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Research Papers: Design and Analysis

Statistical Evaluation of Local Stress and Strain of Three Dimensional Polycrystalline Material at Elevated Temperature

[+] Author and Article Information
Osamu Watanabe

Department of Engineering Mechanics and Energy  University of Tsukuba Tsukuba, Ibaraki 305-8573, Japan

J. Pressure Vessel Technol 134(1), 011208 (Dec 02, 2011) (16 pages) doi:10.1115/1.4004795 History: Received July 15, 2010; Revised June 29, 2011; Accepted June 30, 2011; Published December 02, 2011; Online December 02, 2011

The present paper presents results of numerical simulation for statistical evaluation of stress and strain at elevated temperature from view point of crystal plasticity level by employing a new Voronoi tessellation algorithm in the three dimensional geometry for general grain shape using first order tetrahedron element (four nodes). The elasticity tensors are assumed to include isotropic material and anisotropic material of FCC or BCC crystal using three material constant parameters. The employed finite element formulation is based on the updated Lagrange type expressed in the general form using trapezoidal integration rule in time domain, and the selective numerical integration scheme is used in the present analysis. The obtained numerical examples include the effects of employed finite elements, employed grain aggregate model, grain diameter size, and grain regularity on local stress. The statistical variation around mean value is investigated for the isotropic material and the anisotropic materials having different anisotropy ratio A in elastic range. The inelastic analysis at elevated temperature is also carried out for the anisotropic materials in order to investigate the statistical variation for the anisotropic materials in strain rate effect problem and creep strain program by introducing additional six cubic slip systems into the conventional 12 octahedral slip systems inelastic range.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Region, grain nucleation sites and Delaunay triangulation

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Figure 2

Flow chart of obtaining Voronoi points using Delaunay triangulation

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Figure 3

Voronoi vertices Qi (i = 1,2,3,…) on the bisector plane for points P0 and P1

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Figure 4

Flow chart of mapping of internal point to the boundary surfaces

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Figure 5

Flow chart of mapping of boundary point to the boundary surfaces

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Figure 6

Voronoi mesh-subdivision of “Level 1” having vertices Qi (i = 1,2,3…) on the bisector plane

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Figure 7

Mesh-subdivision for one grain

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Figure 9

Geometry of analysis model

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Figure 10

Regular brick, BCC and FCC grain models

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Figure 11

Random 40, 60, 80, and 100 grain model

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Figure 12

Geometry of analysis model and boundary condition

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Figure 13

Stress distribution in 61 irregular BCC model

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Figure 14

Stress distribution in 40 grain model

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Figure 15

Effect of material model on stress distribution using 100 grain model in Level 2 mesh

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Figure 16

Effect of regular grain model on stress distribution using Nickel in Level 2 mesh

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Figure 17

Effect of random grain model on stress distribution using Nickel in Level 2 mesh

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Figure 18

Effect of mesh model on stress distribution using Nickel material and random 40 grain model with Level 2 mesh

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Figure 19

Stress-strain curve in elasto-plastic analysis of Aluminum (Material constants of AL3-1, AL-2-1, AL2-2, AL2-3 in Table 3)

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Figure 20

Stress and strain distribution in elasto-plastic analysis of Aluminum (Material constants of AL3-1 in Table 3)

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Figure 21

Comparison of continuum model predictions and experimental results (Material constants of SUS-0 in Table 5)

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Figure 22

Comparison of continium model and crystal plasticity analysis using 12 octahedral slip model (Material constants of SUS-1 in Table 5)

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Figure 23

Effects of introducing six cubic slip systems for creep strain under constant load (Material constants of SUS-2 in Table 5)

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Figure 24

Stress and strain distribution for six cubic slip systems in creep strain problem (Material constants of SUS-2 in Table 5)

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Figure 25

Effects of active six cubic slip systems on creep strain problem (Material constants of SUS-3 in Table 5)

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Figure 26

Stress and strain distribution for active six cubic slip systems in creep strain problem (Material constants of SUS-3 in Table 5)

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Figure 8

Deformation gradient of reference configurations

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