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Research Papers

Modeling of Size Effect on Tensile Flow Stress of Sheet Metal in Microforming

[+] Author and Article Information
Daw-Kwei Leu

Department of Mechanical Engineering, Technology and Science Institute of Northern Taiwan, No. 2 Xue Yaun Road, Beitou, Taipei, Taiwan 112, R.O.C.dkleu@tsint.edu.tw

J. Manuf. Sci. Eng 131(1), 011002 (Dec 11, 2008) (8 pages) doi:10.1115/1.3039520 History: Received March 31, 2008; Revised October 01, 2008; Published December 11, 2008

Abstract

This investigation considers the size effect on the deformation behavior of simple tension in microforming and thus proposes a simple model of the tensile flow stress of sheet metal. Experimental results reveal that the measure of the flow stress can be represented as a hyperbolic function $tanh(T/D)$, which is a function of $T/D$ (sheet thickness/grain size). The predicted flow stress agrees very well with the published experiment. Notably, a specimen with smaller grains has lower normalized flow stress for a given $T/D$. Since the material properties of the macroscale specimen do not pertain to the microscale, a critical condition $(T/D)c$ that distinguishes the macroscale from the microscale in the tensile flow stress is subsequently proposed, based on the “affected zone” model, the pile-up theory of dislocations, and the Hall–Petch relation. The distribution of the predicted $(T/D)c$ is similar to the experimental finding that the $(T/D)c$ decreases as the grain size increases. However, the orientation-dependent factor $β$ is sensitive to $(T/D)c$. Hence, further study of the orientation-dependent factor $β$ is necessary to obtain a more accurate $(T/D)c$ and, thus, to evaluate and understand better the tensile flow stress of sheet metal in microforming.

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Figures

Figure 1

Dislocation pile-up at an obstacle

Figure 2

The model of the affected zone (13)

Figure 3

The effect of T/D on the normalized stress S at 20% strain in polycrystalline Al, and the experiment was carried out by Miyazaki (13)

Figure 4

The effect of T/D on the normalized stress S at 20% strain in polycrystalline Cu, and the experiment was carried out by Miyazaki (13)

Figure 5

The effect of T/D on the normalized stress S at 20% strain in polycrystalline Cu–13 at. %Al, and the experiment was carried out by Miyazaki (13)

Figure 6

The effect of T/D on the normalized stress S in polycrystalline Fe for lower yield stress and the experiment was carried out by Miyazaki (13)

Figure 7

The effect of T/D on the normalized stress S in polycrystalline Fe for upper yield stress and the experiment was carried out by Miyazaki (13)

Figure 8

(a) The effect of T/D on the normalized stress S at strain ε=0.05 and D=62 μm in polycrystalline CuZn15, and the experiment was carried out by Geiger (4). (b) The effect of T/D on the normalized stress S at strain ε=0.10 and D=62 μm in polycrystalline CuZn15, and the experiment was carried out by Geiger et al. (4). (c) The effect of T/D on the normalized stress S at strain ε=0.18 and D=62 μm in polycrystalline CuZn15, and the experiment was carried out by Geiger (4).

Figure 9

(a) The effect of grain size D on the critical values (T/D)c for Cu and Cu–13 at. %Al, and the experiment was carried out by Miyazaki (13). (b) The effect of grain size D on the critical values (T/D)c for Fe (upper and lower YS) and Al, and the experiment was carried out by Miyazaki (13).

Figure 10

The effect of grain size D on the orientation-dependent factor β for various materials based on the true values of (T/D)c carried out by Miyazaki (13)

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