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Research Papers

Modeling of the Grain Shape Effect on the Elastic-Inelastic Behavior of Polycrystals With Self-Consistent Scheme

[+] Author and Article Information
A. Abdul-Latif, M. Radi

Laboratoire de Mécanique, Matériaux et Modélisation (L3M), Université Paris 8, 93290 Tremblay-en-France, France

J. Eng. Mater. Technol 132(1), 011008 (Nov 03, 2009) (12 pages) doi:10.1115/1.3184036 History: Received January 07, 2009; Revised March 28, 2009; Published November 03, 2009; Online November 03, 2009

Based on a well established nonincremental interaction law for fully anisotropic elastic-inelastic behavior of polycrystals, tangent formulation-based and simplified interaction laws of softened nature are derived to describe the nonlinear elastic-inelastic behavior of fcc polycrystals. Using the Eshelby’s tensor, the developed approach considers that the inclusion (grain) form is ellipsoidal. It has been clearly demonstrated by Abdul-Latif (2002, “Elastic-Inelastic Self-Consistent Model for Polycrystals,” ASME J. Appl. Mech., 69, pp. 309–316) for spherical inclusion that the tangent formulation-based model requires more calculation time, and is incapable to describe correctly the multiaxial elastic-inelastic behavior of polycrystals in comparison with the simplified model. Hence, the simplified nonincremental interaction is studied considering the grain shape effect. A parametric study is conducted showing principally the influence of the some important parameters (the grain shape (α) and the new viscous parameter γ) and the effect of their interaction on the hardening evolution of polycrystals. Quantitatively, it is recognized that the model describes suitably the grain shape effect together with the new viscous parameter γ on the strain-stress behavior of aluminum and Waspaloy under tensile test.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Effect of the grain shape (α) on the evolution of mean slip system per grain during tensile load

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Figure 3

Comparison between the two selected grains behaviors showing the heterogeneity at the granular level due to the difference in grain orientation

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Figure 4

Effect of the parameter α on the granular heterogeneities of (a) axial stress, (b) axial elastic strain, and (c) axial inelastic strain at the end of loading within the aggregate of 400 grains

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Figure 14

Microstructure of (a) aluminum (42) and (b) Waspaloy (43)

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Figure 15

Plots showing the predictions of the proposed model with corresponding experimental responses for (a) aluminum and (b) Waspaloy in tensile test

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Figure 1

Grain shape effect on the overall polycrystal uniaxial response

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Figure 7

Effect of the grain shape on the intragranular isotropic hardening evolution for a given system and grain

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Figure 8

Effect of the new model parameter γ on the overall polycrystal uniaxial tensile response

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Figure 9

Effect of γ on the evolution of mean slip system per grain during tensile load

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Figure 10

Effect of the parameter γ on the granular heterogeneities of (a) axial stress, (b) axial elastic strain, and (c) axial inelastic strain at the end of loading within the aggregate of 400 grains

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Figure 11

Effect of γ on the interaction type (hard or soft) of a given grain with its matrix for (a) elastic part and (b) plastic part

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Figure 12

Effect of γ on the intragranular isotropic hardening evolution

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Figure 13

Influence of α and γ parameters and their interaction on the evolution of overall yield stress of the polycrystal

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Figure 5

Effect of α on the interaction type (hard or soft) of a given grain with its matrix for (a) elastic part and (b) plastic part

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Figure 6

Effect of the grain shape (α) on the slip evolution for a given system and grain

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