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TECHNICAL PAPERS

# Application of Finite Deformation Theory to the Development of an Orthogonal Cutting Model—Part I: Model Development

[+] Author and Article Information
Yuliu Zheng1

Department of Mechanical Engineering–Engineering Mechanics, Michigan Technological University, Houghton, MI 49931-1295

Xuefei Hu2

Department of Mechanical Engineering–Engineering Mechanics, Michigan Technological University, Houghton, MI 49931-1295

John W. Sutherland

Department of Mechanical Engineering–Engineering Mechanics, Michigan Technological University, Houghton, MI 49931-1295

1

Presently at Manufacturing R&D, Federal Mogul Corporation.

2

Presently at Global Engine Development-NA, Engine Systems, Caterpillar, Inc.

J. Manuf. Sci. Eng 128(3), 760-766 (Nov 14, 2005) (7 pages) doi:10.1115/1.2193555 History: Received January 06, 2005; Revised November 14, 2005

## Abstract

An orthogonal cutting model is developed using the finite deformation theory of continuum mechanics. A family of flowlines is proposed to describe the chip flow during orthogonal cutting, and the shape of the flowlines is described in terms of three parameters, one of which is the shear angle. The velocity, Eulerian strain, and Eulerian strain rate distribution along the assumed flowlines are obtained analytically for the orthogonal cutting operation based on this model. The temperature distribution along the flowline is predicted via a finite difference method. Values for the three flowline parameters are selected that minimize the total power associated with primary shear zone deformation and chip-tool interaction using the Davidon-Fletcher-Powell optimization scheme. The model utilizes a general constitutive equation for material behavior, which is a function of strain, strain rate, and temperature. In Part I of this two-part paper, the continuum mechanics-based model for the orthogonal cutting process is established. Experimental assessment and adequacy checking of the model, including determination of the material constitutive equation using a split Hopkinson pressure bar technique, is presented in Part II of the paper.

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## Figures

Figure 1

The reference coordinate systems

Figure 2

Simulated flowline pattern

Figure 3

Velocity along the flowline

Figure 4

The effective Eulerian strain along a flowline

Figure 5

Strain rate and the effective deformation rate (a) and (b).

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