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Research Papers

A Plasticity Model for Metals With Dependency on All the Stress Invariants

[+] Author and Article Information
George Z. Voyiadjis

Department of Civil and Environmental Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: voyiadjis@eng.lsu.edu

S. H. Hoseini

e-mail: s.hamedhoseini@mech.sharif.edu

G. H. Farrahi

e-mail: farrahi@sharif.edu
School of Mechanical Engineering,
Sharif University of Technology,
Tehran, 11365-8639, Iran

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received March 25, 2012; final manuscript received July 16, 2012; published online December 21, 2012. Editor: Hussein Zbib.

J. Eng. Mater. Technol 135(1), 011002 (Dec 21, 2012) (13 pages) Paper No: MATS-12-1059; doi: 10.1115/1.4007386 History: Received March 25, 2012; Revised July 16, 2012

Recent experiments on metals have shown that all of the stress invariants should be involved in the constitutive description of the material in plasticity. In this paper, a plasticity model for metals is defined for isotropic materials, which is a function of the first stress invariant in addition to the second and the third invariants of the deviatoric stress tensor. For this purpose, the Drucker–Prager yield criterion is extended by addition of a new term containing the second and the third deviatoric stress invariants. Furthermore for estimating the cyclic behavior, new terms are incorporated into the Chaboche's hardening evolution equation. These modifications are applied by adding new terms that include the effect of pervious plastic history of deformation on the current hardening evaluation equation. Also modified is the isotropic hardening rule with incorporating the effect of the first stress invariant. For calibration and evaluation of this plasticity model, a series of experimental tests are conducted on high strength steel, DIN 1.6959. In addition, finite element simulations are carried out including integration of the constitutive equations using the modified return mapping algorithm. The modeling results are in good agreement with experiments.

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Figures

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Fig. 1

Cylindrical coordinate system in the space of the principal stresses

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Fig. 2

Schematic representation of the yield surface in (a) π-plane and (b) 2D plane stress

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Fig. 3

Flow diagram of the return mapping algorithm with the recursive procedure flow

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Fig. 4

(a) The smooth round bar, (b) the notched round bar with medium notch radius, (c) the notched round bar with sharp notch radius, and (d) the doubly grooved plate

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Fig. 5

The change of Young's modulus versus the accumulated plastic strain in tension

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Fig. 6

The change of Young's modulus due to plastic deformation

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Fig. 7

The force–displacement response of the smooth round bar in tension and compression loading, for the compression loading the absolute values are shown

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Fig. 8

The effect of damage and kinematic hardening corrections on the numerical results

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Fig. 9

The comparison between the numerical and the experimental result in cyclic loading

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Fig. 10

The force–displacement response of (a) the medium notch radius specimen and (b) the sharp notch radius specimen under the tension and compression loadings. For the compression loading the absolute values are shown.

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Fig. 11

The effect of the damage and the hardening corrections on the numerical results of (a) the medium notch radius and (b) the sharp notch radius specimen

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Fig. 12

The comparison between the numerical and the experimental results in the cyclic loading of (a) the medium notch radius and (b) the sharp notch radius specimen

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Fig. 13

The force–displacement response of the doubly grooved plate simulations and experimental results under (a) simple tension with and without Lode angle effect and (b) tension and compression loadings. For the compression loading, the absolute values are shown.

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Fig. 14

The effect of damage and the hardening correction on the numerical results

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Fig. 15

The comparison between the numerical and the experimental results in cyclic loading on the doubly grooved plates

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