental free bulge test results and finite element analysis. The comparison between predicted results and experimental data is performed to assess the proposed approach. It is shown that this identification strategy provides appropriate flow stress relationship which can be used to predict accurate plastic deformation behavior during the tube hydroforming process.

Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales

Reliable material models are necessary for accurate analysis of micro-forming and micro-manufacturing processes. The grain-to-feature size ratio ( d/ D c) in micro-forming processes is predicted to have a critical impact on the material behavior in addition to the well-known effect of the grain size ( d) itself as manifested by the Hall–Petch relation. In this study, we investigated the “size effects” on the material flow curve of thin sheet metals under hydraulic bulge testing conditions. The ratio of the sheet thickness to the material grain size ( N= t 0/ d) was used as a parameter to characterize the interactive effects between the specimen and the grain sizes at the micro-scales, while the ratio of the bulge die diameter to the sheet thickness ( M= D c/ t 0) was used to represent the effect of the feature size in the bulge test. Thin sheets of stainless steel 304 (SS304) with an initial thickness ( t 0) of 51 μm and three different grain sizes ( d) of 9.3, 10.6, and 17 μm were tested using five bulge diameters ( D c) of 2.5, 5, 10, 20, and 100 mm. A systematic approach for determining the flow curve of thin sheet metals in bulge testing was discussed and presented. The results of the bulge tests at different scales showed a decrease in the material flow curve with decreasing N value from 5.5 to 3.0, and with decreasing M value from 1961 to 191. However, as M value was decreased further from 191 to 49, an inversed relation between the flow curve and M value was observed; that is, the flow curve was found to increase with decreasing M value from 191 to 49, a new observed phenomenon that has never been reported in any open literature. New material models, both qualitatively and quantitatively, were developed to explain the size effects on the material flow curve by using the N and M as the characteristic parameters of relative size between the grain, the specimen (i.e., sheet thickness), and the part feature (i.e., bulge diameter). The explanation and prediction of the flow curve behavior based on these models were shown to be in good agreement with the bulge test results in this study and in the literature.

Mechanical properties of TiN thin films investigated using biaxial tensile testing

Mechanical properties of TiN thin films were investigated using bulge test measurements performed on square freestanding membranes. For this purpose, both sides of n type Si(1OO) wafers were first coated by a layer of low stress SiN thin films (thickness t = 465 nm). The square windows of side 2a = 4 mm were then made using standard micromachining techniques to obtain freestanding SiN membranes. The edges of the windows were usually aligned with the [110] directions of the underlying Si wafer in order to make perfect squares bounded by (111) planes. These specimens were then coated by a layer of TiNx (0·84 < x < 1·3), using the rf magnetron sputtering method. Bulge testing was first conducted on an SiN film to determine its proper residual stress and Youngs modulus, which were found to be (σi = 227 ± 15 MPa and E = 225 ± lO GPa respectively. Then the composite membrane made of TiNx together with underlying SiNy was bulged and the related load-displacement variation was measured. Finally, using a simple rule of mixtures formula, the elastic mechanical properties of TiNx coatings were determined. Both the Young s modulus and residual stress increased with bias voltage, N/Ti ratio, and coating density. In contrast, the effect of substrate temperature below 600°C was found to be less significant than that of other parameters. Scanning electron microscopy of cross-sectioned specimens showed that coating growth occurs by the formation of equiaxial nanocrystallites, 10-30 nm in size, leading to columnar morphology beyond a thickness of 100-150 nm. The columns are nearly perpendicular to the film surface. The bulge test results are discussed in terms of coating microstructure and chemical composition determined by means of electron probe microscopy.

Effects of deflection on bulge test measurements of enhanced modulus in multilayered films

The bulge test is an experimental method to determine the yield behavior and biaxial elastic modulus of thin films. In a typical bulge test, pressure is applied to a free-standing foil. The bulge height h is measured as function of the applied pressure. The initial height h 0 of the bulge deflection must be considered when analyzing interferometric bulge-height measurements as the range of linearly elastic behavior and the magnitude of biaxial modulus enhancement are directly affected by it. Computation of the biaxial modulus over a linearly elastic range to 0.10% strain is shown to yield rule-of-mixtures values for homogeneous Ag/Pd and Cu/Pd multilayer foils. An apparent 500% modulus enhancement for a 1.47 nm Cu/Pd foil is reduced to 12% using an h 0 correction to produce a linear elastic response to 0.10% offset strain. For a 100% enhancement found in a 2.24 nm Ag/Pd foil, the h 0 correction reduces the enhancement to 51%. Analysis of bulge test results using an h 0 correction shows that modulus enhancement exists in metallic multilayers, but not to the extent found using a non-linear elastic analysis.

Accuracy and Reliability of Bulge Test Experiments

ABSTRACTIn this paper we address possible causes for inconsistencies in bulge test results and describe methods by which the bulge test technique can be made to produce accurate and reliable results. Experiments have been conducted on a variety of materials: polyimide (PIQ13) and polycarbonate (Lexan), silver and silver-palladium multilayers, and silicon nitride. All the materials tested yield biaxial moduli that are in the range of expected values for the bulk material. In addition, the tests show that the technique can be used to differentiate between the elastic properties of materials throughout the range of elastic stiffnesses, with even crystallo-graphic texture having a notable impact on the measured modulus. These results will be presented along with the methods used for preparing bulge test samples.