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Abstract

In order to achieve the precision bending deformation, the effects of process parameters on springback behaviors should be clarified preliminarily. Taking the 21-6-9 high-strength stainless steel tube of 15.88 mm × 0.84 mm (outer diameter × wall thickness) as the objective, the multi-parameter sensitivity analysis and three-dimensional finite element numerical simulation are conducted to address the effects of process parameters on the springback behaviors in 21-6-9 high-strength stainless steel tube numerical control bending. The results show that (1) springback increases with the increasing of the clearance between tube and mandrel C_m, the friction coefficient between tube and mandrel f_m, the friction coefficient between tube and bending die f_b, or with the decreasing of the mandrel extension length e, while the springback first increases and then remains unchanged with the increasing of the clearance between tube and bending die C_b. (2) The sensitivity of springback radius to process parameters is larger than that of springback angle. And the sensitivity of springback to process parameters from high to low are e, C_b, C_m, f_b and f_m. (3) The variation rules of the cross section deformation after springback with different C_m, C_b, f_m, f_b and e are similar to that before springback. But under same process parameters, the relative difference of the most measurement section is more than 20% and some even more than 70% before and after springback, and a platform deforming characteristics of the cross section deformation is shown after springback.

Keywords

Springback 21-6-9 high-strength stainless steel tube numerical control bending sensitivity analysis finite element simulation cross section deformation

Introduction

High-strength 21-6-9 stainless steel (0Cr21Ni6Mn9N) bent tubes currently have been increasingly used in hydraulic, fuel, or oxygen transportation systems for advanced aircraft and spacecraft due to its excellent properties such as high strength, corrosion resistance and oxidation resistance.¹ Among various bending methods such as compress bending, stretch bending, roll bending and push bending, the numerical control (NC) bending, under multi-tool constraints as shown in Figure 1, is a feasible one for achieving stable and accurate bending of the high-strength stainless steel tube (HSSST). When the die is removed, the inevitable springback phenomenon occurs due to the extrados elongation and intrados compression deformation and even shows more significantly due to the high ratio of the yield strength to elastic modulus of the HSSST. The springback causes the decrease of the bending angle and the increase of bending radius and thus affects the connection and sealing performance of tubes with other parts as well as the internal structure compact. Since the springback closely relates to the bending history, and that is affected by process parameters. Therefore, in order to realize the effective control springback and the precision bending, the effects laws and degrees of the process parameters on springback in NC bending of 21-6-9 HSSST should be studied.

Figure 1.

Schematic diagram of NC tube bending.

Up to now, great efforts have been carried out on the springback prediction and control in tube bending using analytical, experimental and numerical methods, while most studies focused on Al-alloy, Ti-alloy and low-strength stainless steel tube. Few concerned the springback of the HSSST. Tang² used plastic deformation theory to calculate the stress distributions and the bending moment for springback calculation. Zhang³ derived an approximate calculation formula for springback angle and radius based on the analyses of stress and strain distribution in tube bending. Al-Qureshi and Russo⁴ deduced an analytical model for the prediction of the springback and residual stress distributions with assumptions of ideal elastic plastic material, plane strain condition, absence of defects and “Bauschinger effect.” E and Liu⁵ presented an analytical model in which time-dependent springback was associated with strain hardening for 1Cr18Ni9Ti stainless steel tube, and the formulae of time-dependent springback, time-independent springback and total springback were deduced using the model. By experiments, Wu et al.⁶ obtained the effects of the temperature, bending speed and grain size on the springback of the wrought magnesium alloy AM30 tubes during rotary draw bending. Li et al.⁷ experimentally studied the effects of forming parameters on springback of thin-walled 6061-T4 Al-alloy tubes in NC bending. Liu et al.⁸ investigated the effects of bending angle, relative bending radius, relative tube diameter and material properties on springback of 1Cr18Ni9Ti, LF6 and T2 tubes in NC bending by experiments.

By the numerical simulation of the whole process (bending tube, retracting mandrel and unloading) for thin-walled 1Cr18Ni9Ti tube,⁹ it was discovered that the total springback angle considering retracting mandrel was much smaller than that not considering retracting mandrel with maximum difference between them being 107.34%. Li et al.¹⁰ revealed the nonlinear springback characterization and behaviors of high strength Ti-3Al-2.5V tube by finite element (FE) analysis. Also by the FE analysis, the geometry-dependent springback behaviors of thin-walled Al-alloy 6061-T4 tube on rotary draw bending were revealed by Li et al.¹¹ Sözen et al.¹² addressed the springback phenomena of steel tube NC bending under the interactions between the geometrical and mechanical parameters and developed a surrogate model to predict fast the springback for a given combination of parameters. Using the numerical simulation, Zhan et al.¹³ investigated the springback mechanism for larger-diameter thin-walled CT20 Ti-alloy tube and proposed a two-level springback compensation method. Jiang et al.¹⁴ studied the coupling effects of material properties and bending angle on springback angle for medium-strength TA18 Ti-alloy tube NC bending based on explicit/implicit FE code of ABAQUS. Recently, Fang et al.¹⁵ achieved the effect rules of material parameters and geometry parameters on springback of 21-6-9 HSSST in NC bending. Zhang et al.¹⁶ analyzed the sensitivity of material parameters on springback of high strength TA18 tube in NC bending using the numerical simulation and the multi-parameters sensitivity analysis method.

In addition, in the aspect of sheet bending springback, Behrouzi et al.¹⁷ presented an analytical approach for springback analysis based on inverse algorithm, and the optimum die shape was obtained for producing the product in a few trials by inverse springback modeling. Lajarin and Marcondes¹⁸ investigated the influences of process and tool parameters on springback of high-strength steel and obtained the significant parameters from high to low were blank holder force, tool radius and friction condition. Choudhury and Ghomi¹⁹ studied the effects of 11 process parameters on springback of aluminum sheet in V-bending by Taguchi orthogonal array design and bending tests. The above results and methods provide beneficial information for springback prediction and control of 21-6-9 HSSST in NC bending.

In order to realize precision NC bending forming of HSSST, in this work, taking the 21-6-9 HSSST of 15.88 mm × 0.84 mm (outer diameter D × wall thickness t) as the objective, using the multi-parameter sensitivity analysis and FE numerical simulation method, the effects rules and the sensitivity degrees of process parameters on springback were studied, and the effects rules of the 21-6-9 HSSST springback on cross section deformation were further clarified.

Research methods

Description of multi-parameter sensitivity analysis method

Sensitivity analysis is a kind of the system analysis method as regards the stability of the system, which shows the trends and degrees of the system characteristics deviating from the benchmark status with the change of the influence factors. In actual system, decisions of the system characteristics for influence factors usually are different physical quantities, which have different units. Thus, the influence factors need to have a dimensionless processing. The relative errors δ_p and $δ_{a_{k}}$ of the system characteristics P = f(a_k) and the influence factors a_k (k = 1, 2,…, n) are defined as equation (1),²⁰ where n is the number of the influence factors

δ_{P} = \frac{| Δ P |}{P}, δ_{a_{k}} = \frac{| Δ a_{k} |}{a_{k}}

(1)

The ratio is defined as the sensitivity value S_k(a_k) of the influence factors a_k,, as shown in equation (2)

S_{k} (a_{k}) = (\frac{| Δ P |}{P}) / (\frac{| Δ a_{k} |}{a_{k}}) = | \frac{Δ P}{Δ a_{k}} | \frac{a_{k}}{P} (k = 1, 2, \dots, n)

(2)

When |Δa_k|/a_k, is in smaller case, S_k(a_k) can be approximate representation as equation (3)

S_{k} (a_{k}) = | \frac{d f_{k} (a_{k})}{d a_{k}} | \frac{a_{k}}{P} (k = 1, 2, \dots, n)

(3)

where S_k(a_k) (k = 1, 2,…, n) are a set of dimensionless non-negative real number, and the higher the value is, the more sensitivity the P to a_k, is. Thus, the sensitivity of P to a_k, can be obtained by comparing the values of S_k(a_k).

Modification of multi-parameter sensitivity analysis

In equation (3), the function relationship f(a_k) between P and a_k must be established before a sensitivity analysis. But not all the P of the research object and the a_k have a certain function relationship. While for the complex system, using numerical method expressed the relationship between the P and the a_k requires a large amount of data to ensure the fitting precision. Thus, equation (3) is modified, and the modified of the multi-parameter sensitivity analysis model is shown in equation (4), namely, every two adjacent fitting date will have a slope value between them, and finally, the average value of these slopes is taken as the sensitivity value

S_{k} (a_{k}) = | \frac{1}{m - 1} \sum_{i = 1}^{m - 1} (\frac{P_{k}^{i} - P_{k}^{i + 1}}{a_{k}^{i} - a_{k}^{i + 1}} \frac{a_{k}^{i + 1}}{P_{k}^{i + 1}}) | (i = 1, 2, \dots, m - 1; k = 1, 2, \dots, n)

(4)

where m is the number of the a_k under each process condition, $a_{k}^{i}$ is the value of the a_k under the i and $P_{k}^{i}$ is the system characteristics value corresponding to the $a_{k}^{i}$ .

For the sensitivity analysis of 21-6-9 HSSST NC bending springback process, the system characteristics P refer to the springback angle Δθ = θ − θ′ and springback radius ΔR = R′ − R (shown in Figure 2), and the influence factors a_k (k = 1, 2,…, n) refer to the process parameters including the clearance between tube and bending die C_b, the clearance between tube and mandrel C_m, the friction coefficient between tube and bending die f_b, the friction coefficient between tube and mandrel f_m and the mandrel extension length e. Because of the influence factors of the HSSST NC bending springback process were so many, and the influences rules were complex, therefore, the FE model was established as a system model under ABAQUS platform, and all of the analysis was carried out by the FE simulation.

Figure 2.

Schematic of tube springback after bending deformation.

Explicit/implicit three-dimensional FE model of the whole NC bending process for HSSST and its validation

According to the actual tube NC bending process, an elastic plastic three-dimensional finite element (3D-FE) model of the whole NC bending process including bending tube, retracting mandrel and unloading is established under ABAQUS platform as shown in Figure 3. The detailed solutions involved in FE modeling can be found in the literature.^21,22 The explicit algorithm was employed for solving the bending tube and retracting mandrel process, while the implicit one was used for unloading computation. The results from bending tube and retracting mandrel simulation in ABAQUS/Explicit were directly imported into ABAQUS/Standard. The geometrical nonlinearity was included, and the specified damping factor was used to stabilize implicit iteration procedure in springback analysis. Double precision was employed for the bending process and the single precision for the springback analysis. The mass scaling factor of 2000 was utilized to improve the computation cost with neglected inertia effect using the convergence analysis in bending simulation.

Figure 3.

Explicit/implicit elastic plastic 3D-FE model of the whole NC bending process for 21-6-9 HSSST.

The tube was discretized by four-node doubly curved thin shell element S4R, while four-node bilinear quadrilateral rigid element R3D4 was used to model the relative rigid dies. Different mesh density was used to the tube and die surfaces with the element size of 1.5 mm × 1.5 mm and 2 mm × 2 mm, respectively. The mechanical properties of the 21-6-9 HSSST (shown in Table 1) were obtained by the uniaxial tension test according to the GB/T228-2002, in which a piece of complete tube specimen was directly cut from the raw tube by the wire cut. And the Ludwigson model $\bar{σ} = K {\bar{ε}}^{n} + Δ$ ( $Δ = \exp (K_{1} + n_{1} \bar{ε})$ ) was used to describe the strain hardening characteristics of tube material.²³ The classical coulomb friction model was used to represent the friction behavior between tube and dies, and the friction coefficients in various contact interfaces were employed for the results of the twist compression test in the literature,²⁴ as shown in Table 2.

Table 1.

Mechanical properties of 21-6-9 HSSST.

Material parameters	Value
Elastic modulus E (GPa)	193
Initial yield strength σ_0.2 (MPa)	994
Ultimate strength σ_b (MPa)	1324
Fracture elongation δ (%)	22
Strength coefficient K (MPa)	1796.5
Hardening exponent n	0.177
Poisson’s ratio ν	0.29
Material constant K₁	5.7
Material constant n₁	−27.4

Table 2.

Friction coefficients in various contact interfaces.

	Contact interface	Friction coefficients
1	Tube/bending die	0.1
2	Tube/pressure die	0.25
3	Tube/clamp die	Rough
4	Tube/mandrel	0.05
5	Tube/wiper die	0.05

Rough means no relative slip between tube and clamp die.

The boundary constraints were applied by two approaches to realize the actual NC bending process: “displacement/rotation” and “velocity/angular velocity”. Both bending die and clamp die were constrained to rotate about the global Z-axis simultaneously; pressure die was constrained to translate only along the global X-axis with the same linear speed as the centerline bending speed of bending die; wiper die was constrained along all degrees of freedom; the mandrel was fixed from all degrees of freedom during bending process, while the mandrel was retracted along the global X-axis after the bending process finished. The smooth step amplitude curves were used to define the smooth loading of the bending die, clamp die, pressure die and mandrel to ensure little inertial effects in explicit FE simulation of the quasi-static process. For the unloading process, all dies were removed and a fixed boundary condition was applied to avoid the rigid motion as shown in Figure 3.

In order to validate the reliability of the FE model, the experiments were carried out by the NC tube bender SB-12 × 3A-2S as shown in Figure 4. The experimental conditions are as follows: the specification of 6.35 mm × 0.41 mm (outer diameter D × wall thickness t) for 21-6-9 HSSST; the bending speed ω is 0.4 rad/s; the push assistant speed of pressure die V_p is 8 mm/s; the bending radius R is 20 mm; the bending angle θ are 30°, 60°, 90°, 120°, 150°, and 180°, respectively; and the dry friction condition is used to the contact interfaces.

Figure 4.

Illustration of NC tube bender SB-12 × 3A-2S.

Figure 5 shows the comparison between experimental results and simulation results. As shown in Figure 5(a), it is found that the FE simulation for springback angles agrees with the experimental results with the maximum relative error of 15.5%. Besides the direct comparisons, the validation of the FE model is also carried out for the cross section deformation degree ΔD,²² as shown in Figure 5(b). The comparisons show that the FE prediction can capture the bending deformation precisely with the maximum relative error less than 7%, which is the basic for reliable prediction of the springback. Thus, the FE model is reliable, which can be used to study the springback law of 21-6-9 HSSST in NC bending.

Figure 5.

Comparison of simulation results and experimental results: (a) springback angle and (b) cross section deformation degree.

Results and discussion

Research procedure

Taking the specification 15.88 mm × 0.84 mm of 21-6-9 HSSST as the objective, the fluctuation ranges of process parameters are used as shown in Table 3 according to the actual situation. The study on the effects rules of process parameters on springback and springback on cross section deformation was carried out. The bending radius R is 47.64 mm, the bending angle θ is 180°, the bending speed ω is 0.4 rad/s, the push assistant speed of pressure die V_p is 19.056 mm/s, the clearance between tube and clamp die is 0 mm, the clearance between tube and mandrel is 0.05 mm, the clearance between tube and other dies is 0.1 mm, the mandrel extension length is 3.5 mm, and the friction coefficients in various contact interfaces are listed in Table 2.

Table 3.

Range of process parameters for analysis.

Process parameters	Fluctuation ranges
Clearance between tube and mandrel C_m (mm)	0.05	0.1	0.2	0.25	0.3
Clearance between tube and bending die C_b (mm)	0.1	0.2	0.25	0.3	0.35
Friction coefficient between tube and mandrel f_m	0.05	0.1	0.2	0.3	0.4
Friction coefficient between tube and bending die f_b	0.05	0.1	0.2	0.3	0.4
Mandrel extension length e (mm)	0	1	2	3.5	5

Value in bold fonts is taken as the standard bending condition.

Effects of process parameters on springback

Figure 6 shows the effects of process parameters on springback of 21-6-9 HSSST in NC bending. As shown in Figure 6(a), with the increasing of the clearance between tube and mandrel C_m, the trends of both springback angle and springback radius increase on the whole. The results are similar to the analysis results of the thin-walled 6061-T4 Al-alloy tube⁷ and the thin-walled 1Cr18Ni9Ti stainless steel tube.²⁵ The reasons are that first, the larger C_m makes the axial tensile force acting on the tube decrease, and then the bending moment increases since the neutral layer shifts toward outside of the bending center. Second, the larger C_m is, the larger cross section deformation (shown in Figure 10(a)), which leads to the bending stiffness decreases. All above reasons make the springback increase.

Figure 6.

Effects of process parameters on springback: (a) C_m, (b) C_b, (c) f_m, (d) f_b and (e) e.

Figure 6(b) shows the springback angle and radius first increase and then remain little changed with the increasing of the clearance between tube and bending die C_b, which is according with the results of the thick-walled medium strength TA18 tube.²⁶ This is because that when the C_b is less than 0.25 mm, the cross section deformation degree increases with the increasing of the C_b as shown in Figure 10(b), then the bending stiffness decreases, and as a result the springback increases. While when the C_b is larger than 0.25 mm, the deformation degree variation is not obvious with the increasing of the C_b. Figure 7 shows that the maximum tangent compressive stress first decreases and then the variation is not obvious with the increasing of the C_b, which further proves the above results.

Figure 7.

Effects of C_b on maximum tangent compressive stress.

Figure 6(c) shows the springback angle and radius increase with the increasing of the friction coefficient between tube and mandrel f_m. The main reasons are that first, the axial tensile force increases with the increasing of the f_m, and then the bending moment decreases, which leads to reduce the springback; second, the wrinkling wave degree η²² increases with the increasing of the f_m as shown in Figure 8, and the wrinkling occurs near clamp side with larger the f_m, which leads to the springback increase significantly.²⁴ Thus, the synthetic action of the both makes the springback increase.

Figure 8.

Effects of f_m on wrinkling wave degree η.

Figure 6(d) shows the effects of the friction coefficient between tube and bending die f_b on springback angle and radius. It is found that the springback angle and radius increase linearly with the increasing of the f_b, which is in line with the analysis results of the thick-walled medium strength TA18 tube.²⁶ This is because that the larger the f_b, the smaller the tube bending deformation force, namely, the axial tensile force decreases and the bending moment increases with the increasing of the f_b, which leads to the springback increase.

Figure 6(e) shows the effects of the mandrel extension length e on springback angle and radius. It is discovered that the springback angle and radius decrease with the increasing of the e. The results are similar to that of the thin-walled 6061-T4 Al-alloy tube,⁷ but different form that of the thin-walled 1Cr18Ni9Ti stainless steel tube.²⁵ These are because that first, the axial tensile force increases with the increasing of the e, and then the bending moment decreases, which causes the springback angle and radius decrease. Second, the cross section deformation decreases with the increasing of the e as shown in Figure 10(e), and then the corresponding bending stiffness increases, which leads to the springback decrease.

Sensitivity analysis for springback

The sensitivity values S_k(a_k) of springback angle Δθ and springback radius ΔR are calculated using equation (4), as shown in Table 4. In order to get a more direct analysis, the sensitivity values in Table 4 are further shown in Figure 9.

Table 4.

Sensitivity values of different process parameters.

P	S (C_m)	S (C_b)	S (f_m)	S (f_b)	S (e)
Δθ	0.2181	0.2397	0.0941	0.1735	0.4110
ΔR	0.3490	0.3336	0.1514	0.3233	0.6978

Figure 9.

Sensitivity comparison between springback angle and springback radius to process parameters.

Figure 9 shows the sensitivity comparison between springback angle and springback radius to the process parameters. It is found that the sensitivity of springback radius to the process parameters is larger than that of springback angle for 21-6-9 HSSST in NC bending process. The most sensitive process parameter for springback of 21-6-9 HSSST in NC bending is the mandrel extension length e, the next are the clearance between tube and bending die C_b, the clearance between tube and mandrel C_m and the friction coefficient between tube and bending die f_b, while the friction coefficient between tube and mandrel f_m is the least one for springback. The reason is that the maximum range of the effect of e on springback angel/radius is (4.55°–7.70°)/(0.73–1.67 mm), and the maximum range difference value is 3.15°/0.94 mm, while that of f_m is (6.27°–7.36°)/(1.16–1.46 mm), and the maximum range difference value is 1.09°/0.3 mm, the others are between the e and the f_m as shown in Figure 6; therefore, the e exhibits the highest sensitivity to the springback behavior while the f_m shows the lowest one.

Effect of springback on cross section deformation

Figure 10(a) shows the effect of springback on cross section deformation with different clearances between tube and mandrel C_m. It is found that the cross section deformation degree increases with the increasing of the C_m before and after springback. The tendency of the cross section deformation is changed under the same C_m before and after springback, and the cross section deformation appears a platform deforming characteristics after springback in middle zone. On the numerical value, the difference of the cross section deformation degree is very significantly under the same C_m before and after springback. It is known that the cross section deformation is induced by the resultant force of the axial tensile force in the outer tube. During the unloading, the axial tensile force is released sharply and thus the cross section deformation degree can be relieved. The calculation shows that the relative difference except a few points is within 30% before and after springback, while that of the most measurement section is more than 50% and some even more than 70%, namely, the springback has a great influence on the cross section deformation under different C_m.

Figure 10.

Effect of springback on cross section deformation with different process parameters: (a) C_m, (b) C_b, (c) f_m, (d) f_b and (e) e.

Figure 10(b) shows the effect of springback on cross section deformation with different clearances between tube and bending die C_b. It is found that the cross section deformation degree increases with the increasing of the C_b before springback, while the variation of the C_b hardly affects the cross section deformation degree after springback. There is an obvious alleviation of the cross section deformation after springback and a platform deforming characteristics of cross section deformation is also shown after springback. The calculation shows that the cross section deformation degree after springback decreases 25% more than that before springback for all case with different C_b, and the relative difference of the most measurement section is more than 50%, namely, the springback also has a great influence on the cross section deformation under different C_b.

Figure 10(c) shows the effect of springback on cross section deformation with different friction coefficients between tube and mandrel f_m. It is found that the cross section deformation degree increases with the increasing of the f_m before and after springback, and the variation tendency of the cross section deformation after springback is similar to that before springback under the same f_m, while the value of the cross section deformation degree is reduced after springback. The relative difference of the cross section deformation degree is more than 20% with different f_m before and after springback, and that of most measurement section is more than 30%, namely, the springback also has a great influence on the cross section deformation under different f_m.

Figure 10(d) shows the effect of springback on cross section deformation with different friction coefficients between tube and bending die f_b. It is found that the cross section deformation decreases with the increasing of the f_b before and after springback, but is not obvious. The tendency of the cross section deformation is changed after springback on the same f_b, and a platform deforming characteristics is also appeared after springback. The springback of the cross section deformation is more serious near the pressure die end. The calculation shows that the relative difference of the cross section deformation is more than 25% for all case with different f_b before and after springback, and that of most measurement section is more than 40%. Namely, the springback has a significant impact on the cross section deformation under different f_b.

Figure 10(e) shows the effect of springback on cross section deformation with different mandrel extension length e. It is found that the cross section deformation degree decreases with the increasing of the e before and after springback. The variation tendency of cross section deformation after springback is similar to that before springback under the same e, while the cross section deformation degree decreases after springback. The cross section deformation degree decreases 20% more than that before springback for the most measurement section with different e. Namely, the springback also has a significant impact on the cross section deformation under different e.

Conclusion

Springback increases with the increasing of the clearance between tube and mandrel, the friction coefficient between tube and mandrel, the friction coefficient between tube and bending die, or with the decreasing of the mandrel extension length, while the springback first increases and then remains little changed with the increasing of the clearance between tube and bending die.

The sensitivity of springback radius to process parameters is larger than that of springback angle for 21-6-9 HSSST in NC bending. And the sensitivity of springback to process parameters from high to low are the mandrel extension length, the clearance between tube and bending die, the clearance between tube and mandrel, the friction coefficient between tube and bending die and the friction coefficient between tube and mandrel.

The variation rules of the cross section deformation after springback with different clearance between tube and mandrel, clearance between tube and bending die, friction coefficient between tube and mandrel, friction coefficient between tube and bending die and mandrel extension length are similar to that before springback. But under same process parameters, the relative difference of the most measurement section is more than 20% and some even more than 70% before and after springback, and a platform deforming characteristics of the cross section deformation is shown after springback.

Footnotes

Acknowledgements

The authors would like to thank the National Natural Science Foundation of China (No. 51164030) and the Key Project of Natural Science Research of Jiangxi Science & Technology Normal University (No. 300098010501) for the support given to this research.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

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Jiang

ZQ.

Deformation laws of medium-strength titanium alloy thick-walled tubes in NC bending processes. PhD Thesis, Northwestern Polytechnical University, Xi’an, China, 2010.

Springback law of high-strength 21-6-9 stainless steel tube in numerical control bending under different process parameters

Abstract

Keywords

Introduction

Research methods

Description of multi-parameter sensitivity analysis method

Modification of multi-parameter sensitivity analysis

Explicit/implicit three-dimensional FE model of the whole NC bending process for HSSST and its validation

Results and discussion

Research procedure

Effects of process parameters on springback

Sensitivity analysis for springback

Effect of springback on cross section deformation

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

References