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Research Papers

Modeling of Grain Shape Effect on Multiaxial Plasticity of Metallic Polycrystals

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

Laboratoire d'Ingénierie des Systèmes
Mécaniques et des Matériaux (LISMMA),
Supméca, 3 rue Fernand Hainaut,
93407 Saint Ouen Cedex, France
e-mail: aabdul@iu2t.univ-paris8.fr

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 20, 2012; final manuscript received January 24, 2013; published online March 25, 2013. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 135(2), 021011 (Mar 25, 2013) (10 pages) Paper No: MATS-12-1150; doi: 10.1115/1.4023779 History: Received June 20, 2012; Revised January 24, 2013

A simplified nonincremental interaction law is used describing the nonlinear elastic-inelastic behavior of FCC polycrystals proposed recently (Abdul-Latif and Radi, 2010, “Modeling of the Grain Shape Effect on the Elastic-Inelastic Behavior of Polycrystals with Self-Consistent Scheme,” ASME J. Eng. Mater. Technol., 132(1), p. 011008). In this scheme, the elastic strain defined at the granular level based on the Eshelby's tensor is assumed to be isotropic, uniform and compressible. Hence, the approach considers that the inclusion (grain) has an ellipsoidal shape of half axes defining by a, b and c such as a ≠ b = c. The granular heterogeneous inelastic strain is locally determined using the slip theory. Both elastic and inelastic granular strains depend on the granular aspect ratio (α = a/b). An aggregate of grains of ellipsoidal shape is supposed to be randomly distributed with a distribution of aspect ratios having a log-normal statistical function. The effect of this distribution on the mechanical behavior is investigated. A host of cyclic inelastic behavior of polycrystalline metals is predicted under uniaxial and multiaxial loading paths. Using the aluminum alloy 2024, an original complex cyclic loading path type is proposed and carried out experimentally. After the model parameters calibration, the elastic-inelastic cyclic behavior of this alloy is quantitatively described by the model. As a conclusion, the model can successfully describe the elasto-inelastic at the overall and local levels.

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Figures

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Fig. 1

Volume weighted grain-shape distribution determined with the mean aspect ratio of 1 with different standard deviations of: (a) S = 0.1, (b) S = 0.01, (c) S = 0.001

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Fig. 2

Employed cyclic loading paths

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Fig. 3

Experimental curves of aluminum alloy 2024 (a): Σ11-E11, (b): Σ12-E12 and (c): Σ1112 for tri-type test up to cyclic stabilization

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Fig. 4

Predicted uniaxial stress-strain for the cyclic steady state for different distributions of grain shape having different standard deviation of S = 0, 0.1, 0.01, and 0.001

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Fig. 5

Programming flow chart of the model

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Fig. 6

Plots showing the correlation of the self-consistent model with corresponding experimental responses (first cycle and stabilized one) for aluminum alloy 2024 under different loading path complexity in: (a) TC, (b) TT90, and (c) butterfly

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Fig. 7

Comparison between the experimental and predicted evolutions at steady-state for aluminum alloy 2024 under Tri-type loading path

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Fig. 8

Comparison between the experimental and predicted evolutions of the maximum von-Mises stress at steady-state for aluminum alloy 2024 under the four employed cyclic loading paths using for the simulations three distributions of grain shape with standard deviations of S = 0, 0.1, 0.01, and 0.001

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