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An analytical model to optimize rotation speed and travel speed of friction stir welding for defect-free joints
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Scripta Materialia 68 (2013) 175–178 www.elsevier.com/locate/scriptamat
An analytical model to optimize rotation speed and travel speed of friction stir welding for defect-free joints Jinwen Qian,a,b Jinglong Li,b,⇑ Fu Sun,b Jiangtao Xiong,b Fusheng Zhangb and Xin Lina a
State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China b Shaanxi Key Laboratory of Friction Welding Technologies, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China Received 28 July 2012; revised 6 October 2012; accepted 8 October 2012 Available online 13 October 2012
Currently the optimum rotation speed and travel speed used in friction stir welding are obtained by trial and error. An analytical model is proposed and tested for optimizing rotation speed and travel speed for defect-free joints. The model is based on the principle of exactly balancing the material flowing from the region ahead of the pin to the rear with an optimum temperature. The calculated optimum operating windows are consistent with experimental results and literature data. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Friction stir welding; Rotation speed; Travel speed; Defect-free; Optimum operating window
Friction stir welding (FSW) is a relatively novel solid-state technique for welding metallic alloys, such as aluminum alloys, magnesium alloys, steels, titanium alloys, and even nickel-based superalloys, as well as metal matrix composites [1,2]. Compared to conventional fusion welding processes, FSW has many metallurgical, environmental and energy benefits, and has therefore been successfully applied in the aerospace, automobile and shipbuilding industries. However, obtaining a defect-free welded joint with good mechanical properties is critical for industrial applications. The formation of FSW defects, such as lack of penetration, lack of fusion, tunnels, voids, surface grooves, excessive flash, surface galling, nugget collapse and kissingbonds, are mainly related to the process parameters including tool design, tool rotation speed, tool travel speed, shoulder plunge depth (or axial force), spindle tilt angle, etc. Much research has been devoted to understanding the effect of process parameters on defect formation in order to optimize the process parameters for FSW. So far, optimization of process parameters is mostly done by trial and error. Arora et al. [3] proposed and tested a criterion for tool geometry design. However, no criteria exist for selecting the tool rotation speed and tool travel speed. This work
⇑ Corresponding
author. Tel.: +86 29 88460673; fax: +86 29 88491426; e-mail: [email protected]
aims to develop an analytical model to find the optimized tool rotation speed and tool travel speed so that defect-free FSWed joints can be obtained. It is found, for a given set of process parameters, that the model produces the optimum speeds of tool rotation and travel that result in defect-free joints; these speeds are consistent with values reported in the literature. During the FSW process, the material undergoes intense plastic deformation at an elevated temperature because of the friction between the tool and workpiece, and the softened material then flows away from the front (or leading side) of the pin to the rear (or trailing side) of the pin with each rotation. When the FSW process is completed, this flowed zone becomes the nugget zone (NZ), and has a width slightly larger than the pin diameter. Figure 1 schematically shows the material flow around the pin during each rotation. The two overlapping circles represent the positions of the pin at this rotation and the subsequent one. When the tool translates along the welding direction during one rotation, a crescent-shaped vacated region is left; meanwhile, a material layer, which appears in Figure 1 as the red crescent-shaped region of thickness d, flows from the front the pin driven by the pin to fill the vacated region. The width (k) of the crescent-shaped region, as shown in Figure 1, equals the weld pitch: v ð1Þ k¼ ; x
1359-6462/$ - see front matter Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2012.10.008
J. Qian et al. / Scripta Materialia 68 (2013) 175–178 y δ
λ ω
0
x
v
Figure 1. Schematic illustration of the material flow around the pin during each rotation.
where v is the tool travel speed and x the tool rotation speed. In order to obtain a defect-free joint, the process must follow the mass conservation law, i.e. there must be an exact balance between the material flowing from the region ahead of the pin and that flowing back into the vacated region behind the pin: d ¼ k:
ð2Þ
The material flow around the pin can be treated as a laminar flow of a non-Newtonian, incompressible and viscoplastic material [4,5]. Therefore, the material flow during FSW is similar to a thin shear boundary layer. Aukrust and LaZghab [6] investigated hot aluminum extruded in a channel. The flow of hot aluminum was idealized as a viscous non-Newtonian incompressible fluid, and a thin shear boundary layer was found that existed at the wall of the channel. Based on the Sheppard– Wright constitutive equation [7] and the equations governing a viscous incompressible fluid, the thickness of the thin shear boundary layer can be evaluated as: r ð3Þ d¼ ; 1 Z 1=n nsinh A where d is the thickness of the thin shear boundary layer, r is the radius of the channel, n and A are material constants, and Z is the Zener–Hollomon parameter [8], which is defined as: Q ; ð4Þ Z ¼ e_ exp RT where e_ is the strain rate, Q is an activation energy, R is the universal gas constant and T is the absolute temperature. However, the thin shear boundary layer forms inside the channel in the model, whereas the material flows around the pin during FSW, i.e. outside the channel. However, the width of the thin shear boundary layer is much smaller than the channel radius. Thus the direct effect of the curvature on boundary layer behavior can be safely neglected. Consequently, the boundary layers formed inside and outside the wall are equal. Therefore, the width of the flowed material driven by the rotation of the pin can also be defined as Eq. (3) with r changed to the radius of the pin. Furthermore, Reynolds [9] pointed out that the size of the NZ increased with the pin diameter, proving that the material flow around the pin is related to the pin diameter. It should be pointed out that T should be the average temperature of the thin material flow layer around the pin in Eq. (3). However, peak temperature will be used instead for the reason that an average temperature-
related model is not available currently but the peak temperature can be obtained from a model as will be mentioned below. Secondly, although large gradients exist in the temperature field in the joint (i.e. plasticized material), the temperature difference across such a thin material flow layer around the pin turns out to be tiny. Thus the error caused by substitution of the average temperature by the peak value can be safely neglected. The temperature T is a key factor that affects the material flow, the defect formation and the joint strength during FSW. Arbegast [10] pointed out that flow-related defects occur outside the acceptable processing window with parameters that are considered either too hot or too cold. Under excessively hot processing conditions, excess material flow would lead to flash formation, surface galling and nugget collapse. However, if the processing temperature is too low, insufficient flowing material results in surface lack of fill, wormholes or lack of consolidation defects on the advancing side. Therefore, the temperature during FSW should be neither too high nor too low, and near but below the solidus temperature. Thus, there must be an optimum temperature range to obtain defect-free joints. However, no previous researchers have specified such a range. Based on work by a number of researchers [11–19], as shown in Figure 2, a linear regression of the temperature ratio Tmax/Ts (where Tmax is the maximum temperature and Ts is the solidus temperature) on Ts was derived: T max T opt ¼ ¼ 1:344 5:917 104 T s ; Ts Ts
ð5Þ
where this temperature range can be thought of as the optimum temperature range, i.e. Tmax = Topt. The correlation has a standard deviation of 0.024. The calculation results in a temperature range Topt = (0.8–0.9) Ts. The rationality of this assumption was verified by experiments and literature data as will be mentioned below. Recently, DebRoy and co-workers [5,20] established a dimensionless correlation of the following form that can be useful for estimating the non-dimensional peak temperature from the non-dimensional heat input [20]: T ¼ 0:151 log10 ðQ Þ þ 0:097:
ð6Þ
where T* is the non-dimensional peak temperature, which is defined as [20]: T ¼
T T0 ; Ts T0
ð7Þ
where T is the peak temperature, T0 is the initial temperature and Q* is the non-dimensional heat input, which is defined as [20]: 0.94
Tmax = 1.344 − 5.917 × 10 − 4 Ts Ts
0.92 0.90
Standard Deviation =0.024
0.88 0.86
Tmax/ Ts
176
0.84 0.82 0.80 0.78 0.76 0.74 720
7075[10] 7075[11] 2024[12] 7050[13] 7050[14] 6082[15] 6061[17] 6061[18] 6063[19] Linear fit 740
760
780
800
820
840
860
880
900
Ts / K
Figure 2. Linear relationship between the ratio of Tmax/Ts and Ts.
J. Qian et al. / Scripta Materialia 68 (2013) 175–178
r8 SxCg ; ð8Þ kv2 where, for conformity of calculation, the unit of x changes from rpm to rad s1 and v from mm min1 to m s1, r8 is the yield stress of the material at a temperature of 0.8TS, S is the cross-sectional area of the tool shoulder, C is the specific heat capacity of the workpiece material, k is the thermal conductivity of the workpiece, and g is the ratio according to which heat generated at the shoulder–workpiece interface is transported between the tool and the workpiece, and is defined as [20]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðkqCÞW ; ð9Þ g¼ ðkqCÞT Q ¼
where q is the density, and the subscripts W and T are used to describe the material properties of the workpiece and tool, respectively. All the material properties are taken at a temperature average between the initial temperature and the solidus temperature. The strain rate e_ is an important factor for understanding the material flow and the microstructure evolution of the stir zone. Therefore, many researchers have attempted to estimate the strain rate during FSW. Jata and Semiatin [21] estimated the average strain rate as the quotient of the shear strain extrapolated from that measured in the thermomechanically affected zone and the deformation time in the stir zone during FSW of Al–Li alloy. In this way, e_ was estimated to be 10 s1. Frigaard et al. [22] suggested that the local strain rate within the plastically deformed region during FSW of 6082 Al alloy and 7108 Al alloy varied from about 1 to 20 s1 by using the measured subgrain size of the stir zone, the computer-simulated maximum temperature, and the relationship between the subgrain diameter and the Z parameter in aluminum alloys. Chang et al. [23] estimated the strain rate during FSW to vary from 1 to 102 s1 according to a simple equation derived from torsional deformation. Masaki et al. [24] suggested that the effective strain rate during FSW would not exceed 100 s1 at most by simulating the recrystallized grains of the stir zone through a combination of the plane-strain compression at various strain rates and the subsequent cooling tracing in the cooling cycle of FSW. Arora et al. [25] estimated the strain rate during FSW as not more than 10 s1 by using numerical simulations. Fratini et al. [26] used a neural network to estimate the strain rate during FSW as not more than 25 s1. Mukherjee and Ghosh [27] reported a maximum observed shear strain rate observed of about 87 s1 by inserting a ductile foil in between two plates to observe the deformation field around the pin. Thus, it is reasonable to estimate the strain rate to be between 10 and 100 s1. Combined Eqs. (1)–(9) and the strain rate of FSW, an analytical model to optimize tool rotation speed and travel speed during FSW of aluminum alloy was proposed: 120pr8 SCg x ¼ 1=n 2 . T T 1 e_ Q k r nsinh A exp RT opt 10^ ToptS T 00 0:097 0:151 ð10Þ
v¼
1000 rx 1=n nsinh1 Ae_ exp RTQopt
177
ð11Þ
where the units of the calculated result for x and v are rpm and mm min1, respectively. Aluminum alloy 1100-H14 and 2024-T3 rolled plates 8 and 3.2 mm in thick, respectively, were welded to verify the proposed model and literature data was also examined. The experiment detail of 1100-H14 was shown in Ref. [28]. The 2024-T3 sheets were joined using a tool with a 10 mm diameter shoulder and a 4 mm diameter pin made of H13 steel at a travel speed of 50–400 mm min1 and a rotation speed of 400– 1200 rpm. The physical parameters of the various alloys are shown in Table 1. During FSW, the optimum temperature and strain rate are not a fixed value, but a range for different aluminum alloys. The strain rate falls between 10 and 100 s1, a range that has been mentioned previously. Arora et al. [3] pointed out that the temperature range commonly used in the FSW of AA6061 is 0.87–0.90Ts, which actually varies within ±10 K. Therefore, it is reasonable to set the optimum temperature range as Topt ±10 K. Based on these assumptions, the optimum operating window can be obtained. Figure 3 shows a comparison of the calculated optimum operating window of rotation speed and travel speed with the experimental results and literature data for 1100, 2024, 6061 [31] and 7050 [13] aluminum alloys, where the calculated optimum operating window is shown by the blue ellipse. It can be seen that the calculated optimum operating windows are consistent with the experimental results and the literature data, Typically, the optimum rotation speed and travel speed as indicated by the calculated optimum operating window can produce joints in, for example, 6061 alloy that are not only defect-free but also possess good mechanical properties. It should be noted that the calculated optimum operating windows are smaller than the experimental results. This phenomenon may be caused by the conservative assumptions of optimum temperature and strain rate range. For example, Gerlich et al. [32] experimentally estimated the strain rate around the pin surface to be between 20 and 650 s1 during friction stir spot welding of 7075 Al. For the analytical model proposed in this study, only the effect of the tool dimension has been taken into account; other effects such as shoulder plunge depth and spindle tilt angle are not considered. However, Zhao et al. [33] and Rajakumar et al. [34] reported that defects can be eliminated by changing tool geometry, shoulder plunge depth (or axial force) or spindle tilt angle with the same rotation speed and travel speed for FSW. Therefore, in the future it will be necessary to improve the model by adding the effect of other process parameters affecting material temperature and flow in the NZ. An analytical model is proposed and tested for optimizing the rotation speed and travel speed for defectfree joints based on the principle of exactly balancing the material flowing from the region ahead of the pin to the rear of the pin using an optimum temperature for the FSW of different aluminum alloys. The optimum temperature is related to the solidus temperature, as
178
J. Qian et al. / Scripta Materialia 68 (2013) 175–178
Table 1. The physical property parameters of the various alloys. Alloy
Ts [29] (K)
Topt (K)
q [29] (kg m3)
C [29] (W m1 k1)
k [29] (W m1 K1)
r8 [29] (MPa)
n [20]
A [30] (s1)
Q [30] (J mol1)
1100 2024 6061 7050
916 775 855 797
727 686 716 695
2710 2770 2700 2830
900 880 900 990
218 120 200 220
1.0 18.0 3.5 15.0
5.66 4.27 3.55 2.86
5.18 1010 4.55 1016 2.41 108 8.39 109
158300 214349 145000 151500
500
400
(a)
350
-1
300
T=727K
250 200
T=737K
150
Defect Defect-free Caculated results
100 50
400
600
800
1000
Travel speed / mm min
-1
T=717K Travel speed / mm min
Defect Defect-free Caculated results
(b) 400
300
T=686K T=696K
100
0
1200
T=676K
200
0
200
400
Rotaion speed / rpm
600
800
1000
1200
1400
1600
Rotation speed / rpm 350
450
(c)
T=726K
-1
Travel speed / mm min
-1
Travel speed / mm min
T=705K
350 300
T=716K 250 200 150 100 400
(d)
300
400
T=706K
Defect Defect-free Defect-free Good mechanical property Caculated results 800
1200
250
T=695K
200
150
T=685K 100
Defect-free Caculated results
50 1600
Rotation speed / rpm
2000
2400
0
200
400
600
800
1000
Rotation speed / rpm
Figure 3. A comparison of the calculated optimum operating window of rotation speed and travel speed with experimental and literature results for (a) 1100, (b) 2024, (c) 6061 [31] and (d) 7050 [13] aluminum alloys with T = Topt ±10 K and e_ = 10–100 s1.
shown in Eq. (5). The optimum operating window is found to be an optimum temperature and strain rate range of Topt ±10 K and 10–100 s1, respectively. The calculated results are consistent with experimental results and literature data. This work was supported by the National Natural Science Foundation of China (51071123 and 51101126), the fund of the State Key Laboratory of Solidification Processing in NWPU (31-TP-2009 and 43-QP-2009) and the 111 Project (B08040). [1] R.S. Mishra, Z.Y. Ma, Mater. Sci. Eng. R 50 (2005) 1. [2] R. Nandan, T. DebRoy, H.K.D.H. Bhadeshia, Prog. Mater. Sci. 53 (2008) 980. [3] A. Arora, A. De, T. DebRoy, Scripta Mater. 64 (2011) 9. [4] R. Nandan, G.G. Roy, T.J. Lienert, T. Debroy, Acta Mater. 55 (2007) 883. [5] A. Arora, T. DebRoy, H.K.D.H. Bhadeshia, Acta Mater. 59 (2011) 2020. [6] T. Aukrust, S. LaZghab, Int. J. Plast. 16 (2000) 59. [7] T. Sheppard, D.S. Wright, Met. Technol. 6 (1979) 215. [8] C. Zener, J.H. Hollomon, J. Appl. Phys. 15 (1944) 22.
[9] A.P. Reynolds, Sci. Technol. Weld. Joining 5 (2000) 120. [10] W.J. Arbegast, Scripta Mater. 58 (2008) 372. [11] M.W. Mahoney, C.G. Rhodes, J.G. Flintoff, R.A. Spurling, W.H. Bingel, Metall. Mater. Trans. A 29 (1998) 1955. [12] K. Nakata, Y.G. Kim, M. Ushio, T. Hasimoto, S. Jyogan, ISIJ Int. 40 (Suppl.) (2000) S15. [13] W. Li, Z. Zhang, J. Li, Y.J. Chao, J. Mater. Eng. Perform. 21 (2012) 1849. [14] A.P. Reynolds, W. Tang, Z. Khandkar, J.A. Khan, K. Lindner, Sci. Technol. Weld. Joining 10 (2005) 190. [15] P. Ulysse, Int. J. Mach. Tool Manuf. 42 (2002) 1549. [16] P. Cavaliere, A. Squillace, F. Panella, J. Mater. Process. Technol. 200 (2008) 364. [17] C.M. Chen, R. Kovacevic, Int. J. Mach. Tool Manuf. 43 (2003) 1319. [18] D.C. Hofmann, K.S. Vecchio, Mater. Sci. Eng. A 465 (2007) 165. [19] Y.S. Sato, M. Urata, H. Kokawa, Metall. Mater. Trans. A 33 (2002) 625. [20] G.G. Roy, R. Nandan, T. DebRoy, Sci. Technol. Weld. Joining 11 (2006) 606. [21] K.V. Jata, S.L. Semiatin, Scripta Mater. 43 (2000) 743. [22] Ø. Frigaard, Ø. Grong, O.T. Midling, Metall. Mater. Trans. A 32 (2001) 1189. [23] C.I. Chang, C.J. Lee, J.C. Huang, Scripta Mater. 51 (2004) 509. [24] K. Masaki, Y.S. Sato, M. Maeda, H. Kokawa, Scripta Mater. 58 (2008) 355. [25] A. Arora, Z. Zhang, A. De, T. DebRoy, Scripta Mater. 61 (2009) 863. [26] L. Fratini, G. Buffa, D. Palmeri, Comput. Struct. 87 (2009) 1166. [27] S. Mukherjee, A.K. Ghosh, Mater. Sci. Eng. A 527 (2010) 5130. [28] J.W. Qian, J.L. Li, J.T. Xiong, F.S. Zhang, W.Y. Li, X. Lin, Sci. Technol. Weld. Joining 17 (2012) 338. [29] Joseph R. Davis (Ed.), ASM Handbook: vol. 2, ASM International, Materials Park, OH, 1992. [30] T. Sheppard, A. Jackson, Mater. Sci. Technol. 13 (1997) 203. [31] S. Lim, S. Kim, C.-G. Lee, S. Kim, Metall. Mater. Trans. A 35 (2004) 2829. [32] A. Gerlich, G. Avramovic-Cingara, T.H. North, Metall. Mater. Trans. A 37 (2006) 2773. [33] Y.-H. Zhao, S.-B. Lin, W. Lin, F.-X. Qu, Mater. Lett. 59 (2005) 2948. [34] S. Rajakumar, C. Muralidharan, V. Balasubramanian, Mater. Des. 32 (2011) 535.
Scripta Materialia 68 (2013) 175–178 www.elsevier.com/locate/scriptamat
An analytical model to optimize rotation speed and travel speed of friction stir welding for defect-free joints Jinwen Qian,a,b Jinglong Li,b,⇑ Fu Sun,b Jiangtao Xiong,b Fusheng Zhangb and Xin Lina a
State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China b Shaanxi Key Laboratory of Friction Welding Technologies, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China Received 28 July 2012; revised 6 October 2012; accepted 8 October 2012 Available online 13 October 2012
Currently the optimum rotation speed and travel speed used in friction stir welding are obtained by trial and error. An analytical model is proposed and tested for optimizing rotation speed and travel speed for defect-free joints. The model is based on the principle of exactly balancing the material flowing from the region ahead of the pin to the rear with an optimum temperature. The calculated optimum operating windows are consistent with experimental results and literature data. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Friction stir welding; Rotation speed; Travel speed; Defect-free; Optimum operating window
Friction stir welding (FSW) is a relatively novel solid-state technique for welding metallic alloys, such as aluminum alloys, magnesium alloys, steels, titanium alloys, and even nickel-based superalloys, as well as metal matrix composites [1,2]. Compared to conventional fusion welding processes, FSW has many metallurgical, environmental and energy benefits, and has therefore been successfully applied in the aerospace, automobile and shipbuilding industries. However, obtaining a defect-free welded joint with good mechanical properties is critical for industrial applications. The formation of FSW defects, such as lack of penetration, lack of fusion, tunnels, voids, surface grooves, excessive flash, surface galling, nugget collapse and kissingbonds, are mainly related to the process parameters including tool design, tool rotation speed, tool travel speed, shoulder plunge depth (or axial force), spindle tilt angle, etc. Much research has been devoted to understanding the effect of process parameters on defect formation in order to optimize the process parameters for FSW. So far, optimization of process parameters is mostly done by trial and error. Arora et al. [3] proposed and tested a criterion for tool geometry design. However, no criteria exist for selecting the tool rotation speed and tool travel speed. This work
⇑ Corresponding
author. Tel.: +86 29 88460673; fax: +86 29 88491426; e-mail: [email protected]
aims to develop an analytical model to find the optimized tool rotation speed and tool travel speed so that defect-free FSWed joints can be obtained. It is found, for a given set of process parameters, that the model produces the optimum speeds of tool rotation and travel that result in defect-free joints; these speeds are consistent with values reported in the literature. During the FSW process, the material undergoes intense plastic deformation at an elevated temperature because of the friction between the tool and workpiece, and the softened material then flows away from the front (or leading side) of the pin to the rear (or trailing side) of the pin with each rotation. When the FSW process is completed, this flowed zone becomes the nugget zone (NZ), and has a width slightly larger than the pin diameter. Figure 1 schematically shows the material flow around the pin during each rotation. The two overlapping circles represent the positions of the pin at this rotation and the subsequent one. When the tool translates along the welding direction during one rotation, a crescent-shaped vacated region is left; meanwhile, a material layer, which appears in Figure 1 as the red crescent-shaped region of thickness d, flows from the front the pin driven by the pin to fill the vacated region. The width (k) of the crescent-shaped region, as shown in Figure 1, equals the weld pitch: v ð1Þ k¼ ; x
1359-6462/$ - see front matter Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2012.10.008
J. Qian et al. / Scripta Materialia 68 (2013) 175–178 y δ
λ ω
0
x
v
Figure 1. Schematic illustration of the material flow around the pin during each rotation.
where v is the tool travel speed and x the tool rotation speed. In order to obtain a defect-free joint, the process must follow the mass conservation law, i.e. there must be an exact balance between the material flowing from the region ahead of the pin and that flowing back into the vacated region behind the pin: d ¼ k:
ð2Þ
The material flow around the pin can be treated as a laminar flow of a non-Newtonian, incompressible and viscoplastic material [4,5]. Therefore, the material flow during FSW is similar to a thin shear boundary layer. Aukrust and LaZghab [6] investigated hot aluminum extruded in a channel. The flow of hot aluminum was idealized as a viscous non-Newtonian incompressible fluid, and a thin shear boundary layer was found that existed at the wall of the channel. Based on the Sheppard– Wright constitutive equation [7] and the equations governing a viscous incompressible fluid, the thickness of the thin shear boundary layer can be evaluated as: r ð3Þ d¼ ; 1 Z 1=n nsinh A where d is the thickness of the thin shear boundary layer, r is the radius of the channel, n and A are material constants, and Z is the Zener–Hollomon parameter [8], which is defined as: Q ; ð4Þ Z ¼ e_ exp RT where e_ is the strain rate, Q is an activation energy, R is the universal gas constant and T is the absolute temperature. However, the thin shear boundary layer forms inside the channel in the model, whereas the material flows around the pin during FSW, i.e. outside the channel. However, the width of the thin shear boundary layer is much smaller than the channel radius. Thus the direct effect of the curvature on boundary layer behavior can be safely neglected. Consequently, the boundary layers formed inside and outside the wall are equal. Therefore, the width of the flowed material driven by the rotation of the pin can also be defined as Eq. (3) with r changed to the radius of the pin. Furthermore, Reynolds [9] pointed out that the size of the NZ increased with the pin diameter, proving that the material flow around the pin is related to the pin diameter. It should be pointed out that T should be the average temperature of the thin material flow layer around the pin in Eq. (3). However, peak temperature will be used instead for the reason that an average temperature-
related model is not available currently but the peak temperature can be obtained from a model as will be mentioned below. Secondly, although large gradients exist in the temperature field in the joint (i.e. plasticized material), the temperature difference across such a thin material flow layer around the pin turns out to be tiny. Thus the error caused by substitution of the average temperature by the peak value can be safely neglected. The temperature T is a key factor that affects the material flow, the defect formation and the joint strength during FSW. Arbegast [10] pointed out that flow-related defects occur outside the acceptable processing window with parameters that are considered either too hot or too cold. Under excessively hot processing conditions, excess material flow would lead to flash formation, surface galling and nugget collapse. However, if the processing temperature is too low, insufficient flowing material results in surface lack of fill, wormholes or lack of consolidation defects on the advancing side. Therefore, the temperature during FSW should be neither too high nor too low, and near but below the solidus temperature. Thus, there must be an optimum temperature range to obtain defect-free joints. However, no previous researchers have specified such a range. Based on work by a number of researchers [11–19], as shown in Figure 2, a linear regression of the temperature ratio Tmax/Ts (where Tmax is the maximum temperature and Ts is the solidus temperature) on Ts was derived: T max T opt ¼ ¼ 1:344 5:917 104 T s ; Ts Ts
ð5Þ
where this temperature range can be thought of as the optimum temperature range, i.e. Tmax = Topt. The correlation has a standard deviation of 0.024. The calculation results in a temperature range Topt = (0.8–0.9) Ts. The rationality of this assumption was verified by experiments and literature data as will be mentioned below. Recently, DebRoy and co-workers [5,20] established a dimensionless correlation of the following form that can be useful for estimating the non-dimensional peak temperature from the non-dimensional heat input [20]: T ¼ 0:151 log10 ðQ Þ þ 0:097:
ð6Þ
where T* is the non-dimensional peak temperature, which is defined as [20]: T ¼
T T0 ; Ts T0
ð7Þ
where T is the peak temperature, T0 is the initial temperature and Q* is the non-dimensional heat input, which is defined as [20]: 0.94
Tmax = 1.344 − 5.917 × 10 − 4 Ts Ts
0.92 0.90
Standard Deviation =0.024
0.88 0.86
Tmax/ Ts
176
0.84 0.82 0.80 0.78 0.76 0.74 720
7075[10] 7075[11] 2024[12] 7050[13] 7050[14] 6082[15] 6061[17] 6061[18] 6063[19] Linear fit 740
760
780
800
820
840
860
880
900
Ts / K
Figure 2. Linear relationship between the ratio of Tmax/Ts and Ts.
J. Qian et al. / Scripta Materialia 68 (2013) 175–178
r8 SxCg ; ð8Þ kv2 where, for conformity of calculation, the unit of x changes from rpm to rad s1 and v from mm min1 to m s1, r8 is the yield stress of the material at a temperature of 0.8TS, S is the cross-sectional area of the tool shoulder, C is the specific heat capacity of the workpiece material, k is the thermal conductivity of the workpiece, and g is the ratio according to which heat generated at the shoulder–workpiece interface is transported between the tool and the workpiece, and is defined as [20]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðkqCÞW ; ð9Þ g¼ ðkqCÞT Q ¼
where q is the density, and the subscripts W and T are used to describe the material properties of the workpiece and tool, respectively. All the material properties are taken at a temperature average between the initial temperature and the solidus temperature. The strain rate e_ is an important factor for understanding the material flow and the microstructure evolution of the stir zone. Therefore, many researchers have attempted to estimate the strain rate during FSW. Jata and Semiatin [21] estimated the average strain rate as the quotient of the shear strain extrapolated from that measured in the thermomechanically affected zone and the deformation time in the stir zone during FSW of Al–Li alloy. In this way, e_ was estimated to be 10 s1. Frigaard et al. [22] suggested that the local strain rate within the plastically deformed region during FSW of 6082 Al alloy and 7108 Al alloy varied from about 1 to 20 s1 by using the measured subgrain size of the stir zone, the computer-simulated maximum temperature, and the relationship between the subgrain diameter and the Z parameter in aluminum alloys. Chang et al. [23] estimated the strain rate during FSW to vary from 1 to 102 s1 according to a simple equation derived from torsional deformation. Masaki et al. [24] suggested that the effective strain rate during FSW would not exceed 100 s1 at most by simulating the recrystallized grains of the stir zone through a combination of the plane-strain compression at various strain rates and the subsequent cooling tracing in the cooling cycle of FSW. Arora et al. [25] estimated the strain rate during FSW as not more than 10 s1 by using numerical simulations. Fratini et al. [26] used a neural network to estimate the strain rate during FSW as not more than 25 s1. Mukherjee and Ghosh [27] reported a maximum observed shear strain rate observed of about 87 s1 by inserting a ductile foil in between two plates to observe the deformation field around the pin. Thus, it is reasonable to estimate the strain rate to be between 10 and 100 s1. Combined Eqs. (1)–(9) and the strain rate of FSW, an analytical model to optimize tool rotation speed and travel speed during FSW of aluminum alloy was proposed: 120pr8 SCg x ¼ 1=n 2 . T T 1 e_ Q k r nsinh A exp RT opt 10^ ToptS T 00 0:097 0:151 ð10Þ
v¼
1000 rx 1=n nsinh1 Ae_ exp RTQopt
177
ð11Þ
where the units of the calculated result for x and v are rpm and mm min1, respectively. Aluminum alloy 1100-H14 and 2024-T3 rolled plates 8 and 3.2 mm in thick, respectively, were welded to verify the proposed model and literature data was also examined. The experiment detail of 1100-H14 was shown in Ref. [28]. The 2024-T3 sheets were joined using a tool with a 10 mm diameter shoulder and a 4 mm diameter pin made of H13 steel at a travel speed of 50–400 mm min1 and a rotation speed of 400– 1200 rpm. The physical parameters of the various alloys are shown in Table 1. During FSW, the optimum temperature and strain rate are not a fixed value, but a range for different aluminum alloys. The strain rate falls between 10 and 100 s1, a range that has been mentioned previously. Arora et al. [3] pointed out that the temperature range commonly used in the FSW of AA6061 is 0.87–0.90Ts, which actually varies within ±10 K. Therefore, it is reasonable to set the optimum temperature range as Topt ±10 K. Based on these assumptions, the optimum operating window can be obtained. Figure 3 shows a comparison of the calculated optimum operating window of rotation speed and travel speed with the experimental results and literature data for 1100, 2024, 6061 [31] and 7050 [13] aluminum alloys, where the calculated optimum operating window is shown by the blue ellipse. It can be seen that the calculated optimum operating windows are consistent with the experimental results and the literature data, Typically, the optimum rotation speed and travel speed as indicated by the calculated optimum operating window can produce joints in, for example, 6061 alloy that are not only defect-free but also possess good mechanical properties. It should be noted that the calculated optimum operating windows are smaller than the experimental results. This phenomenon may be caused by the conservative assumptions of optimum temperature and strain rate range. For example, Gerlich et al. [32] experimentally estimated the strain rate around the pin surface to be between 20 and 650 s1 during friction stir spot welding of 7075 Al. For the analytical model proposed in this study, only the effect of the tool dimension has been taken into account; other effects such as shoulder plunge depth and spindle tilt angle are not considered. However, Zhao et al. [33] and Rajakumar et al. [34] reported that defects can be eliminated by changing tool geometry, shoulder plunge depth (or axial force) or spindle tilt angle with the same rotation speed and travel speed for FSW. Therefore, in the future it will be necessary to improve the model by adding the effect of other process parameters affecting material temperature and flow in the NZ. An analytical model is proposed and tested for optimizing the rotation speed and travel speed for defectfree joints based on the principle of exactly balancing the material flowing from the region ahead of the pin to the rear of the pin using an optimum temperature for the FSW of different aluminum alloys. The optimum temperature is related to the solidus temperature, as
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Table 1. The physical property parameters of the various alloys. Alloy
Ts [29] (K)
Topt (K)
q [29] (kg m3)
C [29] (W m1 k1)
k [29] (W m1 K1)
r8 [29] (MPa)
n [20]
A [30] (s1)
Q [30] (J mol1)
1100 2024 6061 7050
916 775 855 797
727 686 716 695
2710 2770 2700 2830
900 880 900 990
218 120 200 220
1.0 18.0 3.5 15.0
5.66 4.27 3.55 2.86
5.18 1010 4.55 1016 2.41 108 8.39 109
158300 214349 145000 151500
500
400
(a)
350
-1
300
T=727K
250 200
T=737K
150
Defect Defect-free Caculated results
100 50
400
600
800
1000
Travel speed / mm min
-1
T=717K Travel speed / mm min
Defect Defect-free Caculated results
(b) 400
300
T=686K T=696K
100
0
1200
T=676K
200
0
200
400
Rotaion speed / rpm
600
800
1000
1200
1400
1600
Rotation speed / rpm 350
450
(c)
T=726K
-1
Travel speed / mm min
-1
Travel speed / mm min
T=705K
350 300
T=716K 250 200 150 100 400
(d)
300
400
T=706K
Defect Defect-free Defect-free Good mechanical property Caculated results 800
1200
250
T=695K
200
150
T=685K 100
Defect-free Caculated results
50 1600
Rotation speed / rpm
2000
2400
0
200
400
600
800
1000
Rotation speed / rpm
Figure 3. A comparison of the calculated optimum operating window of rotation speed and travel speed with experimental and literature results for (a) 1100, (b) 2024, (c) 6061 [31] and (d) 7050 [13] aluminum alloys with T = Topt ±10 K and e_ = 10–100 s1.
shown in Eq. (5). The optimum operating window is found to be an optimum temperature and strain rate range of Topt ±10 K and 10–100 s1, respectively. The calculated results are consistent with experimental results and literature data. This work was supported by the National Natural Science Foundation of China (51071123 and 51101126), the fund of the State Key Laboratory of Solidification Processing in NWPU (31-TP-2009 and 43-QP-2009) and the 111 Project (B08040). [1] R.S. Mishra, Z.Y. Ma, Mater. Sci. Eng. R 50 (2005) 1. [2] R. Nandan, T. DebRoy, H.K.D.H. Bhadeshia, Prog. Mater. Sci. 53 (2008) 980. [3] A. Arora, A. De, T. DebRoy, Scripta Mater. 64 (2011) 9. [4] R. Nandan, G.G. Roy, T.J. Lienert, T. Debroy, Acta Mater. 55 (2007) 883. [5] A. Arora, T. DebRoy, H.K.D.H. Bhadeshia, Acta Mater. 59 (2011) 2020. [6] T. Aukrust, S. LaZghab, Int. J. Plast. 16 (2000) 59. [7] T. Sheppard, D.S. Wright, Met. Technol. 6 (1979) 215. [8] C. Zener, J.H. Hollomon, J. Appl. Phys. 15 (1944) 22.
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