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Research Papers

Hybrid Digital Image Correlation–Finite Element Modeling Approach for Modeling of Orthogonal Cutting Process

[+] Author and Article Information
Dong Zhang, Han Ding

State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of
Science and Technology,
Wuhan 430074, China

Xiao-Ming Zhang

State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of
Science and Technology,
Wuhan 430074, China
e-mails: zhangxm.duyi@gmail.com;
cheungxm@hust.edu.cn

1Corresponding author.

Manuscript received June 21, 2017; final manuscript received December 22, 2017; published online February 15, 2018. Assoc. Editor: Radu Pavel.

J. Manuf. Sci. Eng 140(4), 041018 (Feb 15, 2018) (14 pages) Paper No: MANU-17-1387; doi: 10.1115/1.4038998 History: Received June 21, 2017; Revised December 22, 2017

Cutting process modeling is still a significant challenge due to the severe plastic deformation of the workpiece and intense friction between the workpiece and tool. Nowadays, a novel experimental approach based on digital image correlation (DIC) technique has been utilized to study the severe deformation of the workpiece. However, the experimentally measured velocity field does not necessarily satisfy the equilibrium equation that is one of the fundamental governing equations in solid mechanics due to the measurement errors; hence, accurate stress fields could hardly be derived. In this paper, we propose a hybrid DIC-FEM approach to optimize the velocity field and generate a stress field that is in an equilibrium state. First, the analysis region for finite element modeling (FEM) is selected according to the captured image, and the DIC results are used to track the deformation history of the material points. Secondly, the deviatoric stresses of the analysis region are calculated by employing the plastic theory. Thirdly, the hydrostatic pressures are acquired through solving over-constrained equations derived through FEM. Finally, the velocity field is optimized to satisfy the equilibrium equation and the boundary conditions (BCs) with the DIC results serving as an initial value of the workpiece velocity field. To validate this approach, the deformations including the velocity and strain yielded by the hybrid method are compared with the DIC results. The stress fields are presented to demonstrate the satisfaction of the equilibrium equation and the BCs. Moreover, cutting forces calculated through the integration of the stress tensors are compared against the FEM simulations and the experimental measurement.

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Figures

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Fig. 1

Experimental setup of orthogonal cutting process

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Fig. 2

Flowchart of the hybrid DIC–FEM approach

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Fig. 3

Demonstration of the classification of FEM nodes

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Fig. 4

Magnitude of the residual nodal force |QR| (N/m) for each cutting condition (a) h = 0.06 mm, (b) h = 0.08 mm, and (c) h = 0.1 mm

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Fig. 5

Differences between the optimized velocity fields and the initial ones where the contour maps (unit in mm/min) indicate the magnitude of the difference and the arrows indicate the directions from the initial velocity vectors to the optimized ones. (a) h = 0.06 mm, (b) h = 0.08 mm, and (c) h = 0.1 mm.

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Fig. 6

Equivalent strain (a) h = 0.06 mm, (b) h = 0.08 mm, and (c) h = 0.1 mm

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Fig. 15

Cutting force integration paths superimposed on the maps of hydrostatic pressure. (a) h = 0.06 mm, (b) h = 0.08 mm, and (c) h = 0.1 mm.

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Fig. 14

Stress fields for cutting condition no. III (h = 0.1 mm)

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Fig. 13

Stress fields for cutting condition no. II (h = 0.08 mm)

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Fig. 12

Stress fields for cutting condition no. I (h = 0.06 mm)

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Fig. 11

Evolutions of Lxx (unit in 1/s) along the red streamline, which passes through the TSZ. (a) h = 0.06 mm, (b) h = 0.08 mm, and (c) h = 0.1 mm.

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Fig. 10

Lxx (unit in 1/s) (a) h = 0.06 mm, (b) h = 0.08 mm, and (c) h = 0.1 mm

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Fig. 9

Comparisons of the strain evolution along the red streamline, which passes through the TSZ. (a) h = 0.06 mm, (b) h = 0.08 mm, and (c) h = 0.1 mm.

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Fig. 8

Comparisons of the strain evolution along the white streamline which passes through the SSZ. (a) h = 0.06 mm, (b) h = 0.08 mm, and (c) h = 0.1 mm.

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Fig. 7

Comparisons of the strain evolution along the black streamline, which passes through the PSZ. (a) h = 0.06 mm, (b) h = 0.08 mm, and (c) h = 0.1 mm.

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Fig. 16

DIC determined velocity fields. (I) h = 0.06 mm, (II) h = 0.08 mm, and (III) h = 0.1 mm.

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Fig. 17

Optimized velocity fields. (I) h = 0.06 mm, (II) h = 0.08 mm, and (III) h = 0.1 mm.

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