Gas Pressure Profile Prediction from Variable Strain Rate Deformation Paths in AA5083 Bulge Forming

Two approaches to gas pressure profile prediction for bulge forming of AA5083 sheet under Quick Plastic Forming (QPF) conditions at 450?°C were investigated. The first was based on an algorithm internal to ABAQUS? wherein the gas pressure results from maintaining a constant effective target strain rate at the dome pole. In the second, the nonlinear long wavelength stability analysis was combined with a single creep mechanism material model that accounts for hardening/softening. A series of stability curves, which denote combinations of strain and strain rate for unmitigated thinning and, ultimately, rupture of an AA5083 bar, were computed. These are based on a parameter that characterizes an assumed geometric non-uniformity, ??. The associated uniaxial strains and strain rates were expressed in terms of von Mises effective strains and strains rates, and pressure profiles were computed. An ancillary approach to variable strain rate path prediction based on a thinning factor was used to suggest a suitable value of ?? in the stability analysis for a reasonable thinning level at the end of forming. Key advantages and disadvantages of both approaches to pressure profile prediction are examined relative to bulge forming time and thinning at a 50-mm dome displacement.     

New approach to gas pressure profile prediction for high temperature AA5083 sheet forming

A new theoretical approach to the prediction of gas pressure profiles that vary smoothly with time in high temperature forming of fine-grained AA5083 sheet is presented. The required pressure-flow stress relationship, which couples the gas pressure profile and the material constitutive model, was implemented in ABAQUS implicit. Forming of a rectangular pan in a die with variable entry radii was simulated with a single creep mechanism model that accounts for hardening/softening in AA5083. Predicted sheet thickness and thinning in a die entry radius region at the end of forming are examined in detail. Results are compared with those from two additional gas pressure schemes. One of these is taken directly from experiments and the other is based upon an algorithm that is internal to ABAQUS. The effect of friction on forming time is explored in the absence of a stability criterion for necking.     

Forming-Limit Diagrams for Hot-Forming of AA5083 Aluminum Sheet: Continuously Cast Material

Fine-grained AA5083 aluminum sheet is used for hot-forming automotive body panels with gas pressure in the superplastic forming (SPF) and quick plastic forming (QPF) processes. Deformation under QPF conditions is controlled by two fundamental creep mechanisms, grain-boundary-sliding (GBS) and solute-drag (SD) creep. The failure mechanisms of AA5083 materials under QPF conditions depend strongly on these deformation mechanisms and on the applied stress state. Failure can be controlled by flow localization, cavitation development or a combination of both. There is interest in using continuously cast (CC) AA5083 materials instead of direct-chill cast (DC) materials in QPF operations as a means of reducing material cost. However, CC and DC AA5083 materials can produce significantly different ductilities under hot forming. Rupture-based forming-limit diagrams (FLDs) have been constructed for a CC AA5083 sheet material under hot-forming conditions. Forming limits are shown to be related to the controlling deformation mechanisms. Differences between FLDs from DC and CC AA5083 materials are investigated. The differences in FLDs between these materials are related to differences in cavitation development. This article was presented at Materials Science & Technology 2006, Innovations in Metal Forming symposium held October 15-19, 2006 Cincinnati, OH.     

Material Models for Simulation of Superplastic Mg Alloy Sheet Forming

Accurate prediction of strain fields and cycle times for fine-grained Mg alloy sheet forming at high temperatures (400-500 °C) is severely limited by a lack of accurate material constitutive models. This paper details an important first step toward addressing this issue by evaluating material constitutive models, developed from tensile data, for high-temperature plasticity of a fine-grained Mg AZ31 sheet material. The finite element method was used to simulate gas pressure bulge forming experiments at 450 °C using four constant gas pressures. The applicability of the material constitutive models to a balanced-biaxial stress state was evaluated through comparison of simulation results with bulge forming data. Simulations based upon a phenomenological material constitutive model developed using data from both tensile elongation and strain-rate-change experiments were found to be in favorable accord with experiments. These results provide new insights specific to the construction and use of material constitutive models for hot deformation of wrought, fine-grained Mg alloys.     

On Practical Forming Limits in Superplastic Forming of Aluminum Sheet

In this paper, the superplastic forming (SPF) potential of two fine-grained 5083 aluminum alloys were studied under various stress states with the use of both high temperature tensile testing and pneumatic bulge testing. Experiments with the pneumatic bulge test were performed at temperatures ranging from 475 to 525 °C under three different strain paths ranging from equi-biaxial to approaching plane strain. The effects of temperature on total elongation, m-value, final thickness distribution, dome height, and cavitation were investigated for the case of uniaxial and equi-biaxial stretching. Increased temperature in bulge forming was found to improve the thickness distribution in the formed parts, but did not have a significant effect on dome height. The shape of the forming limit diagram (FLD) was found to be significantly different than that of FLDs commonly used in room temperature stamping. Results indicate that determination of forming limits in SPF cannot be represented with a simple FLD and additional metrics such as external thinning and internal cavitation need to be considered to determine a material’s SPF potential. This article was presented at Materials Science & Technology 2006, Innovations in Metal Forming symposium held in Cincinnati, OH, October 15-19, 2006.     

Superplastic forming characteristics of fine-grained 5083 aluminum

Superplastic forming characteristics of a fine-grained 5083 aluminum sheet have been investigated by means of gas-pressure forming of a rectangular pan. This part geometry lends itself to a simple representation in terms of nearly one-dimensional sheet stretching and permits reasonably rigorous control of strain rate throughout the forming cycle. This study followed a study of the uniaxial tensile properties carried out on this alloy. A two-stage forming cycle, which comprised a short, rapid prestraining stage followed by a stage of slower rate of superplastic straining, was used because the uniaxial tensile work showed enhancement of superplastic response of this alloy under this condition. The study examined the effect of process parameters such as initial gas pressurization rate, level of hydrostatic pressure, and lubricants on the thinning characteristics of the sheet, especially along the die entry radii. The gas pressure/time cycle was suitably modified to avoid premature sheet failure due to excessive sheet thinning or cavitation. Cavitation under the biaxial forming condition and the effect of hydrostatic pressure on cavitation suppression were evaluated. A defect-free pan with sharp corners was formed.     

Effect of pressurization profile on the deformation characteristics of fine-grained AZ31B Mg alloy sheet during gas blow forming

The deformation characteristics of a 0.6 mm-thick, fine-grained AZ31B Mg alloy sheet were investigated with the intention of reducing forming time during gas blow forming. The sheets were successfully deformed into hemispherical domes at 300, 370, and 420 °C under various pressurization profiles. The results show that the proposed pressurization profiles could achieve the goal of reducing forming time. A stepwise pressurization profile may be a suitable process at lower temperatures, whereas a constant or near constant pressure imposed during forming is a better method at higher temperatures. The pressurization profiles used in this study were not restricted to providing the optimum constant strain rate, which is often used in the traditional superplastic forming. Under the proposed pressurization profiles, maximum stress in the range of 23.5–45.6 MPa and resultant average strain rate in the range of 6.63 × 10⁻³ to 1.56 × 10⁻² s⁻¹ were imposed on the deforming sheet at the apex of the dome. The pressurization profile might not be one of the major factors influencing formability at the same forming temperature but it can significantly affect the forming time. Deviation of the bulged shape from the perfect sphere shape increased with increasing forming temperature.     

Deformation characteristics and cavitation during multiaxial blow forming in superplastic 8090 alloy

This work examined the effect of multiaxial stress on deformation characteristics of a superplastic aluminum alloy 8090 by deforming the sheet into a die with a cylindrical cavity. Several interrupted tests were performed to bulge the sheets to various depths for different strain rates, the formed parts were utilized to evaluate the deformation status, thickness distribution, local strain states, and cavitation. It was found that evolution of cavity volume fraction with forming time could be related to the thinning behavior of the deformed sheet during forming. Decrease in cavity volume fraction at the central region was observed in the later stage of forming as the thickness of the deformed sheet remained constant for all test forming rates.     

Combined experimental and numerical analysis of bulge test at high strain rates using split Hopkinson pressure bar apparatus

High strain rate bulge test technique which is introduced in this paper adopts a rubber-pad as pressure carrying medium to bulge a sheet metal at high velocity using split Hopkinson pressure bar (SHPB) system. The experimental set-up is based on conventional hydraulic bulge test which is modified to mount on SHPB. The thickness thinning of the sheet metal during the test will be considered as a measure of true strain of the bulged sheet. The theoretical approach is developed in this study to attain pressure–strain curves of sheet metals during high strain rate bulge forming process. This approach is followed by a finite element simulation of the process in ABAQUS/Explicit software. To verify the developed method, analytical and finite element methods are compared with experiments.     

Bulge Testing under Constant and Variable Strain Rates of Superplastic Aluminium Alloys

The present paper deals with superplastic forming of aluminium alloy AA5083 sheet metals tested at specific strain rates, temperatures and counter pressures by means of bulge testing using circular and elliptical dies and by the cone-cup testing method. Further, differences from batch to batch can lead to a different strain rates at the maximum m value. It is shown by experimental investigations that pulsating strain rates can lead to higher m values and to increased thickness strains.     

Forming response of AA5052–H32 sheet deformed using a shock tube

The effect of bending pre-strain and pressure on the forming behavior of AA5052–H32 sheets has been studied using a shock tube. Various forming parameters like dome height, effective strain and stress distribution, hardness, and grain size evolution have been measured. Circular grids are printed on the sheets and Hill's 1948 yield criterion is used to calculate the effective strain distribution. The effective stress distribution is calculated by using the Hollomon's power law. The strain evolution during the forming process is monitored by mounting a strain rosette at the mid location of the sheet. The strain–time graph confirms the sharp rise in the peak strain and it increases significantly at higher pressure. The variation in the forming parameters asserts that the material stretches uniformly without strain localization. The optical microstructures also depict that the equiaxed grains are stretched and elongated after the shock deformation. This analysis confirms that the forming behavior of the material is dependent both on the degree of pre-strain and the change in pressure.     

On the thinning variation of a superplastically formed titanium alloy spherical domes

The gas pressure bulging of metal sheets has become an important forming method. As the bulging process progresses, significant thinning in the sheet material becomes obvious. A prior knowledge about non-uniform thinning in the product after forming helps the designer in the selection of initial blank thickness. This paper presents a simple analytical procedure for obtaining the thinning variation of a superplastically formed Ti alloy spherical dome. The procedure is validated with the existing measured data.     

Theoretical and numerical study of strain rate influence on AA5083 formability

With the application of new forming techniques (hydroforming, incremental forming), it is necessary to improve the characterization of the formability of materials and in particular the influence of strain rate. This paper begins with the characterization of material behavior of an aluminum alloy 5083 at high temperatures. To describe its visco-plastic behavior, Swift’s hardening law is used and the corresponding parameter values are identified. Then, two different approaches are introduced to construct FLDs (forming limit diagrams) of this alloy sheet and evaluate the effect of the rate sensitivity index on its formability. The first one is theoretical (the M-K model), and an algorithm is developed to calculate the limit strains by this model. In the second approach, the Marciniak test is simulated with the commercially available finite-element program ABAQUS. Based on FEM results, different failure criteria are discussed and an appropriate one is chosen to determine the onset of localized necking. With the material behavior data corresponding to AA5083 at 150 °C, parametric studies are carried out to evaluate the effect of the strain rate sensitivity index. The comparison of results by these two approaches shows the same tendency that an improvement of the formability with increasing strain rate sensitivity is observed. Finally, by consideration of the compensating effects of the strain hardening and rate sensitivity indices, the FLDs of this sheet at 150, 240 and 300 °C are determined and compared. Results show that the formability of AA5083 seems not to be improved up to a certain temperature (between 240 and 300 °C), above this temperature, the formability is greatly enhanced.     

Superplastic Behavior of Copper-Modified 5083 Aluminum Alloy

An AA5083 aluminum alloy was modified with two different levels of Cu additions, cast by direct-chill method, and thermo-mechanically processed to sheet gauge. Copper additions reduced sheet grain size, decreased tensile flow stress and significantly increased tensile elongation under most elevated temperature test conditions. The high-Cu (0.8 wt.%) alloy had the finest grain size 5.3 μm, a peak strain-rate sensitivity of 0.6 at a strain-rate of 1 × 10⁻² s⁻¹, and tensile elongation values between 259 and 584% over the temperature range, 400-525 °C, and the strain rate range, 5 × 10⁻⁴ to 1 × 10⁻² s⁻¹, investigated. In biaxial pan forming tests, only the Cu-containing alloys successfully formed pans at the higher strain rate 10⁻² s⁻¹. The high-Cu alloy showed the least die-entry thinning. Comparison of ambient temperature mechanical properties in O-temper state showed the high-Cu alloy to have significantly higher yield strength, ultimate strength, and ductility compared to the base 5083 alloy. This article was presented at the AeroMat Conference, International Symposium on Superplasticity and Superplastic Forming (SPF) held in Seattle, WA, June 6-9, 2005.     

Designing superplastic forming process of a developmental AA5456 using pneumatic bulge test experiments and FE-simulation

Relatively low tooling costs, high design complexity coupled with low forming speeds make the superplastic sheet metal forming process attractive, especially for smaller lot sizes. Due to the relatively small lot size, the effort and budget for designing superplastic forming processes is usually limited (Kappes and Liewald in J Mater Sci Eng B1:472?C478, 2011). For this reason the tool design and corresponding pressure profiles in superplastic forming processes are often based on trial and error (Franchitti et al. in 11th international Esaform conference on material forming, 2008; Barnes in J Mater Eng Perform 4:440?C454, 2007). Consequently a process chain should be established to design superplastic forming processes accurately and efficiently. This paper deals with the process chain to form an aluminium part superplastically. At the beginning of the process chain, there is a new, developmental aluminium alloy sheet (AA5456, s₀?=?1.6?mm) designed for superplastic forming supplied by Hydro Aluminium Rolled Products GmbH. The relevant material parameters of this sheet are then determined via pneumatic bulge testing with and without in situ measurement of strains. Using these experimentally determined parameters superplastic forming process can be simulated by FE modelling (PAM-STAMP 2G). Due to in situ measurement of strains during pneumatic bulging, the comparison of experiment and FE-simulation results over the whole pneumatic bulging process could be done. This comparison shows good correlation for the observed conditions. Furthermore a cylindrical cup was simulated, evaluated via determined isobar Superplastic Forming Limit Curve (at fracture) and finally formed by pneumatic bulging. Material characterisation of the bottom of this cup showed that excessive cavitation was observed as a result of the iron-silicon particles. Superplastic forming of a bracket usually formed out of AA5083 was also simulated using material parameters of AA5456. The simulation was able to show that this part is not able to be manufactured out of AA5456 under these forming conditions, which was confirmed by forming trials performed at ALU-SPF AG.     

The effect of stress state on high-temperature deformation of fine-grained aluminum–magnesium alloy AA5083 sheet

The effect of stress state on high-temperature deformation of fine-grained aluminum–magnesium alloy AA5083 sheet is investigated over a range of temperatures and strain rates for which the grain-boundary-sliding and solute-drag creep mechanisms govern plastic flow. Experimental data from uniaxial tension and biaxial tension are used in conjunction with finite-element-method simulations to examine the role of stress state. Three different material constitutive models derived from uniaxial tensile data are used to simulate bulge-forming experiments. Comparison of simulation results with bulge-forming data indicates that stress state affects grain-boundary-sliding creep by increasing creep rate as hydrostatic stress increases. Thus, creep deformation is faster under biaxial tension than under uniaxial tension for a constant effective stress. No effect of stress state is observed for solute-drag creep. A new material model that accounts for the effect of stress state on grain-boundary-sliding creep is proposed.     

Analysis of tube bulge forming in an open die considering anisotropic effects of the tubular material

In this paper, a mathematical model considering the anisotropic effects of the tubular material was proposed to examine the plastic deformation behavior of a thin-walled tube during bulge forming processes in an open die. In the formulation of this mathematical model, the forming tube is considered as an ellipsoidal surface. Non-uniform thinning in the free-bulged region and sticking friction between the tube and die are also considered. In this analytical model, Hill's orthogonal anisotropic theory was adopted for deriving the effective stress and effective strain under a bi-axial stress state. The effects of the anisotropic values on the forming pressure and maximum bulge height were discussed. Experiments of bulge forming using annealed A6011 aluminum tubes were conducted. The analytical results of forming pressure were compared with the finite element simulations and the experimental data. The validity of this newly proposed model was verified.     

On the optimization of superplastic blow-forming processes

The superplastic blow-forming process of thin sheets is analyzed, and an optimal stable deformation path that reduces production time is obtained. The analysis is based on an analytical model for the superplastic forming (SPF) of a long rectangular box made of Ti-6Al-4V alloy at 900 °C use of a microstructure-based constitutive equation for the strain rate and grain growth, a stability criterion, and a variable strain rate control. It is shown that by imposing a variable strain rate control scheme derived from the stability analysis, an optimal forming time can be developed while maintaining a stable deformation path. Some other control schemes also show effectiveness in either reducing the localized thinning in the formed sheet or reducing the required forming time. Effects of friction and initial grain sizes on the forming pressure profile and the thickness distribution of the formed sheet are also investigated.     

Forming limit diagrams of tubular materials by bulge tests

This study uses bulge tests to establish the forming limit diagram (FLD) of tubular material AA6011. A self-designed bulge forming apparatus of fixed bulge length and a hydraulic test machine with axial feeding are used to carry out the bulge tests. Loading paths corresponding to the strain paths with a constant strain ratio at the pole of the bulging tube are determined by FE simulations linked with a self-compiled subroutine and are used to control the internal pressure and axial feeding punch of the test machine. After bulge tests, the major and minor strains of the grids beside the bursting line on the tube surface are measured to construct the forming limit diagram of the tubes. Furthermore, Swift's diffused necking criterion and Hill's localized necking criterion associated with Hill's non-quadratic yield function are adopted to derive the critical principal strains at the onset of plastic instability. The critical major and minor strains are plotted to construct the forming limit curve (FLC). The effects of the exponent in the Hill's non-quadratic yield function and the normal anisotropy of the material on the yield locus and FLC are discussed. Tensile tests are used to determine the anisotropic values in different directions with respect to the tube axis and the K and n values of the flow stress of the tubular material. The analytical FLCs using the n values obtained by tensile tests and bulge tests are compared with the forming limits from the forming limit experiments.     

Electro-hydraulic forming of sheet metals: Free-forming vs. conical-die forming

This work builds upon our recent advances in quantifying high-rate deformation behavior of sheet metals, during electro-hydraulic forming (EHF), using high-speed imaging and digital image correlation techniques. Aluminum alloy AA5182-O and DP600 steel sheets (1 mm thick, ∼152 mm diameter) were EHF deformed by high-energy (up to ∼34 kJ) pressure-pulse in an open die (free-forming) and inside a conical die. The deformation history (velocity, strain, strain-rate, and strain-path) at the apex of the formed domes was quantified and analyzed. The data shows that the use of a die in the EHF process resulted in an amplification, relative to free-forming conditions, of the out-of-plane normal velocity and in-plane strain-rate at the dome apex. This amplification is attributed to the focusing action of the die on account of its conical geometry. Further, while the strain-path at the dome apex was generally linear and proportional, the use of a die resulted in greater strain at the apex relative to the strain during free-forming. The sheet deformation profile in the EHF process was found to be different from that previously observed in electromagnetic forming (EMF) and, thus, the two processes are expected to result in different strain-paths and formability. It is anticipated that quantitative information of the sheet deformation history, made possible by the experimental technique developed in this work, will improve our understanding of the roles of strain-rate and sheet-die interactions in enhancing the sheet metal formability during high-rate forming.