1
Finite element modeling of three-dimensional milling process
2
of Ti–6Al–4V
3 4 5 6 7 8 9 10 11
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
12
Titanium alloys are widely used in the aviation and space sectors, as well as in bio-implants, including
13
knee and hip prostheses and cochlear devices, due to the excellent mechanical and chemical properties
14
and biocompatibility. However, titanium has poor machinability. The cutting temperature, qualit y of
15
the machined surface, burr formation, and tool wear are the major issues, and increase the final
16
product cost. Milling is a mechanical machining process that is widely used to create three-
17
dimensional (3D) free-form features in materials including metals, polymers, and ceramics. The
18
machinability of titanium has been studied experimentally via orthogonal machining, turning, and
19
milling. Haron [1] has reported low tool life during machining of Ti6Al4V. A fine grain tool insert
20
showed comparatively longer tool life. Further, Haron and Jawaid [2] have reported effect of
21
machining on the microstructure of Ti6Al4V. Microhardness of the surface was increased due to the
22
alteration in the microstructures while machining with a dull tool used. Hussain et al. [3], showed
23
mixing of lanthanum with the Ti alloy. This technique helped in formation of segmented chips and
24
further in optimization of the process. However, the works have been limited to experimental analysis.
25
Pittala and Monno [4] reported a face milling simulation by splitting the full circular cut into parts. 2D
26
simulation works have been reported to predict the cutting temperature and forces; for example,
27
Afazov et al. [5] converted the path of the milling cutter into finite parts and calculated the section of
28
each part using 2D simulations of each part in separate windows, which were combined manually to
29
obtain the forces in the milling process. A lot of simulations have been performed and a non linear
30
relationship was defined between cutting force and the uncut chip area and the cutting velocity. High-
31
speed end milling at 400 m/min was reported [6], the effect of coolants on tool life and thermal
32
fatigue was investigated. Sima and Ozel [7] proposed a modified material model for chip formation in
33
Ti6Al4V using orthogonal 2D machining simulations with the Johnson–Cook (JC) plasticity model to
34
describe adiabatic shearing and flow-softening to form a saw tooth chip. Zhang et al. [8] has adopted
35
fracture energy criteria for chip formation and prediction of cutting forces. Temperature dependent
36
flow softening in conjunction with the material constitutive model was proposed [9] to simulate
37
machining process. He showed that the softening started from 350 °C to 500 °C. Patil et al. [10] has
38
presented a FE model of effect of vibration on machining of Ti6Al4V. They showed improved surface
1
1
1
finish with vibration assisted machining of Ti alloy. A microdrill simulation was reported by Guu [11]
2
The stress concentration near the boundary of the hole has been analyzed. Based on the stress
3
distribution the quality of the hole was determined. However, there remains a lack of full circular 3D
4
modeling of the milling process on Ti–6Al–4V that can describe the mechanical and thermal behavior
5
directly.
6
Here, we report a fully coupled thermal-displacement 3D milling simulation of Ti6Al4V using the JC
7
material model proposed by Johnson et al. [12]. This will investigate the plasticity behavior and
8
failure of the material under machining loads. Experiments were car ried out using a vertical CNC
9
milling machine. The model was validated at extreme cases of depth of cut (50 µm and 200 µm), feed
10
rate (50 µm/tooth/rev. and 200 µm/tooth/rev.) and the linear cutting speed (25 m/min and 50 m/min).
11
We found that the simulations showed good agreement with the measured cutting forces, with an error
12
in prediction under 34%. The chip morphology was investigated experimentally and using
13
simulations; the size and shape of the predicted chip was in good agreement with the measured data. A
14
parametric study was carried out using the machining model to analyze the effects of the machining
15
parameters (uncut chip area and linear cutting speed) on the machining response. The uncut chip
16
thickness, feed per tooth per revolution, and linear cutting speed were varied, and the tangential,
17
radial, and axial cutting forces were analyzed. We conclude that rise in the feed rate and depth of cut
18
to achieve a given increase in the uncut chip area gives dissimilar increase in the main cutting force
19
(tangential force). Increase in the feed showed 27% lower tangential force than increase in the depth
20
of cut. Since increasing the tangential force is more problematic than the radial force and axial forces,
21
we recommend increasing the feed rate rather than the axial depth of cut to achieve higher material
22
removal rate.
23
2. FEM model o f the 3D milling process
24
The FEM package Abaqus ® Explicit version 6.12 has been used to model the 3-D milling process.
25
Fig. 1 shows a flow chart describing the modeling process, which contained two key modules: the
26
numerical formulation of the problem and the chip formation mechanism. The numerical formulation
27
consisted of geometrical modeling, interactions between the tool and the workpiece, the loading and
28
boundary conditions and the material properties. Element deletion has been implemented for chip
29
formation. The element deletion was based on the stiffness degradation corresponding to the element.
30
The JC material model was used to define the behavior under machining condition. Chip Formation and Failure
31 32 33
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
2
1
2.1 Material model and chip formation criterion
2
The Johnson-Cook (JC) constitutive material model was applied to define material deformation. The
3
JC model can describe large strains and strain rates, and allows temperature-dependent material
4
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
5
(1) .
6
where A, B, n, C, and m are material constants, ε
7
temperature. The JC constants and material’s mechanical and thermal properties are listed in Table 1
8
and Table 2.
9
Table 1: JC constants for Ti6Al4V, [13, 14]
p
is the strain, ε p is the strain rate, and θ i is the
10
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
11
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)
510
Temperature (°C)
301
396
495
602
698
Thermal conductivity, K (W/m-K) Temperature (°C)
8
9
11
14
16
301
401
500
699
799
Elastic modulus, E (Gpa)
114
109
103
86
73
12 13
Temperature (°C)
15
88
201
422
535
14
The material failure model employs element deletion and removal from the mesh during the process.
15
Figure 2 shows a uniaxial stress–strain curve, which describes the material behavior in the elastic and
16
plastic regions, as well as the post-failure material response for a ductile metal. The region of the
17
curves marked O−A is perfectly elastic. A-B portion of the curve represents a plastic-yielding and
18
strain-hardening region. Damage starts at point B, and point C corresponds to the maximum stress as
19
a result of zero hardening modulus. Fracture occurs at point F (D = 0.7), and point G indicates
20
theoretical fracture at D = 0.99.
3
1 2
Fig. 2: Material behavior under loading
3
The effective stiffness decreases at strains greater than point B. The effective stiffness can be
4
expressed as
5
E f = (1 − D ) E0
(2)
6
where E0 is the initial stiffness, D is the degradation factor (0 < D ≤ 0.99) and E f is the effective
7
stiffness of the material at a given strain.
8
Damage initiation was modeled based on the JC shear failure model using the five failure parameters
9
(D1, D 2, …, D 5) listed in Table 1. Damage occurred at point B (Fig. 2) when the scalar damage
10
parameter, ω, exceeds unity. The scalar damage parameter is defined as:
∆ε p j =1 ε O i j n
ω = ∑
11 12
where ∆ε
13
integration point and
14 15 16
p
(3)
is the increment in the equivalent plastic strain for a given increase in the load at each
&̅() * +,- . , /exp
4
123 5 9 6 78
@AB
: ; ln ? B DE ;
