Modeling of the Size Effects on the Behavior of Metals in Microscale Deformation Processes

[+] Author and Article Information
Gap-Yong Kim, Jun Ni

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109

Muammer Koç1

NSF I/UCR Center for Precision Forming (CPF), Department of Mechanical Engineering, Virginia Commonwealth University (VCU), Richmond, VA 23284


Corresponding author.

J. Manuf. Sci. Eng 129(3), 470-476 (Dec 04, 2006) (7 pages) doi:10.1115/1.2714582 History: Received September 19, 2005; Revised December 04, 2006

For the accurate analysis and design of microforming process, proper modeling of material behavior at the micro/mesoscale is necessary by considering the size effects. Two size effects are known to exist in metallic materials. One is the “grain size” effect, and the other is the “feature/specimen size” effect. This study investigated the feature/specimen size effect and introduced a scaling model which combined both feature/specimen and grain size effects. Predicted size effects were compared with three separate experiments obtained from previous research: a simple compression with a round specimen, a simple tension with a round specimen, and a simple tension in sheet metal. The predicted results had a very good agreement with the experiments. Quantification of the miniaturization effect has been achieved by introducing two parameters, α and β, which can be determined by the scaling parameter n, to the Hall–Petch equation. The scaling model offers a simple way to model the size effect down to length scales of a couple of grains and to extend the use of continuum plasticity theories to micro/mesolength scales.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Illustration of two types of scaling effects: the “grain size effect” and the “feature/specimen size effect”

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Figure 3

Hall–Petch results for the polycrystalline aluminum (31): (1) >99.987 Al (38); (2) 99.992 Al (39); (3) 99.999 Al (36)

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Figure 4

Feature/specimen size effects in round specimens (4-5,15-16,24)

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Figure 5

Feature/specimen size effects in sheet metal (25)

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Figure 2

Stress–strain curves of 99.999% aluminum for various n values (36)

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Figure 6

Illustration of reduction of internal grain boundary length per area (GBi/area) with miniaturization

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Figure 7

Illustration of the Schmid law (45)

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Figure 8

Flow stress (σ) and Hall–Petch constants (σ0 and k) as a function of strain for 99.999% Al (36)

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Figure 9

The average value of orientation factor, M, for aluminum and copper (43)

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Figure 10

Comparison of the experimental (4-5,15-16,24) and calculated results for the case of round specimens

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Figure 11

Comparison of the Hall–Petch constants between the experiment (44) and the values obtained by calculation

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Figure 12

Comparison of flow stresses calculated by Eq. 8 and “surface layer model” by Engel (24)

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Figure 14

Parameters α and β, and their dependence on n=D∕d (D=feature size, d=grain size)

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Figure 13

Calculated results using Eq. 8 based on the experiment by Hansen (36)

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Figure 15

Flow stress predicted and compared for λ=0.5 based on experimentally obtained values at λ=0.1 and λ=1.0 for sheet metal



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