AZ31 Sheet Forming by Clustering Ball Spinning-Analysis of Damage Evolution Using a Modified GTN Model
Abstract
:1. Introduction
2. Materials and Methods
3. Mechanical Analysis and Constitutive Model
3.1. Contact Stress
3.2. Constitutive Model
3.3. Parameters Identification
3.3.1. Elastic-Plastic Behavior
3.3.2. Fractional Factor of GTN Model
3.3.3. The FE Model of Shear-Tensile
4. Results and Discussion
4.1. Step 1
4.2. Step 2
4.3. The Result of Experiment
5. Conclusions
- The material parameters of the GTN model for AZ31 magnesium alloy were determined by experiment, and the reliability of modified GTN model was verified through the comparison of numerical simulation and experimental observation on the shear-tensile process with the AZ31 magnesium alloy. Theoretical formula is conducted to contact stress analysis in the CBS forming process, and it can be found that the stress triaxiality is related to the radius of rigid balls and the thickness of the sheet. Besides, the stress triaxiality was about 0.26 and the Lode parameter was about 0.68 in the AF region, and the forming region was under the negative stress triaxiality in this simulations and experiments.
- The numerical results are compared under different damage parameter , it can be found that the results of damage parameter are similar with that of experiments both in Step 1 and Step 2. The maximum displacement of the rotatable gland stirrer reached 27.3 mm and the effective forming radius reached 24.7 mm in Step 2, which was much higher than that in Step 1 (The maximum displacement was 13.9 mm, and the effective forming radius was 12 mm in Step 1). With spinning of rigid balls, forming limit was improved and the effective forming radius increased.
- To explore the increased forming limit in the CBS forming process, the microstructure of curved surface was tested by electron backscattered scattering detection (EBSD). It is indicated from the microstructure that the deformation of AZ31 sheet using the CBS method is dominated initially by the extension twinning and non-basal slip system is activated with development of forming and the improvement of the temperature. Meanwhile, it can be found that the c-axes in the grains had a small angle rotation which was caused by the shear deformation during CBS process.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Hu, Z.; Guo, C.; Li, H. Influence of AZ31 sheet treated by cryogenic on punch shearing. J. Cent. South Univ. 2019, 26, 1582–1591. [Google Scholar] [CrossRef]
- Hu, Z.; Zheng, X.; An, D.; Zhou, C.; Yang, Y.; Li, R. New analytic buckling solutions of side-cracked rectangular thin plates by the symplectic superposition method. Int. J. Mech. Sci. 2021, 191, 106051. [Google Scholar] [CrossRef]
- Feng, F.; Li, J.; Yuan, P.; Zhang, Q.; Huang, P.; Su, H.; Chen, R. Application of a GTN Damage Model Predicting the Fracture of 5052-O Aluminum Alloy High-Speed Electromagnetic Impaction. Metals 2018, 8, 761. [Google Scholar] [CrossRef] [Green Version]
- Li, H.; Fu, M.W.; Lu, J.; Yang, H. Ductile fracture: Experiments and computations. Int. J. Plast. 2011, 27, 147–180. [Google Scholar] [CrossRef]
- Ma, H.; Xu, W.; Jin, B.C.; Shan, D.; Nutt, S.R. Damage evaluation in tube spinnability test with ductile fracture criteria. Int. J. Mech. Sci. 2015, 100, 99–111. [Google Scholar] [CrossRef]
- Tvergaard, V.; Tvergaard, N. Analysis of the cup-cone fracture in a round tensile bar. Acta Metall. 1984, 32, 157–169. [Google Scholar] [CrossRef]
- Lee, H.W.; Basaran, C. A Review of Damage, Void Evolution, and Fatigue Life Prediction Models. Metals 2021, 11, 609. [Google Scholar] [CrossRef]
- Yan, Y.; Sun, Q.; Chen, J.; Pan, H. The initiation and propagation of edge cracks of silicon steel during tandem cold rolling process based on the Gurson–Tvergaard–Needleman damage model. J. Mater. Processing Technol. 2013, 213, 598–605. [Google Scholar] [CrossRef]
- Riedel, H.; Andrieux, F.; Walde, T.; Karhausen, K.F. The Formation of Edge Cracks during Rolling of Metal Sheet. Steel Res. Int. 2007, 78, 818–824. [Google Scholar] [CrossRef]
- Hambli, R. Comparison between Lemaitre and Gurson damage models in crack growth simulation during blanking process. Int. J. Mech. Sci. 2001, 43, 2769–2790. [Google Scholar] [CrossRef]
- Achouri, M.; Germain, G.; Dal Santo, P.; Saidane, D. Numerical integration of an advanced Gurson model for shear loading: Application to the blanking process. Comput. Mater. Sci. 2013, 72, 62–67. [Google Scholar] [CrossRef] [Green Version]
- Cao, T.S.; Maire, E.; Verdu, C.; Bobadilla, C.; Lasne, P.; Montmitonnet, P.; Bouchard, P.O. Characterization of ductile damage for a high carbon steel using 3D X-ray micro-tomography and mechanical test—Application to the identification of a shear modified GTN model. Comput. Mater. Sci. 2014, 84, 175–187. [Google Scholar] [CrossRef]
- Cao, T.S.; Mazière, M.; Danas, K.; Besson, J. A model for ductile damage prediction at low stress triaxialities incorporating void shape change and void rotation. Int. J. Solids Struct. 2015, 63, 240–263. [Google Scholar] [CrossRef]
- Madou, K.; Leblond, J.-B. A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—I: Limit-analysis of some representative cell. J. Mech. Phys. Solids 2012, 60, 1020–1036. [Google Scholar] [CrossRef] [Green Version]
- Monchiet, V.; Bonnet, G. A Gurson-type model accounting for void size effects. Int. J. Solids Struct. 2013, 50, 320–327. [Google Scholar] [CrossRef]
- Morin, L.; Michel, J.-C.; Leblond, J.-B. A Gurson-type layer model for ductile porous solids with isotropic and kinematic hardening. Int. J. Solids Struct. 2017, 118–119, 167–178. [Google Scholar] [CrossRef]
- Nahshon, K.; Hutchinson, J.W. Modification of the Gurson Model for shear failure. Eur. J. Mech.-A/Solids 2008, 27, 1–17. [Google Scholar] [CrossRef]
- Sun, Q.; Zan, D.; Chen, J.; Pan, H. Analysis of edge crack behavior of steel sheet in multi-pass cold rolling based on a shear modified GTN damage model. Theor. Appl. Fract. Mech. 2015, 80, 259–266. [Google Scholar] [CrossRef]
- Silva, M.B.; Skjoedt, M.; Martins, P.A.F.; Bay, N. Revisiting the fundamentals of single point incremental forming by means of membrane analysis. Int. J. Mach. Tools Manuf. 2008, 48, 73–83. [Google Scholar] [CrossRef]
- Chang, Z.; Chen, J. Investigations on the deformation mechanism of a novel three-sheet incremental forming. J. Mater. Processing Technol. 2020, 281, 116619. [Google Scholar] [CrossRef]
Alloys | Mg | Al | Zn | Mn |
---|---|---|---|---|
AZ31 | 95.7 | 3.0 | 1.0 | 0.3 |
Parameters | Value |
---|---|
The radius of the rotatable gland stirer (mm) | 75 |
The radius of rigid balls (mm) | 4 |
The Rotational speed of rotatable gland stirere (r/min) | 24 |
The radius of the bottom die | 46 |
q1 | q2 | q3 | fN | fc | ff | εN | SN | f0 |
---|---|---|---|---|---|---|---|---|
1.5 | 1 | 2.25 | 0.04 | 0.0732 | 0.1279 | 0.2 | 0.1 | 0.001 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Hu, Z.; Da, L.; Xi, J.; Li, X. AZ31 Sheet Forming by Clustering Ball Spinning-Analysis of Damage Evolution Using a Modified GTN Model. Metals 2022, 12, 220. https://doi.org/10.3390/met12020220
Hu Z, Da L, Xi J, Li X. AZ31 Sheet Forming by Clustering Ball Spinning-Analysis of Damage Evolution Using a Modified GTN Model. Metals. 2022; 12(2):220. https://doi.org/10.3390/met12020220
Chicago/Turabian StyleHu, Zhiqing, Lijia Da, Jia Xi, and Xinchen Li. 2022. "AZ31 Sheet Forming by Clustering Ball Spinning-Analysis of Damage Evolution Using a Modified GTN Model" Metals 12, no. 2: 220. https://doi.org/10.3390/met12020220