- Email: [email protected]
On twist springback of a curved channel with pre-strain effect
International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
Contents lists available at ScienceDirect
International Journal of Lightweight Materials and Manufacture journal homepage: https://www.sciencedirect.com/journal/ international-journal-of-lightweight-materials-and-manufacture
Original Article
On twist springback of a curved channel with pre-strain effect Juan Liao*, Shanshan Chen, Xin Xue, Hongliang Xiang School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, 350116, Fujian, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 July 2019 Received in revised form 14 August 2019 Accepted 15 August 2019 Available online xxx
In the field of automotive lightweight manufacturing, the advanced high-strength steel (AHSS) sheet gets a pivotal position owing to a good match between the plasticity and superior strength. However, in the complex multi-step loadings, the twist springback phenomenon generated by irregular and curved stampings has arisen great concerns. In this article, the material DP500 is adopted for the twist springback analysis in a two-step loading experiment. First, the large bone-shaped specimen is deformed to 4% strain along the rolling direction. Subsequently, the forming blank, cut from the large specimen at different directions, is stamped in a die to form a 3D curved channel. Meanwhile, the simulation analysis of the two-step loading procedure is built for twist springback prediction. An advanced distortional hardening model incorporated with an attenuated modulus model is applied for exactly capturing the deformation features under mutative strain path. A deep analysis with regard to the residual stress and elastic modulus distribution is conducted to evaluate the pre-strain's influence on the twist springback of this curved part. The result shows that mutative strain path induced by the change of the pre-strain axis has a significant impact on the twist springback. © 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
Keywords: Twist DP steel Multi-step loading Strain path change
1. Introduction Advanced high-strength steel sheet (AHSS) gets the wideranging tendency in automotive industry and it is committed to the environmental protection strategies due to its good plasticity and weight reduction. At the same time, the higher elastic recovery phenomenon of the high-strength steel compared with traditional materials has also attracted people's attention. Especially the twist springback phenomenon, generated by non-proportional loading, poses a challenge to the research work. The elastic modulus is a significant factor affecting the springback, which has been addressed in many studies of twodimensional springback issues. A more accurate springback prediction can be obtained by taking into account attenuated elastic modulus models, in which the elastic modulus would gradually decrease when the plastic strain increases. This decrease, addressed in many literatures, could result in a greater springback. The Chord model was universally applied in the simulations in terms of
springback prediction [1e3]. This elastic model improved springback simulation results significantly compared with the constant elastic modulus, and it gets a more consistent trend with the experimental data. In the benchmark 4 of the international conference NUMISHEET 2011 [4], the springback problems on U-shaped parts under the prestrain are proposed. Since then, many scholars have studied the springback problems with pre-strain effect. Multi-step loading method might generate a larger springback phenomenon in consequence of the non-linear strain path. The difference of the stress distribution induced by different loading modes is also the trigger of the twist springback, which is also the core of this work. For the purpose of characterizing the twist springback phenomenon in channel-type products, an asymmetric deep drawing experimental device of a curved channel is designed. The impact of pre-strain that acts on the twist springback is discussed, and how it influences the strain path as well as the elastic modulus is also deeply analysed. 2. Main contents
* Corresponding author. E-mail addresses: [email protected] (J. Liao), [email protected] (S. Chen), [email protected] (X. Xue), [email protected] (H. Xiang). Peer review under responsibility of Editorial Board of International Journal of Lightweight Materials and Manufacture.
In this work, the 0.8 mm thick steel sheet, DP500, is adopted to analyse the twist springback under the pre-strain effect. First, the pre-strain test of the large specimen is performed with alarge universal testing equipment (Fig. 1a). The geometry of the large
https://doi.org/10.1016/j.ijlmm.2019.08.006 2588-8404/© 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: J. Liao et al., On twist springback of a curved channel with pre-strain effect, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.08.006
2
J. Liao et al. / International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
Fig. 1. Experimental device and drawn parts: (a) the tensile testing machine and the strain ε1 distribution after the pre-strain; (b) the forming tool; (c) the formed parts.
specimen is optimized to ensure that the strain in the middle part is uniform [5]. Second, the curved channel forming experiment is conducted on the blank cut from the large specimen. The forming tool maintains a blank holding force of 144 kN by means of the gas spring, which is shown in Fig. 1b. In the light of the included angle between the guide axis of the channel and the direction that the pre-strain is applied, the curved channels are divided into channel (L) and channel (T) (the ‘L’ and ‘T’ respectively denote the ‘longitudinal’ and ‘transverse’ direction to distinguish the channels) that represents the angle is 0 and 90 , respectively. The final drawn parts are shown in Fig. 1c. For a better understanding of the forming methods pertaining to the channels (L and T), the schematic forming process is illustrated in Fig. 2. One of the key factors, causing the phenomenon of twist springback in the intricate multi-stage stampings, is significant changes of the strain path. Previous research work has proved that the combination of the attenuated modulus algorithm and the anisotropic hardening models can significantly improve the accuracy of the springback prediction [6]. For the purpose of better capturing the material behaviours under complex path changes, an advanced distortional hardening (i.e. HAH) model, incorporated with the anisotropic yield criterion Yld2000-2d, is selected in this work to describe characteristic of the material. At the same time, the non-linear Chord model is applied to describe a declining tendency of elastic modulus. It can be expressed by:
Echord ¼ E0 ðE0 Ea Þ 1 exp xεp
(1)
The HAH model, brought forth by Barlat et al. [7], is employed in exquisitely capturing the characteristics of materials under complex paths by the distortion of the yield surface. It can be represented in the following equation:
sðsÞ ¼ fq þ fqh
1 q
¼
The yield equation sðsÞ consists of a stable equation f and a floating equation fh . The q is the constant exponent of the material, b is a microscopic tensor in order f1 and f2 are the state variable. The h to record the history of deformation path. The dislocation densitybased hardening algorithm, containing the evolution equation of dislocation density, can reproduce the hardening stagnation feature during the load reversal [8]. It is merged into the HAH model. All the parameters in regard to the above mentioned models are presented in Table 1. 3. Results and discussions Fig. 3a shows the progressively attenuation trend of elastic modulus, which eventually stabilizes with the plastic strain increases. In the case of 4% true strain, the elastic modulus has already reduced to 162 MPa. For the sake of better representing the elastic modulus distribution among the channels, the elements, selected in different locations of the channel, are analysed and marked as E1, E2…10. It is found that the elastic modulus distribution in formed channels is distinguished. The channel without pre-strain has the larger elastic modulus than that with pre-strain. Especially, the channel (L) has the uneven distribution of elastic modulus that can be reflected by E3, E4, E5 apparently. In terms of the twist springback of the channels based on experimental results (Exp.), the relative twist angle calculated by the principal axis of inertia [6] of the representative cross sections is shown in Fig. 3b, which is served as a way to evaluate the twist springback. It can be found that there is more obvious twist springback phenomenon for channel (L). For the purpose of further probing into the mechanism resulting in twist springback phenomenon, the simulation software ABAQUS, embedded in the subroutines with the above mentioned models, is
(qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q )1 q q b b : sj q þ f q h b : sj q ¼ sðεÞ b : s þ jh : s jh fðs0 Þ2 þ fðs00 Þ2 þ f 1 h 2
(2)
Please cite this article as: J. Liao et al., On twist springback of a curved channel with pre-strain effect, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.08.006
J. Liao et al. / International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
3
Fig. 2. Diagrammatic sketch of two-step loading process of channel (L) and channel (T): the guide axis of formed channel is (a) in the rolling direction and (b) vertical to the rolling direction.
Table 1 Material constitutive coefficients of the DP500 used for constitutive model. Chord model
E0 198
x
Ea 161
92.4
Yld2000-2d
a
a1
a2
a3
a4
a5
a6
a7
a8
HAH
6 q 2
Dislocation density-based model
a
0.90 k 14 m (GPa) 80
1.06 k1 90 b (nm) 0.25
1.03 k2 33.4 t0 (MPa) 121
0.98 k3 0.48 M 3.1
0.96 k4 0.92 K 148
0.74 k5 5 D (mm) 20
0.95 ks 179 F 3.5
1.06 s 0.83 P 0.8
0.5
Fig. 3. (a) The fitting curve of DP500 elastic modulus with Chord model and the elastic modulus distribution in formed channels; (b) The relative twist angles of different channels.
applied to analyse stress conditions of the channels. It is found from the stress nephogram of channel (L) that the stress (s22) in the straight side wall is very inhomogeneous. One element (shows in Fig. 4) is selected in straight side wall to analyse the strain path change from pre-strain to forming process. It could be seen that strain path of channel (L) exhibits cross-loading phenomenon under the two-step loading transition. And the stress s22 in central regions of the channel (L) is 182 MPa that is obviously lower than the channel (T). In curved sidewall, the wide and the narrow side with different stress s11, the former performs as stretching and the latter one is compression. The representative element which selected in curved sidewall is shown in Fig. 5a. Obviously, the channel (L) has the larger stress s11 than channel (T) whether it
is in wide side or in narrow side, which is one of the causes that generate a more drastic twist springback feature of the channel (L) than the one (T). The traced historical values of the element which are compared between channel (L) and channel (T) is shown in Fig. 5a. According to the deformation analysis associated with in-plane stress distribution, the asymmetric longitudinal in-plane stress on the curved transition flange and sidewall is the main source of twist springback occurrence. Thus, an alternative method to reduce or eliminate springback is to use partial draw bead design for Pchannel. This method may be efficient to balance the in-plane stress distribution and reduce springback for the studied case. The work further aims at evaluating the accuracy of the simulated models for the twist springback prediction. The relative twist
Please cite this article as: J. Liao et al., On twist springback of a curved channel with pre-strain effect, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.08.006
4
J. Liao et al. / International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
Fig. 4. Stress distribution s22 in straight sidewall.
Fig. 5. (a) Stress distribution s11 in curved sidewall; (b) Comparison of the different elastic models based on relative twist angles.
angles, used to compare the extent of twist springback, are calculated for channels based on different elastic models, as shown in Fig. 5b. The equation characterizing the average error is also shown in Fig. 5b, in which the Dgi is on behalf of the relative twist angle of 0 the experimental channel, and Dgi is the simulated one. It is found that the HAH model incorporated with the attenuated model (varied E) can capture the twist springback phenomenon better than that of the constant elastic modulus (E0). The average error (marked in ‘Ae’) of the channel (L) is 12%, and the channel (T) is 15%. The simulation based on constant elastic modulus (E0) predicts a lower value of the twist springback universally. It probably ascribes to the overvaluation of elastic modulus of the sheet with pre-strain. The maximum Ae of twist springback prediction is the channel (L) predicted by model (E0), of which the relative twist angle reaches 2 at section 5. It is probably due to the omission of the uneven elastic modulus on the different positions in channel (L) after suffering the intricate strain paths. 4. Conclusions Aiming at addressing the twist springback problems in twostage loading, a large bone-shaped sheet is pre-strained first and
then deformed in a curved channel tool. The main conclusions are drawn as follows: (1) The direction of pre-strain is an important factor that significantly affects the twist springback of the formed channel. If the guide axis of forming channel is consistent with the pre-strain axis, strain path changes, e.g. cross loading condition, will occur, which will generate uneven sidewall stress distribution. It is one of the reasons resulting in the more severe twist springback; (2) The Chord model embedded with the enhanced HAH model and anisotropic yield criterion Yld2000-2d, which can well describe the non-linear elasto-plastic behaviour of materials under complex strain paths, has a better prediction on twist springback of the channel with prestrain effect; (3) The deformation analysis associated with in-plane stress distribution indicates that the asymmetric longitudinal inplane stress field on the curved transition flange and sidewall may be the source of twist springback occurrence. The control strategy to balance the corresponding in-plane stress distribution for the minimization of twist
Please cite this article as: J. Liao et al., On twist springback of a curved channel with pre-strain effect, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.08.006
J. Liao et al. / International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
springback, e.g., tool design related to additional geometric stiffener, will be addressed in terms of individual forming case in the future work.
Conflict of interest The authors declared that they have no conflicts of interest to this work.
Acknowledgement The financial supports from the National Natural Science Foundation of China (NO.51805087), the Natural Science Foundation of Fujian Province of China (NO.2018J01761) and the Major Science and Technology Project in Fujian Province (NO.2017HZ0001-2) are greatly appreciated.
5
References [1] F. Yoshida, T. Uemori, K. Fujiwara, Elasticeplastic behavior of steel sheets under inplane cyclic tensionecompression at large strain, Int. J. Plast. 18 (2002) 633e659. [2] A. Zajkani, H. Hajbarati, Investigation of the variable elastic unloading modulus coupled with nonlinear kinematic hardening in springback measuring of advanced high-strength steel in u-shaped process, J. Manuf. Process. 25 (2017) 391e401. [3] X. Xue, J. Liao, G. Vincze, A.B. Pereira, F. Barlat, Experimental assessment of nonlinear elastic behaviour of dual-phase steels and application to springback prediction, Int. J. Mech. Sci. 117 (2016) 1e15. [4] K. Chung, T. Kuwabara, R.K. Verma, T. Park, H. Huh, G. Bae, BM4: Pre-strain Effect of Spring-Back of 2-D Draw Bending, the NUMISHEET 2011 Benchmark Study of the 8th International Conference and Workshop on Numerical Simulation of 3D Metal Forming Processes, Seoul, Korea, 2011, pp. 171e208. [5] S.B. Zaman, F. Barlat, J.H. Kim, Deformation-induced anisotropy of uniaxially prestrained steel sheets, Int. J. Solids Struct. 134 (2017) 20e29. [6] J. Liao, X. Xue, M.G. Lee, F. Barlat, G. Vincze, A.B. Pereira, Constitutive modeling for path-dependent behavior and its influence on twist springback, Int. J. Plast. 93 (2017a) 64e88. [7] F. Barlat, G. Vincze, J.J. Gracio, M.G. Lee, E.M. Rauch, C.N. Tome, Enhancements of homogenous anisotropic hardening model and application to mild and dualphase steels, Int. J. Plast. 58 (2014) 201e218. [8] E.F. Rauch, J.J. Gracio, F. Barlat, Work-hardening model for polycrystalline metals under strain reversal at large strains, Acta Mater. 33 (2007) 2939e2948.
Please cite this article as: J. Liao et al., On twist springback of a curved channel with pre-strain effect, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.08.006
Contents lists available at ScienceDirect
International Journal of Lightweight Materials and Manufacture journal homepage: https://www.sciencedirect.com/journal/ international-journal-of-lightweight-materials-and-manufacture
Original Article
On twist springback of a curved channel with pre-strain effect Juan Liao*, Shanshan Chen, Xin Xue, Hongliang Xiang School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, 350116, Fujian, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 July 2019 Received in revised form 14 August 2019 Accepted 15 August 2019 Available online xxx
In the field of automotive lightweight manufacturing, the advanced high-strength steel (AHSS) sheet gets a pivotal position owing to a good match between the plasticity and superior strength. However, in the complex multi-step loadings, the twist springback phenomenon generated by irregular and curved stampings has arisen great concerns. In this article, the material DP500 is adopted for the twist springback analysis in a two-step loading experiment. First, the large bone-shaped specimen is deformed to 4% strain along the rolling direction. Subsequently, the forming blank, cut from the large specimen at different directions, is stamped in a die to form a 3D curved channel. Meanwhile, the simulation analysis of the two-step loading procedure is built for twist springback prediction. An advanced distortional hardening model incorporated with an attenuated modulus model is applied for exactly capturing the deformation features under mutative strain path. A deep analysis with regard to the residual stress and elastic modulus distribution is conducted to evaluate the pre-strain's influence on the twist springback of this curved part. The result shows that mutative strain path induced by the change of the pre-strain axis has a significant impact on the twist springback. © 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
Keywords: Twist DP steel Multi-step loading Strain path change
1. Introduction Advanced high-strength steel sheet (AHSS) gets the wideranging tendency in automotive industry and it is committed to the environmental protection strategies due to its good plasticity and weight reduction. At the same time, the higher elastic recovery phenomenon of the high-strength steel compared with traditional materials has also attracted people's attention. Especially the twist springback phenomenon, generated by non-proportional loading, poses a challenge to the research work. The elastic modulus is a significant factor affecting the springback, which has been addressed in many studies of twodimensional springback issues. A more accurate springback prediction can be obtained by taking into account attenuated elastic modulus models, in which the elastic modulus would gradually decrease when the plastic strain increases. This decrease, addressed in many literatures, could result in a greater springback. The Chord model was universally applied in the simulations in terms of
springback prediction [1e3]. This elastic model improved springback simulation results significantly compared with the constant elastic modulus, and it gets a more consistent trend with the experimental data. In the benchmark 4 of the international conference NUMISHEET 2011 [4], the springback problems on U-shaped parts under the prestrain are proposed. Since then, many scholars have studied the springback problems with pre-strain effect. Multi-step loading method might generate a larger springback phenomenon in consequence of the non-linear strain path. The difference of the stress distribution induced by different loading modes is also the trigger of the twist springback, which is also the core of this work. For the purpose of characterizing the twist springback phenomenon in channel-type products, an asymmetric deep drawing experimental device of a curved channel is designed. The impact of pre-strain that acts on the twist springback is discussed, and how it influences the strain path as well as the elastic modulus is also deeply analysed. 2. Main contents
* Corresponding author. E-mail addresses: [email protected] (J. Liao), [email protected] (S. Chen), [email protected] (X. Xue), [email protected] (H. Xiang). Peer review under responsibility of Editorial Board of International Journal of Lightweight Materials and Manufacture.
In this work, the 0.8 mm thick steel sheet, DP500, is adopted to analyse the twist springback under the pre-strain effect. First, the pre-strain test of the large specimen is performed with alarge universal testing equipment (Fig. 1a). The geometry of the large
https://doi.org/10.1016/j.ijlmm.2019.08.006 2588-8404/© 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: J. Liao et al., On twist springback of a curved channel with pre-strain effect, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.08.006
2
J. Liao et al. / International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
Fig. 1. Experimental device and drawn parts: (a) the tensile testing machine and the strain ε1 distribution after the pre-strain; (b) the forming tool; (c) the formed parts.
specimen is optimized to ensure that the strain in the middle part is uniform [5]. Second, the curved channel forming experiment is conducted on the blank cut from the large specimen. The forming tool maintains a blank holding force of 144 kN by means of the gas spring, which is shown in Fig. 1b. In the light of the included angle between the guide axis of the channel and the direction that the pre-strain is applied, the curved channels are divided into channel (L) and channel (T) (the ‘L’ and ‘T’ respectively denote the ‘longitudinal’ and ‘transverse’ direction to distinguish the channels) that represents the angle is 0 and 90 , respectively. The final drawn parts are shown in Fig. 1c. For a better understanding of the forming methods pertaining to the channels (L and T), the schematic forming process is illustrated in Fig. 2. One of the key factors, causing the phenomenon of twist springback in the intricate multi-stage stampings, is significant changes of the strain path. Previous research work has proved that the combination of the attenuated modulus algorithm and the anisotropic hardening models can significantly improve the accuracy of the springback prediction [6]. For the purpose of better capturing the material behaviours under complex path changes, an advanced distortional hardening (i.e. HAH) model, incorporated with the anisotropic yield criterion Yld2000-2d, is selected in this work to describe characteristic of the material. At the same time, the non-linear Chord model is applied to describe a declining tendency of elastic modulus. It can be expressed by:
Echord ¼ E0 ðE0 Ea Þ 1 exp xεp
(1)
The HAH model, brought forth by Barlat et al. [7], is employed in exquisitely capturing the characteristics of materials under complex paths by the distortion of the yield surface. It can be represented in the following equation:
sðsÞ ¼ fq þ fqh
1 q
¼
The yield equation sðsÞ consists of a stable equation f and a floating equation fh . The q is the constant exponent of the material, b is a microscopic tensor in order f1 and f2 are the state variable. The h to record the history of deformation path. The dislocation densitybased hardening algorithm, containing the evolution equation of dislocation density, can reproduce the hardening stagnation feature during the load reversal [8]. It is merged into the HAH model. All the parameters in regard to the above mentioned models are presented in Table 1. 3. Results and discussions Fig. 3a shows the progressively attenuation trend of elastic modulus, which eventually stabilizes with the plastic strain increases. In the case of 4% true strain, the elastic modulus has already reduced to 162 MPa. For the sake of better representing the elastic modulus distribution among the channels, the elements, selected in different locations of the channel, are analysed and marked as E1, E2…10. It is found that the elastic modulus distribution in formed channels is distinguished. The channel without pre-strain has the larger elastic modulus than that with pre-strain. Especially, the channel (L) has the uneven distribution of elastic modulus that can be reflected by E3, E4, E5 apparently. In terms of the twist springback of the channels based on experimental results (Exp.), the relative twist angle calculated by the principal axis of inertia [6] of the representative cross sections is shown in Fig. 3b, which is served as a way to evaluate the twist springback. It can be found that there is more obvious twist springback phenomenon for channel (L). For the purpose of further probing into the mechanism resulting in twist springback phenomenon, the simulation software ABAQUS, embedded in the subroutines with the above mentioned models, is
(qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q )1 q q b b : sj q þ f q h b : sj q ¼ sðεÞ b : s þ jh : s jh fðs0 Þ2 þ fðs00 Þ2 þ f 1 h 2
(2)
Please cite this article as: J. Liao et al., On twist springback of a curved channel with pre-strain effect, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.08.006
J. Liao et al. / International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
3
Fig. 2. Diagrammatic sketch of two-step loading process of channel (L) and channel (T): the guide axis of formed channel is (a) in the rolling direction and (b) vertical to the rolling direction.
Table 1 Material constitutive coefficients of the DP500 used for constitutive model. Chord model
E0 198
x
Ea 161
92.4
Yld2000-2d
a
a1
a2
a3
a4
a5
a6
a7
a8
HAH
6 q 2
Dislocation density-based model
a
0.90 k 14 m (GPa) 80
1.06 k1 90 b (nm) 0.25
1.03 k2 33.4 t0 (MPa) 121
0.98 k3 0.48 M 3.1
0.96 k4 0.92 K 148
0.74 k5 5 D (mm) 20
0.95 ks 179 F 3.5
1.06 s 0.83 P 0.8
0.5
Fig. 3. (a) The fitting curve of DP500 elastic modulus with Chord model and the elastic modulus distribution in formed channels; (b) The relative twist angles of different channels.
applied to analyse stress conditions of the channels. It is found from the stress nephogram of channel (L) that the stress (s22) in the straight side wall is very inhomogeneous. One element (shows in Fig. 4) is selected in straight side wall to analyse the strain path change from pre-strain to forming process. It could be seen that strain path of channel (L) exhibits cross-loading phenomenon under the two-step loading transition. And the stress s22 in central regions of the channel (L) is 182 MPa that is obviously lower than the channel (T). In curved sidewall, the wide and the narrow side with different stress s11, the former performs as stretching and the latter one is compression. The representative element which selected in curved sidewall is shown in Fig. 5a. Obviously, the channel (L) has the larger stress s11 than channel (T) whether it
is in wide side or in narrow side, which is one of the causes that generate a more drastic twist springback feature of the channel (L) than the one (T). The traced historical values of the element which are compared between channel (L) and channel (T) is shown in Fig. 5a. According to the deformation analysis associated with in-plane stress distribution, the asymmetric longitudinal in-plane stress on the curved transition flange and sidewall is the main source of twist springback occurrence. Thus, an alternative method to reduce or eliminate springback is to use partial draw bead design for Pchannel. This method may be efficient to balance the in-plane stress distribution and reduce springback for the studied case. The work further aims at evaluating the accuracy of the simulated models for the twist springback prediction. The relative twist
Please cite this article as: J. Liao et al., On twist springback of a curved channel with pre-strain effect, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.08.006
4
J. Liao et al. / International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
Fig. 4. Stress distribution s22 in straight sidewall.
Fig. 5. (a) Stress distribution s11 in curved sidewall; (b) Comparison of the different elastic models based on relative twist angles.
angles, used to compare the extent of twist springback, are calculated for channels based on different elastic models, as shown in Fig. 5b. The equation characterizing the average error is also shown in Fig. 5b, in which the Dgi is on behalf of the relative twist angle of 0 the experimental channel, and Dgi is the simulated one. It is found that the HAH model incorporated with the attenuated model (varied E) can capture the twist springback phenomenon better than that of the constant elastic modulus (E0). The average error (marked in ‘Ae’) of the channel (L) is 12%, and the channel (T) is 15%. The simulation based on constant elastic modulus (E0) predicts a lower value of the twist springback universally. It probably ascribes to the overvaluation of elastic modulus of the sheet with pre-strain. The maximum Ae of twist springback prediction is the channel (L) predicted by model (E0), of which the relative twist angle reaches 2 at section 5. It is probably due to the omission of the uneven elastic modulus on the different positions in channel (L) after suffering the intricate strain paths. 4. Conclusions Aiming at addressing the twist springback problems in twostage loading, a large bone-shaped sheet is pre-strained first and
then deformed in a curved channel tool. The main conclusions are drawn as follows: (1) The direction of pre-strain is an important factor that significantly affects the twist springback of the formed channel. If the guide axis of forming channel is consistent with the pre-strain axis, strain path changes, e.g. cross loading condition, will occur, which will generate uneven sidewall stress distribution. It is one of the reasons resulting in the more severe twist springback; (2) The Chord model embedded with the enhanced HAH model and anisotropic yield criterion Yld2000-2d, which can well describe the non-linear elasto-plastic behaviour of materials under complex strain paths, has a better prediction on twist springback of the channel with prestrain effect; (3) The deformation analysis associated with in-plane stress distribution indicates that the asymmetric longitudinal inplane stress field on the curved transition flange and sidewall may be the source of twist springback occurrence. The control strategy to balance the corresponding in-plane stress distribution for the minimization of twist
Please cite this article as: J. Liao et al., On twist springback of a curved channel with pre-strain effect, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.08.006
J. Liao et al. / International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
springback, e.g., tool design related to additional geometric stiffener, will be addressed in terms of individual forming case in the future work.
Conflict of interest The authors declared that they have no conflicts of interest to this work.
Acknowledgement The financial supports from the National Natural Science Foundation of China (NO.51805087), the Natural Science Foundation of Fujian Province of China (NO.2018J01761) and the Major Science and Technology Project in Fujian Province (NO.2017HZ0001-2) are greatly appreciated.
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Please cite this article as: J. Liao et al., On twist springback of a curved channel with pre-strain effect, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.08.006