J. Cent. South Univ. Technol. (2011) 18: 1813-1818

DOI: 10.1007/s11771-011-0907-z

Characteristics of thickness distribution of tailor-welded tube hydroforming

CHU Guan-nan(初冠南)^{1, 2}, LIU Gang(刘钢)³, YUAN Shi-jian(苑世剑)³, LIU Wen-jian(刘文剑)²

1. School of Naval Architecture, Harbin Institute of Technology at Weihai, Weihai 264209, China;

2. School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China;

3. State Key Laboratory of Advanced Welding Production Technology,

Harbin Institute of Technology, Harbin 150001, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2011

Abstract: Both experimental and mechanical analyses were carried out to investigate the characteristics of thickness distribution for tailor-welded tube (TWT) hydroforming with dissimilar thickness. Then, the effects of weld-seam position and thickness difference were also revealed. A multiple-diameter tube was formed to reveal the characteristics and the regularity of thickness distribution during TWT hydroforming. It is indicated that there are obvious fluctuations in thickness distribution though the TWTs have the same expansion ratio. The thinning ratio of thinner tube is bigger than that of thicker tube especially in the zone closed to the weld-seam. The difference in thinning ratio between two tube segments can reach 9%. Consequently, sudden and large fluctuation of thickness appears in the zone nearby the weld-seam. The difference in thinning ratio between thinner and thicker tubes enlarges as the thickness difference increases, but improves as length ratio increases. Different strain states are the main reason to induce nonuniform thickness distribution. The difference in thickness is the main reason to induce different strain states on thinner and thicker tubes.

Key words: tailor-welded tube; thickness distribution; hydroforming; weight reduction

1 Introduction

Tube hydroforming becomes more and more attractive in manufacturing of tubular components in aviation, astronavigation and automobile industries due to its advantages such as weight reduction and high utilization of strength and stiffness [1-3]. But there are some disadvantages on producing components with different cross-section perimeters, e.g. multiple-diameter tube. In such case, axial feeding is usually applied to improving the thickness uniformity of final component [4-5]. However, even though an optimal loading path was applied, an obviously uneven thickness appears along the axial direction of a tubular component due to friction effect and difference in expansion ratio [5-6].

Hydroforming of tailor-welded tube (TWT) with dissimilar thickness was therefore put forward to improve the thickness uniformity without complex feeding control [7]. It raises great advantages in simplifying the forming process. But, up to now, relative studies are still scarce.

During the hydroforming of TWT, the difference in thickness induces various stress states, so the evolution of plastic deformation is affected [8]. LIU et al [7] studied the effects of length ratio and thickness ratio on the expansion ratio of two segments through numerical simulation. Simulation results showed that the deformation uniformity would be better if the thickness ratio is less than 2.25. Then NATAL et al [9-10] further demonstrated that the weld-seam displacement and the difference in expansion ratio can be minimized by the optimizing length ratio. Their results could be better convinced if the results were verified through experiments. Some scholars [11-12] studied the weld seam movement during tailor welded tube hydroforming, and pointed out that weld-seam movement would induce nonuniformity thickness distribution. ZHANG et al [13] analyzed the effects of thickness difference on axial deformation of tailor welded tube. Their results indicated that TWT with optimal thickness ratio and the weld line position has better axial mechanical performance than the traditional thin walled tube, which is very important to crashworthiness design of tailor-welded energy absorbing structures. For structure components, uniformity of thickness is a key factor affecting its fatigue life. Among previous studies, the characteristics of TWT thickness distribution were not revealed and analyzed. At the same time, the regularity of weld-seam position and thickness difference are still unknown.

In order to reveal the thickness distribution regularity of TWT, experiment was carried out and the effects of length ratio and thickness ratio were also analyzed. At last, the main reason resulting in thickness fluctuation was given by mechanical analysis.

2 Experimental

The material of the parent tubes was OCr18NI9 stainless steel. The initial outer diameter was d40 mm. In order to avoid effects of anisotropic properties on experiments results, solid solution heat treatment was carried out for both tube segments before welding. The thinner and thicker tubes were welded together by argon-arc welding with argon shield through the whole process.

To facilitate strain and thickness comparison between thinner and thicker tubes, one multiple-diameter tube component was selected as shown in Fig.1(a), whose diameter and length were 52 mm and 180 mm respectively. By forming this component, the effects of weld-seam position and thickness difference on thickness distribution were studied. As shown in Fig.1(b), the tube ends were axially fixed by sealing punches to avoid being pulled into die cavity, which would affect the strain and thickness distribution.

Fig.1 Shape of multiple-diameter tube used in thickness distribution study (L_K: Length of thicker tube; L_N: Length of thinner tube): (a) Shape of multiple-diameter tube; (b) Schematic diagram of die set

During TWT hydroforming with dissimilar thickness, the location of weld-seam directly determines the ratio of the thicker tube length to whole TWT length (so called length ratio), which would induces effects on stress and strain states. Represented by η_l, length ratio can be calculated using equation η_l=L_K/L. TWTs with different length ratios were hydro-bulged to show the effect of length ratio on thickness distribution. The scheme of length ratio is listed in Table 1. The thicknesses of thinner and thicker tubes are 2.3 mm and 2.8 mm, respectively.

Table 1 Schemes of length ratio

Considering the formability decreases rapidly when thickness ratio η_t, which is the ratio of thicker tube thickness (t_K) to thinner tube thickness (t_N), is bigger than 2.25, three kinds of thickness ratios were designed to show the effect of thickness ratio on thickness distribution as listed in Table 2. The weld-seam was placed just right on the middle zone of TWT.

Table 2 Schemes of thickness ratio

3 Thickness distribution

3.1 Regularity of thickness distribution

Considering the different initial thicknesses of the two tube segments, it is indistinct if using the ultimate thickness dimension to compare the thickness variation between two tube segments. However, thinning ratio can help to overcome this difficulty and is effective to compare the thickness variation. Represented by δ, thinning ratio can be calculated using equation δ=Δt/t₀, where Δt is the variation in thickness, and t₀ is the initial thickness of the tube.

Illustrated by the case of TWT with η_l=0.5, η_t=1.6, thickness distribution along the axial direction is shown in Fig.2. It can be seen that the thinning ratio distribution is uneven, although the expansion ratio is the same everywhere and axial constrains are carried out. The average thinning ratio of the thinner tube is higher than that of the thicker tube. Along axial direction, thinning ratio is monotone increasing for thinner tube but monotone decreasing for the thicker tube. As a result, maximum thinning ratio appears on thinner tube near weld-seam. In contrast, minimum thinning ratio appears on thicker tube near weld-seam. The maximum and minimum thinning ratios are 30.5% and 23.1%, respectively. Consequently, sudden and large fluctuation of thickness is brought about in the zone nearby weld-seam.

Fig.2 Thickness distribution of tailor-welded tube with η_l=0.5, η_t=1.6 [14]: (a) Test sample; (b) Thickness distribution

3.2 Effect of length ratio

As shown in Fig.3, effects of length ratio on thickness distribution are illustrated. It can be seen that the thinning ratio increases as length ratio for the thinner tube increases, and the fluctuation range is from 3.2% to 2.5%. But the effect of length ratio is more complex on the thicker tube thickness distribution. With the length ratio increasing, thinning ratio of the thicker tube increases in the zone near weld-seam, but decreases in the zone far away from weld-seam. The fluctuation range of thinning ratio for four kinds of TWTs decreases from 2.5% to 1.2%.

It also can be seen from Fig.3 that the trend of thinning ratio evolution between thinner and thicker tubes is the same. As shown in Fig.4, thinning ratio increases as length ratio increases, and the increment is small. As a result, the difference of thinning ratio between thinner and thicker tubes keeps changeless. Consequently, it can be concluded that thickness distribution improves as length ratio increases.

3.3 Effect of thickness ratio

Figure 5 illustrates the effects of thickness ratio on thickness distribution. It can be seen that as difference in thickness increases, thinning ratio increases rapidly for the thinner tube, but decreases for the thicker tube. This trend is more remarkable for the zone near the weld-seam. As shown in Fig.5, the difference in thinning ratio is only 1% for the zone far from the weld-seam, but 4.5% for the zone near the weld-seam between the TWTs of η_t=1.2 and η_t=1.8. It also can be seen that just opposite trend of thinning ratio evolution between thinner and thicker tubes was obtained when thickness ratio increases, as shown in Fig.6. Thinning ratio difference between two tube segments increases as thickness ratio increases. The maximum difference in thinning ratio is 2.5% for the TWT with η_t=1.2, but increases to 9% when η_t=1.8. It can be concluded that the thickness distribution deteriorates as the thickness ratio increases.

Fig.3 Effect of weld-seam position on thickness distribution (η_t=1.6): (a) Multiple-diameter tubes; (b) Experimental results of thickness distribution

Fig.4 Effect of weld-seam position on peak value of thinning ratio (η_t=1.6)

Fig.5 Effect of thickness difference on thickness distribution (η_l=0.5): (a) Multiple-diameter tube; (b) Experimental results of thickness distribution
 

Fig.6 Effect of thickness difference on peak value of thinning ratio (η_l=0.5)

4 Mechanics of non-uniformity thickness distribution

4.1 Mechanical analysis

In terms of hydro-bulging a thin-wall tube, there is a free surface on the outer side of the tube so that stress state is usually dealt with as a plane stress by assuming the stress through thickness direction (σ_t) as zero. Assuming that σ_z is the stress along the axial direction, and σ_θ is the stress along the hoop direction of the tube, and then according to Von-Misses yield criterion, the yielding condition of the tube under plane-stress state could be described as an ellipse as shown in Fig.7. Based on the simulation results, the stress paths of the typical points N_i (i=1, 2, 3) and K_i (i=1, 2, 3) on thinner and thicker tubes, as shown in Fig.2, can be recorded in Fig.7 for TWT with η_l=0.5, η_t=1.6.

Fig.7 Yielding condition of tube under plane-stress state (η_l=0.5, η_t=1.6)
 

It can be seen that there are biaxial tensile stresses acting on both tube segments, but the stress paths locate in different zones of strain state. The stress paths of thinner tube locate in zone A (where, σ_z>σ_θ/2), with strain states of dε_θ>0 and dε_z>0. Therefore, the deformation pattern of the thinner tube is biaxial elongation along the axial and hoop directions.

Nevertheless, the stress paths of the thicker tube locate in zone B (where, σ_z<σ_θ/2), with strain states of dε_θ>0 and dε_z<0. Therefore, the deformation pattern of the thicker tube is single-axial elongation along the hoop direction.

It can be seen from Fig.7 that stress components of TWT have relationships as inequaiton (1) and inequation (2) all the way through the hydroforming process.

(i=1, 2, 3)                                (1)

(i=1, 2, 3)                                (2)

where  are hoop, axial and thickness stresses of the thinner tube, respectively;  and ? are hoop, axial and thickness stresses of the thicker tube, respectively.

Considering the initial strain is zero and the principal axial strain remains unchanged during the forming process, the relationship of the first, second and third principal strains can be derived as inequation (3) and inequaiton (4).

 (i=1, 2, 3)                                    (3)

 (i=1, 2, 3)                                        (4)

where  are hoop, axial and thickness strains of the thinner tube, respectively;   and  are hoop, axial and thickness strains of thicker tube, respectively.

From the consistent relationship between the stress and strain components [15], it can be derived that

 (i=1, 2, 3)                                                     (5)

 (i=1, 2, 3)                                                     (6)

Because the directions of principal axis of strain keep unvaried during hydroforming and the initial strain is zero, the following inequations are derived:

(i=1, 2, 3; j=1, 2, 3)                         (7)

According to the volume constancy, thickness strains of both thinner and thicker tubes can be described as follows:

 (i=1, 2, 3)                                   (8)

 (i=1, 2, 3)                                   (9)

Because the hoop strain of thinner and thicker tubes is equal,

 (i=1, 2, 3)                                                (10)

Combining inequation (7) and Eqs.(8)-(10), the following equation can be derived:

(i=1, 2, 3)                        (11)

Combining inequations (3), (4) and Eq.(11), the following inequation can be derived:

 (i=1, 2, 3; j=1, 2, 3)                           (12)

For the thinner tube, the thickness strain also can be described as:

 (i=1, 2, 3)                                    (13)

where t_N is the initial thickness of the thinner tube, and Δt_N is the thickness variation of the thinner tube.

For the same reason, thickness strain of the thicker tube also can be described as

                                                      (14)

where t_K is the initial thickness of the thicker tube, and Δt_K is the thickness variation of the thicker tube.

Combining Eqs.(13), (14) with inequation (12):

                                 (15)

The following equation can be derived:

                                                                 (16)

From inequation (16), it can be concluded that the thinning ratio of thinner tube is higher than that of thicker tube during hydroforming process.

4.2 Experiment results

Figure 8 shows the experimental results of the axial strain distribution after hydroforming. It can be seen that the axial strain of the thinner tube is higher than zero, i.e., ε_zN>0. The maximum axial strain appears in the zone near weld-seam, which is about 0.075. On the contrary, axial strain of the thicker tube is less than zero, i.e., ε_zK<0. In the zone adjacent to the weld-seam, the axial strain is obviously larger than other zones, and the maximum strain is about -0.039. The relation of the axial strain between thinner and thicker tubes is ε_zN>0>ε_zK. These results are also consistent with the mechanical analysis.

Fig.8 Axial strain distribution of tailor-welded tube: (a) η_t=1.6; (b) η_l=0.5

5 Conclusions

1) During TWT hydroforming, obvious fluctuation in thickness happens although every zone has the same expansion ratio. Thinning ratio of the thinner tube is higher than that of the thicker tube. Among the expansion zones, thinning ratio increases as approaching the weld-seam for thinner tube, but just contrary for thicker tube. Consequently, the maximum and minimum thinning ratios situate on both sides of the weld-seam respectively and induce sudden thickness fluctuation around the weld-seam.

2) Thinning ratio increases as length ratio increases for thinner tube, but decreases for thicker tube. When thickness ratio is 1.6, the fluctuation amplitude of thinning ratio reaches more than 9%. Thickness uniformity can be improved to some extend by increasing the proportion of thicker tube.

3) Different strain states appear on thinner and thicker tube all the way through the hydroforming process. Variant strain states are the main reason to induce thickness fluctuation. Thickness difference between two segments is the main reason to induce variant strain states.

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(Edited by HE Yun-bin)

Foundation item: Projects(51005054, 50575051) supported by the National Natural Science Foundation of China; Project(HIT.BRETI.2010010) supported by the Fundamental Research Funds for the Central Universities, China; Project(20100471025) supported by the National Science Foundation for Post-doctoral Scientists of China

Received date: 2010-10-26; Accepted date: 2011-02-20

Corresponding author: CHU Guan-nan, PhD; Tel: +86-631-5687830; E-mail: Amrrychu@gmail.com