Application of Finite Deformation Theory to the Development of an Orthogonal Cutting Model—Part II: Experimental Investigation and Model Validation

In Part 1 of this paper, a continuum mechanics model of the orthogonal cutting process was developed based on finite deformation theory. In this part of the paper, constitutive equations for O1 and L6 tool steels are developed using the results from split Hopkinson pressure bar tests. Statistically designed orthogonal cutting experiments are conducted to secure process results across a range of cutting conditions. The continuum mechanics model established in Part 1 of this paper is used to simulate all the cutting tests. All the model outputs are calculated and compared with the corresponding cutting experiment results. Good agreement is observed between the model predictions and the experimental results. The continuum mechanics model is successfully used to predict the cutting force, shear angle, and temperature.

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

Journal of Manufacturing Science and Engineering ◽

10.1115/1.2193555 ◽

2005 ◽

Vol 128 (3) ◽

pp. 760-766

Author(s):

Yuliu Zheng ◽

Xuefei Hu ◽

John W. Sutherland

Keyword(s):

Constitutive Equation ◽

Strain Rate ◽

Continuum Mechanics ◽

Finite Deformation ◽

Deformation Theory ◽

Orthogonal Cutting ◽

Total Power ◽

Eulerian Strain ◽

Finite Deformation Theory ◽

Cutting Model

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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An Orthogonal Cutting Model Based on Finite Deformation Analysis: Part I — Model Development

10.1115/imece1999-0685 ◽

1999 ◽

Author(s):

Y. Zheng ◽

J. W. Sutherland

Keyword(s):

Constitutive Equation ◽

Strain Rate ◽

Finite Deformation ◽

Deformation Theory ◽

Orthogonal Cutting ◽

Total Power ◽

Eulerian Strain ◽

Finite Deformation Theory ◽

Material Constitutive Equation ◽

Cutting Model

Abstract Based on the finite deformation theory of continuum mechanics, the velocity, Eulerian strain, Eulerian strain rate, and deformation rate distributions along a family of assumed streamlines are analytically obtained for an orthogonal cutting operation. An iterative incremental method is used to predict the temperature on the shear plane. The total power in orthogonal cutting may be expressed in terms of three parameters, which are predicted by minimization of the total power. This model allows a general form for the material constitutive equation, which, in general, is a function of strain, strain rate, and temperature. The rotation effect of streamlines on the strain and strain rate calculations is automatically considered using the finite deformation theory of continuum mechanics. In Part I of this paper, the theoretical underpinning for the orthogonal cutting model is established. The verification of the model, including determination of the material constitutive equation using the Hopkinson bar technique, is presented in Part II of this paper.

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Comparison of Various Object Stress Rates under Simple Shear

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.650.407 ◽

2013 ◽

Vol 650 ◽

pp. 407-413 ◽

Cited By ~ 2

Author(s):

Dong Keon Kim ◽

Jong Wan Hu

Keyword(s):

Continuum Mechanics ◽

Simple Shear ◽

Finite Deformation ◽

Deformation Theory ◽

Numerical Results ◽

The Other ◽

Stress Rate ◽

Shear Problem ◽

Finite Deformation Theory ◽

Objective Stress

Object Stress rates to predict the behavior of material have been researched based on numerically and theoretically for researchers who study continuum mechanics due to its complexity. This study focused on the various objective stress rates which assumed the finite deformation theory. Eight object stress rates (Oldroyd, Truesdell, Cotter–Rivlin, Jaumann, Green–Naghdi, Eulerian, grangian, and logarithmic object stress rates) were introduced using continuum mechanics and analyzed to derive the numerical solution to the simple shear problem. Numerical results from each object stress rate were analyzed and compared with the results of the other stress rates. Finally, the appropriate object stress rate for the simple shear problem was determined based on the numerical results from eight objects stress rates.

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Characterizing the Effect of 319 Aluminum Microstructure on Machinability: Part 2 — Model Validation

Manufacturing Engineering and Materials Handling, Parts A and B ◽

10.1115/imece2005-79654 ◽

2005 ◽

Author(s):

Xuefei Hu ◽

John W. Sutherland ◽

James M. Boileau

Keyword(s):

Continuum Mechanics ◽

Cutting Forces ◽

Orthogonal Cutting ◽

Constitutive Relationship ◽

Force Model ◽

Mechanics Model ◽

Paper Disk ◽

New Material ◽

Material Constitutive Equation ◽

Cutting Model

In Part 1 of this paper, a machining force model was developed based on an enhanced version of Zheng’s Continuum Mechanics model that incorporates microstructural effects. Machining experiments identified Secondary Dendrite Arm Spacing (SDAS) as a significant microstructure feature of 319 aluminum in terms of machinability. A new material constitutive relationship that incorporates SDAS microstructure effects on the flow stress was proposed. In this part of the paper, disk turning tests are performed to simulate the orthogonal cutting process. The cutting forces obtained from some of these tests are used in concert with an inverse form of the continuum mechanics machining model to estimate the parameters in the material constitutive equation. The enhanced continuum mechanics orthogonal cutting model is then applied to predict cutting forces when machining Al319. Comparison of the model predicted and experimentally acquired cutting forces is demonstrated to show good agreement.

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