Determining flow stress of tubes

The conventional uniaxial tensile test often is used to determine the properties of tube material for hydroforming. However, a biaxial test is more appropriate for hydroforming applications.

Material data obtained from a uniaxial tensile test using sheet samples cannot be used for process development or simulation in hydroforming for the following reasons:

• In the tensile test, the specimen is subjected to a uniaxial state of stress, which does not accurately reflect the state of deformation encountered in the hydroforming process (both tube and sheet), which subjects the material to a biaxial state of stress.

• The intermediate processes involved in manufacturing a tube from a sheet—roll forming—affects the material formability of the tube.

Therefore, material data for tube hydroforming applications must be obtained by deforming a tubular sample under a biaxial state of stress. Process simulations are used increasingly these days to determine the feasibility of a process or to improve the existing process parameters. For such simulations to yield accurate and reliable results, the material properties (for example, the relation between flow stress, s, and strain, e, in the equation s = Keⁿ) used as input in the simulations, the strength coefficient, K, and the strain-hardening exponent, n, must be accurate.

To set the standards for material formability and expansion and to deliver reliable material data to the industry, the Engineering Research Center for Net Shape Manufacturing (ERC/NSM) at The Ohio State University has developed and implemented the biaxial tube bulge test. This test can be used to determine the formability of various tube materials, including aluminum alloys, stainless steels, carbon steels, and nickel alloys.

Hydraulic Bulge Test

The hydraulic bulge test is used to test tubes in a biaxial state of stress. One major impediment with such a test is machine costs. Even though the hydraulic bulge test was developed many years ago, it has not been implemented successfully in industry to determine material formability.

This is due to the high costs involved in developing the required equipment, such as an advanced pressurization and sealing system to pressurize the tube, a data acquisition system to monitor the experimental results, and a computer program to obtain the flow stress from the tests. The ERC/NSM has developed cost-effective techniques that can determine material formability from biaxial tests for both sheet and tube.

Test Methodology for Hydraulic Bulge Test

A tool set, a simple stand-alone hydraulic bulging unit, was developed to biaxially deform tubular samples.1 Since tube hydroforming applies a biaxial loading to the tubes, a similar approach was used in the design of the test fixture. This tool set is suitable for use with different types of metals, different tube sizes, and different pressure levels.

The basic system consists of a hard tooling set (see Figure 1), hydraulic pressurization system, and data acquisition equipment. Because this system was intended for use by industrial and research institutions, simplicity was emphasized throughout the design process.

Experimental Procedure. The bulge test consists of the following steps:

1. Expand the tube with internal pressure while the ends of the tube are held firmly to prevent axial movement.

2. Measure the internal pressure and bulge height continually during expansion.

3. Convert the data into true stress-strain data using analytical equations.

4. Use the least-squares method to fit the data into known and widely used equation forms to obtain a flow stress curve that is easy to use. The bulge tooling also can be used as a quality control tool. This test, which can determine the formability of tubular material quickly, is suitable for use on the shop floor for evaluating the quality of incoming material before it is released to production. The higher the bulge radius at fracture, the higher the formability of the tube.

Data Collection and Analysis. The internal pressure (P_i) and bulge height (h_i) of the tube are measured continuously using a pressure sensor and linear potentiometer, respectively (see Figure 2). The pressure sensor is located on one end of the rod holding the hydraulic cylinder, and the linear potentiometer is fixed on the upper die. The pressure and bulge height values are collected during the experiment with the help of LABVIEW, a computer data acquisition system.

The data is exported into TUBE_ STRESS, a software program developed at the ERC/NSM to analyze the measured data. This program calculates the true stress and true strain values, which then are curve-fitted into widely used forms of the flow stress curve shown in Equation 1.Analytical Representation of the Flow Curve. By using TUBE_STRESS, it is possible to determine the flow stress (true stress versus true strain) of the tubular material accurately in the following forms:

s = Keⁿor s = K(e₀+ e)ⁿ(1)

where: s = true stress

e = true strain

K = strength coefficient

n = strain-hardening exponent

e₀= prestrain

A flow chart is used for calculating the flow stress of the tube (see Figure 3).²

Forming Limit Diagrams. Forming limit diagrams (FLDs) are widely used fracture criteria for tube hydroforming. The hydraulic bulge test also can be used for determining the right side of the FLDs.³Varying the bulge width (w) of the tube used for the bulge test results in different deformation paths. From this the fracture points for each deformation path can be plotted.

By fitting a regression curve (seeFigure 4) through the fracture points, the right side of the FLDs for the material tested can be determined. Using FLD0, the fracture point at plane strain deformation (minor strain = 0), the left side of the FLDs can be plotted directly using the empirical formula given by North American Deep Drawing Research Group, NADDRG.⁴

Capabilities and Limitations of the Bulge Tooling. The tooling is set up for use with tubing of the following dimensions:

Diameter: 57.15 millimeters (2.25 inches)Length: 203.2 mm (8.0 in.)Wall thickness range: 0.6 to 1.65 mm (0.024 to 0.065 in.)

The tooling can be quickly modified for use with tubes of larger wall thickness and different diameters and lengths. A new set of dies is required for each diameter of tubes to be tested.

The data acquisition system comprises a pressure sensor and a computer data acquisition system. Internal pressure is recorded 10 times per second to measure the pressure precisely, which is used in the analytical equations.

The relevant specifications of the tube-testing fixture are:

Press: 45 tons maximum clamping force provided by a small hydraulic press
• Hydraulic pump: 68.9 megapascals (MPa) (10,000 pounds per square inch [PSI]) max-mum pressure provided by an air-assisted hydraulic pump
• Hydraulic cylinder: 20 tons maximum sealing force
• Flow valve: 12 cubic feet per minute (CFM) flow rate

The fixture can accommodate tubes with the following dimensions:

Diameter: 57.15 to 88.90 mm (2 to 3.5 in.)
• Length: 203.2 to 254 mm (8 to 10 in.)
• Thickness: 0.65 to 3.0 mm (0.026 to 0.118 in.)

Biaxial Better for Hydroforming

The uniaxial tensile test is still useful for its intended applications. However, the data obtained from it is not suitable for every situation. A biaxial tensile test provides more accurate results for hydroforming.

With analytical equations, flow stress data can be calculated simply by measuring the bulge height and internal pressure. The material data obtained from the bulge test is more accurate than the conventional uniaxial tensile test data and should be used for process simulation. The hydraulic bulge test also can be used in tube fabrication shops as a quality control tool for incoming material.

Srikanth Kulukuru and Yingyot Aue-u-lan are graduate research associates and Taylan Altan, Ph.D., is a professor and director of the Engineering Research Center for Net Shape Manufacturing (ERC/NSM), The Ohio State University, 339 Baker Systems, 1971 Neil Ave., Columbus, OH 43210, phone 614-292-5063, fax 614-292-7219, e-mail altan.1@osu.edu, Web site www.ercnsm.org.

This work was partially funded by the Tube Hydroforming Consortium at the ERC/NSM, The Ohio State University, and the NSF Grant No. 9610323. The Ohio State University and the authors would like to acknowledge their support.

1. T. Sokolowski, K. Gerke, M. Koc, M. Ahmetoglu, and T. Altan, "Evaluation of Tube Formability and Material Characteristics in Tube Hydroforming," Report No. THF/ERC/NSM-98-R-025 (Columbus, Ohio: The Ohio State University, 1998).

2. Y. Aue-u-lan, "Determination of Flow Stress and Formability of Tubes for Hydroforming," Report No. THF/ERC/NSM-00-R-11 (Columbus, Ohio: The Ohio State University, 2000).

3. S. Matteo, Y. Aue-u-lan, G. Aiello, and T. Altan, "Determination of the Forming Limit Diagrams for Tubular Materials," Report No. THF/ERC/NSM-00-R-29 (Columbus, Ohio: The Ohio State University, 2000).

4. S.B. Levy, "A Comparison of Empirical Forming Limit Curves for Low Carbon Steel With Theoretical Forming Limit Curves of Ramaekers and Bongaerts," IDDRG, WG3, Ungarn (1996).