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Technical Brief

# Identification of an Empirical Equation for Predicting Free Surface Roughness Evolution in Thin Sheets of Aluminum Alloy and Pure Copper

[+] Author and Article Information
Tsuyoshi Furushima

Institute of Industrial Science,
The University of Tokyo,
4-6-1 Komaba,
Meguro 153-8505, Tokyo, Japan
e-mail: tsuyoful@iis.u-tokyo.ac.jp

Hideki Sato

Department of Mechanical Engineering,
Tokyo Metropolitan University,
1-1 Minami-osawa,
Hachioji 192-0397, Tokyo, Japan

Ken-ichi Manabe

Department of Mechanical Engineering,
Tokyo Metropolitan University,
1-1 Minami-osawa,
Hachioji 192-0397, Tokyo, Japan
e-mail: manabe@tmu.ac.jp

Sergei Alexandrov

Institute for Problems in Mechanics
Moscow 119526, Russia
e-mail: sergeyaleksandrov@yahoo.com

1Present address: 293 Yoshida, Totsuka, Yokohama, Kanagawa 244-0817 Japan. Manuscript received September 28, 2016; final manuscript received December 1, 2017; published online January 25, 2018. Assoc. Editor: Yannis Korkolis.

J. Manuf. Sci. Eng 140(3), 034501 (Jan 25, 2018) (6 pages) Paper No: MANU-16-1522; doi: 10.1115/1.4038822 History: Received September 28, 2016; Revised December 01, 2017

## Abstract

This paper deals with the identification of an empirical equation for predicting free surface roughness evolution. The equation has been proposed elsewhere, and, in contrast to widely used equations, assumes that the evolution of free surface roughness is controlled by two kinematic variables, the equivalent strain, and the logarithmic strain normal to the free surface. Therefore, an experimental program is designed to account for the effect of the mode of deformation on free surface roughness evolution. Thin sheets of aluminum alloy A5052-O and pure copper C1220P-O alloys are used to conduct the experimental program. In addition, numerical simulation is performed to calculate the evolution of free surface roughness under the same conditions. Comparison of experimental and numerical results shows that the accuracy of the numerical results is good enough. Then, numerical simulation is extended to the domain in which no experimental results are available. Discrete functions so found are fitted to polynomials. As a result, continuous functions that represent the empirical equation for predicting free surface roughness evolution for A5052-O and C1220P-O alloys are determined. These equations can be used in conjunction with solutions to boundary value problems in plasticity for predicting the evolution of free surface roughness in metal forming processes.

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## References

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## Figures

Fig. 1

Illustration of the function Ω involved in Eq. (1)

Fig. 2

Isotropy of free surface roughness evolution in A5052-O sheets

Fig. 3

Isotropy of free surface roughness evolution in C1220P-O sheets

Fig. 4

Evolution of free surface roughness in the plane strain tension test of (a) A5052-O and (b) C1220P-O sheets

Fig. 5

Evolution of free surface roughness in the biaxial tension test of (a) A5052-O and (b) C1220P-O sheets

Fig. 6

Representative element for finite element simulation of free surface roughness evolution

Fig. 7

Discrete and continuous functions Ω involved in Eq. (1) for (a) A5052-O and (b) C1220P-O sheets

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