0
TECHNICAL PAPERS

# 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

1

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

## Abstract

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.

<>

## Figures

Figure 1

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

Figure 2

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

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)

Figure 4

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

Figure 5

Feature/specimen size effects in sheet metal (25)

Figure 6

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

Figure 7

Illustration of the Schmid law (45)

Figure 8

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

Figure 9

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

Figure 10

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

Figure 11

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

Figure 12

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

Figure 13

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

Figure 14

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

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

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections