Abstract
The aim of this work is to develop a unified and rational formulation of isotropic and anisotropic hardening with;_n the framework of the tensor functions representation theory. We consider the evolution of the yield criteria during plastic deformations and we assume that this evolution depends on the strain history only through the present value of the plastic strain. For more complicated situations, the proposed concepts can be developed in a straightforward manner.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BACKHAUS, G., Zur Fliessgrenze bei Allgemeiner Verfestigung, ZAMM, 48 (1968): 99–108.
BALTOV, A. and SAWCZUK A., A Rule of Anisotropic Hardening, Acta Mech., 1 (1965): 81–92.
BOEHLER, J.P., Contributions Théoriques et Expérimentales à l’Etude des Milieux Plastiques Anisotropes, Thèse de Doctorat ès-Sciences, Grenoble, 1975.
BOEHLER, J.P., Lois de Comportement Anisotrope des Milieux Continus, J. de Mécanique, 17 (2), (1978): 153–190.
BOEHLER, J.P., A Simple Derivation of Representations for Non-Polynomial Constitutive Equations in Some Cases of Anisotropy, ZAMM, 59 (1979): 157–167.
BOEHLER, J.P., On a General Concept of Isotropic and Anisotropic Hardening. Part I: Theoretical (in preparation).
BOEHLER, J.P., On a General Concept of Isotropic and Anisotropic Hardening. Part II: Examples (in preparation).
BOEHLER, J.P. and RACLIN J., Ecrouissage Anisotrope des Matériaux Orthotropes Prédéformés, J. Mécanique Théorique et Appliquée, Numéro Spécial, 1982, 23–44.
BOEHLER, J.P. and RACLIN J., Anisotropic Hardening of Prestrained Rolled Sheet-Steel. In: Current Advances in Mechanical Design and Production, Proc. 2 nd Cairo Un. MDP Conf., Cairo University, 1982, 483–492.
BOEHLER, J.P. and RACLIN J., A Unified Theoretical and Experimental Study of Anisotropic Hardening, Trans. 6th Int. Conf. on SMIRT,North-Holland, Amsterdam, 1982, Invited Lecture L3/2.
CHABOCHE, J.L., Le Concept de Contrainte Effective Appliqué à l’Elasticité et à la Viscosité en Présence d’un Endommagement Anisotrope. In: Mechanical Behavior of Anisotropic Solids, Proc. Euromech Coll. 115-CNRS Int. Coll. 295 (Villard-de-Lans, June 1979 ), (Ed. J.P. Boehler ), Editions du CNRS (Paris) and Martinus Nijhoff, The Hague. 1982, 737–760.
Hill, R., The Mathematical Theory of Plasticity, Oxford University Press, Oxford, 1950.
HODGE, P.G., Discussion on W. Prager Paper “A New Method of Analyzing Stresses and Strains in Work-Hardening Plastic Solids”, J. Appl. Mech., 24 (1957): 482–483.
KACHANOV, L. M., Time of Rupture Process under Creep Conditions, Izv. Akad. Nauk SSR Otd. Tekh. Nauk,8 (1958), 26-31 (in Russian).
LEMAITRE J. and CHABOCHE J.L., Aspect Phénoménologique de la Rupture par Endommagement, J. Mécanique Appliquée, 2 (3), 1978, 317–365.
MURAKAMI S. and OHNO N., A Continuum Theory of Creep and Creep Damage. In: Creep in Structures, Proc. IUTAM Symp. (Leicester, Sept. 1980 ), (Ed. A.R.S. Ponter and D.R. Hayhurst), Springer, Berlin, 1981, 422444.
MURAKAMI, S. and SAWCZUK A., On Description of Rate-Independent Behavior for Prestrained Solids, Arch. Mech., 32 (1979): 251–264.
PRAGER, W., A New Method of Analyzing Stresses and Strains in Work-hardening Plastic Solids, J. Appl. Mech., 23 (4) (1956): 493–496.
REES, D.W.A., A Survey of Hardening in Metallic Materials. In: Failure Criteria of Structured Media, Proc. CNRS Int. Coll. 351 (Villard-de-Lans, June 1983), in press.
RIVLIN, R.S., Further Remarks on the Stress-Deformation Relations for Isotropic Materials, J. Rat. Mech. Anal. 4 (1955): 681–702.
SPENCER, A.J.M., The Formulation of Constitutive Equations for Anisotropic Solids. In: Mechanical Behavior of Anisotropic Solids, Proc. Euromech. Coll. 115-CNRS Int. Coll. 295 (Villard-de-Lans, June 1979 ), (Ed. J.P. Boehler ), Editions du CNRS (Paris) and Martinus Nijhoff, The Hague, 1982, 3–26.
SVENSSON, J.L., Anisotropy and the Bauschinger Effect in Cold Rolled Aluminium, J. Mech. Engng Sci., 8 (1966): 162–172.
TOUATI A., Comportement Mécanique des Sols Pulvérulents sous Fortes Contraintes, Thèse de Docteur-Ingénieur, Ecole Nationale des Ponts et Chaussées, Paris, 1982.
YOSHIMURA, Y., Hypothetical Theory of Anisotropy and the Bauschinger Effet Due to Plastic Strain History, Aero. Res. Inst.,Tokyo University, 349 (1959): 224–246.
ZIEGLER, H., A Modification to Prager’s Hardening Rule, Q.J. Appl. Math., 17 (55), (1959): 55–65.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Wien
About this chapter
Cite this chapter
Boehler, J.P. (1987). On a Rational Formulation of Isotropic and Anisotropic Hardening. In: Boehler, J.P. (eds) Applications of Tensor Functions in Solid Mechanics. International Centre for Mechanical Sciences, vol 292. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2810-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2810-7_6
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81975-3
Online ISBN: 978-3-7091-2810-7
eBook Packages: Springer Book Archive