ON THE PHENOMENOLOGICALMODELLING OF YIELD SURFACE DISTORTION

ON THE PHENOMENOLOGICALMODELLING OF YIELD SURFACE DISTORTION

Shutov, A. V.; Ihlemann, J.

Full Article:

A simple phenomenological approach to metal plasticity, including the description of the strain-induced plastic anisotropy, is considered. The advocated approach is exemplified by a two-dimensional rheological analogy. This analogy provides insight into modelling of nonlinear kinematic hardening of Armstrong-Frederick type combined with a nonlinear distortional hardening. In the previous publications of the authors, an interpolation rule between the undistorted yield surface of a virgin material and the saturated yield surface of a pre-deformed material was considered. In the current publication, a somewhat more flexible approach is considered. Given a set of convex symmetric key surfaces which correspond to different hardening stages, the form of the yield surface is smoothly interpolated between these key surfaces. Thus, any experimentally observed sequence of symmetric convex yield surfaces can be rendered. In particular, an arbitrary sharpening of the yield locus in the loading direction combined with a flattening on the opposite side can be taken into account. Moreover, the yield locus evolves smoothly and its convexity is ensured at each hardening stage.

A simple phenomenological approach to metal plasticity, including the description of the strain-induced plastic anisotropy, is considered. The advocated approach is exemplified by a two-dimensional rheological analogy. This analogy provides insight into modelling of nonlinear kinematic hardening of Armstrong-Frederick type combined with a nonlinear distortional hardening. In the previous publications of the authors, an interpolation rule between the undistorted yield surface of a virgin material and the saturated yield surface of a pre-deformed material was considered. In the current publication, a somewhat more flexible approach is considered. Given a set of convex symmetric key surfaces which correspond to different hardening stages, the form of the yield surface is smoothly interpolated between these key surfaces. Thus, any experimentally observed sequence of symmetric convex yield surfaces can be rendered. In particular, an arbitrary sharpening of the yield locus in the loading direction combined with a flattening on the opposite side can be taken into account. Moreover, the yield locus evolves smoothly and its convexity is ensured at each hardening stage.

Palavras-chave:

DOI: 10.5151/meceng-wccm2012-18507

Referências bibliográficas

• [1] Dafalias Y.F., Schick D., Tsakmakis C., “A simple model for describing yield surface evolution”. Lecture note in applied and computational mechanics, K. Hutter and H. Baaser, eds., Springer, Berlin. 169-201, 2002.
• [2] Dafalias Y.F., Feigenbaum H.P., “Directional distortional hardening in plasticity within thermodynamics”. Recent Advances in Mechanics 61-78, 2011.
• [3] Dannemeyer S., “Zur Veränderung der Fließfläche von Baustahl bei mehrachsiger plastischer Wechselbeanspruchung”. Braunschweig (Carolo- Wilhelmina University) 1999.
• [4] Feigenbaum H.P., Dafalias Y.F., “Directional distortional hardening in metal plasticity within thermodynamics”. International Journal of Solids and Structures 44, 7526-7542, 2007.
• [5] Feigenbaum H.P., Dafalias Y.F., “Simple model for directional distortional hardening in metal plasticity within thermodynamics”. Journal of Engineering Mechanics 134 9, 730- 738, 2008.
• [6] Franc¸ois M., “A plasticity model with yield surface distortion for non proportional loading”. International Journal of Plasticity 17, 703-717, 2001.
• [7] Grewolls G., Kreißig R., “Anisotropic hardening – numerical application of a cubic yield theory and consideration of variable r-values for sheet metal”. European Journal of Mechanics A/Solids 20, 585-599, 2001.
• [8] Khan A.S., Pandey A., Stoughton T., “Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part II: A very high work hardening aluminum alloy (annealed 1100 Al)”. International Journal of Plasticity 26, 1421-1431, 2010.
• [9] Khan A.S., Pandey A., Stoughton T., “Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part III: Yield surface in tension-tension stress space (Al 6061T 6511 and annealed 1100 Al)”. International Journal of Plasticity 26, 1432-1441, 2010.
• [10] Lion A., “Constitutive modelling in finite thermoviscoplasticity: a physical approach based on nonlinear rheological elements”. International Journal of Plasticity 16, 469- 494, 2000.
• [11] Noman M., Clausmeyer T., Barthel C., Svendsen B., Huetink J., Riel, M., “Experimental characterization and modeling of the hardening behavior of the sheet steel LH800”. Materials Science and Engineering A 527, 2515-2526, 2010.
• [12] Ortiz M., Popov E.P., “Distortional hardening rules for metal plasticity”. J. Engng Mech. 109, 1042-1058, 1983.
• [13] Panhans S., Kreißig R., “A viscoplastic material model of overstress type with a nonquadratic yield function”. European Journal of Mechanics A/Solids 25, 283-298, 2006.
• [14] Phillips A., Tang J.-L., “The effect of loading path on the yield surface at elevated temperatures”. Int. J. Solids Structures. 8, 463-474, 1972.
• [15] Pietryga M.P., Vladimirov I.N., Reese S., “A finite deformation model for evolving flow anisotropy with distortional hardening including experimental validation”. Mechanics of Materials 44, 163-173, 2012.
• [16] Plesek J., Feigenbaum H.P., Dafalias Y.F., “Convexity of yield surface with directional distortional hardening rules”. Journal of Engineering Mechanics 136 4, 477-484, 2010.
• [17] Shutov A.V., Panhans S., Kreißig R., “A phenomenological model of finite strain viscoplasticity with distortional hardening”. ZAMM 91 8, 653-680, 2011.
• [18] Shutov A.V., Ihlemann J., “A viscoplasticity model with an enhanced control of the yield surface distortion”. arXiv-preprint http://arxiv.org/abs/1204.0086 2012.
• [19] Steck E., Ritter R., Peil U., Ziegenbein A., “Plasticity of Materials: Experiments, Models”. Deutsche Forschungsgemeinschaft, Computation (Wiley-VCH Verlag GmbH), 2001.
• [20] Wegener K., Schlegel M., “Suitability of yield functions for the approximation of subsequent yild surfaces”. International Journal of Plasticity 12, 1151-1177, 1996

Como citar:

Shutov, A. V.; Ihlemann, J.; "ON THE PHENOMENOLOGICALMODELLING OF YIELD SURFACE DISTORTION", p-1662-1670. In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 23580828, DOI 10.5151/meceng-wccm2012-18507