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Finite element modeling of three-dimensional milling process
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of Ti–6Al–4V
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Vivek Bajpai1,#, Ineon Lee1,+ and Hyung Wook Park 1,* School of Mechanical and Advanced Materials Engineering, Ulsan National Institute of Science and Technology, UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan, Republic of Korea, 689-798 # Email:
[email protected], + Email:
[email protected] *Corresponding author: Tel: +82-52-217-2319, Fax: +82-52-217-2409, Email:
[email protected] and hyungwo
[email protected] 1. Introduction
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Titanium alloys are widely used in the aviation and space sectors, as well as in bio-implants, including
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knee and hip prostheses and cochlear devices, due to the excellent mechanical and chemical properties
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and biocompatibility. However, titanium has poor machinability. The cutting temperature, qualit y of
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the machined surface, burr formation, and tool wear are the major issues, and increase the final
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product cost. Milling is a mechanical machining process that is widely used to create three-
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dimensional (3D) free-form features in materials including metals, polymers, and ceramics. The
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machinability of titanium has been studied experimentally via orthogonal machining, turning, and
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milling. Haron [1] has reported low tool life during machining of Ti6Al4V. A fine grain tool insert
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showed comparatively longer tool life. Further, Haron and Jawaid [2] have reported effect of
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machining on the microstructure of Ti6Al4V. Microhardness of the surface was increased due to the
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alteration in the microstructures while machining with a dull tool used. Hussain et al. [3], showed
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mixing of lanthanum with the Ti alloy. This technique helped in formation of segmented chips and
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further in optimization of the process. However, the works have been limited to experimental analysis.
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Pittala and Monno [4] reported a face milling simulation by splitting the full circular cut into parts. 2D
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simulation works have been reported to predict the cutting temperature and forces; for example,
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Afazov et al. [5] converted the path of the milling cutter into finite parts and calculated the section of
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each part using 2D simulations of each part in separate windows, which were combined manually to
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obtain the forces in the milling process. A lot of simulations have been performed and a non linear
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relationship was defined between cutting force and the uncut chip area and the cutting velocity. High-
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speed end milling at 400 m/min was reported [6], the effect of coolants on tool life and thermal
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fatigue was investigated. Sima and Ozel [7] proposed a modified material model for chip formation in
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Ti6Al4V using orthogonal 2D machining simulations with the Johnson–Cook (JC) plasticity model to
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describe adiabatic shearing and flow-softening to form a saw tooth chip. Zhang et al. [8] has adopted
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fracture energy criteria for chip formation and prediction of cutting forces. Temperature dependent
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flow softening in conjunction with the material constitutive model was proposed [9] to simulate
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machining process. He showed that the softening started from 350 °C to 500 °C. Patil et al. [10] has
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presented a FE model of effect of vibration on machining of Ti6Al4V. They showed improved surface
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finish with vibration assisted machining of Ti alloy. A microdrill simulation was reported by Guu [11]
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The stress concentration near the boundary of the hole has been analyzed. Based on the stress
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distribution the quality of the hole was determined. However, there remains a lack of full circular 3D
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modeling of the milling process on Ti–6Al–4V that can describe the mechanical and thermal behavior
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directly.
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Here, we report a fully coupled thermal-displacement 3D milling simulation of Ti6Al4V using the JC
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material model proposed by Johnson et al. [12]. This will investigate the plasticity behavior and
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failure of the material under machining loads. Experiments were car ried out using a vertical CNC
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milling machine. The model was validated at extreme cases of depth of cut (50 µm and 200 µm), feed
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rate (50 µm/tooth/rev. and 200 µm/tooth/rev.) and the linear cutting speed (25 m/min and 50 m/min).
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We found that the simulations showed good agreement with the measured cutting forces, with an error
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in prediction under 34%. The chip morphology was investigated experimentally and using
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simulations; the size and shape of the predicted chip was in good agreement with the measured data. A
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parametric study was carried out using the machining model to analyze the effects of the machining
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parameters (uncut chip area and linear cutting speed) on the machining response. The uncut chip
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thickness, feed per tooth per revolution, and linear cutting speed were varied, and the tangential,
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radial, and axial cutting forces were analyzed. We conclude that rise in the feed rate and depth of cut
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to achieve a given increase in the uncut chip area gives dissimilar increase in the main cutting force
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(tangential force). Increase in the feed showed 27% lower tangential force than increase in the depth
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of cut. Since increasing the tangential force is more problematic than the radial force and axial forces,
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we recommend increasing the feed rate rather than the axial depth of cut to achieve higher material
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removal rate.
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2. FEM model o f the 3D milling process
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The FEM package Abaqus ® Explicit version 6.12 has been used to model the 3-D milling process.
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Fig. 1 shows a flow chart describing the modeling process, which contained two key modules: the
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numerical formulation of the problem and the chip formation mechanism. The numerical formulation
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consisted of geometrical modeling, interactions between the tool and the workpiece, the loading and
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boundary conditions and the material properties. Element deletion has been implemented for chip
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formation. The element deletion was based on the stiffness degradation corresponding to the element.
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The JC material model was used to define the behavior under machining condition. Chip Formation and Failure
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Johnson cook model for plasticity behavior and damage modeling
FE Modeling
Model Validation
Parametric Study
Numerical Formulation
•Geometry (Interactions and constraints) •Loading and Boundary Conditions •Material Properties
Fig. 1: Overview of the 3D FEM simulation process
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2.1 Material model and chip formation criterion
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The Johnson-Cook (JC) constitutive material model was applied to define material deformation. The
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JC model can describe large strains and strain rates, and allows temperature-dependent material
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properties to be used. The equivalent stress can be expressed in the JC model as follows m ε& p θ w − θ0 σ jc = [ A + B(ε ) ]× 1 + C ln & p × 1 − ε 0 θm − θ0 p n
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(1) .
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where A, B, n, C, and m are material constants, ε
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temperature. The JC constants and material’s mechanical and thermal properties are listed in Table 1
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and Table 2.
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Table 1: JC constants for Ti6Al4V, [13, 14]
p
is the strain, ε p is the strain rate, and θ i is the
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B Constant A n C m D1 D 2 D3 D4 D5 Value 1098 MPa 1092 MPa 0.93 0.014 1.1 -0.09 0.25 -0.5 0.014 3.87
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Table 2: Mechanical and thermal properties of Ti6Al4V, [15] Properties
Density, ρ (kg/m3) Tmelt (°C) Inelastic heat fraction, β Poisson’s ratio, ν Friction coefficient, µ
Value
4500
1640
0.9
0.32
0.6 (dry)
535
562
585
611
650 799
Temperature dependent material properties: Specific heat capacity, Cm (J/Kg-K)
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Temperature (°C)
301
396
495
602
698
Thermal conductivity, K (W/m-K) Temperature (°C)
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9
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14
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301
401
500
699
799
Elastic modulus, E (Gpa)
114
109
103
86
73
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Temperature (°C)
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88
201
422
535
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The material failure model employs element deletion and removal from the mesh during the process.
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Figure 2 shows a uniaxial stress–strain curve, which describes the material behavior in the elastic and
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plastic regions, as well as the post-failure material response for a ductile metal. The region of the
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curves marked O−A is perfectly elastic. A-B portion of the curve represents a plastic-yielding and
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strain-hardening region. Damage starts at point B, and point C corresponds to the maximum stress as
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a result of zero hardening modulus. Fracture occurs at point F (D = 0.7), and point G indicates
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theoretical fracture at D = 0.99.
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Fig. 2: Material behavior under loading
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The effective stiffness decreases at strains greater than point B. The effective stiffness can be
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expressed as
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E f = (1 − D ) E0
(2)
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where E0 is the initial stiffness, D is the degradation factor (0 < D ≤ 0.99) and E f is the effective
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stiffness of the material at a given strain.
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Damage initiation was modeled based on the JC shear failure model using the five failure parameters
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(D1, D 2, …, D 5) listed in Table 1. Damage occurred at point B (Fig. 2) when the scalar damage
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parameter, ω, exceeds unity. The scalar damage parameter is defined as:
∆ε p j =1 ε O i j n
ω = ∑
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where ∆ε
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integration point and
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p
(3)
is the increment in the equivalent plastic strain for a given increase in the load at each
&̅() * +,- . , /exp
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123 5 9 6 78
@AB
: ; ln ? B DE ;