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Benchmark 3 - Springback of an Al-Mg alloy in warm forming conditions

Accurate prediction of springback is a long-standing challenge in the field of warm forming of aluminium sheets. The objective of this benchmark is to predict the effect of temperature on the springback process through the use of the split-ring test [1] with an Al-Mg alloy. This test consists in determining the residual stress state by measuring the opening of a ring cut from the sidewall of a formed cylindrical cup. Cylindrical cups are drawn with a heated die and blank-holder at temperatures of 20, 150 and 240°C. The force-displacement response during the forming process, the thickness and the earing profiles of the cup as well as the ring opening and the temperature of the blank are used to evaluate numerical predictions submitted by the benchmark participants. Problem description, material properties, and simulation reports with experimental data are summarized.


INTRODUCTION
Nowadays, aluminium alloys are increasingly used in the automotive industry, since they allow weight reduction in body-in-white. However, the large springback that occurs after aluminium alloy sheets have been formed at room temperature is one of the main reasons why this material has not been more widely used. In order to overcome this issue, good results on the stamping process are obtained for aluminium alloys when the temperature is elevated up to an intermediate temperature, below the recrystallisation temperature. This process is called warm forming, that promoted a great interest during the last few years, especially with the 5xxx series (Al-Mg alloys). The warm forming process has now become a widely used alternative to the classical forming processes performed at room temperature.
The aim of this benchmark is to investigate experimentally springback tests performed on an AA5086 alloy under warm forming conditions, such as to serve as a reference to compare the results obtained by numerical simulations. An experimental setup has been designed to perform the deep drawing of a cylindrical cup by heating the tools separately. Indeed, several authors have shown that the formability increases when selective localized heating strategies are applied to the forming tools, causing an inhomogeneous distribution of the temperature in the blank. Therefore, the aim is to confirm this improvement of the formability and to study the effects of warm forming conditions on residual stresses and springback. For that purpose, the springback is determined by measuring the opening of a ring cut from the sidewall of a drawn cylindrical cup (see Fig.1). This is the so-called split-ring test that was first presented by Demeri et al. [1]. It provides a simple and effective way of predicting the forming and springback properties of alloys based on experimental measurements.
Cylindrical cups are drawn with a heated die and blank-holder at temperatures of 20 (room temperature), 150 and 240°C. The force-displacement response during the forming process, the thickness and the earing profiles of the cup as well as the ring opening and the temperature of the blank are used to evaluate numerical predictions submitted by the benchmark participants. To simulate this process, a temperature-dependent anisotropic constitutive model is required for the material. The parameters of hardening models and strain rate dependency can be identified using data given in uniaxial tensile and shear tests at various temperatures and strain rates as well as biaxial expansion test, in order to account for temperature, viscous effects and anisotropy in a coupled thermomechanical constitutive law. Shell elements, solid elements, or solid-shell elements are recommended for this benchmark with careful control of the incremental punch stroke, with sufficient number of elements in the mesh to reproduce the curvature of the die and to capture plastic strain accurately. The analysis in this benchmark is highly non-linear, including thermal, viscosity and anisotropy. It is recommended to use a simple isotropic material model (such as von-Mises yield function) before attempting an advanced anisotropic material model. This benchmark study has the main objective of predicting springback after warm forming, cutting and opening. Different challenging outputs will be required as a function of forming temperature: i) Prediction of earing after the warm forming operation due to the plastic anisotropy of the material; ii) Prediction of thickness profiles for several orientation to the rolling direction after the warm forming operation; iii) Prediction of springback through ring opening; iv) Prediction of punch force-punch stroke and temperature of the blank evolutions.

DESCRIPTION OF FORMING OPERATIONS
This section contains a description of the warm forming, cutting and opening operations for this benchmark.

Drawing operation
The benchmark is based on a paper presented in [2]. Cylindrical cup forming tests (Swift tests) are carried out on a Zwick/Roell Amsler BUP 200 sheet metal testing machine. A diagram of the deepdrawing procedure is presented in Fig.1. The blanks can be heated between the die and the blankholder up to 240°C. Heating is obtained using electrical rods embedded both in the die and in the blank-holder. Axial water input and output channels are machined into the punch that allow controlling the temperature of the punch. An ejector located inside the punch is used to eject the cup from the punch at the end of the forming process. Type K thermocouples (TC) are used to control the temperature of the blank, the punch, the die and the blank-holder.
The geometry of the tools is given in Fig.2. The material is a rolled sheet of AA5086 aluminium alloy of 0.8 mm thick. The circular blank has an initial diameter of D=60 mm. At the beginning of the test, an oil lubricant (Jelt Oil) is applied manually on both sides of the blanks. To fully draw the cup, a punch displacement of 32.5 mm is imposed with a constant punch travel speed of 5 mm/s. The punch force, the punch stroke and the blank-holder force are recorded during the test. All the tools are axisymmetric. The blank-holder force at the beginning of the deep drawing operation is set to 5 kN, and this force is maintained until the cup is fully drawn. Heating is applied using electrical heating rods as shown in Fig.3. The set of tools used includes: i) A draw die composed of two inserts containing a resistance coil and a copper plate; ii) A blank-holder machined with a suitable upper annular insert for placing the heating rods; iii) The punch and the internal ejector; iv) A base used to support previous parts, connected to the BUP 200 machine.
The positions of thermocouples used to control the temperature of the punch, the die and the blankholder are shown in Fig. 3. In the die, the thermocouple (TC-Die) is located on a diameter φ TC-Die = 38.4 mm, 1 mm from the contact surface. In the blank-holder, TC-BH is located on a diameter φ TC-BH = 47.3 mm, 1 mm from the contact surface and for the punch, TC-Punch is located under the ejector, on a diameter φ TC-Punch = 16 mm, 1.5 mm from the contact surface. The evolution of the temperature of the tools is supposed homogeneous around the circumference and as those of the thermocouples, and is given as a function of the punch stroke in the file BM3_Process.xlsx for each temperature. The resulting temperature of the blank is measured on the side in contact with the die, at a location of φ TC-Blank = 11.5 mm for the orientation of 22.5° to the rolling direction.

Springback
Rings are cut from the sidewall of a formed cylindrical cup and split perpendicularly to the circle plane, in the rolling direction (RD). The cutting and splitting operations are carried out using a wire electro-erosion machine. Ring gap measurements are performed along the straight line connecting the two ends of the split rings (see Fig.1) in order to characterize residual stress state and to measure the springback effect.

Experimental Measurements
The distributions of the thickness of the cup are measured in several directions (rolling direction RD, transverse direction TD, diagonal direction DD) from the center to the outer diameter every 1 mm in curvilinear distance, using a 3-D measuring machine. The curvilinear distance corresponds to the length of the average fiber of the cup. The earing profiles of the cups are also recorded and the cup height is plotted from the bottom of the cup as a function of the angular position (every 5°) to the RD. The punch force-displacement curves as well the temperature of the tools and the blank are recorded during the forming test. To help participants, the evolutions of temperatures of the tools as well as the temperature of the blank during the forming process are given in BM3_Process.xlsx file (see Fig.4).
For example, these temperatures may be used to estimate the contact heat transfer coefficient. Thus, the participants can evaluate the relevance of their thermomechanical simulations on the temperature of the blank. Rings of 5 mm high are cut 7 mm from the bottom of the cups (see Fig.1), perpendicularly to the revolution axis of the cup. Ring gap measurements are performed along the straight line connecting the two ends of the split rings in order to evaluate the springback.

BLANK MATERIAL
The material used is sampled from a rolled sheet of 0.8 mm thick AA5086-H111 aluminium alloy. This material presents, at least at room temperature, the Portevin-Le Châtelier (PLC) effect. This effect is no more present for temperatures above 200°C. For the material parameters required in the constitutive models, the material is characterized under different conditions (temperature and strain rate) and strain paths (tensile, shear, bulge). Uniaxial tensile tests are performed under isothermal conditions at room temperature (20), 150 and 240°C. Tensile tests at room temperature are performed on a hydraulic Instron 8803 machine while the tests at 150 and 240°C are carried out with a Gleeble 3500 testing machine where the specimen is heated by Joule effect [3]. On this last machine, a constant crosshead velocity is difficult to achieve and the strain rate is thus non linear. For all the tensile tests, the participants can calculate the strain rate by fitting the time-strain signal. For the strain rate effects, a decade has been imposed between two consecutive tests, denoted by x1, x10 and x100.
Monotonous and reverse shear tests for several values of pre-strains are provided in order to evaluate Bauschinger effect and therefore kinematic hardening. Shear tests are performed with a tensile machine, using a specific shear device placed in a heating furnace [4]. But due to experimental considerations, it was not possible to reach temperatures higher than 150°C. Shear samples have been machined at dimensions: 60x15mm 2 and the shear width is constant equal to 3mm (see [4] for details). Finally, biaxial tests are carried out in a hydraulic bulge test setup only at room temperature. The material data necessary to identify the influence of temperature, anisotropy and strain rate is given in Section 5 and in the Excel file AA5086-H111.xlsx.

BENCHMARK REPORT
All results are expected to be reported using the benchmark report template BM3_Report.xlsx, which can be downloaded from the conference website, and when completed, uploaded to the website at a later date to submit the entry. The report file contains the following informations:

Simulation results
1) Earing profiles plotted through Cup height (h mm) after the warm forming operation for each temperature (RT,150,240°C), measured from the lower surface to the upper edge of the cup around the circumference starting from the rolling direction (0°) to 360°, reported every 5° 2) Plot of punch load (kN) vs punch stroke (mm) during the cup forming operation for each temperature (RT,150,240°C). The zero punch stroke is defined as the position when the punch makes initial contact with the blank with no interaction forces 3) Blank surface temperature as a function of punch stroke on the side in contact with the die, during the test for RT, 150 and 240°C. The temperatures of the tools should also be given for each test temperature 4) Thickness distribution (mm) vs curvilinear distance from the cup center after the forming operation, in the rolling direction (0°), transverse direction (90°) and diagonal direction (45°) for each temperature (RT, 150, 240°C). For the curvilinear distance, the medium thickness should be considered. The experimental values are the average between the four quarters of the cup 5) The ring opening (mm) for each temperature (RT, 150, 240°C) measured as the straight line connecting the two ends of the ring. As the ring may be slightly conical, the distance should be measured at the mid-height of the ring.   Blank-Holder force (kN) 5