1. Exercises in Hydraulic Bulge Testing H.S. Kim H. Lim Mike Sumption Ted Collings The Ohio State University Dept of Materials Science and Engineering Center for Superconducting and Magnetic Materials (CSMM) Research funded by the U.S. Dept. of Energy through Grant No. DE-SC0004217

2. OUTLINE Description of the hydraulic bulge test Purpose of the test Summary of the presentation Experimental materials Tensile test results FE simulation of bulge based on tensile test results Bulge test results Analysis of the bulge test results Concluding summary

3. The Hydraulic Bulge Test Data Acquired: Hydraulic pressure: manually adjusted, gauge measured Bulge height: laser sensor Tube thickness: ultrasonic gauge, sliding under gravity

4. Press: Max. clamping force of 45 tons, provided by a small hydraulic press Hydraulic Pump: Max. pressure of 69 MPa, provided by an air assisted hydraulic pump Hydraulic cylinder: Max. sealing force of 20 tons OSU’s Press for Hydraulic Bulge Testing

5. Purpose of the Bulge Test The purpose of the bulge test is to obtain realistic information about the materials properties of a tube, using a procedure as close as possible to the hydroforming process. Hydraulic pressure is applied and the maximum bulge height and wall thickness are measured. The data are used to calculate the flow stress, σ, as function of effective strain, ε, as they appear in the equation σ = Kε n. The test is used to determine forming limit diagrams and forming limit stress diagrams directly from tubes rather than sheet material.

6. welded nine-cell cavity hydroformed nine-cell cavity Purpose – continued: Testing the hydroformability of tube in preparation for the hydroforming of multi-cell cavities

7. Research Progress Part-I: Creation of an FEM-based “virtual bulge”. Analysis of the bulge using the procedures of Fuchizawa, Koc et al., and Bordot et al, respectively. Kim et al., Adv. Cryo. Eng. (Materials) 58 305 – 312 (2012) The procedure of Koç et al is selected for future analysis Part-II: Burst test of as-received copper pipe. Experiment completed but not reported here Part-III: Bulge testing of annealed copper pipe. The subject of this presentation. Bulge results analysed by the procedure of Koç et al

8. Tube Bulge test - Pressure - Bulge height - Thickness Tensile test - Force - Displacement Flow stress curve Analytical model Comparison Summary Flow stress curve

9. Experiment Materials 1. The Tube - OD: 2.5” = 63.5 mm - Thickness: 0.065” = 1.65 mm - Heat treated at 500 °C for 1 hr 2. The tensile sample - Tensile test specimens were cut from the tube with an ASTM standard dimension. - Strain rate: 0.002 /s

10. Orientation Image Mapping (OIM) Results (b) Thickness direction No preferred orientation -> Isotropic material (a) (a) As received (b) Heat treated at 500 °C for 1 hr

11. Tensile Test Results Tube: Heat treated at 500 °C for 1 hr

12. 1)Program: Abaqus 2)Geometry - Axisymmetry cross-section of the tube - Only half tube was modeled - The ends of the tube were constrained - Four-noded solid elements (CAX4R) 3) Elastic properties - Elastic Modulus: 110 GPa 4) Plastic Properties - True stress – True plastic strain 5) Yield function: Isotropy (Von Mises) Copper Tube Finite Element Analysis

13. FEA Results Simulation result using flow stress curve from tensile test

14. Bulge Test Results Tube: Heat treated at 500 °C for 1 hr

15. Analyze Koc et al.

16. Results Bulge test results Analytical model Effective Stress – Effective Strain Plastic constitutive equation TensileBulge ( Koc) K 563.11479.78 n 0.4420.432 Hollomon format The strain range for fitting: 0.02 ~ 0.32 for tensile 0.02 ~ 0.12 for bulge

17. FEA Results Combined simulation results using flow stress curve from tensile test and bulge test

18. The empirical plastic constitutive equation are obtained from tensile test and tube bulge test. Ko Ç method is used for determining constitutive equation from tube bulge test. Next Step Based on these results, bulge test using niobium tube will be carried out. Conclusion Thank you