Development of a New Biaxial Testing System for Generating Forming Limit Diagrams for Sheet Metals Under Hot Stamping Conditions
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Conventional experimental approaches used to generate forming limit diagrams (FLDs) for sheet metals at different linear strain paths are not applicable to hot stamping and cold die quenching processes because cooling occurs prior to deformation and consistent values of heating rate, cooling rate, deformation temperature and strain rate are not easy to obtain. A novel biaxial testing system for use in a Gleeble testing machine has been adopted to generate forming limits of sheet metals, including aluminium alloys, magnesium alloys and boron steel, under practical hot stamping conditions in which heating and cooling occur. For example, the soaking temperature is about 900 °C and the deformation temperature range is 550–850 °C for boron steel  and the soaking temperature is about 535 °C and the deformation temperature range is 370–510 °C for AA6082 . Resistance heating and air cooling were introduced in this pioneering system and the thermal analysis of different heating and cooling strategies was investigated based on a type of cruciform specimen. FE models with a UAMP subroutine were used to predict temperature fields on a specimen in ABAQUS 6.12. Digital image correlation (DIC) system was used to record strain fields of a specimen by capturing images throughout the deformation history and its post-processing software ARAMIS was used to determine forming limits according to ISO standards embedded in the software. Heating and cooling strategies were determined after the analysis. Preliminary results of forming limit curves at the designated temperatures are presented in order to verify the feasibility of this new method.
KeywordsSheet metal forming Hot stamping Formability tests Forming limit diagram (FLD) Novel biaxial testing system Thermal analysis
Weight reduction can improve the performance of automobiles and can directly reduce energy consumption . Two potential routes for reducing the weight of sheet metal parts in automobile body structures are the use of high strength steel, which enables a thinner gauge sheet to be used and the use of sheet of low density, such as aluminium alloys. High strength steel is difficult to form and aluminium alloys have low formability at room temperature and, to deal with this, hot forming technologies have been developed; they are hot stamping and cold die quenching for steel and solution heat treatment, forming and in-die quenching (HFQ®), for lightweight alloys .
The hot stamping and cold die quenching process, conventionally abbreviated to hot stamping, is used to obtain complex shaped components with high mechanical properties. In the hot stamping process, heat treatable metal sheet is heated to a temperature at which it is a solid solution with a single phase, transferred to a press and simultaneously formed and quenched in a cold tool . The control of die temperature, cooling rate, forming speed and metallic sheet temperature are critical conditions for the success of these processes. The technique can be applied to both quenchable steels, such as boron steel , and heat treatable low density sheet metals, such as aluminium alloys  and magnesium alloys . For the latter application, a patented process named HFQ® has been developed . In the HFQ® process, a metal sheet is heated to a temperature at which its microstructure is a solid solution and then transferred to a press and simultaneously formed and quenched in a cold tool from which it emerges with a microstructure of solid solution virtually completely retained [9, 10]. This novel process is beneficial to forming complex shaped parts in one operation at a low cost. To be successful, forming conditions, such as heating rate, cooling rate, forming temperature and strain rate, need to be controlled .
In the out-of-plane test, such as the Nakazima test (Fig. 1(b)) , waisted specimens with different parallel shaft lengths are stretched by a rigid hemispherical punch. The application of the out-of-plane test at ambient temperature has been standardised and has also been used to obtain FLDs at high temperature. Ayres et al.  used this experimental method to investigate temperature and strain rate effects on the formability of AA5182 by heating the spherical punch and die to a temperature of 130 and 200 °C, respectively. Bagheriasl  used this test to obtain the FLD of AA3003 at 100–350 °C and strain rates of 0.003–0.1 /s. Circular grid patterns of 2 mm diameter were etched on specimens prior to forming, and the digital image correlation (DIC) technique  was adopted to measure strains. DIC enables full-field strains to be measured at different stages of forming by comparing the digital images of a pattern sprayed on a specimen. Min et al.  obtained the left-hand side of an FLD for boron steel at a temperature of approximately 800 °C for hot stamping applications. However, deformation temperature cannot be controlled precisely in the transfer of specimen from furnace to cold tooling. Pneumatic stretching was used by Abu-Farha et al.  to determine the formability of magnesium AZ31B sheet heated to 400 °C. In contrast to isothermal testing, the need to simultaneously quench and form, to simulate HFQ® conditions makes testing in a furnace impractical. For the in-plane test, such as the Marciniak test (Fig. 1(c)) , specimens are stretched over a flat-bottomed punch of cylindrical or elliptical cross section without imposing any bending within the central region of the specimen. A carrier blank with a central hole is often used to eliminate frictional contact between specimen and the punch. Li and Ghosh  preformed a biaxial warm forming investigation of AA5754, AA5182 and AA6111 by forming rectangular parts at a rapid rate of 1 /s and a temperature range of 200–350 °C. No data was obtained at temperatures over 350 °C. Kim et al.  established the FLD of Al5182+Mn alloy at three different temperature levels (250 °C, 300 and 350 °C) for isothermal conditions. Palumbo et al.  performed isothermal warm formability tests using an electrically heated punch which heated the specimen by heat transfer. FLDs of AA5754 were obtained in the temperature range of 20–300 °C. Neither current conventional out-of-plane nor in-plane methods of determining FLDs are suitable for hot stamping and cold die quenching conditions. Using a planar biaxial machine with a cruciform specimen could be an alternative approach to determine the forming limits. Hannon and Tiernan  reviewed planar biaxial tensile test systems for sheet metal and classified the test machines to two types i.e. stand-alone biaxial testing machines and link mechanism attachments for biaxial testing. Zidane et al.  proposed a new cruciform design for formability tests and obtained the FLD of AA5086 at room temperature based on a servo-hydraulic biaxial test machine. Naka et al.  used biaxial tensile tests and hot air blow heating with cruciform specimens to investigate the effects of strain rate and temperature on yield locus of AZ31.
These methods are usually used to determine FLDs at room temperature and only a few investigations concentrate on formability tests at elevated temperature. In cold stamping conditions, the FLD of a material contains only one curve. However, the FLD of a material at elevated temperature consists of many curves, relating to process conditions . It is very difficult to obtain the FLD of a material under hot stamping and cold die quenching conditions at varying deformation rates because extra heating and cooling facilities are needed, control of heating rate, cooling rate, temperature and strain rate are hard to obtain precisely and the problem of the difficulty of strain measurement in a hot environment needs to be solved. The work described in this paper concerns a novel system for dealing with these problems.
In this paper, a novel biaxial testing system, for use on a Gleeble materials simulator is described, for obtaining FLDs of alloy sheet under hot stamping conditions. Different proportional strain paths can be achieved and friction effects can be avoided. A cruciform specimen was proposed for the biaxial testing. A thermal analysis of the resistance heating method adopted is presented, in order to improve the uniformity of temperature distribution in the specimen during the testing. Different strain paths are verified to be linear and results of an experimental FLD are shown in this paper to prove the feasibility of this new testing system for hot stamping and cold die quenching applications.
The Principles of the Experimental Design
Biaxial Testing Apparatus
Compared with the conventional out-of-plane and in-plane formability tests, the present method overcomes their obvious drawbacks of the presence of friction and formed shape complexity. The mechanism has a relatively simple configuration and is employable within limited space on conventional tensile test machines. The heating rate and cooling rate can be controlled precisely by a Gleeble for complex forming process applications. A controllable temperature distribution can be created in the gauge region of a specimen. The maximum temperature to which a sheet metal specimen can be heated using this testing system mainly depends on the nature of test material, dimensions of test-piece, and heating power. A steel test-piece of the current design (with thickness ≤3 mm) can be heated to 1000 °C. The relationship of time and input displacement from a Gleeble can be defined accurately in advance in order to keep a constant effective strain rate on a specimen during testing. Different linear strain paths can be achieved easily by varying the lengths and orientations of rigid connecting rods in the apparatus and the strain path is independent of specimen dimensions. The testing system enables the DIC system to be used so that deformation history of a specimen can be captured.
Development of Specimen Design
A dog-bone type of specimen with a 98 mm parallel length was used for uniaxial testing in the determination of an FLD of AA6082 under the HFQ® conditions. The thickness of the specimen was 1.5 mm and other dimensions were as shown in Fig. 6(a). The dimensions of cruciform specimens, including clamping regions, are shown in Fig. 6(b). Fillets of 10 mm exist at the intersection of two adjacent arms, to reduce stress concentration in the corners. The thickness of the specimen was 1.5 mm except for the 17 mm diameter central circular gauge region where it was reduced to 0.7 mm, by recessing each face by 0.4 mm. Slots 1.4 mm wide and 28 mm long were cut into the arms in order to distribute the load more uniformly to the central gauge region. The distance between each slot is 6 mm and the distance from the mid-length of the specimen to the ends of the slots is 16.5 mm, marked in Fig. 6(b).
Specimen Temperature Tests
Figure 8a shows the temperature at location 3 to be over 10 °C higher than that at location 1 because of large geometric changes from the end of the slot to the recess in the centre for the first type of heating and cooling strategy. This may cause localised necking to start from the region around location 3 with stress concentration but not from the gauge section, which is not acceptable for the biaxial tension. For the second type of heating and cooling strategy, the temperature difference within the recessed region is within 8 °C, which indicates a sufficiently uniform temperature distribution was created (Fig. 8(b)). The temperature at location 4 is around 20 °C lower than that at location 1, which is perhaps beneficial to postponing localised necking outside the gauge section. Regarding the third type of heating and cooling strategy, the temperature at location 1 is 30 °C lower than that at location 2 (Fig. 8(c)). When the average temperature in the central region is much lower than that of the arms of the specimen, premature localised necking might occur in them. Further investigation is needed to verify the uniformity of deformation within the gauge length region.
Different strategies of heating and cooling have their own advantages and drawbacks. In order to obtain entire temperature fields, which could not be readily obtained experimentally FE simulation was carried out to further investigate the uniformity of temperature distribution and thus enable selection of the best heating and cooling strategy.
Values of constant K j in the UAMP subroutine
K1 (Heating process)
K2 (Soaking process)
K3 (Cooling process)
K4 (Deformation process)
The FE simulations were carried out for the three types of heating and cooling strategies. In order to obtain agreement between the FE computed results and the experimental results of temperature profiles, the conduction heat transfer coefficient was defined as 8000 Wm−2K−1 and the sink temperature within clamping region was defined as 150 °C. These two values were determined empirically for the best fit of the thermal simulation results to the experimental temperature data obtained for selected positions along the gauge section of the specimen. The initial temperature of all elements was set to the room temperature of 20 °C. Conduction heat transfer was used for the clamping area to simulate heat loss. The gauge area of the specimen was meshed finely and the coarseness of the mesh increased from the centre-line to the clamped end, in order to reduce calculation time. A 4-node linear coupled thermo-electrical tetrahedron element was used.
Comparison of experimental and simulated results of temperatures at different locations on specimens of AA6082 for different types of heating and cooling strategies
In Fig. 10(b), an isothermal temperature field can be observed within the gauge region but different temperature distributions exist on the four arms of the specimen. The temperature distribution outside the recess region is not symmetric and consistent because the gradient of electrical potential on the specimen decreased from the positive electrodes to the negative electrodes. The temperature distribution outside the gauge region would have an effect on the deformation of the central region. The average temperature in region A is 4 °C lower than that in region B along the section I-I and about 20 °C higher than that in region C along the section II-II. A higher temperature within the gauge area is beneficial to inducing fracture starts in this region.
In Fig. 10(c), the temperature field is symmetrical and uniform within regions A and B. The temperature difference within region A is 8.2 °C. The average temperature in region A is 32.8 °C which is lower than the maximum temperature in region B along section I-I. When the average temperature in the central region is much lower than that on the arms of the specimen, the arms might deform prematurely.
The thermo-electrical FE model was used to obtain the temperature fields on specimens. Based on the analysis above, the second type strategy is the most acceptable one compared with the other two since fractures could occur in the central region but not in the arms by consideration of temperature distribution on a specimen.
Biaxial Tensile Tests
In order to overcome the weaknesses associated with conventional methods for the determination of FLDs at elevated temperatures for application to industrial hot stamping and cold die quenching processes, a new in-plane biaxial testing system was designed and used on a Gleeble materials simulator machine. This new testing system enables formability data to be generated under complex heating and cooling conditions. Designed uniaxial and cruciform specimens were used in formability tests under different linear strain paths. By comparison of temperature distributions obtained from different types of resistance heating and air cooling strategies, it was found that connecting two adjacent arms of the cruciform specimen to positive electrodes gave the most acceptable temperature field within the gauge region. Specimen design could be further improved since the temperature distribution on the arms of the cruciform specimen is not exactly uniform and symmetric. Representative forming limit curves for AA6082 at temperatures of 400 and 500 °C and strain rate of 0.1 /s were obtained on solution heat treated and cooled material, which proved the feasibility of this novel method for the determination of FLD of sheet metals under hot stamping conditions. This method can be used to determine the hot formability of many sheet metals up to a maximum temperature of 1000 °C, on a Gleeble materials simulator.
Financial support from Impression Technologies Ltd for this research project is gratefully acknowledged by the authors. In addition, the research was supported by the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 604240, project title ‘An industrial system enabling the use of a patented, lab-proven materials processing technology for Low Cost forming of Lightweight structures for transportation industries (LoCoLite)’.
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