Available online at www.sciencedirect.com
ScienceDirect Procedia CIRP 46 (2016) 428 – 431
7th HPC 2016 – CIRP Conference on High Performance Cutting
Numerical modelling of microstructure evolution in Ti6Al4V alloy by ultrasonic assisted cutting Wei Baia, Ronglei Suna*, Jürgen Leopoldb a
The State Key Lab of Digital Manufacturing Equipment and Technology, School of Mechanical Science & Engineering, Huazhong University of Science and Technology, 1037 Luoyu Road, 430074 Wuhan, China b TBZ-PARIV GmbH; 09126 Chemnitz, Germany
* Corresponding author. Tel.: +86-18986129289 ; fax: +86-027-87559416. E-mail address:
[email protected]
Abstract This paper aims to reveal the influence of ultrasonic assisted cutting (UAC) on the microstructure of machined surface in Ti6Al4V alloy. In order to investigate the microstructure evolution, an enhanced material constitutive model with the temperature dependent material properties of Ti6Al4V alloy is presented. The study also performs a comparison of cutting and thrust forces in conventional cutting (CC) by using three models, and the Calamaz modified Johnson-Cook model meets the experimental results well. The Johnson-Mehl-Avrami-Kolmogorov (JMAK) model for Ti6Al4V alloy is utilized to predict dynamic recrystallization (DRx) and resultant grain size. Five points under machined surface are tracked to reflect the evolution of dynamic recrystallization grain size and average grain size subjected to CC and UAC. Further simulations of different vibration amplitudes and cutting parameters are performed, and the comparison between CC and UAC presents the change of average grain size of UAC is smaller than that of CC, thus showing the UAC can achieve low damage processing. 2016The TheAuthors. Authors. Published by Elsevier © 2016 Published by Elsevier B.V B.V. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the International Scientific Committee of 7th HPC 2016 in the person of the Conference Chair Prof. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Matthias Putz. under responsibility of the International Scientific Committee of 7th HPC 2016 in the person of the Conference Chair Peer-review Prof. Matthias Putz Keywords: Ultrasonic, Cutting, Microstructure, Dynamic Recrystallization, Low Damage Process
1. Introduction Ultrasonic assisted cutting (UAC) is a promising process over conventional cutting (CC) in terms of cutting force, cutting temperature, cutting stability, tool wear, surface roughness and so on [1]. UAC has been proven to be an efficient technique for improving the machinability of several aeronautic materials [2, 3]. The microstructure of machined surface and subsurface strongly affect the performance and fatigue life of components in aerospace. Microstructure modelling of cutting has been the interest of many researchers [4, 5]. The cutting tool separates from workpiece cyclically in UAC which may lead to different microstructure from CC. Thus, the investigation of microstructure evolution in Ti6Al4V alloy by UAC is needed. The paper is organized as follows: in order to reveal the microstructure evolution of UAC, an accurate finite element (FE) model is required. In Section 2, an enhanced material
constitutive model was presented and validated by cutting forces. The Johnson-Mehl-Avrami-Kolmogorov (JMAK) microstructure model was used to predict the dynamic recrystallization and resultant grain size of UAC and CC in Section 3. In Section 4, the experiments were performed and the average grain size of UAC and CC in different amplitudes and cutting parameters were predicted. The paper ended with some concluding remarks in Section 5. 2. FE-based orthogonal CC and validation In numerical model, a material constitutive model is required to calculate the flow stress. The Johnson-Cook (J-C) material model is widely used for calculating the flow stress of machining process. However, Johnson-Cook material model is limited at high strains. A modified Johnson-Cook material model is presented by Calamaz et al. [6]. Then Sima and Özel [7] added a parameter
2212-8271 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the International Scientific Committee of 7th HPC 2016 in the person of the Conference Chair Prof. Matthias Putz doi:10.1016/j.procir.2016.03.122
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of the equation. The modified material flow stress is expressed as follows: s m ⎡ ⎡ ⎛ ⎞⎤ ⎤ ⎡ ⎛ 1 ⎞⎤ ⎡ ε& ⎤ ⎡ ⎛ T − Tr ⎞ ⎤ ⎢ 1 ⎥ σ = ⎢ A + Bε n ⎜ 1 + C ln ⎥ ⎢1 − ⎜ ⎥ D + (1 − D ) ⎢ tanh ⎜ ⎟ r ⎟⎥ a ⎟⎥ ⎢ ⎜ (ε + p ) ⎟⎥ ⎥ , ε&0 ⎦ ⎢ ⎝ Tm − Tr ⎠ ⎥ ⎢ ⎝ exp(ε ) ⎠⎦ ⎣ ⎣ ⎝ ⎠⎦ ⎦ ⎣ ⎦⎣ ⎣⎢
where
⎛T ⎞ D = 1− ⎜ ⎟ ⎝ Tm ⎠
d
and
⎛T ⎞ p=⎜ ⎟ ⎝ Tm ⎠
b
(1)
where σ is the equivalent flow stress, ε is the equivalent strain, ε& is the equivalent strain rate, ε&0 is the reference equivalent strain rate, T is the workpiece temperature, Tr is the room temperature, Tm is the material melting temperature, A , B , C , n , m , a , b , d , r and s are material constants. It modified strain hardening function of Johnson-Cook model by including flow softening at high strains, modified thermal softening function by including temperature-dependent flow softening. The parameters of Calamaz modified Johnson-Cook (Calamaz J-C) model were optimized by simulation experiments [8]. The flow stress curves of this model are shown in Fig. 1.
different feeds (0.0762mm/rev, 0.1016mm/rev, 0.127mm/rev) were studied for each model. The orthogonal CC of Ti6Al4V alloy experiments under the same cutting parameters had been implemented by Sima and Özel [7]. Thus the simulated cutting and thrust forces of three different material models and experimental data have been presented in Fig. 2. It should be mentioned that the depth of cut in simulation and experiment should be convert to the same value.
Fig. 2. Simulated cutting and thrust forces and experimental results.
As shown in Fig. 2, the cutting forces at three different feeds by Calamaz J-C material model show the minimal errors compared with experimental results. The thrust forces by Deform-2D material model show the minimal errors; however, the thrust forces using Calamaz J-C model also can be accepted. Thus the Calamaz J-C model meets the experimental results well. It will be imported into the FE model of microstructure evolution. 3. Numerical modelling of microstructure evolution Fig. 1. Flow stress curves of Calamaz modified Johnson-Cook material model.
According to the flow stress curves shown in Fig. 1, the flow softening is evident at high strains and high temperatures. The stresses reach to the peak value then decrease, until a strain around 2 after which the constant stresses are obtained. To study the microstructure evolution of CC and UAC, an accurate FE model is required. The updated Lagrangian software (Deform-2D) is used to achieve continuous remeshing. The three material models (J-C material model, Deform-2D material model and Calamaz J-C material model) of Ti6Al4V alloy are integrated into Deform-2D for orthogonal cutting. A plane-strain thermo-mechanical coupled analysis is performed. The material properties of Ti6Al4V are defined as temperature dependent [7]. In this paper, the serrated chip formation is simulated by employing Cockroft and Latham’s fracture criterion [9]. It is expressed as:
∫
εf
0
σ 1d ε = Dc
(2)
where ε f is the effective strain, σ1 is the maximum principle stress, Dc is the material constant. The damage value Dc is suggested as 245 in this paper. The FE-based orthogonal CC of Ti6Al4V alloy were performed using uncoated tungsten carbide (WC) tools with sharp edges (5μm edge radius) at cutting speed 121.9m/min. The rake angle and relief angle of tool is 0°and 11°. Three
The orthogonal cutting with ultrasonic vibration in the direction of the cutting velocity is shown in Fig. 3. In the model the workpiece moves at a cutting speed of 40m/min. The bottom side of the workpiece is provided with kinematic boundary, and the top surface is free.
Fig. 3. Relative movement of the tool and workpiece in orthogonal UAC.
The cutting tool (rake angle of 0°relief angle of 7° and edge radius of 0.05mm) is rigid and immovable for the simulations of CC. However, the vibration in the direction of cutting velocity is applied to the tool in the simulations of UAC as given by:
v x = 2π fAx sin ( 2π ft ) , v y = 0
(3)
where the frequency f is 20kHz and amplitude Ax is 20μm.The maximum tool vibration speed 2π fAx (2513mm/s) is larger
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than cutting speed (666.7mm/s). Thus the tool will separate from workpiece in each cycle. The JMAK microstructure model is used to study the microstructure evolution of UAC. The main idea of the JMAK model is to calculate the recrystallized volume fraction inside the material and use the initial grain size information to model the microstructure. The dynamic recrystallization volume fraction is defined with the Avrami equation as given by: kd ⎡ ⎛ ε − a10ε p ⎞ ⎤ X DRx = 1 − exp ⎢ − β d ⎜ ⎟ ⎥ ⎢⎣ ⎝ ε 0.5 ⎠ ⎥⎦
(4)
where ε is the strain, ε p is the peak strain, ε 0.5 symbolizes the strain for X DRx = 0.5 , as: ⎛Q m ⎞ ε 0.5 = a5d 0h5ε n5ε& m5 exp ⎜ act 5 ⎟ + c5 ⎝ RT ⎠
(5)
where R is the universal gas constant. Dynamic recrystallization occurs when the critical strain ε c =a2ε p is reached, where the peak strain ε p is defined by: ⎛Q m ⎞ ε p = a1d0h1ε&m1 exp ⎜ act 1 ⎟ + c1 ⎝ RT ⎠
(6)
The recrystallized grain size is given by: ⎛Q m ⎞ d DRx = a8d 0h8 ε n8 ε& m8 exp ⎜ act 8 ⎟ + c8 ⎝ RT ⎠
(7)
The average grain size is calculated from the mixture as: d avg = d 0 (1 − X DRx ) + d DRx X DRx
(8)
The JAMK model parameters a1 , h1 , m1 , Qact , c1 , a5 , h5 , n5 , m5 , c5 , a8 , h8 , n8 , m8 , c8 , β d , a10 and kd of Ti6Al4V alloy are provided by running sensitivity analysis on Deform FE simulations [10]. The microstructure of Ti6Al4V alloy consists of two phase: α and β . The α - grains have typical average grain size of d 0 = 20μm . The β - grains are matrix which contain net structures and hard to count. In this paper, the average grain size is counted from α - grains, and phase-transition is not considered.
Fig. 5. Microstructure evolution of (a) dynamic recrystallization grain size in CC, (b) dynamic recrystallization grain size in UAC, (c) average grain size in CC, and (d) average grain size in UAC.
As shown in Fig. 5, the zones of translucent rectangle represent the period that the tool passes. The dynamic recrystallization grain size of UAC is much different from CC as shown in Fig. 5(a) and (b). The recrystallization grain size of UAC is obvious smaller than CC, and eventually the recrystallization grain size of UAC changes towards zero. It is because the tool separates from workpiece each cutting cycle in UAC, thus resulting the rapid change of strain rate and undulation of temperature. However, the strain rate and temperature have great impact on dynamic recrystallization and dynamic recovery. The recrystallization grain size cannot grow continuously due to the alternately predominant of dynamic recrystallization and recovery. In addition, the dynamic recrystallization volume fraction has the same mechanism and trend of evolution. From equation (8), it can be concluded that the average grain size subjected to UAC is larger than that of CC as shown in Fig. 5(c) and (d). The average grain size of surface and subsurface (Point 1 and 2) in CC decreases dramatically when the tool passes. After the tool passes, the average grain size increases slowly due to the recovery, after which a constant grain size is obtained. Eventually the average grain size of machined surface in UAC is larger than that in CC. 4. Experimental results and discussions
Fig. 4. The distribution of five track points.
Five points under the machined surface have been determined to track the microstructure evolutions. The points distributed in the depth of machined surface by 0.005mm, 0.015mm, 0.050mm, 0.100mm, 0.200mm as shown in Fig. 4. The microstructure evolution of machined surface subjected to CC and UAC are compared as shown in Fig. 5. The five points’ variables of dynamic recrystallization grain size and average grain size are tracked.
In this study, orthogonal CC and UAC with the cutting speed at 20m/min and feed at 0.1mm/rev have been tested. The microstructures under machined surface were illustrated in Fig. 6. As shown in Fig. 6, the five points under machined surface were marked and average grain size was measured using the linear intercept method. The simulated and experimental results of average grain size under machined surface in CC and UAC were compared in Table 1, where d 0 is 16.22μm . Table 1 shows the predicted and measured average grain sizes are very close in five different depths. Otherwise, the average grain size in UAC is larger, and is more close to d 0 .
Wei Bai et al. / Procedia CIRP 46 (2016) 428 – 431
Fig. 6. Microstructure under machined surface with respect to cutting speed at 20m/min, feed at 0.1mm/rev (a) CC, (b) UAC with amplitude at 7.7μm. Table 1.Comparision between numerically and experimentally obtained average grain size in CC and UAC.
CC UAC
FEM Exp FEM Exp
p1 15.10 15.03 15.50 15.48
p2 15.10 15.21 15.50 15.91
p3 15.20 15.15 15.60 15.72
p4 15.30 15.57 15.70 16.10
p5 15.70 15.57 16.00 16.11
In order to reveal the influence of cutting and vibration parameters on microstructure subjected to CC and UAC, a series of simulations are performed. Fig. 7 shows the average grain size of the selected five points under machined surface in CC and UAC at different vibration amplitudes, feeds and cutting speeds. As shown in Fig. 7, the average grain size in UAC is a bit larger than that in CC at different amplitudes and cutting parameters. In addition, the effects of vibration amplitude, feed and cutting speed on average grain size are unapparent. It is also indicated that the difference between five points in UAC is smaller than that in CC. Thus the comparison shows the UAC can achieve low damage processing. 5. Conclusions In this paper, the numerical model for microstructure of machined surface in Ti6Al4V alloy by UAC is investigated. The Calamaz modified Johnson-Cook material model is used which considers the flow softening at high strains and high temperatures. The dynamic recrystallization and resultant grain size for Ti6Al4V alloy are predicted by JMAK model. The comparison of average grain size under machined surface in CC and UAC shows that the change of average grain size of UAC is smaller than that of CC, thus showing the UAC can achieve low damage processing.
Fig. 7. Comparison of average grain size of five points under machined surface in CC and UAC with respect to (a) cutting speed at 20m/min, feed at 0.1mm/rev, (b) cutting speed at 60m/min, amplitude at 20μm and (c) amplitude at 20μm, feed at 0.1mm/rev.
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