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The aim of the paper is to formulate physically well founded yield condition for initially anisotropic solids revealing the asymmetry of elastic range. The initial anisotropy occurs in material primarily due to thermo-mechanical pre-processing and plastic deformation during the manufacturing processes. Therefore, materials in the “as-received” state become usually anisotropic. After short account of the known limit criteria for anisotropic solids and discussion of mathematical preliminaries the energy-based criterion for orthotropic materials was formulated and confronted with experimental data and numerical predictions of other theories. Finally, possible simplifications are discussed and certain model of isotropic material with yield condition accounting for a correction of shear strength due to initial anisotropy is presented. The experimental verification is provided and the comparison with existing approach based on the transformed-tensor method is discussed.
Wydawca
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Rocznik
Tom
Strony
771--778
Opis fizyczny
Bibliogr. 41 poz., rys., tab., wzory
Twórcy
autor
- Institute of Fundamental Technological Research, Polish Academy of Sciences, 5B Pawińskiego Str., 02-106 Warszawa, Poland
autor
- Laboratory of Microstructure Studies and Mechanics of Materials, UMR-CNRS 7239, Lorraine University, 7 Rue Félix Savart, BP 15082, 57073 Metz Cedex 03, France
autor
- French-German Research Institute of Saint-Louis (ISL), 5 Général Cassagnou Str., 68301 Saint-Louis, France
autor
- Institute of Fundamental Technological Research, Polish Academy of Sciences, 5B Pawińskiego Str., 02-106 Warszawa, Poland
autor
- Institute of Fundamental Technological Research, Polish Academy of Sciences, 5B Pawińskiego Str., 02-106 Warszawa, Poland
Bibliografia
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- [2] W. Burzyński, PhD thesis, Studium nad hipotezami wytężenia, Akademia Nauk Technicznych, Lwów (1928).
- [3] W. Burzyński. Selected passages from Włodzimierz Burzyński’s doctoral dissertation Study on material effort hypotheses, Eng.Trans. 57,185-215 (2009).
- [4] R. M. Caddell, R. S. Raghava, A. G. Atkins, A yield criterion for anisotropic and pressure dependent solids such as oriented polymers, J. Mater. Sc. 11, 1641-1646 (1973).
- [5] S. Federico, Volumetric-distortional decomposition of deformation and elasticity tensor, Math. Mech. Solids 15, 672-690 (2010).
- [6] T. Fras, PhD thesis. Modelling of plastic yield surface of materials accounting for initial anisotropy and strength differential effect on the basis of experiments and numerical simulation, Université de Lorraine and AGH University of Science and Technology in Krakow, Metz (2013).
- [7] T. Fras, M. Nishda, A. Rusinek, R. B. Pęcherski, N. Fukuda, Description of the yield state of bioplastics on examples of starch-based plastics and PLA/PBAT blends, Engng. Trans. 62, 329-354 (2014).
- [8] R. Hill, A theory of the yielding and plastic flow of anisotropic metals, Proc. R. Soc. London 193, 281-297 (1948).
- [9] O. Hoffman, The brittle strength of orthotropic materials, J. Comp. Mat. 1, 200-206 (1967).
- [10] M. T. Huber, Właściwa praca odkształcenia jako miara wytężenia materiału, in: XXII, Lwów, Organ Towarzystwa Politechnicznego we Lwowie, (Proceedings of Lwów Polytechnic Society), XXII, No. 3, No. 4, No. 5, No. 6:80-81; 49-50; 61-62; 80-81 (1904).
- [11] M. T. Huber, Specific work of strain as a measure of material effort, (translated from the original paper in Polish), Arch. Mech. 56, 173-190 (2004).
- [12] K. Kowalczyk, J. Ostrowska-Maciejewska, R. B. Pęcherski, Anenergy-based yield criterion for solids of cubic elasticity andorthotropic limit state, Arch. Mech. 55 (5-6), 431-448 (2003).
- [13] K. Kowalczyk-Gajewska, J. Ostrowska-Maciejewska, Review onspectral decomposition of Hooke’s tensor for all symmetry groups of linear elastic materials, Engn. Trans. 57, 145-183 (2009).
- [14] A. C. Lund, C. A. Schuh, Strength asymmetry in nanocrystalline metals under multiaxial loading. Acta Materialia 53, 3193-3205 (2005).
- [15] R. Mises, Mechanik der plastischen Formänderung von Kristallen, ZAMM 8, 161-185 (1928).
- [16] F. Moayyedian, M. Kadkhodayan, Modified Burzynski criterion with non-associated flow rule for anisotropic asymmetric metals in plane stress problems, Appl. Math. Mech. 36 (3), 303-318 (2015).
- [17] F. Moayyedian, M. Kadkhodayan, A modified Burzynski criterion for anisotropic pressure-dependent materials, Sādhanā 42 (1), 95-109 (2017).
- [18] K. Nalepka, Material symmetry: a key to specification of interatomic potentials, Bull. Pol. Ac.-Tech. 61, 441-450 (2013).
- [19] K. Nalepka, K. Sztwiertnia, P. Nalepka, R. B. Pęcherski, The strength analysis of Cu/α-Al2O3 interfaces as a key for rational composite design, Arch. Metall. Mater. 60, 1953-1956 (2015).
- [20] K. T. Nalepka, R. B. Pęcherski, Modelling of the interatomic interactions in the copper crystal applied in the structure (111)Cu-(0001) Al2O3, Arch. Metall. Mater. 54, 511-522 (2009).
- [21] Z. Nowak, M. Nowak, R. B. Pęcherski, A plane stress elastic-plasticanalysis of sheet metal cup deep drawing processes, SSTA 2013, in: W. Pietraszkiewicz and J. Górski (Eds.), 10th Jubilee Conference on Shell Structures - Theory and Applications 3, 129-132 (2014).
- [22] S. Oller, E. Car, J. Lubliner, Definition of a general implicit orthotropic yield criterion, Comput. Meth. Appl. Mech. Eng. 192, 895-912 (2003).
- [23] W. Olszak, J. Ostrowska-Maciejewska, The plastic potential in the theory of anisotropic elastic-plastic solids, Eng. Fract. Mech. 21, 625-632 (1985).
- [24] J. Ostrowska-Maciejewska, R. B. Pęcherski, P. Szeptyński, Limit condition for anisotropic materials with asymmetric elastic range, Eng. Trans. 60, 125-138 (2012).
- [25] J. Ostrowska-Maciejewska, P. Szeptyński, R. B. Pęcherski, Mathematical foundations of limit criterion for anisotropic materials, Arch. Metall. Mater. 58, 1223-1235 (2013).
- [26] R. B. Pęcherski, Relation of microscopic observations to constitutive modelling of advanced deformations and fracture initiationof viscoplastic materials, Arch. Mech. 35, 257-277 (1983).
- [27] R. B. Pęcherski, Macroscopic measure of the rate of deformation produced by micro-shear banding, Arch. Mech. 49, 385-401 (1997).
- [28] R. B. Pęcherski, Macroscopic effects of micro-shear banding in plasticity of metals, Acta Mech. 131, 203-224 (1998).
- [29] R. B. Pęcherski, K. Nalepka, T. Frąś, M. Nowak, Inelastic Flow and Failure of Metallic Solids. Material Effort: Study Across Scales, in: Łodygowski T., Rusinek A. (Eds), Constitutive Relations under Impact Loadings, CISM International Centre for Mechanical Sciences 552, Springer, Vienna (2014).
- [30] O. R. Richmond, W. A. Spitzig. Pressure dependence and dilatancy of plastic flow, in: Proceedings of the 15th International Congress of Theoretical and Applied Mechanics, Toronto, Ont., Canada, North-Holland Publ. Co., Amsterdam, The Netherlands, pp. 377-386 (1980).
- [31] J. Rychlewski, Elastic energy decomposition and limit criteria, Uspekhi Mech. (in Russian) 7, 51-80 (1984).
- [32] J. Rychlewski, Elastic energy decomposition and limit criteria, Eng. Trans. (translated from the original paper in Russian) 59 (1), 31-63 (2011).
- [33] W. A. Spitzig, R. J. Sober, O. R. Richmond, The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory, Metall. Trans. 7A, 1704-1710 (1976).
- [34] P. Szeptyński, Energy-based yield criteria for orthotropic materials, exhibiting strength- differential effect. Specification for sheets under plane stress state, Arch. Metall. Mater. 62, 729-736 (2017).
- [35] P. Szeptyński, R. B. Pęcherski, Proposition of a new yield criterion for orthotropic metal sheets accounting for asymmetry of elastic range, Rudy i Metale (in Polish) 57, 243-250 (2012).
- [36] T. C. T. Ting, Can a linear anisotropic elastic material have a uniform contraction under a uniform pressure?, Math. Mech. Solids 6, 235-243 (2001).
- [37] S. W. Tsai, E. M. Wu, A general theory of strength for anisotropic materials, J. Comp. Mat. 5, 58-80 (1971).
- [38] G. Vadillo, J. Fernandez-Sáez, R. B. Pęcherski, Some applications of Burzyński yield condition in metal plasticity, Mat. Design 32, 628-635 (2011).
- [39] C. D. Wilson, A critical reexamination of classical metal plasticity, J. Appl. Mech. 69, 63-68, (2002).
- [40] M. Szymczyk, M. Nowak, W. Sumelka, Numerical study of dynamic properties of fractional viscoplasticity model, Symmetry 10 (282), 1-17 (2018).
- [41] W. Sumelka, M. Nowak, On a general numerical scheme for the fractional plastic flow rule, Mechanics of Materials 116, 120-129 (2018).
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a05c9708-9a4e-4e74-ad44-2d073d720d32