Investigation on Granular Medium Forming Formability of TA1 Titanium Alloy Cylinder-Shaped Parts


 In order to investigate the formability of the granular medium forming (GMF), based on the Mohr-Coulomb constitutive model with the tri-axial compression test of granular medium and the true stress-strain curves of TA1 titanium alloy from uniaxial tensile tests, the numerical simulation of TA1 titanium alloy sheet deep drawing with finite element method was performed, and the deep drawing tests were also carried out. Simulation analysis and test results show that the GMF process is suitable for titanium alloy sheets, and can effectively improve the uniformity of the wall thickness of the formed parts, reduce the tendency of wrinkles and improve the forming quality.

The GMF process, which uses granules as a pressure-transfer medium in order to form a workpiece, is a newly proposed flexible die-forming technique [5][6][7][8][9] . Because the application of this process can fully exploit recent advances in the formability of lightweight materials at elevated temperatures, as well as overcome the limitations that the heat-resistant oil used in warm hydroforming operations can withstand temperatures of no more than 350•C [10][11][12] and that the inert gas used at higher temperatures in hot pneumatic bulging processes usually causes leakage problems [13,14] , the GMF process has recently attracted considerable attention by several researchers [15][16][17][18] .
The principle of the GMF technology is shown in Figure 1. A sheet is placed on the concave die; The charging barrel is pressed on the sheet, thus playing the role of edge pressing and sealing; Then the granular medium is loaded into the charging barrel, and pressure is applied to the convex die block, so that the granular forming pressure under the pressure of the block, which are transferred to the sheet through the granular; The middle part of sheet firstly produce plastic deformation because it is subjected to the action of bidirectional tensile stress under the action of forming pressure, and then the flange material gradually enters the die under the action of radial tensile stress, and finally the sheet is completely attached to the die and formed into the cavity shape of the die [5] . Cylinder-shaped part is the most classic and the most representative part, which can well show the uniformity of wall thickness and wrinkle phenomenon of parts. Many researchers take cylinder-shaped parts as the research object to study the forming process formability. Zhao [19] et al. conducted an experimental study on the granular soft die deep drawing of cylinder-shaped parts, and found that the thickness of each part of the forming parts decreased and the thinning amount increased with the increase of the depth of the drawing. Chen [20] et al. took cylinder-shaped parts as the research object, and studied the influence of liquid chamber pressure loading path, forming liquid chamber pressure, blank holder force and blank holder clearance on the sheet hydroforming effect. It is found that the reasonable pressure loading path and blank holder gap of the liquid chamber can effectively control the wrinkle in the flange area of the part and prevent the punch from cracking. At present, the researchers mainly used the cylinder-shaped parts to study the hydroforming process and the granular soft die forming process formability, however, very few investigation concentrates on the GMF process formability, which is a main target of this research.
To study the formability of the GMF process, this paper takes cylinder-shaped parts as the research object, and carries out the simulation calculation and experimental verification of its forming process. In order to improve the accuracy of simulation calculation, the Mohr-Coulomb constitutive model with the tri-axial compression test of granular medium and the mechanical property data of TA1 titanium alloy sheet obtained by uniaxial tensile test were used as the required parameters of the simulation model.

Tri-axial Compression Test of Granular Medium
In order to explore the flow and deformation characteristics of granular medium in the forming process, domestic and foreign scholars have used a variety of measurement methods, including axial static pressure transmission formability test, direct shear test and so on [5,16] , however, these methods are unable to reflect the dynamic flow properties of the material during the compression deformation process, and its applicability is not good for the GMF process. The tri-axial compression test, which is a relatively mature geotechnical test method, is suitable for measuring the dynamic compression deformation characteristics of granular materials under the condition of triaxial compressive stress. Therefore, in order to determine the parameters of the Mohr-Coulomb model of granular materials, the tri-axial compression test is selected to determine the deformation characteristics and pressure transmission laws of granular materials.
When the Mohr-Coulomb strength theory index is obtained by using the tri-axial In addition, it should be noted that the positive direction of each coordinate axis is the direction of compressive stress, which is opposite to the symbol in the calculation of metal plastic deformation. In the three-dimensional stress space, the Mohr-Coulomb yield surface function is expressed as follows [21] : Where 、 are the internal friction angle and cohesion of the material respectively, Θ are the polar deflection angles of the stress state point of the material in the π plane, and p、q、r are the invariants of the first, second, and third stress states respectively: The parameters of Mohr-Coulomb model obtained by tri-axial compression test are shown in Figure   heating length of the furnace was 300mm, and the clamping scheme of superalloy pin was adopted. High temperature uniaxial tensile tests were carried out at same temperatures (500℃) and at different strain rates (0.1s -1 , 0.02s -1 , 0.005s -1 ).
The uniaxial tensile specimen used in the test generally has a rectangular section and a certain length of parallel section. The strain value of sheet specimen in the deformation process can be measured by using an extensometer clamped in the width and length direction of uniaxial tensile specimen, and then the stress can be calculated by obtaining the real-time tension at both ends of the tensile testing machine [22][23] .
However, the accuracy of the stress and strain measurement method is based on the deformation uniformity of the specimen. When the uniaxial tensile specimen exhibits dispersive instability (necking), the measured stress-strain curve will have errors.
Therefore, the extensometer measurement method can only obtain the material flow stress variation before necking. For sheet metal plastic deformation process, especially the forming process of bulging and deep drawing with the characteristics of two-way drawing deformation, the ultimate strain of the material in the uniform deformation stage is often much larger than the strain value in uniaxial tensile test. In the simulation analysis of forming process, if the material mechanical behavior before necking obtained by uniaxial tensile test is used as the basis to predict the plastic deformation process of sheet metal, a large error will be generated. In order to obtain the accurate stress-strain curve of titanium alloy TA1 material after necking, a reverse modeling algorithm which is based on FEA method proposed by Lang [24] et al. was adopted in this paper. The reverse modeling process flow chart is shown in Figure 4. Figure 5 shows the stress-strain curves optimized by iterative steps in reverse modeling at different strain rates (0.005s -1 , 0.02s -1 , 0.1s -1 ). It can be seen that , under the condition of 500℃, the lower the strain rate, then the higher the maximum elongation, however, different strain rates have no significant effect on the hardening curve. To further study the strength and fracture failure mechanism of the material, the microstructure of uniaxial tensile specimens under different temperature conditions (normal temperature, 500℃, 550℃, 600℃) was analyzed by SEM in this paper. The observation results of SEM were shown in Figure 6. It is obvious that the uniaxial tensile fracture morphology of titanium alloy TA1 has a large number of dimples and holes distribution in all temperature ranges, indicating that the fracture process of titanium alloy TA1 appeared microscopic pore nucleation, growth and polymerization deformation mechanism. Figure 6a shows that the fracture tearing morphology at room temperature. Under such temperature conditions, the dimples of titanium alloy TA1 in uniaxial tensile fracture are many and small, and the dimples are shallow, which is a typical character for microporous aggregated ductile fracture. With the increase of temperature (Figure 6b, Figure 6c), the number of dimple holes decreases and the depth increases, indicating that with the increase of temperature, the plasticity of titanium alloy TA1 material increases, the nucleation rate of microholes decreases and the toughness increases.

Numerical Simulation of GMF Process
The thickness uniformity of the parts formed by the traditional hot stamping process is poor, and wrinkles are prone to occur, so it is difficult to meet the processing needs of the cylinder-shaped parts. The optimum forming temperature of titanium alloy is generally higher than 500℃, while the highest heat-resistant temperature of heat transfer oil does not exceed 350℃. Therefore, the hydraulic oil widely used in the conventional liquid-filled forming process no longer meets the requirements of titanium alloy thermal medium forming, and low melting point alloy, viscous medium or nonmetallic ceramic particles must be used as the forming medium. In consideration of safety and sealing, non-metallic ceramic particles are selected as the force transmission medium.  In this paper, the material parameters of titanium alloy obtained from hightemperature uniaxial tensile test and the pressure transfer parameters of granular medium obtained from tri-axial compression test were used to establish the calculation model of the GMF process as shown in Figure 8. The thickness of TA1 plate is 1mm, the test temperature is selected as 500℃, and the fixed gap between blank holder and die is 1.2mm. The cavity in the central part of the blank holder is filled with liquid granular material with particle size of 0.117mm~0.14mm [25] .

Analysis of Simulation Results
The calculation and analysis results are shown in Figure 9. It can be seen that under the conditions of different billet diameters (160mm, 180mm) and different forming heights (42.5mm, 44mm, 58.3mm, 81mm), the forming parts all show good forming formability.
It can also be seen that during the GMF process, the minimum wall thickness appears in the central area of the pass bottom, and the wall thickness value increases uniformly from this area to the edge of the part. The formed part has good uniformity of wall thickness, and its maximum thinning rate is only 18%.

Experimental Equipment and Material
In order to evaluate the accuracy of simulation calculation of the GMF process, the high-temperature GMF experiment was carried out on YRJ-50 sheet metal experimental machine independently developed by Beijing University of Aeronautics and Astronautics. The inner diameter of charging barrel is 80mm, the inner diameter of the die is 85mm, the thickness of TA1 titanium alloy sheet is 1mm, and the blank holder clearance is 1.2mm. The diagram of the high-temperature GMF test die is shown in Figure 10. Under the condition of 500℃, TA1 titanium alloy sheet with blank diameter of 160mm and 180mm was formed with different depth of drawing.
Under the condition of high-temperature, colloid graphite water agent are selected as lubricant, which smear on the surface of the blank and wait for drying. Graphite water agent not only plays the role of lubrication, but also can effectively prevent oxidation on the surface of titanium alloy plate under high-temperature conditions. The forming process is controlled by constant drawing rate, and the drawing rate is 5mm/min.  (1) The GMF technology using granular instead of rigid die can achieve hightemperature processing forming of titanium alloy parts, and forming temperature can reach more than 500℃.
(2) The results of simulation and experiment show that the cylinder-shaped parts of titanium alloy formed by the GMF process have good uniformity of wall thickness.
(3) Under the action of compressive stress in the thickness direction, the wrinkling tendency of titanium alloy parts is effectively suppressed and the forming quality is improved. Mohr-Coulomb yield surface in 3D stress space Fracture morphology of TA1 specimen after tensile test Diagram of the process of deep drawing with granular medium Figure 8 Numerical model of the granular medium forming process Results of numerical simulation Figure 10 Diagram of experimental equipment for hot granular medium forming Figure 11 Fabricatd TA1 part by GMF method at 500 Figure 12 Comparison of shape dimension and thickness distribution between numerical simulation and experimental results (a) Comparison of shape dimension between numerical simulation and experimental results (b) Comparison of thickness distribution between numerical simulation and experimental results