Abstract
The simulation of polycrystalline materials provides detailed insight into the material characteristic. Sheet-bulk metal forming is a complex process that needs comprehensive information about the formed metallic material. Further, transient hardening and Bauschinger effects make this process even more challenging. In order to accurately predict the forming process and the final shape of the formed part under these circumstances, one needs to consider sophisticated elastoplastic material models. Plastic deformation is based on a microscopic length scale phenomenon that involves the dislocation activities within the microstructure. Therefore, a physically motivated dislocation density-based material model is developed to consider the effect of plastic deformation for polycrystalline materials. However, the resolution of the material at a microscopic length scale quickly leads to limitations regarding computation time and cost. Due to the high geometrical resolution, it is impossible to simulate large geometries and resolve the complex plastic transformation at the micro-level within the entire domain. Therefore, based on insights gained with representative volume element simulations of the microstructure an effective plasticity model is developed as well. The effective material model can be applied in coarse scale simulations. It can also provide an accurate mechanical response under non-proportional loading while considering isotropic, as well as kinematic hardening. Additionally, this effective material model can be easily extended to anisotropic yield functions. Both length-scale models are used to validate the mechanical response of ferritic steels under cyclic loading.
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References
Romain, Q., Paul, D., Fabrice, B.: Large-scale 3D random polycrystals for the finite element method: generation, meshing and remeshing. Comput. Methods Appl. Mech. Eng. 200, 1729–1745 (2011)
Taylor, G., Elam, C.: The distortion of iron crystals. In: Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 112(761), 337–361 (1926)
Spitzig, W., Keh, A.: The role of internal and effective stresses in the plastic flow of iron single crystals. Metallurgical Trans. 1(12), 3325–3331 (1970)
Bertram, A.: Finite thermoplasticity based on isomorphisms. Int. J. Plasticity 19(11), 2027–2050 (2003)
Bertram, A.: Elasticity and Plasticity of Large Deformations, Springer, Heidelberg (2012)
Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.H., Chu, E.: Plane stress yield function for aluminum alloy sheets|part 1: theory. Int. J. Plasticity 19(9), 1297–1319 (2003)
Barlat, F., Lege, D.J., Brem, J.C.: A six-component yield function for anisotropic materials. Int. J. Plasticity 7(7), 693–712 (1991)
Banabic, D.: Sheet Metal Forming Processes (2010)
Bachmann, F., Hielscher, R., Schaeben, H.: Texture Analysis with MTEX - Free and Open Source Software Toolbox. Solid State Phenomena, 160, 63–68 (2010)
Huber, J.E.: Micromechanical modelling of ferroelectrics. Current Opinion in Solid State Mater. Sci. 9(3), 100–106 (2005)
Zeller, S., Baldrich, M, Gerstein G., Nuernberger F., Loehnert, S., Maier H.J., Wriggers, P.: Material models for the thermoplastic material behaviour of a dual-phase steel on a microscopic and a macroscopic length scale. J. Mech. Phys. Solids, 129, 205–228 (2019). ISSN 0022-5096
Barlat, F., Yoon, J.W., Cazacu, O.: On linear transformations of stress tensors for the description of plastic anisotropy. Int. J. Plasticity 23(5), 876–896 (2007)
Boeff, M.: Micromechanical modelling of fatigue crack initiation and growth. Dissertation, Ruhr-Universität Bochum (2016)
Baldrich, M., Loehnert, S., Wriggers, P.: Developing a model for the microscopic material behaviour of a tailored formed joining zone of an aluminium-steel hybrid solid component, 2018, PAMM, Proc. Appl. Math. Mech. https://doi.org/10.1002/pamm.201800329
Brands, D., Balzani, D., Scheunemann, L., Schröder, J., Richter, H., Raabe, D.: Computational modeling of dual-phase steels based on representative three-dimensional microstructures obtained from EBSD data. Arch. Appl. Mech. 86(3), 575–598 (2015). https://doi.org/10.1007/s00419-015-1044-1
Brunner, D., Diehl, J.: Strain-rate and temperature dependence of the tensile flow stress of high-purity-iron above 250 K (regime I) studied by means of stress-relaxation tests. Physica Status Solidi 124(1), 155–170 (1991)
Rivlin, R.: Large elastic deformations of isotropic materials. I. fundamental concepts. Philosophical Trans. Royal Soc. London. Series A, Math. Phys. Sci. 240(822), 459–490 (1948)
Wang, H., Yan, Yu., Wan, M., Chen, Z., Li, Q., He, D.: A quadratic yield function with multi-involved-yield surfaces describing anisotropic behaviors of sheet metals under tension/compression. Acta Mech. Solida Sin. 30(6), 618–629 (2017). https://doi.org/10.1016/j.camss.2017.10.004
Zeller, S.: Material models for the thermoplastic material behavior of a dual-phase steel DP600 on microscopic and macroscopic length scale, Ph.D. thesis, Hannover: Institut für Kontinuumsmechanik (2017). ISBN: 978-3-941302-22-8
Korelc, J., Wriggers, P.: Automation of Finite-Element-Methods. Springer, Cham (2016)
Acknowledgment
This project was supported by the German Research Foundation (DFG) within the scope of the Transregional Collaborative Research Centre 73 for sheet-bulk metal forming (TCRC 73, Subproject C2) under grant number TRR73/3 68237143. The authors are also grateful to all laboratory assistants and students who supported the execution of this work.
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Ahmed, S., Lyu, T., Löhnert, S., Wriggers, P. (2021). Multilevel Material Modeling to Study Plastic Deformation for Sheet-Bulk Metal Forming Under Different Loading Histories. In: Merklein, M., Tekkaya, A.E., Behrens, BA. (eds) Sheet Bulk Metal Forming . TCRC73 2020. Lecture Notes in Production Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-61902-2_15
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