1 School of Materials Science & Engineering, Harbin Institute of Technology at Weihai, Weihai 264209, China; 2 School of Materials Science & Engineering, Harbin Institute of Technology, Harbin 150001, China; 3 Center for Precision Engineering, Harbin Institute of Technology, Harbin 150001, China

Due to the increasing demands for lightweight parts in various fields, such as bicycle, automotive, aircraft and aerospace industries, hydroforming processes have become popular in recent years. Since tubular materials during tube hydroforming are under a bi-axial even tri-axial stress state, which is different from that in the tensile test, it is necessary to test the mechanical properties of the material under bi-axial stress state. Tube bulging test is an advanced method for characterizing the mechanical properties of tubular materials under bi-axial stress state. But there are excessive physical quantities in the theoretical model of tube bulging test for testing the mechanical properties of tubes under bi-axial stress state which are difficult to be obtained during the experiment. In order to solve the problems, a method for directly testing the mechanical properties of tubes under bi-axial stress state was proposed in this work, which will be referred to as "one point method". Because of circular model is characterized by a dominant function expression, theoretical models of both the pole axial curvature radius and the pole thickness during bulging test are derived under supposing the geometrical models for bulging zone as circular. Thus, the mechanical properties of tubes under bi-axial stress state can be obtained only through measuring the bulging height at the pole point during the bulging test, which laid the foundation for the establishment of a simple and reliable method for testing the mechanical properties of the tube online. Based on the above proposed method, the extruded aluminum alloy tubes AA6061 were tested. The results showed that both the pole axial curvature radius and the pole thickness during bulging test can be expressed as display functions pertaining to the bulging height at the pole point. For the theoretical model of the pole axial curvature radius, as the bulging rate increases, the prediction accuracy increases at beginning, and decreases at the end when using circular as the theoretical geometrical models for bulging zone. The prediction accuracy is the highest as the bulging rate is about 13%, the prediction accuracy decreases after the bulging rate is more than 20%. Fortunately, the overall prediction error is small. The maximum error does not exceed ±0.9%. The prediction accuracy of the pole thickness using the theoretical model is almost unaffected by the specimen geometry. When the ratios of length to diameter and diameter to thickness change, the difference is very small, the prediction error is not more than 0.8%. This is very helpful to ensure the accuracy of mechanical testing under bi-axial loading conditions. Using the "one point method", the stress and strain components along the circumferential and axial directions can be simultaneously measured, this laid the foundation for further analysis of the anisotropic property impacting on the flow and subsequent yield under complex stress state.

Fund: Supported by National Natural Science Foundation of China (Nos.51405102 and 51475121), China Postdoctoral Science Foundation (No.2015M570286), Fundamental Research Funds for the Central Universities (No.HIT.NSRIF.2016093) and Scientific Research Foundation of Harbin Institute of Technology at Weihai (No.HIT(WH)201414)

Yanli LIN, Zhubin HE, Guannan CHU, Yongda YAN. A New Method for Directly Testing the Mechanical Properties of Anisotropic Materials in Bi-Axial Stress State by Tube Bulging Test. Acta Metall Sin, 2017, 53(9): 1101-1109.

Fig.1 Schematic of tube bulging test and the corresponding geometric parameters (r and z—two coordinate axes, L_{0}—length of bulging region, t_{0}—initial thickness of the tube, R_{0}—initial outer radius, h—bulging height of the middle point, R_{P}—outer radius of the middle point during bulging, t_{P}—real-time pole thickness, ρ_{z}_{P}—pole axial curvature radius, R_{d}—radius of the die)

Fig.2 Die-related arc profile model for tube bulging test (P—pole point of the tube, a—ordinate of the center of the bulging region circle)

Fig.3 Flow chart for testing flow stress-strain curve on line based on one point method

Fig.4 Photos of AA6061 aluminum tubes after bul-ging test with ratios of length-to-diameter λ=1.4 (a) and λ=1.8 (b)

Fig.5 Axial contour measuring of tested tubes(a) hoop cross section (b) schematic of contour measuring

Fig.6 Axial contour of AA6061 aluminum tubes after bulging test obtained by experiments and theoretical analysis with λ=1.4 (a) and λ=1.8 (b) (η—tube expansion, η=h/R_{0}100%)

Fig.7 Error analyses of tangency circle geometric model to fit the axial contour of AA6061 aluminum tubes in bulging test with λ=1.4 (a) and λ=1.8 (b)

λ=L_{0}/D_{0}

δ=D_{0}/t_{0}

D_{0} / mm

L_{0} / mm

t_{0} / mm

1.6

27.8

50

80

1.8

2.0

27.8

50

100

1.8

1.6

33.3

60

96

1.8

1.8

33.3

60

108

1.8

2.0

33.3

60

120

1.8

Table 1 Experimental schemes for tube bulging tests of AA6061 tubes

Fig.8 Experimental results of pole thickness and bulging height with different length-to-diameter ratios under D_{0}=60 mm and t_{0}=1.8 mm

Fig.9 Error analyses of pole thickness and bulging height with different length-to-diameter ratios under D_{0}=60 mm and t_{0}=1.8 mm

Fig.10 Experimental results of pole thickness and bulging height with different initial outer diameters under t_{0}=1.8 mm and λ=1.6 (a), λ=2.0 (b)

Fig.11 Error analyses of pole thickness and bulging height with different initial outer diameters under t_{0}=1.8 mm and λ=1.6 (a), λ=2.0 (b)

Fig.12 Bulging height at the middle point variation with the internal pressure (D_{0}=60 mm, t_{0}=1.8 mm, λ=1.6)

Fig.13 Flow stress-strain curve (D_{0}=60 mm, t_{0}=1.8 mm,λ=1.6)

Fig.14 Equivalent stress- strain curves of AA6061 tubes (D_{0}=60 mm, t_{0}=1.8 mm, λ=1.6)

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