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Erschienen in:
Measurement Principles and Structures Kapitel lesen Erstes Kapitel lesen

2006 | OriginalPaper | Buchkapitel

18. Continuum Constitutive Modeling

verfasst von : Shoji Imatani

Erschienen in: Springer Handbook of Materials Measurement Methods

Verlag: Springer Berlin Heidelberg

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Abstract

Constitutive models play an important role when characterizing structural materials in order to evaluate their thermomechanical behavior. The experimental characterization of materials (using techniques discussed in Part C of this Handbook) involves measuring and controlling macroscopic variables such as force, displacement and temperature. Concise models are also of great use when characterizing the continuous media used to create structural materials, because phenomenological modeling can be carried out regardless of the internal material structure. This continuum modeling usually successfully describes the behavior of various classes of material under complex boundary conditions.
This chapter presents phenomenological constitutive models from both macroscopic and microscopic viewpoints:
  • Starting from viscoplasticity models, model performance is reviewed in order to predict the mechanical response under creep–plasticity interaction conditions, taking into account internal state variables.
  • Material anisotropy is discussed; mathematical modeling of initial anisotropy and induced anisotropy based on the representation theorem for higher order isotropic tensors is presented.
  • Thermomechanical coupling phenomena involving phase transformations predominate in engineering applications of heat treatment and material processing. A continuum model is presented that takes into account the way structural rearrangement evolves in materials.
  • Finally, microscopic analysis based on crystal plasticity, which relates the resolved shear stress to crystal slip, is applied to describe the inhomogeneous deformation process in polycrystalline materials.

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Vorheriges Kapitel Molecular Dynamics
Nächstes Kapitel Finite Element and Finite Difference Methods
Literatur
18.1.
L. E. Malvern: Introduction to the Mechanics of a Continuous Medium (Prentice-Hall, Englewood 1969)
18.2.
P. Perzyna: Thermodynamic theory of viscoplasticity, Adv. Appl. Mech. 11, 313–354 (1971)CrossRef
18.3.
A. K. Miller: Unified Constitutive Equations for Creep and Plasticity (Elsevier, London 1987)
18.4.
A. S. Krausz, K. Krausz: Unified Constitutive Laws of Plastic Deformation (Academic, San Diego 1996)
18.5.
J. Lemaitre, J. L. Chaboche: Mechanics of Solid Materials (Cambridge Univ. Press, Cambridge 1994)
18.6.
G. A. Maugin: Thermomechanics of Plasticity and Fracture (Cambridge Univ. Press, Cambridge 1995)
18.7.
A. K. Miller: An inelastic constitutive model for monotonic, cyclic, and creep deformation, Trans ASME J. Eng. Mater. Technol. 98, 97–105 (1976)CrossRef
18.8.
M. C. M. Liu, E. Krempl: A uniaxial viscoplastic model based on total strain and overstress, J. Mech. Phys. Solids 27, 377–391 (1979)CrossRef
18.9.
S. R. Bodner, A. Merzer: Viscoplastic constitutive equations for copper with strain rate history and temperature effects, Trans. ASME J. Appl. Mech. 100, 388–394 (1978)
18.10.
Y. Estrin, H. Mecking: An extension of the Bodner-Partom model of plastic deformation, Int. J. Plasticity 1, 73–85 (1985)
18.11.
K. C. Valanis: A theory of viscoplasticity without a yield surface, Arch. Mech. 23, 517–551 (1971)
18.12.
D. Kujawski, Z. Mroz: A viscoplastic material model and its application to cyclic loading, Acta Mech. 36, 213–230 (1980)CrossRef
18.13.
Y. F. Dafalias, E. P. Popov: A model for nonlinear hardening materials for complex loading, Acta Mech. 21, 173–192 (1975)CrossRef
18.14.
N. Ohno: A constitutive model for cyclic plasticity with a nonlinear strain region, Trans. ASME, J. Appl. Mech. 49, 721–727 (1982)CrossRef
18.15.
O. Watanabe, S. N. Atluri: Constitutive modeling of cyclic plasticity and creep using internal time concept, Int. J. Plasticity 2, 107–134 (1986)CrossRef
18.16.
T. Inoue, N. Ohno, A. Suzuki, T. Igari: Evaluation of inelastic constitutive models under plasticity-creep interaction for 2.1/4Cr-1Mo steel, Nucl. Eng. Des. 114, 295–309 (1989)CrossRef
18.17.
T. Inoue, F. Yoshida, N. Ohno, M. Kawai, Y. Niitsu, S. Imatani: Evaluation of inelastic constitutive models under plasticity-creep interaction in multiaxial stress state, Nucl. Eng. Des. 126, 1–11 (1991)CrossRef
18.18.
T. Inoue, S. Imatani, Y. Fukuda, K. Fujiyama, K. Aoto, K. Tamura: Inelastic stress-strain response for notched specimen of 2.1/4Cr-1Mo steel at 600°C, Nucl. Eng. Des. 150, 129–139 (1994)CrossRef
18.19.
A. J. M. Spencer: Theory of invariants. In: Continuum Physics, Vol. 1, ed. by C. A. Eringen (Academic, New York 1971) pp. 239–353
18.20.
A. J. M. Spencer: Isotropic invariants of tensor functions. In: Application of Tensor Functions in Solid Mechanics, CISM Courses and Lectures, Vol. 292, ed. by J. P. Boehler (Springer, Berlin, Heidelberg 1987) pp. 141–169
18.21.
R. Hill: The Mathematical Theory of Plasticity (Oxford Univ. Press, Oxford 1950)
18.22.
Y. Tomita, A. Shindo: Onset and growth of wrinkles in thin square plates subjected to diagonal tension, Int. J. Mech. Sci. 30, 921–931 (1988)CrossRef
18.23.
S. Imatani, T. Saitoh, K. Yamaguchi: Finite element analysis of out-of-plane deformation in laminated sheet metals based on an anisotropic plasticity model, Mater. Sci. Res. Int. 1, 89–94 (1995)
18.24.
A. Phillips, R. Kasper: On the foundation of thermoplasticity; an experimental investigation, Trans. ASME J. Appl. Mech. 40, 891–896 (1973)CrossRef
18.25.
E. Shiratori, K. Ikegami: Studies of the anisotropic yield condition, J. Mech. Phys. Solids 17, 473–491 (1969)CrossRef
18.26.
A. Baltov, A. Sawczuk: A rule of anisotropic hardening, Acta Mech. 1, 81–92 (1965)CrossRef
18.27.
J. F. Williams, N. L. Svensson: A rationally based yield criterion for workhardening materials, Meccanica 6, 104–114 (1971)CrossRef
18.28.
D. W. A. Rees: The theory of scalar plastic deformation function, Z. Angew. Math. Mech. 63, 217–228 (1983)CrossRef
18.29.
D. C. Drucker: Relation of experiments to mathematical theories of plasticity, Trans. ASME, J. Appl. Mech. 16, 349–357 (1949)
18.30.
P. Mazilu, A. Meyers: Yield surface description of isotropic materials after cold prestrain, Ing. Archiv. 55, 213–220 (1985)CrossRef
18.31.
S. Imatani, M. Teraura, T. Inoue: An inelastic constitutive model accounting for deformation-induced anisotropy, Trans. JSME A 55, 2042–2048 (1989)
18.32.
N. Ohno, J. D. Wang: Kinematic hardening rules with critical state of dynamic recovery, Int. J. Plasticity 9, 375–390 (1993)CrossRef
18.33.
T. Inoue, Z. G. Wang: Coupling between stresses, temperature and metallic structures during processes involving phase transformation, Mater. Sci. Tech. 1, 845–850 (1985)
18.34.
R. M. Bowen: Theory of mixture. In: Continuum Physics, Vol. 3, ed. by C. A. Eringen (Academic, New York 1976) pp. 1–127
18.35.
T. Inoue, T. Yamaguchi, Z. G. Wang: Stresses and phase transformations occurring in quenching of carburized steel gear wheel, Mater. Sci. Tech. 1, 872–876 (1985)
18.36.
P. Ding, T. Inoue, S. Imatani, D. Y. Ju, E. de Vries: Simulation of the forging process incorporating strain-induced phase transformation using the finite volume method (Part I: Basic theory and numerical methodology), Mater. Sci. Res. Int. 7, 19–26 (2001)
18.37.
S. Bhattacharyya, G. Kehl: Isothermal transformation of austenite under externally applied tensile stress, Trans. ASM 47, 351–379 (1955)
18.38.
M. Fujita, M. Suzuki: The effect of high pressure on the isothermal transformation in high purity Fe-C alloys and commercial steels, Trans. ISIJ 14, 44–53 (1974)
18.39.
S. V. Radcliffe, M. Schatz: The effect of high pressure on the martensitic reaction in iron-carbon alloys, Acta. Metall. Mater. 10, 201–207 (1962)CrossRef
18.40.
W. A. Johnson, F. R. Mehl: Reaction kinetics in processes of nucleation and growth, Trans. AIME 135, 416–458 (1939)
18.41.
C. L. Magee: The nucleation of martensite. In: Phase Transformation, ed. by H. I. Aaronson (ASM Int., Metals Park, OH 1968)
18.42.
K. Shinagawa, H. Nishikawa, T. Ishikawa, Y. Hosoi: Deformation-induced martensitic transformation in type 304 stainless steel during cold upsetting, Iron Steel 3, 156–162 (1990)
18.43.
P. Ding, D. Y. Ju, T. Inoue, S. Imatani, E. de Vries: Simulation of the forging process incorporating strain-induced phase transformation using the finite volume method (Part II: Effects of strain rate on structural change and mechanical behavior), Mater. Sci. Res. Int. 7, 27–33 (2001)
18.44.
G. I. Taylor: Plastic strain in metals, J. Inst. Metals 62, 307–324 (1938)
18.45.
R. J. Asaro: Micromechanics of crystals and polycrystals, Adv. Appl. Mech. 23, 1–115 (1983)CrossRef
18.46.
J. W. Hutchinson: Bounds and self-consistent estimates for creep of polycrystalline materials, Proc. R. Soc. London A 348, 101–127 (1976)CrossRef
18.47.
J. R. Rice: Inelastic constitutive relations for solids, J. Mech. Phys. Solids 19, 433–455 (1971)CrossRef
18.48.
T. Inoue, S. Torizuka, K. Nagai, K. Tsuzaki, T. Ohashi: Effect of plastic strain on grain size of ferrite transformed from deformed austenite in Si-Mn steel, Mater. Sci. Tech. 17, 1580–1588 (2001)
18.49.
E. van der Giessen, V. Tvergaard: A creep rupture model accounting for cavitation at sliding grain boundaries, Int. J. Fracture 48, 153–178 (1991)CrossRef
18.50.
G. Beer: An isoparametric joint/interface element for finite element analysis, Int. J. Num. Meth. Eng. 21, 585–600 (1985)CrossRef
18.51.
R. Kawakami, S. Imatani, R. Maeda: Effects of crystal grain and grain boundary sliding on the deformation of polycrystal, J. Soc. Mater. Sci. Jpn. 52, 112–118 (2003)
Metadaten
Titel
Continuum Constitutive Modeling
verfasst von
Shoji Imatani
Copyright-Jahr
2006
Buch
Springer Handbook of Materials Measurement Methods

Print ISBN: 978-3-540-20785-6

Electronic ISBN: 978-3-540-30300-8

Copyright-Jahr: 2006

DOI
https://doi.org/10.1007/978-3-540-30300-8_18

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