Jie MENG, Feng CHEN, You-qing DING

(1College of Mechanical and Power Engineering, Chongqing University of Science and Technology, Chongqing 401331, China)(2 CNNC Nuclear Power Operation Management Co.,Ltd., Haiyan 314300, China)

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Finite element modelling and simulation of micro side cutting process

Jie MENG1*, Feng CHEN2, You-qing DING1

(1CollegeofMechanicalandPowerEngineering,ChongqingUniversityofScienceandTechnology,Chongqing401331,China)(2CNNCNuclearPowerOperationManagementCo.,Ltd.,Haiyan314300,China)

This paper presented a 2D finite element model of AISI 4340 for micro side cutting. Johnson-Cook constitutive model and Johnson-Cook shear failure model are combined to simulate a complete side cutting cycle for one flute rotation. The flow stress which is calculated from Johnson-Cook constitutive model is smaller if the size effect is neglected. Therefore, the strain gradient plasticity model is developed. The chip formation, von Mises stress and temperature fields are predicted. Compare to the Johnson-Cook constitutive model, simulation results show that size effect exists in the micro side cutting process and the strain gradient plasticity model can describe it well. Finally, the flow stress from the finite element simulation is compared with theoretical calculation results, which is validated the correctness of finite element model.

Johnson-Cook constitutive model, Strain gradient plasticity model, AISI 4340, Micro side cutting

1 Introduction

Medium carbon steel AISI 4340 which was hardened to 40-60 HRC by heat treatment is a general-purpose steel having a wide range of application in automobile and related industries by virtue of its good harden ability enabling it to be used in fairly large sections [1]. It is well known for its ductility and high strength.

Micro milling is an advantage industrial technologies and has been widely used in biomedical, medicine, electronic, optic, aerospace, defense industry and so on. It also could be used for the machining of hardened steel, micro dies and molds. Cutting force, size effect, burr formation, surface roughness and tool wear are the critical factors which will affect the micro machining quality and are concerned by many researchers.

Dhanorker et al. [2-3] and ?zel et al. [4-5] presented experimental and modelling studies on meso/micro-milling of AISI 4340 steel. Experiment is used to measure dynamic force and the finite element modelling is conducted to predict chip formation and temperature fields. Meanwhile, a model-based micro-end milling process planning guideline for machining micro mold cavities are proposed to facilitate proper selections of the process parameters. Furthermore, experiments and finite element method-based process simulations for micro milling of AISI 4340 steel with and without the laser assistance are conducted to study the influence of the pulsed laser thermal softening on cutting forces and the temperature rise in the cutting tool.

Afazov et al. [6] predicted the cutting forces in micro-milling of AISI 4340 steel using a number of FE simulations of an orthogonal cutting model, which covered a wide range of cutting conditions with the range of uncut chip thickness from 0 to 20 μm and cutting velocity from 0.1 to 4.7 m/s.

Woon et al. [7] developed a 2D orthogonal cutting finite element model to study the influence of the tool edge radius on chip formation for a homogeneous AISI 4340 steel. The results show that the chip is formed by extrusion along the tool edge radius when the depth of cut is lower than a broken value and confirm that the tool cannot be considered sharp in micro-milling.

Most publications on micro milling of AISI 4340 have conducted investigations on cutting force, surface roughness, chip formation and temperature fields for the micromachining process during 2D orthogonal cutting or slotting.

In this paper, micro side cutting of AISI 4340 is discussed. Finite element model is used to simulate the process of tungsten carbide tool micromachining AISI 4340 bulk. Because Johnson-Cook constitutive model cannot describe the size effect during micro side cutting process, the strain gradient plasticity model is developed. The chip formation, von Mises stress and temperature fields are predicted as well.

2 Finite element model of AISI4340

2.1Johnson-CookconstitutivemodelofAISI4340

AISI 4340, which was hardened by heat treatment, is difficult to machine from the moderate speed to high speed. Finite element analysis, which is easier and cheaper than experiment, is usually used to simulate the micro machining process. In order to study the characters of AISI 4340 during micro milling process, 2D FE model is set up to simulate the two flute end mill, which is made by tungsten carbide micro side cutting AISI 4340 bulk. The diameter of end mill is 100 μm and its cutting edge radius is 0.5 μm. As shown in Fig.1, two flute end mill which has symmetrical structure is simplified to one flute with the actual geometry parameters. During the cutting process, the uncut chip thickness is set to 0.83 μm. The angular velocity of 60 000 rpm is applied to the cutting tool. The radical and axial depth of cut are 5 and 100 μm, respectively. The workpiece material properties are modelled by using the Johnson-Cook constitutive model. The material crack and separation as chip are simulated through using the Johnson-Cook shear failure model. The simulation parameters are shown in Table 1 and Table 2. Therefore, a complete side cutting cycle for one flute rotation could be simulated.

Fig.1 2D FE model for one flute of end mill micro side cutting AISI 4340 bulk

Table 1 Johnson-Cook behavior and damage law parameters of AISI 4340[8-10]

A/MPaB/MPanCmTm/Kd1d2d3d4d57925100.260.01401.0317930.053.44-2.120.0020.61

Table 2 Material properties of tungsten carbide tool [11]

Density/(g·cm-3)Specificheat/(J·kg-1℃-1)Thermalconductivity/(W·m-1K-1)Thermalexpansion/(μm·m-1℃-1)Young’smodulus/GPaPoisson’sratio14.526028.45.26960.25

During one side cutting cycle for one flute rotation, chip formation, propagation and separation are about 20 degree. The total simulation time is 56 μs. Fig.2 shows the simulation results at 20 μs, 50 μs and 56 μs, respectively. It can be seen that the maximum von Mises stress is about 1 797 MPa at this condition.

2.2 Strain gradient plasticity model of AISI 4340

Constitutive model is the fundamental of FE simulations and is required to represent the features of material behaviors during the deformation process. Johnson-Cook is one of the most widely used models. It provides good description of metal material behaviors undertaking large strains, high strain rate and temperatures. It describes the flow stress of work material with the product of strain, strain rate and temperature effects that could be individually determined as follows [12-13],

(1)

However, the stress based on the Johnson-Cook constitutive model is independent to the length scale. Therefore, the model cannot describe the size effect. For micro machining, size effect is a dominant factor. Considerer the size effect, the flow stress based on the strain gradient plasticity theory is shown as follows.

(2)

The strain gradient plasticity is programmed as a subroutine in the finite element model. The strain gradient plasticity model is set up and used to simulate the side cutting under the same condition. Table 3 shows the parameters of strain gradient model for AISI 4340.

Fig.2 Chip formation during one side cutting cycle

Table 3 Strain gradient parameters for AISI 4340[14-15]

G/GPab/nmαμ800.2480.50.38

Fig.3 shows flow stress and temperature fields of strain gradient plasticity model at 20 μs. As compared to the Johnson-Cook constitutive model, the maximum von Mises stress of the strain gradient plasticity model is 2 614 MPa. Room temperature is used as the initial temperature condition in the simulation. The maximum temperatures on the chip and tool are around 67℃ and 50℃ at 20 μs, respectively.

2.3 Validate finite element simulation of AISI 4340

The flow stress based on Johnson-Cook constitutive model and strain gradient plasticity model are obtained by using finite element simulation, respectively. In order to prove correctness of the model and the subroutine of simulation, the flow stress of Johnson-Cook constitutive model and strain gradient plasticity model are calculated by using equation (1) and (2), respectively. The results are shown in Fig.4.

Fig.3 Strain gradient plasticity model for AISI 4340

Fig.4 Calculation results of flow stress for AISI 4340

Theoretical calculation:

σJC-S=1.711×103MPa

σSG-S=2.672×103MPa

Simulation results:

σJC-C=1.797×103MPa

σSG-C=2.617×103MPa

Error:

The relative errors for both simulation results are less than 5%, respectively. Therefore, the FEM are correct and could be used to simulate the micro side cutting process.

3 Conclusions

In this paper, a finite element model is introduced to simulate the micro side cutting. Johnson-Cook constitutive model and strain gradient plasticity model are developed for simulation of chip formation. For a complete side cutting cycle of AISI 4340 by tungsten carbide tool, flow stress and temperature fields are obtained. Compare Johnson-Cook constitutive model with strain gradient plasticity model, the maximum simulated von Mises stress of strain gradient plasticity model is much higher due to the size effect during the micro side cutting. However, the cutting temperature is lower than that of conventional model due to the smaller cutting parameters, higher thermal conductivity of tungsten carbide tool and AISI 4340.

Acknowledgements

This paper is supported by Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2013jcyjA70004), Scientific and Technological Research Program of Chongqing Municipal Education Commission (No.KJ1501314), and Chongqing University of Science & Technology (No.CK2014Z27).

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10.3969/j.issn.1001-3881.2015.24.015 Document code: A

TG501

微細(xì)側(cè)銑過程的有限元建模與仿真

孟杰1*, 陳鋒2, 丁又青1

1.重慶科技學(xué)院 機(jī)械與動(dòng)力工程學(xué)院, 重慶401331 2.中核核電運(yùn)行管理有限公司, 浙江 海鹽314300

建立了AISI 4340 微細(xì)側(cè)銑的二維有限元模型。將Johnson-Cook本構(gòu)模型與Johnson-Cook剪切失效模型相結(jié)合，對銑削刃旋轉(zhuǎn)過程中的一個(gè)完整側(cè)銑周期進(jìn)行了仿真。由于沒有考慮尺寸效應(yīng)的影響，所得到的流動(dòng)應(yīng)力值偏小。因此，建立了應(yīng)變梯度塑性模型，并應(yīng)用其預(yù)測了切屑的形成、馮米斯應(yīng)力和溫度場。仿真結(jié)果顯示：微細(xì)側(cè)銑過程中存在尺度效應(yīng)，與Johnson-Cook本構(gòu)模型相比，應(yīng)變梯度塑性模型能夠很好地描述微細(xì)側(cè)銑過程中的尺寸效應(yīng)。最后，將仿真結(jié)果與理論計(jì)算結(jié)果相比較，驗(yàn)證了所建模型的正確性。

Johnson-Cook本構(gòu)模型；應(yīng)變梯度塑性理論；AISI 4340；微細(xì)側(cè)銑

29 June 2015; revised 2 August 2015;

Jie MENG, Associate Professor. E-mail: mj8101@163.com

accepted 6 August 2015

Hydromechatronics Engineering

http://jdy.qks.cqut.edu.cn

E-mail: jdygcyw@126.com