Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing

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Original Article

Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing Jian Zhao a,b , Zhanqiang Liu a,b,∗ a

School of Mechanical Engineering, Shandong University, Jinan 250061, China Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MOE/Key National Demonstration Center for Experimental Mechanical Engineering Education, Jinan 250061, Shandong, China

b

a r t i c l e

i n f o

a b s t r a c t

Article history:

A hybrid machining technology with rotary ultrasonic roller burnishing process has been

Received 3 April 2019

developed. There is no material removal when the machined surface is generated by the

Accepted 23 December 2019

hybrid ultrasonic burnishing as comparing with other conventional cutting processes. The

Available online xxx

kinematic mechanism for plastic flow during surface generation in hybrid rotary ultrasonic burnishing Ti-6Al-4V with cylindrical roller tool was revealed in this paper. Firstly, the

Keywords:

machining experiments were carried out for surface generation with hybrid rotary ultra-

Rotary ultrasonic burnishing

sonic burnishing Ti-6Al-4V. Then, the experimental analysis was conducted and it showed

Surface generation

that, there was little change in dimension of the rotary ultrasonic roller burnished workpiece

Kinematic mechanism

compared to that of milled workpiece. Finally, a 3D finite element (FE) model was proposed

Plastic flow

to simulate the surface generation in hybrid rotary ultrasonic roller burnishing process. Three machining zones including pile-up deformation area, tensile deformation area, and compressive deformation area were selected for the analysis of the material plastic flow. It was found that the surface generated by rotary ultrasonic burnishing was mainly attributed to the plastic flow of material in these three deformation zones. The FE simulation results showed good agreements with the experimental ones. The proposed research results are helpful for the analysis and diagnosis of the surface generation in ultrasonic burnishing process. © 2019 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/).

1.

Introduction

Ti-6Al-4V is one of the widely popular titanium alloys because of the excellent corrosion resistance and high spe-

∗

cific strength. However, the low thermal conductivity and high chemical reactivity increase the machining difficulty of Ti6Al-4V. The machining mechanisms of the novel machining technologies should be explored to improve the machining of Ti-6Al-4V. Burnishing process is a finishing operation and it has been extensively used to enhance mechanical properties of the machined surfaces [1]. The application of burnishing technology has been extended to the fields of military industry

Corresponding author. E-mail: [email protected] (Z. Liu). https://doi.org/10.1016/j.jmrt.2019.12.071 2238-7854/© 2019 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/). Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071

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Fig. 1 – Research framework of this paper. Nomenclature for symbols in Fig. 1. U U1 U2 U3 FN Ff dx dy dz vx vy vz

Difference of profile height between burnished surface and milled surface Displacement of workpiece material along radial direction of roller parallel to its free surface Displacement of workpiece material along axial direction of roller Displacement of workpiece material perpendicular to free surface Normal force acting on contact surface of roller and workpiece Friction between roller and workpiece along rotation direction of roller Displacement of an arbitrary point on cylindrical surface of roller along x direction Displacement of an arbitrary point on cylindrical surface of roller along y direction Displacement of an arbitrary point on cylindrical surface of roller along z direction Velocity of an arbitrary point on cylindrical surface of roller along x direction Velocity of an arbitrary point on cylindrical surface of roller along y direction Velocity of an arbitrary point on cylindrical surface of roller along z direction

and aerospace. With more and more complicate service environment of the workpiece, the increasing requirement for the workpiece surface has been proposed. Hybrid burnishing has been widely appreciated and trends to replace the conventional burnishing technology, such as deep cold rolling [2], laser assisted burnishing [3], electrochemical assisted burnishing [4] and ultrasonic assisted burnishing [5]. Ultrasonic assisted burnishing superimposes the ultrasonic vibration on the conventional burnishing. The assistance of ultrasonic vibration introduces the smaller surface roughness [6], larger and deeper compressive residual stress [7,8] and hardness [9] distributions while decreasing the burnishing force [10]. There is no material removal during burnishing process. Plastic flow of material is the main deformation behavior in burnishing process. Two typical plastic flow of material phenomena can be observed in burnishing process. The first one is the material pile-up surrounding the indenter during burnishing process [11,12]. The pile-up of material is influenced by the pressure and the work hardening property of material [13]. Fu et al. [14] explored the depth and width of burnishing tracks at various pressures. They observed the pile-up phenomenon in experiment, but there was no pile-

up in simulation. They thought the reason was the lacking of the sliding effect of burnishing tool in simulation. Low [15] also found the formation of material pile-up in roller burnishing polyoxymethylene and polyurethane. Teimouri and Amini [16] analyzed the surface quality of aluminum 6061-T6 in ultrasonic burnishing. They observed the material pile-up when the burnishing depth exceeded 0.075 mm. It means the material pile-up occurs when the burnishing depth reaches a threshold. The other typical plastic flow of material phenomena is the material sink-in on the burnishing passage. Li et al. [17] analyzed the sink-in effect of AA 7075 and AISI 5140 after burnishing. Then, they predicted the surface roughness at various burnishing forces. Okada et al. [18] found the inclined roller burnishing reduced the sink-in effect on the burnished surface. The result indicated that the synergistic effect of rolling and sliding can improve the sink-in phenomenon in burnishing. Other researchers also explored the influence of rolling effect and sliding effect on the plastic flow of material during various burnishing process [19–21]. The pile-up and sink-in caused by the plastic flow of material influence the surface morphology in burnishing. For the

Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071

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Fig. 2 – RURB experimental setup (a) and burnishing tool with four rollers (b).

cylindrical samples, the roundness is a typical parameter to characterize the plastic flow of material in burnishing [22]. Huuki et al. [23] conducted a detailed research on the outof-roundness of metal shafts for three different materials in ultrasonic burnishing. Result showed that the out-ofroundness decreased an average of 7.18 ␮m. Besides, the plastic flow of material also influences the microstructure of workpiece in burnishing, such as reducing the number of voids within the material [24]. The assistance of ultrasonic vibration causes the local severe plastic flow of material in the surface layer [25]. The research of the plastic flow behavior of material in the ultrasonic burnished surface layer is crucial to understand the surface generation mechanism of ultrasonic burnishing. In this research work, with the kinematic analysis of rotary ultrasonic roller burnishing (RURB), the surface generation mechanism is proposed and clarified from the plastic flow of material in three selected machining areas. The morphologies of rotary ultrasonic roller burnished surface are compared with the milled surface morphology. Fig. 1 shows the research frame of this paper.

2.

Experimental setup

The rotary ultrasonic roller burnishing equipment can realize the rotary of ultrasonic transducer with the vibration along the axial direction [26,27]. The ultrasonic generator and bur-

nishing tool are separated. Electrical signal from ultrasonic generator is transmitted to ultrasonic transducer via the noncontact conductive device. Then, it will be converted into mechanical signal. With the adjustment of ultrasonic frequency, appropriate mechanical vibration will be exported via the amplitude transformer. Finally, the burnishing tool accomplishes the machining process with this mechanical vibration. Face milling as a pretreatment process is used to ensure the flatness of workpiece surface to be machined. All the experimental studies were performed on DAEWOOAACE-500 CNC machining center. The experimental setup and burnishing tool of RURB system are shown in Fig. 2. A commercial burnishing tool with four rollers was applied into this research. The roller is made of hardened steel. Compared with conventional burnishing tool with single roller or ball, the multi-roller burnishing tool can accomplish much more burnishing during one feeding cycle. It is beneficial to obtain the smoother machined surface [28]. The fixture was mounted on a base, which was clamped on the machine tool. The experimental parameters are presented in Table 1. The vibration amplitude of burnishing tool was measured with the laser displacement sensor LK G30. Z-axis positioner was applied to ensure the accuracy of machining depth for the whole experiments. The plastic flow of material in the burnished surface layer was observed with a laser confocal microscope (type VK-X250 K) after machining. The dimensions of all the samples were kept as 40 × 60 × 35 mm. Difference of the profile height between burnished surface and milled surface U was selected as measuring object. To ensure the measurement accuracy of experimental results, each set of experiment was repeated three times. The mean value was calculated as the final experimental result.

3.

Kinematic analysis of RURB process

3.1.

General assumptions

The kinematic analysis for burnishing tool is critical to understand the mechanism of surface generation in RURB. To simplify the kinematic analysis of burnishing tool, several assumptions were proposed. Firstly, the friction coefficient between burnishing tool and workpiece materials were regarded as constant in the stabilized phase. Secondly, the rotational speed ωr of the roller around its axis was considered as constant. Thirdly, the ultrasonic vibration of burnishing tool was considered as a simple harmonic motion and the initial phase was set at zero. To facilitate kinematic analysis, three cross sections at different directions were introduced to describe the kinematics

Table 1 – Experimental parameters.

Pretreatment Machining

Process method

Vibration frequency (kHz)

Vibration direction

Vibration amplitude (␮m)

Feeding speed (mm/min)

Machining depth (mm)

Spindle rotation speed (r/min)

Milling RURB

/ 20

/ Axial

/ 10

50 50

0.1 0.1

500 500

Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071

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Fig. 3 – Selected three cross sections at different directions.

Fig. 4 – Schematic of trajectory of burnishing tool in RURB (a) and comparison of trajectories of roller in line ab with and without ultrasonic vibration (trajectory 1 and trajectory 2) (b).

Fig. 5 – Cylindrical coordinate system and rectangular coordinate system in RURB.

of roller and plastic flow of workpiece material during RURB process. Fig. 3 shows the positions of three cross sections at different directions. The selections of three cross sections were based on the positions of roller. A-A was a longitudinal section along the radial direction of roller. B–B was a longitudinal section along the axial direction of roller. C–C was a transverse section paralleling to the free surface of workpiece. The mechanism of surface generation was discussed from the viewpoint of plastic flow of material in the three cross sections.

3.2.

Kinematic analysis of RURB with single roller

The chosen burnishing tool has four identical rollers in the working face. The four rollers present a symmetrical distribution as shown in Fig. 2(b). The motion trajectories of the four rollers are identical during RURB process. Therefore, only the motion of single roller was analyzed in this section. The motion of single roller can be split into four separate movements during RURB. The four separated movements include ultrasonic vibration perpendicular to the workpiece surface, linear motion along the feed direction, rotation around the spindle axis, and rotation of roller around its own axis, respectively.

Fig. 4 shows the schematic of trajectory of burnishing tool in RURB. Continuous spiral areas with different colors represent the burnished regions along the feed direction in Fig. 4 (a). The parameters h, v and ␻ indicate the burnishing depth, the feeding speed and the spindle rotation speed, respectively. The line segment ab as a representative was chosen to analyze the trajectory of roller as shown in Fig. 4 (b). Trajectory 1 and trajectory 2 were induced by roller without and with ultrasonic vibration, respectively. It is shown that the vibration of burnishing tool changes the topography on the machined surface. The plastic deformation of material is the crucial to the generation of surface topography in RURB. However, the plastic flow of material will be inevitably influenced by the ultrasonic vibration. The motion along the Z direction only has a single ultrasonic vibration. However, the other motions are complex as a plane problem in X–Y coordinate plane. Thus, a cylindrical coordinate system was introduced to simplify the kinematic analysis of single roller as shown in Fig. 5. Rectangular and cylindrical coordinates were established in the B B and C C cross sections, respectively. Fig. 5 (a) shows the relative locations of B B and C C cross sections. Fig. 5 (b) demonstrates the relative position between cylindrical coordinate system and rectangular coordinate system. The center of working surface

Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071

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Fig. 6 – Velocity components vx , vy and vz of arbitrary point p at different positions during one rotation period of burnishing tool (r = L0 + Lr = 14 mm).

of burnishing tool was chosen as the origins of two coordinate systems. The parameter  was the angle between roller and polar coordinate. Regardless of the self-rotation of roller, the displacement components of an arbitrary point p of cylindrical surface of roller can be expressed by Eq. (1).

⎧ dx (r, ) = vt + r cos  − r = v/ω + r cos  ⎪ ⎪ ⎪ ⎨ −r, (L0 ≤ r ≤ L0 + Lr ) dy (r, ) = r sin  ⎪ ⎪ ⎪ ⎩

(1)

Fig. 6 shows the variations of vx , vy and vz in the range of  from 0◦ to 360◦ . It can be seen that the values of vy and vz followed the cosinusoidal changing law, while the value of vx varies in a sinusoidal trend. It also can be observed that the extreme values of vz are larger than ones of vx and vy during one rotation period of burnishing tool. It is the result of the assistance of ultrasonic vibration of burnishing tool along the z direction. Considering the self-rotation of roller, the motion of point p became more complex. A polar coordinate system was set up on the A–A cross section of roller as shown in Fig. 7 (a). The center of cross section of roller was selected as the pole. The direction of polar axis was parallel to the workpiece surface and same with rotation direction of burnishing tool. The displacement components of point p can be expressed with Eq. (3).

⎧ dx (r, , ˛) = vt + r cos  − r + R cos ˛ sin  = v/ω ⎪ ⎪ ⎪ +r cos  − r + R cos ˛ sin  ⎪ ⎪ ⎨ dy (r, , ˛) = r sin  + R cos ˛ cos 

⎪ ⎪ ⎪ ⎪ ⎪ ⎩ dz (, ˛) = Au sin(2fu t + ϕ) + R sin ˛

The velocity components of point p can be described by Eq.

(3)

= Au sin(ϕ + 2fu /ω) + R sin ˛

The velocity components of point p can be described with Eq. (4).

⎧ vx (r, , ˛) = f + ωr sin  − ωr R sin ˛ sin  ⎪ ⎪ ⎪ ⎪ ⎨ vy (r, , ˛) = −ωr cos  − ωr R sin ˛ cos  ⎪ vz (, ˛) = 2fu Au cos(ϕ + 2fu /ω) − ωr R cos ˛ ⎪ ⎪ ⎪ ⎩

dz () = Au sin(2fu t + ϕ) = Au sin(ϕ + 2fu /ω)

5

(4)

ωr R = ωr/2

(2).

⎧ v (r, ) = v − ωr sin  ⎪ ⎨ x ⎪ ⎩

vy (r, ) = −ωr cos 

(2)

vz () = 2fu Au cos(2fu t + ϕ) = 2fu Au cos(ϕ + 2fu /ω)

where dx , dy and dz are displacement components of point p at x, y, z directions, respectively. vx , vy and vz are the velocity components of point p at x, y, z directions, respectively. fu and r are the frequency of ultrasonic vibration and the distance from point p to the coordinate origin, respectively. ϕ is the initial phase of ultrasonic vibration.

where ␻r is the rotation angular velocity of roller, ˛ is the polar angle from point p to polar axis along the angular velocity direction. R is the radius of roller. Considering the machining depth h, the range of polar angle ˛ is decided from ˛1 to ˛2 in Fig. 7 (b). The relative movement between roller and workpiece only can be observed in the shadow area as shown in Fig. 7 (b). The minimum value ˛1 and the maximum value ˛2 are calculated by Eqs. (5) and (6), respectively. ˛1 = 90◦ − arcsin(

R−h ) = 71.81◦ R

(5)

Fig. 7 – Polar coordinate system (a) and the range of polar angle ˛ (˛1 < ˛ < ˛2 ) (b) on the A-A cross section of roller. Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071

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value of vy augmented, while the value of vx was still close to zero. However, the velocity components along x direction were equal and opposite when  was 90◦ and 270◦ . With the increase of ˛, the value of vx continued increasing but the value of vy was close to zero. The variation of vz showed a decreasing tendency with the change of ˛ when  was 0◦ and 270◦ . However, it showed an increasing tendency along the when  was 90◦ and 180◦ . It also be subjected to the variation of , which is in agreement with the results as shown in Fig. 6.

4. Theoretical analysis of surface generation during RURB process Fig. 8 – Four critical positions of roller during RURB process (a)  = 0◦ ; (b)  = 90◦ ; (c)  = 180◦ ; (d)  = 270◦ .

˛2 = 90◦ + arcsin(

R−h ) = 108.19◦ R

(6)

A pile-up phenomenon of workpiece material was observed in front of roller during RURB process. It had also been observed around the burnishing ball in ball burnishing by Kuznetsov et al. [29]. To analyze the plastic flow of pile-up of workpiece material, four critical positions of roller during RURB process were selected as shown in Fig. 8. The four critical positions were chosen based on the feed and rotation of burnishing tool, which were  = 0◦ ,  = 90◦ ,  = 180◦ ,  = 270◦ . The velocity components of point p were discussed in four critical positions as shown in Fig. 9. Seven average values were selected in the range of ˛ from 71.81◦ to 108.19◦ . It can be found that the velocity components along y direction were equal and opposite when  was 0◦ and 180◦ . With an increment of ␣, the

Without chip generation, plastic flow is the main form of surface generation of material in RURB process. On the base of kinematic analysis of roller, plastic flow of workpiece material can be divided into three areas on the burnished surface layer. The three areas include area I in front of the roller, area II in sides of roller and area III in back of roller as shown in Fig. 10. Pile-up of workpiece material was generated in area I by the movement of roller. The lateral plastic flow of workpiece material occurred in area II. The area III represents the subsidence region resulting from the compression of roller during RURB process. Gomez-Gras et al. [30] reported that the final topography of the burnished surface would be affected by the plastic flow of material in burnishing process. The typical plastic flow of material included the pile-up phenomenon on the edges of burnishing path and the subsidence phenomenon on the burnishing path. The workpiece material burnished by the former roller would be burnished again due to the rotational feed of burnishing tool. Thus, the area III would be influenced by the pile-up generated by the previous burnishing feed [31]. The generation of finial burnished surface can be ascribed to the

Fig. 9 – Analysis of vx , vy and vz of point p in the range from ˛1 to ˛2 considering self-rotation of roller (r = L0 + Lr = 14 mm;  = 0◦ , 90◦ , 180◦ , 270◦ ). Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071

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Fig. 10 – Description of plastic deformation area I, area II and area III.

plastic flow of workpiece material in these three areas. The material pile-up phenomenon in area I has been observed by several researchers [28,30,32]. Low and Wong [33] found that the bulged edges on the sides of burnishing tool (area II) is caused by the adhesive pull out and stretching action resulting from tensile forces. The material in the area III is subject to the compressive stress during burnishing process [28]. It is the reason for the surface layer presents the distribution of compressive residual stress after burnishing process. Therefore, area I, area II and area III can be defined as pile-up deformation area, tensile deformation area and compressive deformation area, respectively.

4.1. Plastic flow of workpiece material in pile-up deformation area Fig. 11 demonstrates the static analysis for plastic flow of pileup and the movement of roller in A–A section. The pile-up can be divided into regions AB and BC as shown in Fig. 11 (a).

7

Points A’ and B’ of roller correspond to points A and B of workpiece material, respectively. According to the self-rotation of roller, the plastic flow direction of material in region AB can be presumed as arrowheads shown in Fig. 11 (a). However, the direction of plastic flow of pile up depends on the direction of burnishing resultant force loaded on region AB. The plastic flow of pile-up can be obtained with the local mechanical analysis of burnishing force as shown in Fig. 11 (b) and (c). The burnishing force loaded on region A’ B’ can be divided into thrust force along the feed direction of roller, pressure along the vibration direction, friction along the rotation direction of roller and reaction force perpendicular to the region A’ B’ . It had been found that the components of burnishing force in x and y directions were smaller than that in z direction as demonstrated Wang et al. [34]. Therefore, the direction of burnishing resultant force is shown in Fig. 11 (b). Fig. 11 (c) shows the reaction force on the region AB. Fig. 11 (d) presents the guess of plastic flow of pile-up based on the continuity and conservation of plastic flow momentum for workpiece material. With the movement of roller, the new surface of workpiece material is generated by the plastic flow of pile-up. Considering the ultrasonic vibration and feed motion of roller, dynamic analysis of pile-up was conducted. Workpiece material deformation layer can be divided into three parts as shown in Fig. 12 (a), which were active plastic flow layer, passive elastic-plastic flow layer and elastic deformation layer. The depth of active plastic flow layer was determined by burnishing depth h and ultrasonic vibration amplitude Au. The elastic deformation behavior of material would begin to disappear in the active plastic flow layer under the compression of roller. Fig. 12 (a) also presents the interaction between roller and workpiece materials in one period of ultrasonic vibration. The blue zone means the vibration range of roller in a cycle of ultrasonic vibration. The pile-up moved from point C to point D along the free surface during this period. By calculating the movement of roller in one cycle of ultrasonic vibration, the displacement of roller under the feed effect of burnishing tool can be ignored from Eqs. (7)–(10) based

Fig. 11 – Rotary movement of roller in A–A section (a), mechanical analysis of roller (b), mechanical analysis of workpiece (c) and schematic diagram of plastic flow of pile-up (d). Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071

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Fig. 12 – Analysis of plastic flow of pile-up in one vibration cycle (a), simplification of motion of roller (b) and dynamic analysis of pile-up (c) during RURB.

on the experimental parameters. Because Lf is much smaller than Lω and Lu . Lf means the displacement of roller under the feed effect of burnishing tool. Lω means the displacement of roller under the rotation effect of burnishing tool. Lu means the displacement of roller under the ultrasonic vibration effect of burnishing tool. Lf = Tu ∗ f /60 = 0.04m

(7)

Lω = ωr ∗ Tu = 36.65m

(8)

Lu =



 

R2 − (R − h − Au )2 −

|CD| = Lω + Lu = 66.65m

R2 − (R − h)2

 u

= 30m

(9) (10)

It means that the minimum cycle movement length of roller was |CD| as shown in Fig. 12 (b). If the spiral trajectory of roller was unfolded into a linear one, the roller motion can be considered to be comprised of a series of successive displacement |CD|. Fig. 12 (c) indicates the plastic flow of pile-up in one cycle of ultrasonic vibration. Ultrasonic vibration is only considered in Fig. 12 (c). The plastic flow of pile-ups can be divided into three zones (I, II, III) as shown in Fig. 12 (c). Zone I represents the origin position of pile-up before roller moves, Zone III means the new position of pile-up after roller moves, and Zone II belongs to the transition region. During one cycle of ultrasonic vibration, the workpiece material in these three zones would happen the plastic flow behaviors as presented

in Fig. 12 (c). It is a relatively closed loop flow based on the mass conservation with no material removal.

4.2. Plastic flow of workpiece material in tensile deformation area During RURB process, the surface of roller will get into touch with the workpiece material. Fig. 13 (a) shows the plastic flow of workpiece material in tensile deformation area during RURB process. With the effect of FL , the workpiece material in tensile deformation area tends to flow to the roller. The existence of fillet of roller diminishes the occurrence of stress concentration effectively. The initiation and development of crack caused by stress concentration can then be avoided, which can suppress the generated surface be damaged. Fig. 13 (b) shows the plastic flow of workpiece material in the tensile deformation area by roller and ball burnishing. Considering the structure characteristic of burnishing tool, the plastic flow of workpiece material by roller burnishing is different from that by ball burnishing. A small part of workpiece material flows to two sides of roller during roller burnishing compared with that does during ball burnishing. It is because that the spherical contact surface is conducive to the forming of lateral force. The lateral force can lead to workpiece material flowing to two sides of ball that causes the accumulation of material at each side of ball. It can form a protrusion at each side of ball in ball burnishing observed by Balland et al. [32], but it cannot be observed at each side of roller due to the small of fillet.

Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071

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Fig. 13 – Plastic flow of material in tensile deformation area (area II).

Fig. 14 – Plastic flow of workpiece material in compressive deformation area (area III).

4.3. Plastic flow of workpiece material in compressive deformation area Fig. 14 shows the theoretical analysis of the plastic flow of workpiece material in the compressive deformation area (area III). Considering the spiral feeding of roller, the compressive deformation area as the unfinished burnished surface will be burnished repeatedly by four rollers during RURB process. Former pile-up and latter pile-up are generated from the movement of former roller and latter roller, respectively. Latter pile-up will be pushed to the compressive deformation area caused by the former roller as shown in Fig. 14. Balland et al. [32] observed the same plastic flow of material phenomenon in burnishing process. The latter burnishing passage tended to raise the compressive deformation area (area III) created by the former burnishing passage. The raised material formed a new pile-up in front of the latter roller. The final morphology of the burnished surface was affected by the plastic flow and elastic recovery of workpiece material. The plastic flow of material means the accumulation of material towards the edges of the burnishing passage in the area I and area II [30]. Another factor influenced and to be formatted the final morphology of the burnished surface is the elastic recovery of workpiece material in the area III [30].

5.

Finite element modeling of RURB process

5.1.

Geometry and meshing, material modeling

The deformation behavior of material is not a linear problem in RURB process. ABAQUS/Explicit is beneficial to analyze the non-linear problem of converge. Therefore, the threedimensional simulation of RURB process was developed using ABAQUS commercial software with explicit solution. The

Fig. 15 – RURB FEM by one roller in one cycle of ultrasonic vibration (a) and simulation steps (b).

schematic diagram of RURB simulation model was shown in Fig. 15. Considering the periodic characteristic of RURB, the plastic flow of workpiece material is analyzed in one cycle of ultrasonic vibration. The dimensions of workpiece were shown in Fig. 15. As the roller endured less deformation, a rigid cylinder was modeled as the roller with a diameter of 4 mm. The length of roller was 10 mm. Fig. 15 (a) shows the local mesh refinement was applied in the simulation model. Double bias mesh refinement method was used in the burnished region. 3000 CPE4R elements were employed in the workpiece model. The material property of roller model was defined as a rigid body. RURB is a large strain and large strain rate process with the effect of ultrasonic vibration. J–C model is adopted here. The RURB process had been simulated in two-dimensional plane in the previous research [35]. The same mechanical properties of Ti-6Al-4V was applied in this simulation. The J–C stress strain constitutive relation is shown in Eq. (11).

 = (A+Bεn )

·

1 + C ln

ε ·

ε0

(1 − (T − Trm ) / (Tm − Trm ))

(11)

Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071

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Table 2 – Coefficients in J–C model for Ti-6Al-4V [36]. A/MPa

B/MPa

C

n

m

ε0

Tm /◦ C

Tr /◦ C

907

656

0.0128

0.5

0.8

1

1933

20

where A is the yield strength of material, B is the hardening modulus, C is the strain rate sensitivity coefficient, n is the hardening coefficient, m is the thermal softening, ε is the true ·

·

stress, ε0 is the reference shear strain rate, ε is the true strain rate, Tm is the melt temperature, Tr is the room temperature and T is the working temperature. The values of these relevant coefficients for Ti-6Al-4V are shown in Table 2.

5.2.

Boundary conditions and interactions

To simulate RURB process, four steps including preloading step, loading step, burnishing step and unloading step were combined as shown in Fig. 15 (b). The four step times were 0.02 s, 0.0018 s, 0.02 s and 0.02 s, respectively. The preloading depth is 0.01 mm. Considering the similarity of movements of roller, shortest distance was chosen to analyze the plastic flow of workpiece material on the surface layer. To analyze the plastic flow of workpiece material in compressive deformation area accurately, the second burnishing would be performed. After the first unloading step, roller moved 0.1 mm along the opposite direction of the y axis. Then, the second burnishing process began. All the displacements and rotation were applied to the roller to realize the burnishing process. Ultrasonic vibration was added to the displacement of roller in z direction. The displacements of roller included three feeds along x, y and z directions. The feed along x direction means the rotation of burnishing tool. The feed along y direction means the linear feed of burnishing tool. The feed along z direction means the feed of burnishing depth. The bottom surface and four lateral surfaces of workpiece were fixed in all directions. However, the degree of freedom is not limited on the top surface. The surface to surface contact type was chosen to define the contact between workpiece and roller. The kinematic contact method was chosen as the constraint condition. Displacements and velocities of roller were defined by the experimental parameters. The ultrasonic frequency and vibration amplitude were 20 KHz, 10 ␮m, respectively. The feeds of roller along the x, y, z directions were 733.04 mm/s (␻×r), -50 mm/min, 50 mm/min, respectively.

6.

Results and discussion

The relative movement between the roller and workpiece material belongs to the three-dimensional kinematics. The plastic flow behavior of workpiece material should be discussed from the perspective of three-dimensional analysis. Two kinds of node paths were chosen to record the displacements of workpiece material, which were radial path and axial path. Five node paths were selected along the radial or axial direction and mean values were taken as the results. The displacements U1, U2 and U3 were used to describe the plastic flow of workpiece material along the two kinds of paths. Then, the surface generation mechanism during RURB process can be explained.

Fig. 16 – Displacement U1 along the radial direction of roller in FEM.

6.1. Plastic flow behavior of workpiece material at U1 direction In order to analyze the plastic flow phenomenon in the pileup deformation area (area I) and the compressive deformation area (area III), the displacement U1 of workpiece material would be discussed. Fig. 16 shows the variation of U1 along the radial path during the burnishing step. Five consecutive time nodes were chosen to analyze the variation of U1. Step 3-0 means the beginning time of burnishing step. It can be found that U1 is negative in the compressive deformation area because of the compaction and friction effect of roller. Comparatively, U1 in the pile-up deformation area is positive with the ploughing effect of roller. The position of the maximum U1 value moves along the movement direction of roller. It indicates the movement tendency of pile-up. It can be seen that the difference of the maximum U1 values continues decreasing at the adjacent moments. The maximum displacement U1 is 0 mm, 0.053 mm, 0.180 mm, 0.310 mm and 0.357 mm successively at the five adjacent moments. Furthermore, an increasing slope is observed after the maximum U1 value point along with the movement of roller. It means that the pile-up tends to be steady. The workpiece material just below the roller is mainly subject to the normal pressure. Consequently, the curves overlapping parts mean the trajectory of roller along the radial path on the free surface. The displacement U1 almost trends to zero on the unmachined workpiece area because of the smaller interaction force within the workpiece material.

6.2. Plastic flow behavior of workpiece material at U2 direction Fig. 17 shows the displacements U2 of workpiece material along the direction of axial path on the free surface. It can be seen that the displacements U2 of workpiece material in the compressive deformation area (area III) are always negative. The mean displacement U2 in the area III is −0.328 ␮m in RURB. Due to the lateral extrusion of roller, some of the workpiece material in the tensile deformation area (area II)

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Fig. 17 – Displacement U2 along axial direction of roller in FEM.

flows into the compressive deformation area that caused the workpiece material in the compressive deformation area flows into the opposite direction of U2. The fluctuation of displacement U2 becomes greater in the tensile deformation area. The reason is that the extrusion of roller is greater than the resistance from internal workpiece material. The feed motion of workpiece material can also influence the displacement U2 of material. However, compared with the rotary motion of the roller, the influence of feed motion of workpiece material is smaller. The tensile deformation area becomes a gradient transition zone from compressive deformation area to the unmachined area. The interaction within material is the main phenomenon in the gradient transition. It causes the larger fluctuation of displacement U2 of workpiece material. Besides, because of the lateral effect of roller and the plasticity of Ti-6Al-4V, the grains in tensile deformation area will be stretched along the axial direction of roller. The displacement U2 are positive in the unmachined area. It increases rapidly and then decreases slowly. The maximum displacement U2 is 9.74 ␮m in the unmachined area. It is because material far away from the tensile deformation area will be subject to smaller interaction. However, compared with the plastic flow of material along the radial direction of roller in Fig. 16, little material flows into the unmachined region. It is related with the shape of roller and the rotary motion of burnishing tool.

6.3.

Plastic flow of workpiece material at U3 direction

Considering the characteristic of rotary ultrasonic roller burnishing (RURB), the workpiece material will be burnished repeatedly by roller in the compressive deformation area (area III). Fig. 18 shows the variation of displacement U3 of workpiece material along the axial path after the first and second burnishing. As shown in Fig. 18, the U3 values collected in the compressive deformation area presents a sine wave curve. It can be attributed to the interactions among the grains and the effect of ultrasonic vibration. Meanwhile, due to the elastic recovery of workpiece material, the maximum displacement

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Fig. 18 – Displacement U3 along axial path after the first and second burnishing in FEM.

Fig. 19 – Displacement U3 along radial path after twice burnishing processes in FEM.

U3 in the compressive deformation area is less than the burnishing depth after the first burnishing. The displacements U3 of workpiece material is almost unchanged in the repeated burnished area. However, the height difference between the residual burnished surface and the milled surface decreases to 0.025 mm after the second burnishing. It is the result of the plastic flow of workpiece material during the second burnishing. With the lateral compaction effect of roller, a sloping surface is formed in the tensile deformation area (area II). The gradient k1 of the sloping surface is 0.96 after the first burnishing. The gradient k2 of new sloping surface decreases to 0.88 after the second burnishing. Due to the hardening effect induced by the first burnishing decreases the plastic flow of workpiece material during the second burnishing [11]. Some workpiece material is piled up at the border of the tensile deformation area and unmachined area as shown in Fig. 18. The height of the pile-up is 0.019 mm and 0.017 mm during the first and second burnishing processes, respectively. They are both much less than the burnishing depth 0.1 mm. It suggests that little workpiece material flows into the un-machined area

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Fig. 20 – Comparison of height of milled surface and burnished surface (a) 3D, (b) 2D.and (c) measurement from experiments.

during RURB process. The width of the pile-up is 0.118 mm and 0.443 mm in the first and second burnishing processes, respectively. It has a good agreement with the analytical result mentioned above. Fig. 19 shows the variation of displacement U3 of workpiece material along the radial path after twice burnishing processes. In Fig. 19, the black line means the position of milled surface, the red line means the machined surface after first RURB and the green line means the machined surface after twice RURB. The unmachined area close to the initial position of roller appears a little protrusion. Because the deformed workpiece material close to the unmachined area is extruded and flows toward the unmachined area during the roller load-

ing phase [37]. The height of the protrusion is 0.014 mm and 0.013 mm during the first and second burnishing processes, respectively. The displacement U3 of workpiece material in the unmachined area decreases to zero at 0.832 mm from the area III during the first burnishing process. It decreases to zero at 0.533 mm from the area III in the second burnishing process. The work hardening effect causes the reduction of the plastic flow of workpiece material in the unmachined area during the second burnishing process [38]. The compressive deformation area can be divided into two regions as shown in Fig. 19. The yellow region means the burnished region. It can be seen that the fluctuation of U3 values is very small in the burnished region. The blue region means the instantaneous position of

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roller during RURB process. The maximum U3 value in the blue region is 0.097 mm during the first burnishing process, while it is 0.094 mm during the second burnishing process. They are almost up to the theoretical burnishing depth 0.1 mm. However, the corresponding maximum U3 value in the yellow region is 0.08 mm and 0.077 mm, respectively. They are both lower than the maximum depths in the blue region, which is because of the elastic recovery of workpiece material after burnishing. Salahshoor and Guo [39] found that the average 8% elastic recovery for MaCa0.8 alloy in the applied burnishing pressure ranging from 2 to 6 MPa. The maximum U3 value of pile-up is also up to the burnishing depth in the pile-up deformation area. It can be attributed to the fact that little workpiece material flowing into the sides of the burnished region as already been mentioned above. Fig. 19 shows the second burnishing will extrude the workpiece material in front of roller and take it into the compressive deformation area that is formed after first burnishing. As a result, the height of the compressive deformation area formed by the first burnishing is elevated. Little workpiece material in the burnished region flows into the unmachined region. With the law of conservation of matter and constant volume, the burnished workpiece material finishes mainly the behavior of plastic flow in the burnished region. It means that the height of compressive deformation area after RURB changes a little as compared the previous RURB process as shown in Fig. 19. Fig. 20 shows the comparison of the surface elevation between the burnished region and milled region. Fig. 20 (a) shows the three-dimensional morphology diagram of the adjacent burnished region and milled region. The height of surface morphology in the junctional region was measured as shown in Fig. 20 (b). The red region means the junctional region. Six different junctional regions were chosen and five measurements were conducted in every junctional region. Fig. 20 (c) shows one of the measurements in the junctional region. The average value of all the measurements was treated as the result, which was 27.0 ␮m. It is slightly larger than the above obtained simulation result of 25.3 ␮m and their difference is 6.3%. It is also influenced by the plastic deformation and elastic recovery of workpiece material [36]. It can be seen that the height of burnished surface has a little change as compared the milled surface shown in Fig. 20 (a). The results have a good agreement with the FEM simulation results.

6.4.

Plastic flow of pile-up

Fig. 21 (a) depicts the difference in values of displacements of workpiece material along U1 and U3 directions at the adjacent moments from step 3-1 to step 3–4. It can be used to interpret the plastic flow of pile-up. Solid lines and dashed lines mean the difference in values of displacements along U1 and U3 directions, respectively. The black solid line plots the displacement difference U1 between the step 3-1 moment and step 3-2 moment. The red solid line plots the displacement difference U1 between the step 3-2 moment and step 3-3 moment. The green solid line plots the displacement difference U1 between the step 3-3 moment and step 3–4 moment. The displacement difference U3 curves are also same with these. With the effect of ultrasonic vibration, the extreme value of U3 has a fluctuation as shown in Fig. 21 (a). The whole lines

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Fig. 21 – Difference values of displacements of material along U1 and U3 directions in FEM.

in Fig. 21 have a trend to move along the U1 direction with the effect of roller burnishing. The positions of A, B and C points in pile-up have been marked by the example of U1 values as shown in Fig. 21(a). Then, the plastic flow of workpiece material in pile-up was analyzed from AB region and BC region separately. In order to explore the plastic flow of pileup, the differences of absolute difference values U1 and U3 are discussed as shown in Fig. 21(b). With the effect of ultrasonic vibration, the differences of absolute difference values vary between the positive and negative intervals in the compressive deformation area, but U1 values are always larger than U3 values. However, the values of |U1| are also always greater than that of |U3| in the pile-up deformation area. It means that for an arbitrary point in the pile-up deformation area, the displacement U1 is larger than the displacement U3 during the same time, which determines the trend of the plastic flow of pile-up as shown in Fig. 22. The plastic flow direction of workpiece material is close to the free surface from A1 B1 to A2 B2 in AB region, but plastic flow direction of workpiece material is away from the free surface from B1 C1 to B2 C2 in BC region. In Fig. 22, A1 B1 means the location of AB region at the previous step moment. A2 B2 means the location of AB region at the

Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071

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(51425503 and 91860207). This work was also supported by grants from Taishan Scholar Foundation.

Appendix A. Supplementary data Supplementary material related to cle can be found, in the online doi:https://doi.org/10.1016/j.jmrt.2019.12.071. Fig. 22 – Plastic flow of material in AB and BC regions in FEM.

current step moment. According to the comparative analysis of the locations in the two moments, the plastic flow of workpiece material in AB region is obtained as shown in Fig. 22. In the same way, the plastic flow of workpiece material in BC region is obtained. The plastic flow of pile-up obtained with FEM has a good agreement with the theoretical result analyzed above. The study result illustrates that surface generation mechanism of material is mainly attribute to the plastic flow of pile-up in RURB process.

7.

Conclusion

The surface generation mechanism during RURB has been revealed and elaborated through kinematic analysis and finite element simulation. The burnished region has been divided into three deformation areas which include the pile-up deformation area, tensile deformation area, and compressive deformation area. The plastic flow of workpiece material in these three deformation areas has been analyzed and discussed. The following major conclusions could be drawn from the study. • With the kinematic characteristics of RURB, small part of material flows into the unmachined region. It would lead to a little change in dimensions of workpiece. The experimental measurement of height difference between burnished surface and milled surface is 27.0 ␮m. The simulation result is 25.3 ␮m. The error is 6.3%. • The surface generation could be attributed to the plastic flow of pile-up in the burnished region during RURB process. • The regularity of plastic flow behavior of pile-up has been analyzed and obtained by the theoretical model and FEM. The theoretical analysis result had a good agreement with the simulated one.

Conflicts of interest The authors declare no conflicts of interest.

Acknowledgement The authors would like to acknowledge the financial support from the National Natural Science Foundation of China

this artiversion, at

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Please cite this article in press as: Zhao J, Liu Z. Plastic flow behavior for machined surface material Ti-6Al-4V with rotary ultrasonic burnishing. J Mater Res Technol. 2019. https://doi.org/10.1016/j.jmrt.2019.12.071