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Simulation analysis and experimental study of milling surface residual stress of Ti-10V-2Fe-3Al
Journal of Manufacturing Processes 32 (2018) 530–537
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Simulation analysis and experimental study of milling surface residual stress of Ti-10V-2Fe-3Al Qiong Wu ∗ , Dong-Jian Xie, Yu Si, Yi-Du Zhang, Lei Li, Ying-Xin Zhao State Key Laboratory of Virtual Reality Technology and Systems, School of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, PR China
a r t i c l e
i n f o
Article history: Received 12 May 2017 Received in revised form 8 March 2018 Accepted 13 March 2018 Keywords: FE simulation Milling parameter Residual stress Ti-10V-2Fe-3Al
a b s t r a c t Nowadays, Ti-10V-2Fe-3Al is widely used in aerospace field because of its high specific strength, good breaking property, low forging temperature, and excellent stress corrosion resistance. However, these properties render Ti-10V-2Fe-3Al a hard-to-cut material. Moreover, the low thermal conductivity of Ti10V-2Fe-3Al results in high temperature on the tool face, which causes the wear of cutting tool. This paper presents a simulation analysis and an experimental validation on the milling surface residual stress of Ti10V-2Fe-3Al. The formation mechanism and influence of cutting parameters on the residual stress in the end milling of Ti-10V-2Fe-3Al are investigated through orthogonal experiments. The interaction effect of cutting parameters on forming residual stress is studied by analyzing the finite element (FE) simulation results. Moreover, relevant experiments are carried out to validate the accuracy of FE simulation. On the basis of these data, a formulation describing the interaction effect is proposed. © 2018 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
1. Introduction Titanium alloy is considered a industrial high-strength material because of its high specific strength, good breaking properties, low forging temperature, and excellent stress corrosion resistance. Hence, titanium alloy is widely used in aerospace field. However, titanium alloy is difficult to be milled because of the excellent properties mentioned above. Machining titanium alloy is expensive. Thus, many studies have investigated the milling process and surface integrity of titanium alloy to improve milling efficiency. Some studies focused on the effect of milling tool. Wagner et al. [1] studied the tool wear mechanisms of Ti-1023 milling by using toroidal tool and established the relation among cutting conditions, milling tool geometry, and tool life. Rao et al. [2] performed experimental and numerical studies on the face milling of Ti-6Al-4V titanium alloy to characterize tool performance and surface integrity. Thepsonthi et al. [3] proposed an integrated method in selecting toolpath and optimized the process parameters to improve the performance of micro-milling Ti-6Al-4V alloy. Pan et al. [4] investigated the performance of polycrystalline diamond tools in the end milling of titanium alloys and analyzed the relationship between cutting force
∗ Corresponding author. E-mail addresses: [email protected] (Q. Wu), [email protected] (D.-J. Xie), [email protected] (Y. Si), [email protected] (Y.-D. Zhang), [email protected] (L. Li), [email protected] (Y.-X. Zhao).
and cutting parameters. Li et al. [5] presented a 3D finite element method (FEM) of Ti-6Al-4V milling for the design and optimization of solid carbide end milling. Thepsonthi et al. [6] carried out experiments and finite element (FE) simulation to show that the cBN-coated carbide tool outperforms the uncoated carbide tool in generating tool wear and cutting temperature during Ti-6Al4V micro-milling. Nouari et al. [7] studied the effect of third-body particles on the tool-chip contact and tool-wear behavior during the dry cutting of aeronautical titanium alloys. Thepsonthi et al. [8] conducted the 3D FE modeling and simulation of micro-end milling for Ti-6Al-4V titanium alloy to characterize chip flow and tool wear. The simulation results agreed with the experimental data. Rao et al. [9] focused on the measurement of specific cutting energy, surface integrity and tool performance with the experimental and numerical study of face milling of Ti-6Al-4V titanium alloy. Some studies focused on the deformation and cutting chip in the milling process. Bajpai et al. [10] studied the cutting forces and chip morphology through 3D FE simulation and experiments. Wu et al. [11] developed a 3D FE model for the complex milling of titanium alloy Ti-6Al-4V with ABAQUS and compared the chip formation, cutting force, and milling temperature obtained from simulation with those obtained from experiments. Liu et al. [12] established a 3D FE model of a helical tool and a thin-walled part with a cantilever to predict the cutting deformation of a titanium alloy Ti-6Al-4V thin-walled part during milling. The accuracy of this model can be validated by experimental cutting deformation. Calamaz et al. [13]
https://doi.org/10.1016/j.jmapro.2018.03.015 1526-6125/© 2018 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
Q. Wu et al. / Journal of Manufacturing Processes 32 (2018) 530–537
implemented a new material constitutive law in a 2D FE model to analyze the chip formation and shear localization when machining titanium alloys. Moreover, some studies performed experiments and FE simulations to establish the relationship between milling parameters and face integrity. Ma et al. [14] employed the FEM to investigate the effects of cutting conditions in corner up milling on the temperature of the tool rake face. Wyen et al. [15] studied the influence of the cutting edge radius on surface integrity in terms of residual stress, micro-hardness, surface roughness and optical characterization of the surface, and near surface area in up and down milling of the titanium alloy. Wu et al. [16] presented the effect of machined surface quality and cutting parameters on residual stress distribution in 7075 aluminum alloy. Yao et al. [17] investigated the formation mechanism and influence of cutting parameters on residual stress in the flank milling of Ti-10V-2Fe3Al through orthogonal experiments. Daymi et al. [18] conducted a series of end milling experiments to characterize comprehensively the surface integrity of titanium alloy Ti-6Al-4V with TiAlN-coated carbide cutting tools under various milling conditions. Mantle et al. [19] studied the surface integrity of a high-speed ball end milled gamma titanium aluminide. Yang et al. [20] utilized a hybrid technique combining the FEM to study the effect of cutting speed and feed rate on the residual stress of Ti-6Al-4V (TC4). Miguélez et al. [21] investigated the influence of cutting speed on the induced machining residual stresses of TC4. Wu et al. [22] determined the effects of machined surface quality and cutting parameters on the residual stress distribution in a silicon carbide particle-reinforced metal matrix composite through FEM and experiments. Xin et al. [23] numerically analyzed the impact of cutting factors on residual stress. Li et al. [24] adopted non-dominated sorting genetic algorithm-II to established empirical models of tool life, residual stress and roughness according to TC4 milling parameters. The empirical models were utilized for optimization of production cost and surface quality. Yang et al. [25] developed a hybrid technique combining the finite element method and the statis-
531
tical model for residual stress prediction in peripheral milling of TC4. The sensitivity to cutting speed and feed rate of four key features of the residual stress profile including surface residual stress, compressive stress peak value and location, response depth were investigated. Although each of above studies has its features and merits, only a few of them focus on the empirical formula about residual stress and milling parameters. And they mostly focus on the titanium of TC4. Besides, cutting depth, which is one of the four key milling parameters, is less investigated. The purpose of this paper is to provide an empirical formula about the relationship between residual stress and cutting speed, feed rate and cutting depth. In this work, several experiments were performed to acquire the specific parameters of the Johnson–Cook material model of Ti10V-2Fe-3Al. Then, the Johnson–Cook material model was applied into FE software DEFORM to validate its accuracy. FE simulations and relevant experiments under various end milling conditions were conducted to explore the relationship between the residual stress and milling parameters of Ti-10V-2Fe-3Al. After comparing the results obtained from FE simulations and experiments, a good agreement between the two data was found. Furthermore, the variation tendency of residual stress with the changes in feed speed, cutting depth, and cutting speed was discussed and analyzed. The results of this study may serve as a reference for future studies to improve the milling efficiency of Ti-10V-2Fe3Al. 2. Johnson–Cook material model In this study, the Generalized Johnson–Cook model was adopted to simulate Ti-10V-2Fe-3Al in FE software DEFDORM. To obtain an accurate simulation result, several experiments were carried out to obtain the relevant parameters of the Generalized Johnson–Cook model for the Ti-10V-2Fe-3Al. Moreover, we appropriately modified the parameters to fit the data from experiments, and the following is the process.
Fig. 1. Tensile test.
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Fig. 2. Simulation result of the tensile test.
The Generalized Johnson–Cook material model [26] shows the following formulation:
= A + Bε
n
· 1 + Cln
•
ε •
ε0
·
•
ε •
˛
· D-ETm ∗
(1)
ε0
where A, B, n, C, and m are the parameters, which we should confirm. means the effective stress, and ε represents the effective •
•
plastic strain. ε means the effective plastic strain rate, and ε0 is the reference strain rate. D and E are the relevant temperature coefficients. T∗ is a dimensionless temperature that is converted from the current temperature and the melting point of Ti-10V-2Fe-3Al. In this simulation, the job is used to describe the milling process under room temperature. Thus, D and E are 1, and ␣ is 0. The right side of Formulation (1) represents the influences of equivalent plastic strain, strain rate, and temperature on flow stress. In this simulation, the job is used to describe the milling process under room temperature. To obtain parameters, a tensile test of Ti-10V-2Fe-3Al is conducted. Ti-10V-2Fe-3Al is tested under conference strain rate and conference temperature. When the yield n point of workpiece of the tensile test is obtained, ε = 0 and A = . Parameters B and n can be identified by fitting the equivalent effective strain and stress. Meanwhile, when the tensile test is conducted under current temperature, parameters C and m can be identified by the tensile test under different strain rates and temperatures. On the basis of the relation mentioned above, relevant workpieces are selected to conduct the tensile experiments. The experimental set-up is shown in Fig. 1, and the data of stress and
Fig. 3. Stress–strain curve.
strain are recorded under conference strain and temperature. From the data, the experimental stress–strain curve is obtained. Then, the value of other parameters can be obtained by fitting the equivalent effective stress curve under different conditions. The tensile test of Ti-10V-2Fe-3Al is simulated using the Generalized Johnson–Cook material model of DEFORM FE software, and the result is shown in Fig. 2. Moreover, the simulation stress–strain curve is drawn in Fig. 3. A comparison of the experimental and simulation results in Fig. 3 reveals a good agreement on the slope of the stress–strain curve. However, the maximums of the two stress–strain curves are different. The main reason for the difference is the state of the work-
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Fig. 4. Results of the contraction test:(a) under different strain rates; (b) under different temperature.
Table 1 Mechanical properties of Ti-10V-2Fe-3Al. Density(kg/m3)
Hardness (HRC)
Tensile Strength (MPa)
Yield Strength(MPa)
Percentage of Elongation
Young’s Modulus (GPa)
Poisson’s ratio
Shear Strength (MPa)
4400
53
910
860
16%
117
0.31
680
Table 2 Mechanical properties of carbide tool. Young’s Modulus (MPa)
Poisson’s ratio
Linear Expansivity (10−6 /◦ C)
Specific Heat (J/kg ◦ C)
Thermal Coefficient (W/m K)
6.5E + 5
0.25
6.2
226
59
piece enters the non-linear phase after the strain is greater than 0.01. In the non-linear phase, properties of the material decrease. Due to these factors cannot be considered by simulation, the maximum value of simulation is higher than that of experiment. When the strain is greater than 0.01 later, the difference between the maximum of the two curves is relatively stable. The Johnson-Cook parameter is based primarily on the slope of the curve before strain is less than 0.01. Thus the difference in values between the simulation and experimental curves can be accepted. After considering the experimental results, the Johnson–Cook parameters are optimized to obtain accurate simulation results. Moreover, a contraction test is conducted to verify the accuracy of the parameters. The contraction test is carried out under different strain rates and different temperatures, and the results are shown in Fig. 4. Through this test, the accuracy of the Generalized Johnson–Cook model is verified, and the values of the parameters are finally identified as follows: A = 976.9, B = 502.3, C = 0.028, n = 0.22,m = 1
(2)
3. Simulation The Lagrangian solution-based FE software for deformation is utilized to construct the 3D FE model for the end milling of Ti10V-2Fe-3Al. Constitutive material modeling is highly important because it exhibits thermal and strain softening at elevated strain and temperatures. Through the experiments mentioned above, we obtain the accurate Johnson–Cook material model for Ti-10V2Fe-3Al. Then, the FE simulation can be carried out. Before the simulation, we establish the models of tool and workpiece in Solidworks software in accordance with the actual characters of solid carbide and experimental workpiece displayed. The models are imported into the FE analysis software DEFORM. The pre-settings of the models are completed on the basis of the mechanical properties of Ti-10V-2Fe-3Al and carbide tool (listed in Tables 1 and 2).
Table 3 Relevant milling parameters. Number
Feed Rate fz /(mm z−1 )
Cutting Speed vc /(m min−1 )
Cutting Depth ap /(mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12
30 30 30 60 60 60 90 90 90 30 30 30 60 60 60 90 90 90 30 30 30 60 60 60 90 90 90
0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0
After the pre-settings, the obtained accurate Generalized Johnson–Cook model is applied into the simulation. The object type of Ti-10V-2Fe-3Al is defined as elasto-plastic, whereas the object type of carbide tool is defined as rigid. This study analyzes the influence of various milling conditions on residual stress. According to the practical industrial demands of this work, the relevant milling parameters are identified (Table 3).
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Fig. 5. Simulation process of stress.
Simulating the jobs with relevant milling parameters, we obtain the results of stress and strain. The simulation process is shown in Fig. 5, and the simulation residual stress of each group is recorded. 4. Experiment The relevant experiments are carried out to validate the accuracy of the FE simulation of Ti-10V-2Fe-3Al. In accordance with the milling parameters listed in Table 3, the carbide milling cutter and combined machine tool are selected to complete the milling process. The type of tool is SANDVIK R390. The diameter of the tool is 50 mm and the length is 150 mm. In addition, a low-stress tongs is designed to reduce the assembly stress. The method of measuring residual stress is X-ray diffraction (XRD). Utilizing the diffraction of electron to X-ray, the lattice strain is measured. Then the residual stress can be calculated based on the Hooke’s law and the theory of elastic mechanics.
Before milling, the work pieces have been machined into 30 × 20 × 20 (mm) cuboids (Fig. 6). The experiment consists of three parts. The first step is to wipe off the work hardening of Ti-10V-2Fe-3Al. Second, these work pieces are milled in order as listed in Table 3. After milling, each workpiece is marked with the number of experiment group, and the residual stress of the relevant region is measured by an X-ray stress detector (Fig. 7). Each measure experiment was repeated three times in different locations. The residual stress data obtained are compared with the simulation results (Fig. 8). Fig. 8 shows that the simulation residual stress is the compressive stress and that the variation range is [−260, −121] MPa. With the feed rate varying from 0.04 mm/z to 0.12 mm/z, the range of compressive residual stress is [−182, −121], [−260, −142], and [−227, −163] MPa, which decreases after the initial increase. Fig. 8 also shows that the average experiment residual stress is −200 MPa and that the average error of this experiment is 39.6 MPa.
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Fig. 6. Experiment setup for milling: (a) Low-stress tongs; (b) Combined machine tool.
Fig. 7. Measurement of residual stress: (a) X-ray stress detector; (b) Measurement of marked workpiece.
3Al milling is accurate and can help predict the residual stress of real Ti-10V-2Fe-3Al milling. According to the experiment data, Fig. 9 is set to investigate the influence on residual stress from the change of milling parameters. From the picture, a positive correlation can be found between not only residual stress and feed rate, but also residual stress and cutting speed. However, with the increase of cutting depth, residual stress becomes smaller. On the basis of the simulation data, a formulation is proposed referring to the previous studies [17,24,25] to evaluate the influence of cutting speed, cutting depth, and feed rate accurately. The relevant simulation results are used to fit a curve, which is described as r = a · fbz · vc · adp
Fig. 8. Comparison of experiment and simulation values.
This result validates the accuracy of the FE simulation. As the experiment group increases, the error varies considerably. The variation range of experiment residual stress is [−283, −75] MPa, which is larger than the simulation range. This finding may be attributed to the wear of carbide tool and initial distortion of lattice. The 27 experiment groups can be divided into three levels based on the feed rate. The errors are 47, 28, and 43 MPa when the feeds rate are 0.04, 0.08, and 0.12 mm/z. The smallest error is found at the feed rate of 0.08 mm/z. Furthermore, the error becomes small when the cutting speed becomes large, which verifies the proposed milling condition mentioned above. Thus, this FE simulation of Ti-10V-2Fe-
(3)
where r means the residual stress, fz stands for the feed rate, v represents the cutting speed, and ap means the cutting depth. According to the fitted curve, the relevant parameters are defined as a = −184.949, b = 0.2071, c = 0.1115, d = −0.0723
(4)
From Formulation (3), the influence of feed rate is larger than that of the cutting speed ignoring the wear of carbide tool. In addition, the cutting depth affects the residual stress the least. There is a good agreement between Fig. 10 and Formulation (3). Then the detail interaction influence of feed rate, cutting speed, and cutting depth is described as colorful surfaces shown in Fig. 10. Fig. 10 shows that the residual stress increases with increasing feed rate and cutting speed. In addition, the residual stress
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Q. Wu et al. / Journal of Manufacturing Processes 32 (2018) 530–537
Fig. 9. Influence on residual stress from the change of milling parameters.
Fig. 10. Interaction influence of feed rate and cutting speed: (a) ap = 0.2 mm; (b) ap = 0.6 mm; (c) ap = 1.0 mm; (e) v = 30 m/min; (f) v = 60 m/min; (g) v = 90 m/min; (h) fz = 0.04 mm/z; (i) fz = 0.08 mm/z; (j) fz = 0.12 mm/z.
decreases with increasing cutting depth. The residual stress is more sensitive to feed rate than the cutting speed. The cutting depth affects the residual stress the least because higher feed rate or cutting speed corresponds to higher milling temperature. However, the workpiece cannot conduct much heat because of the low thermal conductivity of Ti-10V-2Fe-3Al, which induces the effect
of thermal plastic deformation. However, a larger cutting depth means more areas to conduct the cutting heat, and the added effect of thermal plastic deformation reduces the milling surface residual stress. Moreover, we propose a large feed rate, high cutting speed, and small cutting depth to obtain the appropriate residual stress of the superficial machining layer.
Q. Wu et al. / Journal of Manufacturing Processes 32 (2018) 530–537
5. Conclusions A series of simulation and experiment studies was conducted to determine the relationship between the milling conditions and milling surface residual stress of Ti-10V-2Fe-3Al. The simulation and experiment results indicate the effects of feed rate, cutting speed, and cutting depth on surface residual stress. The effect mechanism is discussed, and some conclusions have been drawn: (1) The milled surfaces exhibit compressive residual stress under both simulation and experimental conditions. The range of residual stress is [−260, −121] MPa under simulation conditions and [−283, −75] MPa under experimental conditions. The relative error between simulation and experiment results is 19.5%, which indicates that this simulation is accurate. (2) When the feed rate is 0.08 mm/z, the relative error between the simulation and experiment results is the smallest. (3) The effects of feed rate, cutting speed, and cutting depth on the residual stress can be described as a formulation. The residual stress increases with increasing feed rate and cutting speed. The residual stress reduces with increasing cutting depth. (4) To obtain the appropriate residual stress of Ti-10V-2Fe-3Al workpiece, high feed rate, high cutting speed, and small cutting depth are proposed. Acknowledgements This study was financially supported by National Natural Science Foundation of China (Grant No. 51105025), Defense Industrial Technology Development program (Grant No. A0520110009), National Science and Technology Major Project (Grant No. 2014ZX04001011). References [1] Wagner V, Duc E. Study of Ti-1023 milling with toroidal tool. Int J Adv Manuf Technol 2014;75:1473–91. [2] Rao B, Dandekar CR, Shin YC. An experimental and numerical study on the face milling of Ti–6Al–4V alloy: Tool performance and surface integrity. J Mater Process Technol 2011;211:294–304. [3] Thepsonthi T, Özel T. An integrated toolpath and process parameter optimization for high-performance micro-milling process of Ti–6Al–4V titanium alloy. Int J Adv Manuf Technol 2014;75:57–75. [4] Pan W, Kamaruddin A, Ding S, Mo J. Experimental investigation of end milling of titanium alloys with polycrystalline diamond tools. Geophysics 2014;228:832–44. [5] Li A, Zhao J, Pei Z, Zhu N. Simulation-based solid carbide end mill design and geometry optimization. Int J Adv Manuf Technol 2014;71:1889–900.
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[6] Thepsonthi T, Özel T. Experimental and finite element simulation based investigations on micro-milling Ti-6Al-4V titanium alloy: effects of cBN coating on tool wear. J Mater Process Technol 2013;213:532–42. [7] Nouari M, Iordanoff I. Effect of the third-body particles on the tool–chip contact and tool-wear behaviour during dry cutting of aeronautical titanium alloys. Tribol Int 2007;40:1351–9. [8] Thepsonthi T, Özel T. 3-D finite element process simulation of micro-end milling Ti-6Al-4V titanium alloy: Experimental validations on chip flow and tool wear. J Mater Process Technol 2015;221:128–45. [9] Rao B, Dandekar CR, Shin YC. An experimental and numerical study on the face milling of Ti–6Al–4V alloy: Tool performance and surface integrity. J Mater Process Technol 2011;211:294–304. [10] Bajpai Vivek, Lee Ineon, Wook Park Hyung. Finite element modeling of three-dimensional milling process of Ti-6Al-4V. Adv Manuf Processes 2014;29:564–71. [11] Wu HB, Zhang SJ. 3D FEM simulation of milling process for titanium alloy Ti6Al4V. Int J Adv Manuf Technol 2014;71:1319–26. [12] Liu G. Study on deformation of titanium thin-walled part in milling process. J Mater Process Technol 2009;209:2788–93. [13] Calamaz M, Coupard D, Girot F. A new material model for 2D numerical simulation of serrated chip formation when machining titanium alloy Ti–6Al–4V. Int J Mach Tool Manuf 2013;48:275–88. [14] Ma J, Andrus P, Condoor S, Lei S. Numerical investigation of effects of cutting conditions and cooling schemes on tool performance in up milling of Ti-6AL-4V alloy. Int J Adv Manuf Technol 2015;78:361–83. [15] Wyen CF, Jaeger D, Wegener K. Influence of cutting edge radius on surface integrity and burr formation in milling titanium. Int J Adv Manuf Technol 2013;67:589–99. [16] Wu Q, Li DP. Analysis, X-ray measurements of cutting residual stresses in 7075 aluminum alloy in high speed machining. Int J Precis Eng Manuf 2014;15:1499–506. [17] Yao C, Wu D, Tan L, Ren J, Shi K, Yang Z. Effects of cutting parameters on surface residual stress and its mechanism in high-speed milling of TB6. Proc Inst Mech Eng Part B J Eng Manuf 2013;227:483–93. [18] Daymi A, Boujelbene M, Amara AB, Bayraktar E, Katundi D. Surface integrity in high speed end milling of titanium alloy Ti–6Al–4V. Mater Sci Technol 2011;27:387–94. [19] Mantle AL, Aspinwall DK. Surface integrity of a high speed milled gamma titanium aluminide. J Mater Process Tech 2001;118:143–50. [20] Yang D, Liu Z, Ren X, Zhuang P. Hybrid modeling with finite element and statistical methods for residual stress prediction in peripheral milling of titanium alloy Ti-6Al-4V. Int J Mech Sci 2016;108-109:29–38. [21] Miguélez H, Zaera R, Cheriguene R, Molinari A. Numerical analysis of the influence of cutting speed in machined induced residual stresses in aero-engine alloys. Bioinformatics (Oxford, England) 2009;19(Suppl. 2):i246–55. [22] Wu Q, Si Y, Wang GS, Wang L. Machinability of a silicon carbide particlereinforced metal matrix composite. RSC Adv 2016;6:21765–75. [23] Xin H, Shi Y, Ning L, Zhao T. Residual stress and affected layer in disc milling of titanium alloy. Adv Manuf Processes 2015;31:1645–53. [24] Li J, Yang X, Ren C, Chen G, Wang Y. Multiobjective optimization of cutting parameters in Ti-6Al-4V milling process using nondominated sorting genetic algorithm-II. Int J Adv Manuf Technol 2015;76:941–53. [25] Yang D, Liu Z, Ren X, Zhuang P. Hybrid modeling with finite element and statistical methods for residual stress prediction in peripheral milling of titanium alloy Ti-6Al-4V. Int J Mech Sci 2016;108-109:29–38. [26] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures; 1983.
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Simulation analysis and experimental study of milling surface residual stress of Ti-10V-2Fe-3Al Qiong Wu ∗ , Dong-Jian Xie, Yu Si, Yi-Du Zhang, Lei Li, Ying-Xin Zhao State Key Laboratory of Virtual Reality Technology and Systems, School of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, PR China
a r t i c l e
i n f o
Article history: Received 12 May 2017 Received in revised form 8 March 2018 Accepted 13 March 2018 Keywords: FE simulation Milling parameter Residual stress Ti-10V-2Fe-3Al
a b s t r a c t Nowadays, Ti-10V-2Fe-3Al is widely used in aerospace field because of its high specific strength, good breaking property, low forging temperature, and excellent stress corrosion resistance. However, these properties render Ti-10V-2Fe-3Al a hard-to-cut material. Moreover, the low thermal conductivity of Ti10V-2Fe-3Al results in high temperature on the tool face, which causes the wear of cutting tool. This paper presents a simulation analysis and an experimental validation on the milling surface residual stress of Ti10V-2Fe-3Al. The formation mechanism and influence of cutting parameters on the residual stress in the end milling of Ti-10V-2Fe-3Al are investigated through orthogonal experiments. The interaction effect of cutting parameters on forming residual stress is studied by analyzing the finite element (FE) simulation results. Moreover, relevant experiments are carried out to validate the accuracy of FE simulation. On the basis of these data, a formulation describing the interaction effect is proposed. © 2018 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
1. Introduction Titanium alloy is considered a industrial high-strength material because of its high specific strength, good breaking properties, low forging temperature, and excellent stress corrosion resistance. Hence, titanium alloy is widely used in aerospace field. However, titanium alloy is difficult to be milled because of the excellent properties mentioned above. Machining titanium alloy is expensive. Thus, many studies have investigated the milling process and surface integrity of titanium alloy to improve milling efficiency. Some studies focused on the effect of milling tool. Wagner et al. [1] studied the tool wear mechanisms of Ti-1023 milling by using toroidal tool and established the relation among cutting conditions, milling tool geometry, and tool life. Rao et al. [2] performed experimental and numerical studies on the face milling of Ti-6Al-4V titanium alloy to characterize tool performance and surface integrity. Thepsonthi et al. [3] proposed an integrated method in selecting toolpath and optimized the process parameters to improve the performance of micro-milling Ti-6Al-4V alloy. Pan et al. [4] investigated the performance of polycrystalline diamond tools in the end milling of titanium alloys and analyzed the relationship between cutting force
∗ Corresponding author. E-mail addresses: [email protected] (Q. Wu), [email protected] (D.-J. Xie), [email protected] (Y. Si), [email protected] (Y.-D. Zhang), [email protected] (L. Li), [email protected] (Y.-X. Zhao).
and cutting parameters. Li et al. [5] presented a 3D finite element method (FEM) of Ti-6Al-4V milling for the design and optimization of solid carbide end milling. Thepsonthi et al. [6] carried out experiments and finite element (FE) simulation to show that the cBN-coated carbide tool outperforms the uncoated carbide tool in generating tool wear and cutting temperature during Ti-6Al4V micro-milling. Nouari et al. [7] studied the effect of third-body particles on the tool-chip contact and tool-wear behavior during the dry cutting of aeronautical titanium alloys. Thepsonthi et al. [8] conducted the 3D FE modeling and simulation of micro-end milling for Ti-6Al-4V titanium alloy to characterize chip flow and tool wear. The simulation results agreed with the experimental data. Rao et al. [9] focused on the measurement of specific cutting energy, surface integrity and tool performance with the experimental and numerical study of face milling of Ti-6Al-4V titanium alloy. Some studies focused on the deformation and cutting chip in the milling process. Bajpai et al. [10] studied the cutting forces and chip morphology through 3D FE simulation and experiments. Wu et al. [11] developed a 3D FE model for the complex milling of titanium alloy Ti-6Al-4V with ABAQUS and compared the chip formation, cutting force, and milling temperature obtained from simulation with those obtained from experiments. Liu et al. [12] established a 3D FE model of a helical tool and a thin-walled part with a cantilever to predict the cutting deformation of a titanium alloy Ti-6Al-4V thin-walled part during milling. The accuracy of this model can be validated by experimental cutting deformation. Calamaz et al. [13]
https://doi.org/10.1016/j.jmapro.2018.03.015 1526-6125/© 2018 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
Q. Wu et al. / Journal of Manufacturing Processes 32 (2018) 530–537
implemented a new material constitutive law in a 2D FE model to analyze the chip formation and shear localization when machining titanium alloys. Moreover, some studies performed experiments and FE simulations to establish the relationship between milling parameters and face integrity. Ma et al. [14] employed the FEM to investigate the effects of cutting conditions in corner up milling on the temperature of the tool rake face. Wyen et al. [15] studied the influence of the cutting edge radius on surface integrity in terms of residual stress, micro-hardness, surface roughness and optical characterization of the surface, and near surface area in up and down milling of the titanium alloy. Wu et al. [16] presented the effect of machined surface quality and cutting parameters on residual stress distribution in 7075 aluminum alloy. Yao et al. [17] investigated the formation mechanism and influence of cutting parameters on residual stress in the flank milling of Ti-10V-2Fe3Al through orthogonal experiments. Daymi et al. [18] conducted a series of end milling experiments to characterize comprehensively the surface integrity of titanium alloy Ti-6Al-4V with TiAlN-coated carbide cutting tools under various milling conditions. Mantle et al. [19] studied the surface integrity of a high-speed ball end milled gamma titanium aluminide. Yang et al. [20] utilized a hybrid technique combining the FEM to study the effect of cutting speed and feed rate on the residual stress of Ti-6Al-4V (TC4). Miguélez et al. [21] investigated the influence of cutting speed on the induced machining residual stresses of TC4. Wu et al. [22] determined the effects of machined surface quality and cutting parameters on the residual stress distribution in a silicon carbide particle-reinforced metal matrix composite through FEM and experiments. Xin et al. [23] numerically analyzed the impact of cutting factors on residual stress. Li et al. [24] adopted non-dominated sorting genetic algorithm-II to established empirical models of tool life, residual stress and roughness according to TC4 milling parameters. The empirical models were utilized for optimization of production cost and surface quality. Yang et al. [25] developed a hybrid technique combining the finite element method and the statis-
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tical model for residual stress prediction in peripheral milling of TC4. The sensitivity to cutting speed and feed rate of four key features of the residual stress profile including surface residual stress, compressive stress peak value and location, response depth were investigated. Although each of above studies has its features and merits, only a few of them focus on the empirical formula about residual stress and milling parameters. And they mostly focus on the titanium of TC4. Besides, cutting depth, which is one of the four key milling parameters, is less investigated. The purpose of this paper is to provide an empirical formula about the relationship between residual stress and cutting speed, feed rate and cutting depth. In this work, several experiments were performed to acquire the specific parameters of the Johnson–Cook material model of Ti10V-2Fe-3Al. Then, the Johnson–Cook material model was applied into FE software DEFORM to validate its accuracy. FE simulations and relevant experiments under various end milling conditions were conducted to explore the relationship between the residual stress and milling parameters of Ti-10V-2Fe-3Al. After comparing the results obtained from FE simulations and experiments, a good agreement between the two data was found. Furthermore, the variation tendency of residual stress with the changes in feed speed, cutting depth, and cutting speed was discussed and analyzed. The results of this study may serve as a reference for future studies to improve the milling efficiency of Ti-10V-2Fe3Al. 2. Johnson–Cook material model In this study, the Generalized Johnson–Cook model was adopted to simulate Ti-10V-2Fe-3Al in FE software DEFDORM. To obtain an accurate simulation result, several experiments were carried out to obtain the relevant parameters of the Generalized Johnson–Cook model for the Ti-10V-2Fe-3Al. Moreover, we appropriately modified the parameters to fit the data from experiments, and the following is the process.
Fig. 1. Tensile test.
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Fig. 2. Simulation result of the tensile test.
The Generalized Johnson–Cook material model [26] shows the following formulation:
= A + Bε
n
· 1 + Cln
•
ε •
ε0
·
•
ε •
˛
· D-ETm ∗
(1)
ε0
where A, B, n, C, and m are the parameters, which we should confirm. means the effective stress, and ε represents the effective •
•
plastic strain. ε means the effective plastic strain rate, and ε0 is the reference strain rate. D and E are the relevant temperature coefficients. T∗ is a dimensionless temperature that is converted from the current temperature and the melting point of Ti-10V-2Fe-3Al. In this simulation, the job is used to describe the milling process under room temperature. Thus, D and E are 1, and ␣ is 0. The right side of Formulation (1) represents the influences of equivalent plastic strain, strain rate, and temperature on flow stress. In this simulation, the job is used to describe the milling process under room temperature. To obtain parameters, a tensile test of Ti-10V-2Fe-3Al is conducted. Ti-10V-2Fe-3Al is tested under conference strain rate and conference temperature. When the yield n point of workpiece of the tensile test is obtained, ε = 0 and A = . Parameters B and n can be identified by fitting the equivalent effective strain and stress. Meanwhile, when the tensile test is conducted under current temperature, parameters C and m can be identified by the tensile test under different strain rates and temperatures. On the basis of the relation mentioned above, relevant workpieces are selected to conduct the tensile experiments. The experimental set-up is shown in Fig. 1, and the data of stress and
Fig. 3. Stress–strain curve.
strain are recorded under conference strain and temperature. From the data, the experimental stress–strain curve is obtained. Then, the value of other parameters can be obtained by fitting the equivalent effective stress curve under different conditions. The tensile test of Ti-10V-2Fe-3Al is simulated using the Generalized Johnson–Cook material model of DEFORM FE software, and the result is shown in Fig. 2. Moreover, the simulation stress–strain curve is drawn in Fig. 3. A comparison of the experimental and simulation results in Fig. 3 reveals a good agreement on the slope of the stress–strain curve. However, the maximums of the two stress–strain curves are different. The main reason for the difference is the state of the work-
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Fig. 4. Results of the contraction test:(a) under different strain rates; (b) under different temperature.
Table 1 Mechanical properties of Ti-10V-2Fe-3Al. Density(kg/m3)
Hardness (HRC)
Tensile Strength (MPa)
Yield Strength(MPa)
Percentage of Elongation
Young’s Modulus (GPa)
Poisson’s ratio
Shear Strength (MPa)
4400
53
910
860
16%
117
0.31
680
Table 2 Mechanical properties of carbide tool. Young’s Modulus (MPa)
Poisson’s ratio
Linear Expansivity (10−6 /◦ C)
Specific Heat (J/kg ◦ C)
Thermal Coefficient (W/m K)
6.5E + 5
0.25
6.2
226
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piece enters the non-linear phase after the strain is greater than 0.01. In the non-linear phase, properties of the material decrease. Due to these factors cannot be considered by simulation, the maximum value of simulation is higher than that of experiment. When the strain is greater than 0.01 later, the difference between the maximum of the two curves is relatively stable. The Johnson-Cook parameter is based primarily on the slope of the curve before strain is less than 0.01. Thus the difference in values between the simulation and experimental curves can be accepted. After considering the experimental results, the Johnson–Cook parameters are optimized to obtain accurate simulation results. Moreover, a contraction test is conducted to verify the accuracy of the parameters. The contraction test is carried out under different strain rates and different temperatures, and the results are shown in Fig. 4. Through this test, the accuracy of the Generalized Johnson–Cook model is verified, and the values of the parameters are finally identified as follows: A = 976.9, B = 502.3, C = 0.028, n = 0.22,m = 1
(2)
3. Simulation The Lagrangian solution-based FE software for deformation is utilized to construct the 3D FE model for the end milling of Ti10V-2Fe-3Al. Constitutive material modeling is highly important because it exhibits thermal and strain softening at elevated strain and temperatures. Through the experiments mentioned above, we obtain the accurate Johnson–Cook material model for Ti-10V2Fe-3Al. Then, the FE simulation can be carried out. Before the simulation, we establish the models of tool and workpiece in Solidworks software in accordance with the actual characters of solid carbide and experimental workpiece displayed. The models are imported into the FE analysis software DEFORM. The pre-settings of the models are completed on the basis of the mechanical properties of Ti-10V-2Fe-3Al and carbide tool (listed in Tables 1 and 2).
Table 3 Relevant milling parameters. Number
Feed Rate fz /(mm z−1 )
Cutting Speed vc /(m min−1 )
Cutting Depth ap /(mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12
30 30 30 60 60 60 90 90 90 30 30 30 60 60 60 90 90 90 30 30 30 60 60 60 90 90 90
0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0 0.2 0.6 1.0
After the pre-settings, the obtained accurate Generalized Johnson–Cook model is applied into the simulation. The object type of Ti-10V-2Fe-3Al is defined as elasto-plastic, whereas the object type of carbide tool is defined as rigid. This study analyzes the influence of various milling conditions on residual stress. According to the practical industrial demands of this work, the relevant milling parameters are identified (Table 3).
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Fig. 5. Simulation process of stress.
Simulating the jobs with relevant milling parameters, we obtain the results of stress and strain. The simulation process is shown in Fig. 5, and the simulation residual stress of each group is recorded. 4. Experiment The relevant experiments are carried out to validate the accuracy of the FE simulation of Ti-10V-2Fe-3Al. In accordance with the milling parameters listed in Table 3, the carbide milling cutter and combined machine tool are selected to complete the milling process. The type of tool is SANDVIK R390. The diameter of the tool is 50 mm and the length is 150 mm. In addition, a low-stress tongs is designed to reduce the assembly stress. The method of measuring residual stress is X-ray diffraction (XRD). Utilizing the diffraction of electron to X-ray, the lattice strain is measured. Then the residual stress can be calculated based on the Hooke’s law and the theory of elastic mechanics.
Before milling, the work pieces have been machined into 30 × 20 × 20 (mm) cuboids (Fig. 6). The experiment consists of three parts. The first step is to wipe off the work hardening of Ti-10V-2Fe-3Al. Second, these work pieces are milled in order as listed in Table 3. After milling, each workpiece is marked with the number of experiment group, and the residual stress of the relevant region is measured by an X-ray stress detector (Fig. 7). Each measure experiment was repeated three times in different locations. The residual stress data obtained are compared with the simulation results (Fig. 8). Fig. 8 shows that the simulation residual stress is the compressive stress and that the variation range is [−260, −121] MPa. With the feed rate varying from 0.04 mm/z to 0.12 mm/z, the range of compressive residual stress is [−182, −121], [−260, −142], and [−227, −163] MPa, which decreases after the initial increase. Fig. 8 also shows that the average experiment residual stress is −200 MPa and that the average error of this experiment is 39.6 MPa.
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Fig. 6. Experiment setup for milling: (a) Low-stress tongs; (b) Combined machine tool.
Fig. 7. Measurement of residual stress: (a) X-ray stress detector; (b) Measurement of marked workpiece.
3Al milling is accurate and can help predict the residual stress of real Ti-10V-2Fe-3Al milling. According to the experiment data, Fig. 9 is set to investigate the influence on residual stress from the change of milling parameters. From the picture, a positive correlation can be found between not only residual stress and feed rate, but also residual stress and cutting speed. However, with the increase of cutting depth, residual stress becomes smaller. On the basis of the simulation data, a formulation is proposed referring to the previous studies [17,24,25] to evaluate the influence of cutting speed, cutting depth, and feed rate accurately. The relevant simulation results are used to fit a curve, which is described as r = a · fbz · vc · adp
Fig. 8. Comparison of experiment and simulation values.
This result validates the accuracy of the FE simulation. As the experiment group increases, the error varies considerably. The variation range of experiment residual stress is [−283, −75] MPa, which is larger than the simulation range. This finding may be attributed to the wear of carbide tool and initial distortion of lattice. The 27 experiment groups can be divided into three levels based on the feed rate. The errors are 47, 28, and 43 MPa when the feeds rate are 0.04, 0.08, and 0.12 mm/z. The smallest error is found at the feed rate of 0.08 mm/z. Furthermore, the error becomes small when the cutting speed becomes large, which verifies the proposed milling condition mentioned above. Thus, this FE simulation of Ti-10V-2Fe-
(3)
where r means the residual stress, fz stands for the feed rate, v represents the cutting speed, and ap means the cutting depth. According to the fitted curve, the relevant parameters are defined as a = −184.949, b = 0.2071, c = 0.1115, d = −0.0723
(4)
From Formulation (3), the influence of feed rate is larger than that of the cutting speed ignoring the wear of carbide tool. In addition, the cutting depth affects the residual stress the least. There is a good agreement between Fig. 10 and Formulation (3). Then the detail interaction influence of feed rate, cutting speed, and cutting depth is described as colorful surfaces shown in Fig. 10. Fig. 10 shows that the residual stress increases with increasing feed rate and cutting speed. In addition, the residual stress
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Fig. 9. Influence on residual stress from the change of milling parameters.
Fig. 10. Interaction influence of feed rate and cutting speed: (a) ap = 0.2 mm; (b) ap = 0.6 mm; (c) ap = 1.0 mm; (e) v = 30 m/min; (f) v = 60 m/min; (g) v = 90 m/min; (h) fz = 0.04 mm/z; (i) fz = 0.08 mm/z; (j) fz = 0.12 mm/z.
decreases with increasing cutting depth. The residual stress is more sensitive to feed rate than the cutting speed. The cutting depth affects the residual stress the least because higher feed rate or cutting speed corresponds to higher milling temperature. However, the workpiece cannot conduct much heat because of the low thermal conductivity of Ti-10V-2Fe-3Al, which induces the effect
of thermal plastic deformation. However, a larger cutting depth means more areas to conduct the cutting heat, and the added effect of thermal plastic deformation reduces the milling surface residual stress. Moreover, we propose a large feed rate, high cutting speed, and small cutting depth to obtain the appropriate residual stress of the superficial machining layer.
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5. Conclusions A series of simulation and experiment studies was conducted to determine the relationship between the milling conditions and milling surface residual stress of Ti-10V-2Fe-3Al. The simulation and experiment results indicate the effects of feed rate, cutting speed, and cutting depth on surface residual stress. The effect mechanism is discussed, and some conclusions have been drawn: (1) The milled surfaces exhibit compressive residual stress under both simulation and experimental conditions. The range of residual stress is [−260, −121] MPa under simulation conditions and [−283, −75] MPa under experimental conditions. The relative error between simulation and experiment results is 19.5%, which indicates that this simulation is accurate. (2) When the feed rate is 0.08 mm/z, the relative error between the simulation and experiment results is the smallest. (3) The effects of feed rate, cutting speed, and cutting depth on the residual stress can be described as a formulation. The residual stress increases with increasing feed rate and cutting speed. The residual stress reduces with increasing cutting depth. (4) To obtain the appropriate residual stress of Ti-10V-2Fe-3Al workpiece, high feed rate, high cutting speed, and small cutting depth are proposed. Acknowledgements This study was financially supported by National Natural Science Foundation of China (Grant No. 51105025), Defense Industrial Technology Development program (Grant No. A0520110009), National Science and Technology Major Project (Grant No. 2014ZX04001011). References [1] Wagner V, Duc E. Study of Ti-1023 milling with toroidal tool. Int J Adv Manuf Technol 2014;75:1473–91. [2] Rao B, Dandekar CR, Shin YC. An experimental and numerical study on the face milling of Ti–6Al–4V alloy: Tool performance and surface integrity. J Mater Process Technol 2011;211:294–304. [3] Thepsonthi T, Özel T. An integrated toolpath and process parameter optimization for high-performance micro-milling process of Ti–6Al–4V titanium alloy. Int J Adv Manuf Technol 2014;75:57–75. [4] Pan W, Kamaruddin A, Ding S, Mo J. Experimental investigation of end milling of titanium alloys with polycrystalline diamond tools. Geophysics 2014;228:832–44. [5] Li A, Zhao J, Pei Z, Zhu N. Simulation-based solid carbide end mill design and geometry optimization. Int J Adv Manuf Technol 2014;71:1889–900.
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