Yield criterion accounting for the third invariant of stress tensor deviator. Part I. Proposition of the yield criterion based on the concept of influence functions

• Autorzy: Nowak M. , Ostrowska-Maciejewska J. , Pęcherski R. B. , Szeptyński P.
• Języki publikacji: EN

Abstrakty

EN

A proposition of an energy-based hypothesis of material effort for isotropic materials ex-hibiting strength-differential (SD) e?ect, pressure-sensitivity and Lode angle dependence is discussed. It is a special case of a general hypothesis proposed by the authors in [11] for anisotropic bodies, based on Burzyński’s concept of influence functions [2] and Rychlewski’s concept of elastic energy decomposition [16]. General condition of the convexity of the yield surface is introduced, and its derivation is given in the second part of the paper. Limit condition is specified for Inconel 718 alloy, referring to the experimental results published by Iyer and Lissenden [7].

Słowa kluczowe

EN

yield criterion; stress

PL

kryterium plastyczności; naprężenie

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2011
• Tom: Vol. 59, iss. 4
• Strony: 273--281
• Opis fizyczny: Bibliogr. 21 poz., rys., wykr.

Twórcy

autor

Nowak M.

autor

Ostrowska-Maciejewska J.

autor

Pęcherski R. B.

autor

Szeptyński P.

• Universit´e Lille Nord de France F-59000 Lille, France

Bibliografia

• 1. J. P. Bardet, Lode dependences for isotropic pressure sensitive materials, J. Appl. Mech., 57, 498–506, 1990.
• 2. W. Burzyński, Studium nad hipotezami wytężenia, Akademia Nauk Technicznych, Lwów, 1928; see also: Selected passages from Włodzimierz Burzyński’s doctoral dissertation “Study on material effort hypotheses”, Engng. Trans., 57, 3–4, 185–215, 2009.
• 3. D. C. Drucker, W. Prager, Soil mechanics and plastic analysis for limit design, Quart. Appl. Math., 10, 2, 157–165, 1952.
• 4. R. Hill, A theory of the yielding and plastic flow of anisotropic metals, Proc. Roy. Soc. London, 193, 281–297, 1948.
• 5. O. Hoffman, The brittle strength of orthotropic materials, J. Comp. Mater., 1, 200–206, 1967.
• 6. M. T. Huber, Właściwa praca odkształcenia jako miara wytężenia materyału, Czasopismo Techniczne, 15, Lwów, 1904; see also: Specific work of strain as a measure of material effort, Arch. Mech., 56, 3, 173–190, 2004.
• 7. S. K. Iyer, C. J. Lissenden, Multiaxial constitutive model accounting for the strengthdifferential in Inconel 718, Int. J. Palst., 19, 2055–2081, 2003.
• 8. C. Lexcellent, A. Vivet, C. Bouvet, S. Calloch, P. Blanc, Experimental and numerical determinations of the initial surface of phase transformation under biaxial loading in some polycrystalline shape-memory alloys, J. Mech. Phys. Sol., 50, 2717–2735, 2002.
• 9. R. von Mises, Mechanik der festen K¨orper im plastisch deformablen Zustand, Gottin Nachr. Math. Phys., 1, 582—592, 1913.
• 10. R. von Mises, Mechanik der plastischen Form¨anderung von Kristallen, Z. Angew. Math. u. Mech., 8, 161–185, 1928.
• 11. J. Ostrowska–Maciejewska, R. B. Pęcherski, P. Szeptyński, Limit condition for anisotropic materials with asymmetric elastic range, Engng. Trans. (submitted for publication).
• 12. R. B. Pęcherski, P. Szeptyński, M. Nowak, An extension of Burzyński hypothesis of material effort accounting for the third invariant of stress tensor, Arch. Metall. Mat., 56, 2, 503–508, 2011.
• 13. J. Podgórski, Limit state condition and the dissipation function for isotropic materials, Arch. Mech., 36, 3, 323–342, 1984.
• 14. B. Raniecki, Z. Mróz, Yield or martensitic phase transformation conditions and dissipation functions for isotropic, pressure-insensitive alloys exhibiting SD effect, Acta. Mech., 195, 81–102, 2008.
• 15. J. Rychlewski, ”CEIIINOSSSTTUV” Matematicheskaya struktura uprugih tel, Preprint 217, IPM AN SSSR, Moscow, 1983.
• 16. J. Rychlewski, Razlozheniya uprugoi energii i kriterii predelnosti, Uspehi mehaniki, 7, 51–80, 1984; see also: Elastic energy decomposition and limit criteria, Engn. Trans., 59, 1, 31–63, 2011.
• 17. P. Szeptyński, Yield criterion accounting for the influence of the third invariant of stress tensor deviator. Part II: Analysis of convexity condition of the yield surface, Engng. Trans., 59, 4, 283–297, 2011.
• 18. P. Szeptyński, Some remarks on Burzyński’s failure criterion for anisotropic materials, Engng. Trans., 59, 2, 119–136, 2011.
• 19. P. S. Theocaris, The elliptic paraboloid failure criterion for cellular solids and brittle foams, Acta Mech., 89, 93–121, 1991.
• 20. S. W. Tsai, E. M. Wu, A general theory of strength for anisotropic materials, J. Comp. Mater., 5, 58–80, 1971.
• 21. M. Życzkowski, Combined loadings in the theory of plasticity, PWN, Warszawa, 1981.