×

zbMATH — the first resource for mathematics

Modeling the effect of notch geometry on the deformation of a strongly anisotropic aluminum alloy. (English) Zbl 07212914
Summary: In this study, an elastic-plastic model with yielding described by a newly proposed orthotropic yield criterion was used to model the unusual deformation of a strongly textured AA6060 alloy. Available experimental data from tension tests and results of crystal plasticity simulations were used to determine the anisotropy coefficients involved in the yield criterion. Virtual material tests using a recent polycrystalline model were performed to obtain flow stresses for loadings where experimental data were not available. The capability of the elastic-plastic model to account for the distinct anisotropy of the material is demonstrated through comparison of finite element simulations and experimental tests on both smooth and notched axisymmetric specimens of the AA6060 alloy. Specifically, for the smooth specimen, the model predicts that the minimum cross-section evolves from a circle to an ellipse while for the notched specimens, the minimum cross-section evolves from a circular shape to an approximately rectangular, or rhomboidal shape, respectively as observed in the experiments. This model can be easily implemented in finite element codes, requires reduced CPU time compared to crystal plasticity finite element simulations, and can be applied in simulations of large-scale structural applications.
MSC:
74 Mechanics of deformable solids
Software:
ABAQUS
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abaqus, User’s Manual for Version 6.8 Vols. I-V (2009), Dassault Systemes Simulia Corp.: Dassault Systemes Simulia Corp. Providence, RI
[2] Barlat, F.; Aretz, H.; Yoon, J. W.; Karabin, M. E.; Brem, J. C.; Dick, R. E., Linear transformation-based anisotropic yield functions, Int. J. Plast., 21, 1009-1039 (2005) · Zbl 1161.74328
[3] Cazacu, O., New yield criteria for isotropic and textured metallic materials, Int. J. Solid Struct., 139, 200-210 (2018)
[4] Cazacu, O.; Barlat, F., Generalization of drucker’s yield criterion to orthotropy, Math. Mech. Solid, 6, 613-630 (2001) · Zbl 1128.74303
[5] Cazacu, O.; Revil-Baudard, B.; Chandola, N., A yield criterion for cubic single crystals, Int. J. Solid Struct., 151, 9-19 (2018)
[6] Cazacu, O.; Revil-Baudard, B.; Chandola, N., Plasticity-Damage Couplings: from Single Crystal to Polycrystalline Materials (2019) · Zbl 1405.74001
[7] Chandola, N.; Cazacu, O.; Revil-Baudard, B., New polycrystalline modeling as applied to textured steel sheets, Mech. Res. Commun., 84, 98-101 (2017)
[8] Chandola, N.; Cazacu, O.; Revil-Baudard, B., Prediction of plastic anisotropy of textured polycrystalline sheets using a new single-crystal model, Compt. Rendus Mec., 346, 756-769 (2018)
[9] Engler, O.; Randle, V., Introduction to Texture Analysis: Macrotexture, Microtexture, and Orientation Mapping (2009), CRC press, Taylor & Francis Group
[10] Fourmeau, M.; Børvik, T.; Benallal, A.; Hopperstad, O. S., Anisotropic failure modes of high-strength aluminium alloy under various stress states, Int. J. Plast., 48, 34-53 (2013)
[11] Fourmeau, M.; Børvik, T.; Benallal, A.; Lademo, O. G.; Hopperstad, O. S., On the plastic anisotropy of an aluminium alloy and its influence on constrained multiaxial flow, Int. J. Plast., 27, 2005-2025 (2011) · Zbl 1426.74069
[12] Frodal, B. H.; Pedersen, K. O.; Børvik, T.; Hopperstad, O. S., Influence of pre compression on the ductility of AA6xxx aluminium alloys, Int. J. Fract., 206, 131-149 (2017)
[13] Green, A. E.; Naghdi, P. M., A general theory of an elastic-plastic continuum, Arch. Ration. Mech. Anal., 18, 251-281 (1965) · Zbl 0133.17701
[14] Hannard, F.; Pardoen, T.; Maire, E.; Le Bourlot, C.; Mokso, R.; Simar, A., Characterization and micromechanical modelling of microstructural heterogeneity effects on ductile fracture of 6 xxx aluminium alloys, Acta Mater., 103, 558-572 (2016)
[15] Hosford, W. F., A generalized isotropic yield criterion, J. Appl. Mech., 39, 607-609 (1972)
[16] Hughes, T. J., Numerical implementation of constitutive models: rate-independent deviatoric plasticity, Theoretical Foundation for Large-Scale Computations for Nonlinear Material Behavior, 29-63 (1984), Springer: Springer Dordrecht
[17] I-Shih, L., On representations of anisotropic invariants, Int. J. Eng. Sci., 20, 1099-1109 (1982) · Zbl 0504.73001
[18] Khadyko, M.; Dumoulin, S.; Børvik, T.; Hopperstad, O. S., Simulation of large-strain behaviour of aluminium alloy under tensile loading using anisotropic plasticity models, Comput. Struct., 157, 60-75 (2015)
[19] Khadyko, M.; Dumoulin, S.; Cailletaud, G.; Hopperstad, O. S., Latent hardening and plastic anisotropy evolution in AA6060 aluminium alloy, Int. J. Plast., 76, 51-74 (2016)
[20] Kohar, C. P.; Brahme, A.; Hekmat, F.; Mishra, R. K.; Inal, K., A computational mechanics engineering framework for predicting the axial crush response of Aluminum extrusions, Thin-Walled Struct., 140, 516-532 (2019)
[21] Morin, D.; Fourmeau, M.; Børvik, T.; Benallal, A.; Hopperstad, O. S., Anisotropic tensile failure of metals by the strain localization theory: an application to a high-strength aluminium alloy, Eur. J. Mech. A Solids, 69, 99-112 (2018) · Zbl 1406.74155
[22] Smith, G. F.; Rivlin, R. S., The strain-energy function for anisotropic elastic materials, Trans. Am. Math. Soc., 88, 175-193 (1958) · Zbl 0089.23505
[23] Wang, C.-C., A new representation theorem for isotropic functions: an answer to Professor GF Smith’s criticism of my papers on representations for isotropic functions, Arch. Ration. Mech. Anal., 36, 166-197 (1970) · Zbl 0327.15030
[24] Zhang, H.; Diehl, M.; Roters, F.; Raabe, D., A virtual laboratory using high resolution crystal plasticity simulations to determine the initial yield surface for sheet metal forming operations, Int. J. Plast., 80, 111-138 (2016)
[25] Zhang, K.; Holmedal, B.; Hopperstad, O. S.; Dumoulin, S.; Gawad, J.; Van Bael, A.; Van Houtte, P., Multi-level modelling of mechanical anisotropy of commercial pure aluminium plate: crystal plasticity models, advanced yield functions and parameter identification, Int. J. Plast., 66, 3-30 (2015)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.