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[+] Author and Article Information
Sergei Alexandrov

A. Yu. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Prospect Vernadskogo, Moscow 119526, Russiasergei_alexandrov@yahoo.com

Ken-Ichi Manabe

Department of Mechanical Engineering, Tokyo Metropolitan University, 1-1 Minamiosawa, Hachioji-shi, Tokyo 192-0397, Japanmanabe@tmu.ac.jp

Tsuyoshi Furushima

Department of Mechanical Engineering, Tokyo Metropolitan University, 1-1 Minamiosawa, Hachioji-shi, Tokyo 192-0397, Japanfurushima-tsuyoshi@tmu.ac.jp

J. Manuf. Sci. Eng 133(1), 014503 (Feb 08, 2011) (5 pages) doi:10.1115/1.4003477 History: Received May 12, 2010; Revised January 11, 2011; Published February 08, 2011; Online February 08, 2011

## Abstract

A new empirical relation for the conventional measures of free surface roughness is proposed. Its geometric interpretation is a surface in three-dimensional space. A set of tests feasible for practical realization is discussed. Some available experimental and numerical results are used to reveal various qualitative features of the geometric surface. In particular, a reasonable assumption is that it is a ruled surface for a class of materials. A typical cross section of the surface, which is a curve, has an axis of symmetry if the roughening rate is independent of the sense of the strain rate normal to the material surface, where the roughness parameters should be predicted. The curve has a minimum at the axis of symmetry. Finally, there are two points, where the curve has a maximum. A simple analytic expression to specify the relation proposed for a given material is provided to fit experimental data.

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## Figures

Figure 1

Difference in free surface roughness at concave (closed circles) and convex (open circles) surfaces in four point bending

Figure 2

Typical paths to reveal effect of the mode of deformation of free surface roughness

Figure 3

Illustration of tests to be completed for determining the function Ω involved in Eq. 10

Figure 4

Typical shape of the function Ω introduced in Eq. 10

Figure 5

Linear approximation of numerical results obtained in Ref. 15

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