Elasto-viscoplastic constitutive equations for polycrystalline metals: Application to tantalum

We attempt to formulate the elasto-plastic constitutive equations which reflect the basic features of the microscopic mechanism of plastic deformation and at the same time remains sufficiently simple to be applicable in FEM solution of the practical problems. The constitutive equations are based on a simplified verison of polycrystal plasticity. In modeling of the properties of single crystal grains of the polycrystal attention is paid to active and latent hardenings, and especially to the Bauschinger effect. The stress response along three sets of typical examples of complex deformation histories are predicted and compared with precise data of tension-torsion tests. The predictions are in good agreement with the observed behavior.

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A Study on a Semimicroscopic Formulation of Inelastic Constitutive Equations of Polycrystalline Metals Subjected to a Large Deformation

Journal of Engineering Materials and Technology ◽

10.1115/1.3226469 ◽

1989 ◽

Vol 111 (3) ◽

pp. 294-298 ◽

Cited By ~ 3

Author(s):

M. Tokuda ◽

K. Yamada ◽

F. Havlicek

Keyword(s):

Large Deformation ◽

Constitutive Equations ◽

Deformation Process ◽

Grain Shape ◽

Shape Change ◽

Strain Range ◽

Small Strain ◽

Polycrystalline Metal ◽

Polycrystalline Metals ◽

Hardening Mechanisms

Work-hardening mechanisms of a polycrystalline metal significant in a large deformation range are different from those in a small strain range. That is, a texture development and an effect of grain shape change may be typical and important mechanisms in the large deformation process. In this paper, a set of inelastic constitutive equations incorporating two effects are derived theoretically on the basis of crystal plasticity.

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A TEM study of the microstructure of avian eggshells

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100130146 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1102-1103

Author(s):

S. Q. Xiao ◽

S. Baden ◽

A. H. Heuer

Keyword(s):

Electron Microscope ◽

Calcium Carbonate ◽

Nucleation And Growth ◽

Growth Mechanisms ◽

Shell Surface ◽

Thin Sections ◽

Polycrystalline Metals ◽

Transmission Electron ◽

Nucleation And Growth Mechanisms

The avian eggshell is one of the most rapidly mineralizing biological systems known. In situ, 5g of calcium carbonate are crystallized in less than 20 hrs to fabricate the shell. Although there have been much work about the formation of eggshells, controversy about the nucleation and growth mechanisms of the calcite crystals, and their texture in the eggshell, still remain unclear. In this report the microstructure and microchemistry of avian eggshells have been analyzed using transmission electron microscope (TEM) and energy dispersive spectroscopy (EDS).Fresh white and dry brown eggshells were broken and fixed in Karnosky's fixative (kaltitanden) for 2 hrs, then rinsed in distilled H2O. Small speckles of the eggshells were embedded in Spurr medium and thin sections were made ultramicrotome.The crystalline part of eggshells are composed of many small plate-like calcite grains, whose plate normals are approximately parallel to the shell surface. The sizes of the grains are about 0.3×0.3×1 μm3 (Fig.l). These grains are not as closely packed as man-made polycrystalline metals and ceramics, and small gaps between adjacent grains are visible indicating the absence of conventional grain boundaries.

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On the Validity of the Maxwell Model and Related Constitutive Equations; a Study Based on the First Normal Stress Coefficient

Journal de Physique I ◽

10.1051/jp1:1997153 ◽

1997 ◽

Vol 7 (12) ◽

pp. 1523-1533

Author(s):

H.-P. Wittmann

Keyword(s):

Normal Stress ◽

Constitutive Equations ◽

Maxwell Model ◽

Stress Coefficient

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Prediction of Tread Pattern Wear by an Explicit Finite Element Model3

Tire Science and Technology ◽

10.2346/1.2804913 ◽

2007 ◽

Vol 35 (4) ◽

pp. 276-299 ◽

Cited By ~ 18

Author(s):

J. C. Cho ◽

B. C. Jung

Keyword(s):

Finite Element ◽

Wear Rate ◽

Tangential Stress ◽

Rate Equation ◽

Constitutive Equations ◽

Slip Velocity ◽

Test Results ◽

Explicit Finite Element ◽

Driving Condition ◽

Driving Conditions

Abstract Tread pattern wear is predicted by using an explicit finite element model (FEM) and compared with the indoor drum test results under a set of actual driving conditions. One pattern is used to determine the wear rate equation, which is composed of slip velocity and tangential stress under a single driving condition. Two other patterns with the same size (225/45ZR17) and profile are used to be simulated and compared with the indoor wear test results under the actual driving conditions. As a study on the rubber wear rate equation, trial wear rates are assumed by several constitutive equations and each trial wear rate is integrated along time to yield the total accumulated wear under a selected single cornering condition. The trial constitutive equations are defined by independently varying each exponent of slip velocity and tangential stress. The integrated results are compared with the indoor test results, and the best matching constitutive equation for wear is selected for the following wear simulation of two other patterns under actual driving conditions. Tens of thousands of driving conditions of a tire are categorized into a small number of simplified conditions by a suggested simplification procedure which considers the driving condition frequency and weighting function. Both of these simplified conditions and the original actual conditions are tested on the indoor drum test machines. The two results can be regarded to be in good agreement if the deviation that exists in the data is mainly due to the difference in the test velocity. Therefore, the simplification procedure is justified. By applying the selected wear rate equation and the simplified driving conditions to the explicit FEM simulation, the simulated wear results for the two patterns show good match with the actual indoor wear results.

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