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Relationship between microstructure and properties for ultrasonic surface mechanical attrition treatment
SMM 10574
No. of Pages 4
26 March 2015 Available online at www.sciencedirect.com
ScienceDirect Scripta Materialia xxx (2015) xxx–xxx www.elsevier.com/locate/scriptamat
Relationship between microstructure and properties for ultrasonic surface mechanical attrition treatment ⇑
W.Y. Tsai,a J.C. Huang,a, Yu Jia Gao,b Y.L. Chungb and Guan-Rong Huangc a
Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung 804, Taiwan b Metal Industries Research & Development Centre, Kaohsiung 811, Taiwan c Department of Physics, National Taiwan University, Taipei 106, Taiwan Received 3 January 2015; revised 10 March 2015; accepted 12 March 2015
The analytic modeling and one experimental assess of the ultrasonic surface mechanical attrition treatment are presented. The bombarding ball speed, induced energy, hardness and grain size are incorporated into this model, based on harmonic longitudinal vibration motion of ultrasonicwave-driven impact. There appear some optimum attrition working parameters for the best attrition effect; beyond which, the sample surface would be subject to bombarding microcracking and the grain size would not be further reduced. The benefits from attrition would become lower. Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain refining; Nanocrystalline microstructure; Hardness; Stainless steels; SMAT
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Metal surfaces are frequently treated by shot peening in order to induce tougher and harder surface layers with compressive residual stresses in enhancing the fatigue properties [1,2]. The steel balls are typically of the size of 0.2– 1 mm and are accelerated by compressed air. The flying velocity and bombard frequency are typically 50–100 m/s and 20–100 Hz. The accelerated balls are directed from a specific direction on the surface, mostly perpendicular. A modified version of the shot peening, termed as the surface mechanical attrition treatment (SMAT), was firstly reported in 1999 [3,4]. The balls are resonated and accelerated by the vibration of the ultrasonic motor. The ball size, flying velocity and bombarding frequency are typically 1– 10 mm, 1–20 m/s and 10–100 kHz. The balls are bombarding from 3D random directions onto the entire surface, resulting in grain refinement, gradient structure and attractive mechanical performance [5–9]. And this process has been applied to iron [5], titanium [10], copper [11], cobalt [8], aluminum alloy [12], magnesium alloy [13] and stainless steel [6]. The analytic expressions for common severe plastic deformation processes have been proposed widely for ball milling mechanical alloying, equal channel angular pressing, high-ratio extrusion, torsion, friction stir processing or accumulative roll bonding [14–17]. However, there has not been well established relationship for the SMAT processing parameters with respect to the microstructural
⇑ Corresponding
author. Tel.: +886 7 525 4070; fax: +886 7 525 4099; e-mail: [email protected]
and mechanical properties. In this paper, attempt is made on the modeling and experimental assessment of the proposed analytic relationship. The harmonic longitudinal vibration motion can be expressed by x = 2pm, where x is the angular frequency and m the vibration frequency of the motor. The velocity of the ultrasonic motor top, vm, can be expressed by vm = xAsin(xt) = 2pmAsin(xt), where A and t are the wave amplitude and time of the harmonic longitudinal vibration. The balls inside the chamber will be firstly accelerated by the motor, resulting in an induced velocity vb. For simplicity, it is postulated that vb should be much lower than vm since the kinetic energy would be transformed from the vibrating balls onto the sample. Then the flying balls will hit the motor again and be accelerated, resulting in a new ball velocity, vb0 , which can be derived by collision law by regarding them as elastic collisions, i.e., v0b ¼
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ðmb mm Þvb þ 2mm vm ¼ 2vm vb / 2vm mb þ mm
/ mA sinðxtÞ
ð1Þ
where mb and mm are the mass of the ball and motor. Since mm is much greater than mb, vb0 can be simplified as 2vm vb. Since it is assumed above that vb is much lower than vm, it is also simplified that vb0 would also be close to 2vm, and proportional to mA. Based on basic kinetic motion theory, the bombarding input energy E from the vibrating balls should be simply related to the ball mass and ball velocity, or E = (mvb0 2)/ 2. The ball mass m can also be expressed in terms of ball
http://dx.doi.org/10.1016/j.scriptamat.2015.03.003 1359-6462/Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: W.Y. Tsai et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.03.003
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radius r (1/2 of the ball diameter D), m = (4pr3d)/3, where d is the ball density. Since most balls are all made of bearing steel, this d parameter can be considered as a constant. The total ball number N is also an important parameter. For common SMAT experiments, the balls will occupy a fixed surface coverage in the chamber, about 25%. Thus, under the fixed 25% surface coverage, the total ball number for larger balls will be lower, or N is related to ball radius r. The total ball mass M is simply M = Nm. With the fixed surface coverage, the total weight w of the total installed balls would be different. For simplicity, by dividing w by the volume of each spherical ball and its density d, N can be expressed as w N¼ ð2Þ 4pr3 d=3 Practically, each bombarding input-energy will only act on a specific sample area, not the whole sample surface. Thus, the effective overall input energy should be proportional to the total ball number N, the ball mass and the ball velocity, i.e., 1 02 1 4 3 E ¼ mvb ¼ N pr dv02b N dr3 ðmAÞ2 ð3Þ 2 2 3
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Thus, with fixed d and m for most SMAT experiments, E would be directly related to N, r3, and A2. The more rigorous deviation is presented in the Appendix. The SMAT working temperature T may be measured from the sample surface, but the temperature should be a gradient profile from the outer surface to the inner portion of the sample. Since the grain sizes in many SMAT metals or alloys are in the nano- to micro-scale with no pronounced grain growth, the experienced temperature is thought to be around or less than 0.2Tm, where Tm is the melting temperature. In this study, the 304 stainless steel was adopted as the tested material. A plate measuring 40 20 1 mm was set on the top of the SMAT cylindrical chamber measuring 70 mm in diameter and 20 mm in height. The SUJ2 bearing steel balls with smooth surface and high hardness in the RC scale of 62 are applied as the energy deliverer and are vibrated by a vibration generator with a fixed vibration frequency m = 20 kHz at the bottom of the chamber. The vibration generator is a horn powered by compressed air, as shown in the drawing in the Appendix. The vibration amplitude, A, was chosen to vary in three levels, 40, 60 and 80 lm. Three sizes of the balls were selected, namely, 1, 2 and 3 mm in diameter, as summarized in Table 1. The density of these balls of different sizes, d, is fixed to be 7.8 g/cm3. In order to maintain the fixed ball coverage area of 25% inside the chamber, the 1 mm ball case would install 5 g of the total ball weight (i.e. M = 5 g), the 2 mm case for 10 g and the 3 mm case for 15 g, respectively. The SMAT time duration is set to be 15 min. The SMAT samples were investigated by X-ray diffractometry (XRD) with the Cu-Ka radiation. Mechanical polishing and electrochemical polishing were also conducted. The field-emission scanning electron microscopy (SEM) was conducted, with the electron back scattering diffraction (EBSD) function. The cross-sectional transmission electron microscopy (TEM) foils were fabricated using the dual-beam focused-ion-beam (FIB) system with an operating voltage of 30 kV and an ion beam current of 1 pA. The TEM foils were examined by the field emission transmission electron
microscopy with an operating voltage of 200 kV. The hardness of the SMAT specimens from the cross-sectional surface was measured by the MTS Nano Indenter XP System, operated with a displacement rate 10 nm/s with the allowable vibration drift below 0.05 nm/s. The key material characterization tasks are the hardness H, grain size d, and depth of the affected zone L from the free surface, as a function of the SMAT ball size D and ultrasonic vibration amplitude A. Figure 1(a) and (b) shows some representative SEM micrographs taken from the cross-section of sample 4. The grain size is varied with a gradient trend from 20–100 nm near the free surface up to 20 lm in the deeper region without the influence of SMAT bombarding. The grains are basically equiaxed in shape with mostly high angle grain boundaries. Figure 1(c) and (d) presents the typical EBSD images taken from the cross-section of sample 7 at the positions 20 and 500 lm in depth. They are mostly high angle grain boundaries. The detailed grain structures in regions close to the free surface were also characterized by TEM, as shown in Figure 1(e) and (f). The nano-scaled grains contain both high-angle and low-angle boundaries. The average grain size varies from 100–150 nm in those samples SMATed with a lower input energy, such as samples 1–4, to 20– 50 nm in samples SMATed with a higher input energy, such as samples 6 or 8. The hardness was measured by nanoindentation. Two representative plots showing the gradient variation of the hardness are presented in Figure 2(a) and (b). The hardness near the surface directly subject to the ball attrition has the readings about 6 GPa, well above the 304 SS sample before SMAT (about 2.7 GPa). The increment is more than 2 times. Based on the systematic SEM micrographs and the hardness measurements, the depth of the attrition affected zone, L, can be accurately and reliably defined, and can be plotted against the ball size D and amplitude A, as shown in Figure 2(c) and (d). With increasing D or A, L is seen to continuously increase within the experimental range. Figure 2(e) and (f) illustrates the dependence of the hardness and Figure 2(g) and (h) shows the dependence of the grain size (measured at a fixed depth of 100 lm) as a function of the ball size D and amplitude A. Again, basically, with increasing D or A, the hardness would increase and the resulting grain size would decrease, but there are some data deviating this basic trend. This phenomenon needs to be more carefully examined. The resulting hardness and grain size data are plotted in order to explore if they still follow the Hall–Petch relationship, as shown in Figure 3(a). The datum points for the unaffected inner portion (with H 2.7 GPa) and the free surface (with H 6 GPa) are both included. Though the basic dependence is still positively increasing, the trend does not follow the Hall–Petch relation. The measured hardness readings are all higher than the Hall–Petch line, suggesting there is contribution other than grain size hardening. With the severe SMAT attrition at the controlled temperatures below 0.2Tm, work hardening by dislocations and twins contributed appreciably to the observed hardness. In most previous severe plastic deformation experiments, such as ECAP or FSP, the resulting hardness H and grain size d should be related to the input work W or input energy E acting on the sample. Based on the above analytical modeling, the input energy E can be simplified to be related to the overall bombarding events N, the ball
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Table 1. Summary of the major SMAT parameters adopted in this study. Sample
Ball diameter D (mm)
SMAT amplitude A (lm)
Ball average speed v (m/s)
Strain rate e_ (s1)
Input energy E (mJ)
#1 #2 #3 #4 #5 #6 #7 #8 #9
1 2 3 1 2 3 1 2 3
40 40 40 60 60 60 80 80 80
5±1 5±1 5±1 8±1 8±1 8±1 10 ± 1 10 ± 1 10 ± 1
3 102 4 102 5 102 3 102 4 102 5 102 3 102 4 102 5 102
9±1 19 ± 2 28 ± 2 24 ± 2 48 ± 4 71 ± 5 38 ± 3 75 ± 6 110 ± 10
200 µm
6
5
4
3
Untresated H=2.7 GPa
(a)
1 µm
2
(b)
0
100
(c)
Affected depth (µm)
(d)
500
600
0
100
400 300 200
(c)
100
600
2
200 100
(d) 40
5.0
5.0
4.5 4.0
A=40 µm A=60 µm A=80 µm
3.5
(e) 1.0
1.5
2.0
50
60
70
2.5
4.5 4.0
3.0 2.5
3.0
D=1 mm D=2 mm D=3 mm
3.5
(f) 40
Ball size (mm)
50
60
70
210
220
80
Amplitude (µm)
25
25
15 10 5
D=1 mm D=2 mm D=3 mm
20
Grain size (µm)
A=40 µm A=60 µm A=80 µm
20
15 10 5
(g)
radius r, and the ultrasonic vibration amplitude A (i.e., N, r3, and A2). In the current experiment, the attrition time, vibration frequency and ball density are all fixed. The total ball number N needs to be quantified. By inputting the installed total ball weight and ball radius, N for the 1 mm, 2 mm, and 3 mm balls are calculated by Eq. (2) to be 153, 38, and 17. With the smaller ball size and a higher ball number for the 1 mm balls to cover the 25% coverage area inside the chamber, the total ball number is higher. After substituting all experimental parameters into above equations, the ball velocity and the input energy for various specimens can be calculated, as summarized in Table 1. The average ball speed for specimens 1–3, with the same vibration motion frequency (m = 20 kHz) and amplitude (A = 40 lm), remains the same as 5 ± 1 m/s. In parallel, the speed is 8 ± 1 m/s for specimens 4–6, and 10 ± 1 m/s for specimens 7–9. The ball speed range is in good agreement with those measured by the high speed camera [18]. The kinetic energy can also be calculated based on Eq. (3), as tabulated in Table 1. The values vary from
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Amplitude (µm) 5.5
0
600
300
3
3.0
Grain size (µm)
Figure 1. Typical cross-sectional SEM micrographs taken from sample 4: (a) low magnitude whole view, (b) 20 lm under the SMAT-treated surfaces. Typical EBSD images taken from sample 7: (c) 20 lm under the SMAT-treated surfaces, and (d) 500 lm under the SMAT-treated surfaces. (e, f) Examples of the TEM bright field micrographs, showing the fine grains near the free surface (about 0.5–1 lm in depth), taken from sample 4.
500
400
5.5
2.5
(b) 400
500
0 1
Hardness (GPa)
Hardness (GPa)
(f)
300
D=1 mm D=2 mm D=3 mm
700
Ball size (mm)
(e)
200
Depth (µm)
500
0
3
2
600
A=40 µm A=60 µm A=80 µm
700
2 µm
300 400 Depth (µm)
4
Untreated H=2.7 GPa
(a)
200
Sample 7 Sample 8 Sample 9
5
800
800
µm 25 µm
Hardness (GPa)
Sample 1 Sample 2 Sample 3
Affected depth (µm)
Hardness (GPa)
6
1.0
1.5
2.0
2.5
Ball size (mm)
3.0
0
(h) 40
50
60
70
80
Amplitude (µm)
Figure 2. (a, b) The variation of the hardness of selected SMAT 304 SS samples in (a, b). The variation of the affected depth L in (c, d), hardness H in (e, f), and grain size in (g, h) versus ball size D and amplitude A.
9 ± 1 mJ for specimen 1 to 110 ± 1 mJ for specimen 9. Note that there are only about 17 balls (N = 17) for the 3 mm balls. The input energy for these 17 balls, 3 mm in diameter and 80 lm in amplitude, has already reached 110 mJ. This input energy level is consistent with the finding in [18] where the SMAT condition was 50 balls that are 3 mm in diameter and 80 lm in amplitude, resulting in an energy of 275 mJ. The resulting affected depth, hardness and grain size are all plotted against the input energy, as shown in Figure 3(b) and (d). It can be seen that the affected depth is monotonically proportional to the input energy in Figure 3(b), a rather simple trend well expected.
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Figure 3. (a) The Hall–Petch relationship using the data measured from the depths of 20 lm, 100 lm and 200 lm from the SMAT surface, plus the datum of the unaffected inner portion. The variation of the (b) affected depth L, (c) hardness H, and (d) grain size d as a function of input energy.
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250
But the hardness shows a more complicated trend in Figure 3(c), increasing initially until an upper limit, and then deceasing gradually. As the input energy is over the optimum condition (as for samples 6, 8 or 9), the hardness would start to decrease, showing the work softening phenomenon. This effect can be further visualized by the plot of grain size in Figure 3(d). At the highest input energy, the grain size is obviously larger than the expected trend, as a result of grain growth. From Figure 3(c) and (d), it is demonstrated that, with the high input energy, the hardness could start to decline and the grain size could start to grow. In samples 8 and 9, the affected depth has reached about 550 lm, one half of the sample thickness. Thus, the heat generated inside the sample would become difficult to be released rapidly. The accumulated heat would increase the sample temperature (likely above 100 °C), resulting in more efficient dislocation recovery and grain growth. As for the strain rate (_e) level, it can be estimated by et mt P ei ¼ ¼ m P ei ð4Þ t t where et is the overall strain accumulated by numerous bombarding events, ei is the strain for each bombarding (estimated to be about 0.15, 0.20, and 0.25 for the 1, 2 and 3 mm balls), P is the probability for the balls to impact the sample surface, (0.1 for the current experiment). The calculated strain rate range is found to vary from 3 102 to 5 102 s1. This range is already approaching to the lower end of high rate deformation (103 s1), but not yet the explosive shock loading (105 to 106 s1) [19]. We believe this strain rate level at 3–5 102 s1 is logical since in our experiment there is no sign of severe adiabatic heating effect making the microstructure full of checkerboard-like shear banding [20]. Note that the 304 steel is a work-hardening material. During the 15 min SMAT, the surface region would e_ ¼
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undergo gradual hardening. Fortunately, the current SMAT time period is only 15 min. For simplicity, we assume that the material evolution over the 15 min would still follow one similar evolution trend. If the SMAT processing time period reaches, for example, 60 min, the material evolution should be treated to vary for four stages, each with gradually hardened and finally saturated microstructures. The current simplified modeling has not considered the material hardening (or softening) effect, and can be modified in future. In summary, there appear some optimum SMAT working parameters for the best effect. For the 304 stainless steel, it locates within 8–10 m/s for the ball speed, 4–5 102 s1 for the strain rate, and 70–75 mJ for the input energy. Beyond the optimum SMAT parameters, the sample surface could be subject to microcracking (seen from samples 6, 8 or 9) and the grain size would not be further reduced. The benefits from SMAT would become lower. This optimum SMAT parameters need to be established for various metals. The current model can be served as the tool in searching the optimum SMAT working parameters.
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The authors acknowledge the sponsorship from Metal Industries Research & Development Centre, under project No. A0071601, and from Ministry of Science and Technology of Taiwan, under project No. NSC101-2120-M-110-007. 300
Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.scriptamat. 2015.03.003. [1] M. Kobayashi, T. Matsui, Y. Murakami, Int. J. Fatigue 20 (1998) 351. [2] P. Zhang, J. Lindemann, Scripta Mater. 52 (2005) 1011. [3] N.R. Tao, M.L. Sui, J. Lu, K. Lu, Nanostruct. Mater. 11 (1999) 433. [4] G. Liu, J. Lu, K. Lu, Mater. Sci. Eng., A 286 (2000) 91. [5] N.R. Tao, Z.B. Wang, W.P. Tong, M.L. Sui, J. Lu, K. Lu, Acta Mater. 50 (2002) 4603. [6] N.W. Zhang, Z.K. Hei, G. Liu, J. Lu, K. Lu, Acta Mater. 51 (2003) 1871–1881. [7] K. Lu, J. Lu, Mater. Sci. Eng., A. 375 (2004) 38. [8] X. Wu, N. Tao, Y. Hong, G. Liu, B. Xu, J. Lu, K. Lu, Acta Mater. 53 (2005) 681. [9] T. Roland, D. Retraint, K. Lu, J. Lu, Scripta Mater. 54 (2006) 1949. [10] K.Y. Zhu, A. Vassel, F. Brisset, K. Lu, J. Lu, Acta Mater. 52 (2004) 4101. [11] K. Wang, N.R. Tao, G. Liu, J. Lu, K. Lu, Acta Mater. 54 (2006) 5281. [12] X. Wu, N. Tao, Y. Hong, B. Xu, J. Lu, K. Lu, Acta Mater. 50 (2002) 2075. [13] H.Q. Sun, Y.-N. Shi, M.-X. Zhang, K. Lu, Acta Mater. 55 (2007) 975. [14] H.K. Lin, J.C. Huang, Mater. Trans. 43 (2002) 2424. [15] C.I. Chang, C.J. Lee, J.C. Huang, Scripta Mater. 51 (2004) 509. [16] V.M. Segal, Mater. Sci. Eng., A 271 (1999) 322. [17] R.Z. Valiev, T.G. Langdon, Prog. Mater Sci. 51 (2006) 881. [18] H.L. Chan, H.H. Ruan, A.Y. Chen, J. Lu, Acta Mater. 58 (2010) 5086. [19] D.E. Grady, J.R. Asay, J. Appl. Phys. 53 (1982) 7350. [20] J.C. Huang, G.T. Gray, Metall. Trans. 20A (1989) 1065.
Please cite this article in press as: W.Y. Tsai et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.03.003
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26 March 2015 Available online at www.sciencedirect.com
ScienceDirect Scripta Materialia xxx (2015) xxx–xxx www.elsevier.com/locate/scriptamat
Relationship between microstructure and properties for ultrasonic surface mechanical attrition treatment ⇑
W.Y. Tsai,a J.C. Huang,a, Yu Jia Gao,b Y.L. Chungb and Guan-Rong Huangc a
Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung 804, Taiwan b Metal Industries Research & Development Centre, Kaohsiung 811, Taiwan c Department of Physics, National Taiwan University, Taipei 106, Taiwan Received 3 January 2015; revised 10 March 2015; accepted 12 March 2015
The analytic modeling and one experimental assess of the ultrasonic surface mechanical attrition treatment are presented. The bombarding ball speed, induced energy, hardness and grain size are incorporated into this model, based on harmonic longitudinal vibration motion of ultrasonicwave-driven impact. There appear some optimum attrition working parameters for the best attrition effect; beyond which, the sample surface would be subject to bombarding microcracking and the grain size would not be further reduced. The benefits from attrition would become lower. Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain refining; Nanocrystalline microstructure; Hardness; Stainless steels; SMAT
20
30
40
Metal surfaces are frequently treated by shot peening in order to induce tougher and harder surface layers with compressive residual stresses in enhancing the fatigue properties [1,2]. The steel balls are typically of the size of 0.2– 1 mm and are accelerated by compressed air. The flying velocity and bombard frequency are typically 50–100 m/s and 20–100 Hz. The accelerated balls are directed from a specific direction on the surface, mostly perpendicular. A modified version of the shot peening, termed as the surface mechanical attrition treatment (SMAT), was firstly reported in 1999 [3,4]. The balls are resonated and accelerated by the vibration of the ultrasonic motor. The ball size, flying velocity and bombarding frequency are typically 1– 10 mm, 1–20 m/s and 10–100 kHz. The balls are bombarding from 3D random directions onto the entire surface, resulting in grain refinement, gradient structure and attractive mechanical performance [5–9]. And this process has been applied to iron [5], titanium [10], copper [11], cobalt [8], aluminum alloy [12], magnesium alloy [13] and stainless steel [6]. The analytic expressions for common severe plastic deformation processes have been proposed widely for ball milling mechanical alloying, equal channel angular pressing, high-ratio extrusion, torsion, friction stir processing or accumulative roll bonding [14–17]. However, there has not been well established relationship for the SMAT processing parameters with respect to the microstructural
⇑ Corresponding
author. Tel.: +886 7 525 4070; fax: +886 7 525 4099; e-mail: [email protected]
and mechanical properties. In this paper, attempt is made on the modeling and experimental assessment of the proposed analytic relationship. The harmonic longitudinal vibration motion can be expressed by x = 2pm, where x is the angular frequency and m the vibration frequency of the motor. The velocity of the ultrasonic motor top, vm, can be expressed by vm = xAsin(xt) = 2pmAsin(xt), where A and t are the wave amplitude and time of the harmonic longitudinal vibration. The balls inside the chamber will be firstly accelerated by the motor, resulting in an induced velocity vb. For simplicity, it is postulated that vb should be much lower than vm since the kinetic energy would be transformed from the vibrating balls onto the sample. Then the flying balls will hit the motor again and be accelerated, resulting in a new ball velocity, vb0 , which can be derived by collision law by regarding them as elastic collisions, i.e., v0b ¼
50
60
ðmb mm Þvb þ 2mm vm ¼ 2vm vb / 2vm mb þ mm
/ mA sinðxtÞ
ð1Þ
where mb and mm are the mass of the ball and motor. Since mm is much greater than mb, vb0 can be simplified as 2vm vb. Since it is assumed above that vb is much lower than vm, it is also simplified that vb0 would also be close to 2vm, and proportional to mA. Based on basic kinetic motion theory, the bombarding input energy E from the vibrating balls should be simply related to the ball mass and ball velocity, or E = (mvb0 2)/ 2. The ball mass m can also be expressed in terms of ball
http://dx.doi.org/10.1016/j.scriptamat.2015.03.003 1359-6462/Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: W.Y. Tsai et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.03.003
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radius r (1/2 of the ball diameter D), m = (4pr3d)/3, where d is the ball density. Since most balls are all made of bearing steel, this d parameter can be considered as a constant. The total ball number N is also an important parameter. For common SMAT experiments, the balls will occupy a fixed surface coverage in the chamber, about 25%. Thus, under the fixed 25% surface coverage, the total ball number for larger balls will be lower, or N is related to ball radius r. The total ball mass M is simply M = Nm. With the fixed surface coverage, the total weight w of the total installed balls would be different. For simplicity, by dividing w by the volume of each spherical ball and its density d, N can be expressed as w N¼ ð2Þ 4pr3 d=3 Practically, each bombarding input-energy will only act on a specific sample area, not the whole sample surface. Thus, the effective overall input energy should be proportional to the total ball number N, the ball mass and the ball velocity, i.e., 1 02 1 4 3 E ¼ mvb ¼ N pr dv02b N dr3 ðmAÞ2 ð3Þ 2 2 3
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Thus, with fixed d and m for most SMAT experiments, E would be directly related to N, r3, and A2. The more rigorous deviation is presented in the Appendix. The SMAT working temperature T may be measured from the sample surface, but the temperature should be a gradient profile from the outer surface to the inner portion of the sample. Since the grain sizes in many SMAT metals or alloys are in the nano- to micro-scale with no pronounced grain growth, the experienced temperature is thought to be around or less than 0.2Tm, where Tm is the melting temperature. In this study, the 304 stainless steel was adopted as the tested material. A plate measuring 40 20 1 mm was set on the top of the SMAT cylindrical chamber measuring 70 mm in diameter and 20 mm in height. The SUJ2 bearing steel balls with smooth surface and high hardness in the RC scale of 62 are applied as the energy deliverer and are vibrated by a vibration generator with a fixed vibration frequency m = 20 kHz at the bottom of the chamber. The vibration generator is a horn powered by compressed air, as shown in the drawing in the Appendix. The vibration amplitude, A, was chosen to vary in three levels, 40, 60 and 80 lm. Three sizes of the balls were selected, namely, 1, 2 and 3 mm in diameter, as summarized in Table 1. The density of these balls of different sizes, d, is fixed to be 7.8 g/cm3. In order to maintain the fixed ball coverage area of 25% inside the chamber, the 1 mm ball case would install 5 g of the total ball weight (i.e. M = 5 g), the 2 mm case for 10 g and the 3 mm case for 15 g, respectively. The SMAT time duration is set to be 15 min. The SMAT samples were investigated by X-ray diffractometry (XRD) with the Cu-Ka radiation. Mechanical polishing and electrochemical polishing were also conducted. The field-emission scanning electron microscopy (SEM) was conducted, with the electron back scattering diffraction (EBSD) function. The cross-sectional transmission electron microscopy (TEM) foils were fabricated using the dual-beam focused-ion-beam (FIB) system with an operating voltage of 30 kV and an ion beam current of 1 pA. The TEM foils were examined by the field emission transmission electron
microscopy with an operating voltage of 200 kV. The hardness of the SMAT specimens from the cross-sectional surface was measured by the MTS Nano Indenter XP System, operated with a displacement rate 10 nm/s with the allowable vibration drift below 0.05 nm/s. The key material characterization tasks are the hardness H, grain size d, and depth of the affected zone L from the free surface, as a function of the SMAT ball size D and ultrasonic vibration amplitude A. Figure 1(a) and (b) shows some representative SEM micrographs taken from the cross-section of sample 4. The grain size is varied with a gradient trend from 20–100 nm near the free surface up to 20 lm in the deeper region without the influence of SMAT bombarding. The grains are basically equiaxed in shape with mostly high angle grain boundaries. Figure 1(c) and (d) presents the typical EBSD images taken from the cross-section of sample 7 at the positions 20 and 500 lm in depth. They are mostly high angle grain boundaries. The detailed grain structures in regions close to the free surface were also characterized by TEM, as shown in Figure 1(e) and (f). The nano-scaled grains contain both high-angle and low-angle boundaries. The average grain size varies from 100–150 nm in those samples SMATed with a lower input energy, such as samples 1–4, to 20– 50 nm in samples SMATed with a higher input energy, such as samples 6 or 8. The hardness was measured by nanoindentation. Two representative plots showing the gradient variation of the hardness are presented in Figure 2(a) and (b). The hardness near the surface directly subject to the ball attrition has the readings about 6 GPa, well above the 304 SS sample before SMAT (about 2.7 GPa). The increment is more than 2 times. Based on the systematic SEM micrographs and the hardness measurements, the depth of the attrition affected zone, L, can be accurately and reliably defined, and can be plotted against the ball size D and amplitude A, as shown in Figure 2(c) and (d). With increasing D or A, L is seen to continuously increase within the experimental range. Figure 2(e) and (f) illustrates the dependence of the hardness and Figure 2(g) and (h) shows the dependence of the grain size (measured at a fixed depth of 100 lm) as a function of the ball size D and amplitude A. Again, basically, with increasing D or A, the hardness would increase and the resulting grain size would decrease, but there are some data deviating this basic trend. This phenomenon needs to be more carefully examined. The resulting hardness and grain size data are plotted in order to explore if they still follow the Hall–Petch relationship, as shown in Figure 3(a). The datum points for the unaffected inner portion (with H 2.7 GPa) and the free surface (with H 6 GPa) are both included. Though the basic dependence is still positively increasing, the trend does not follow the Hall–Petch relation. The measured hardness readings are all higher than the Hall–Petch line, suggesting there is contribution other than grain size hardening. With the severe SMAT attrition at the controlled temperatures below 0.2Tm, work hardening by dislocations and twins contributed appreciably to the observed hardness. In most previous severe plastic deformation experiments, such as ECAP or FSP, the resulting hardness H and grain size d should be related to the input work W or input energy E acting on the sample. Based on the above analytical modeling, the input energy E can be simplified to be related to the overall bombarding events N, the ball
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Table 1. Summary of the major SMAT parameters adopted in this study. Sample
Ball diameter D (mm)
SMAT amplitude A (lm)
Ball average speed v (m/s)
Strain rate e_ (s1)
Input energy E (mJ)
#1 #2 #3 #4 #5 #6 #7 #8 #9
1 2 3 1 2 3 1 2 3
40 40 40 60 60 60 80 80 80
5±1 5±1 5±1 8±1 8±1 8±1 10 ± 1 10 ± 1 10 ± 1
3 102 4 102 5 102 3 102 4 102 5 102 3 102 4 102 5 102
9±1 19 ± 2 28 ± 2 24 ± 2 48 ± 4 71 ± 5 38 ± 3 75 ± 6 110 ± 10
200 µm
6
5
4
3
Untresated H=2.7 GPa
(a)
1 µm
2
(b)
0
100
(c)
Affected depth (µm)
(d)
500
600
0
100
400 300 200
(c)
100
600
2
200 100
(d) 40
5.0
5.0
4.5 4.0
A=40 µm A=60 µm A=80 µm
3.5
(e) 1.0
1.5
2.0
50
60
70
2.5
4.5 4.0
3.0 2.5
3.0
D=1 mm D=2 mm D=3 mm
3.5
(f) 40
Ball size (mm)
50
60
70
210
220
80
Amplitude (µm)
25
25
15 10 5
D=1 mm D=2 mm D=3 mm
20
Grain size (µm)
A=40 µm A=60 µm A=80 µm
20
15 10 5
(g)
radius r, and the ultrasonic vibration amplitude A (i.e., N, r3, and A2). In the current experiment, the attrition time, vibration frequency and ball density are all fixed. The total ball number N needs to be quantified. By inputting the installed total ball weight and ball radius, N for the 1 mm, 2 mm, and 3 mm balls are calculated by Eq. (2) to be 153, 38, and 17. With the smaller ball size and a higher ball number for the 1 mm balls to cover the 25% coverage area inside the chamber, the total ball number is higher. After substituting all experimental parameters into above equations, the ball velocity and the input energy for various specimens can be calculated, as summarized in Table 1. The average ball speed for specimens 1–3, with the same vibration motion frequency (m = 20 kHz) and amplitude (A = 40 lm), remains the same as 5 ± 1 m/s. In parallel, the speed is 8 ± 1 m/s for specimens 4–6, and 10 ± 1 m/s for specimens 7–9. The ball speed range is in good agreement with those measured by the high speed camera [18]. The kinetic energy can also be calculated based on Eq. (3), as tabulated in Table 1. The values vary from
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Amplitude (µm) 5.5
0
600
300
3
3.0
Grain size (µm)
Figure 1. Typical cross-sectional SEM micrographs taken from sample 4: (a) low magnitude whole view, (b) 20 lm under the SMAT-treated surfaces. Typical EBSD images taken from sample 7: (c) 20 lm under the SMAT-treated surfaces, and (d) 500 lm under the SMAT-treated surfaces. (e, f) Examples of the TEM bright field micrographs, showing the fine grains near the free surface (about 0.5–1 lm in depth), taken from sample 4.
500
400
5.5
2.5
(b) 400
500
0 1
Hardness (GPa)
Hardness (GPa)
(f)
300
D=1 mm D=2 mm D=3 mm
700
Ball size (mm)
(e)
200
Depth (µm)
500
0
3
2
600
A=40 µm A=60 µm A=80 µm
700
2 µm
300 400 Depth (µm)
4
Untreated H=2.7 GPa
(a)
200
Sample 7 Sample 8 Sample 9
5
800
800
µm 25 µm
Hardness (GPa)
Sample 1 Sample 2 Sample 3
Affected depth (µm)
Hardness (GPa)
6
1.0
1.5
2.0
2.5
Ball size (mm)
3.0
0
(h) 40
50
60
70
80
Amplitude (µm)
Figure 2. (a, b) The variation of the hardness of selected SMAT 304 SS samples in (a, b). The variation of the affected depth L in (c, d), hardness H in (e, f), and grain size in (g, h) versus ball size D and amplitude A.
9 ± 1 mJ for specimen 1 to 110 ± 1 mJ for specimen 9. Note that there are only about 17 balls (N = 17) for the 3 mm balls. The input energy for these 17 balls, 3 mm in diameter and 80 lm in amplitude, has already reached 110 mJ. This input energy level is consistent with the finding in [18] where the SMAT condition was 50 balls that are 3 mm in diameter and 80 lm in amplitude, resulting in an energy of 275 mJ. The resulting affected depth, hardness and grain size are all plotted against the input energy, as shown in Figure 3(b) and (d). It can be seen that the affected depth is monotonically proportional to the input energy in Figure 3(b), a rather simple trend well expected.
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Figure 3. (a) The Hall–Petch relationship using the data measured from the depths of 20 lm, 100 lm and 200 lm from the SMAT surface, plus the datum of the unaffected inner portion. The variation of the (b) affected depth L, (c) hardness H, and (d) grain size d as a function of input energy.
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But the hardness shows a more complicated trend in Figure 3(c), increasing initially until an upper limit, and then deceasing gradually. As the input energy is over the optimum condition (as for samples 6, 8 or 9), the hardness would start to decrease, showing the work softening phenomenon. This effect can be further visualized by the plot of grain size in Figure 3(d). At the highest input energy, the grain size is obviously larger than the expected trend, as a result of grain growth. From Figure 3(c) and (d), it is demonstrated that, with the high input energy, the hardness could start to decline and the grain size could start to grow. In samples 8 and 9, the affected depth has reached about 550 lm, one half of the sample thickness. Thus, the heat generated inside the sample would become difficult to be released rapidly. The accumulated heat would increase the sample temperature (likely above 100 °C), resulting in more efficient dislocation recovery and grain growth. As for the strain rate (_e) level, it can be estimated by et mt P ei ¼ ¼ m P ei ð4Þ t t where et is the overall strain accumulated by numerous bombarding events, ei is the strain for each bombarding (estimated to be about 0.15, 0.20, and 0.25 for the 1, 2 and 3 mm balls), P is the probability for the balls to impact the sample surface, (0.1 for the current experiment). The calculated strain rate range is found to vary from 3 102 to 5 102 s1. This range is already approaching to the lower end of high rate deformation (103 s1), but not yet the explosive shock loading (105 to 106 s1) [19]. We believe this strain rate level at 3–5 102 s1 is logical since in our experiment there is no sign of severe adiabatic heating effect making the microstructure full of checkerboard-like shear banding [20]. Note that the 304 steel is a work-hardening material. During the 15 min SMAT, the surface region would e_ ¼
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undergo gradual hardening. Fortunately, the current SMAT time period is only 15 min. For simplicity, we assume that the material evolution over the 15 min would still follow one similar evolution trend. If the SMAT processing time period reaches, for example, 60 min, the material evolution should be treated to vary for four stages, each with gradually hardened and finally saturated microstructures. The current simplified modeling has not considered the material hardening (or softening) effect, and can be modified in future. In summary, there appear some optimum SMAT working parameters for the best effect. For the 304 stainless steel, it locates within 8–10 m/s for the ball speed, 4–5 102 s1 for the strain rate, and 70–75 mJ for the input energy. Beyond the optimum SMAT parameters, the sample surface could be subject to microcracking (seen from samples 6, 8 or 9) and the grain size would not be further reduced. The benefits from SMAT would become lower. This optimum SMAT parameters need to be established for various metals. The current model can be served as the tool in searching the optimum SMAT working parameters.
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The authors acknowledge the sponsorship from Metal Industries Research & Development Centre, under project No. A0071601, and from Ministry of Science and Technology of Taiwan, under project No. NSC101-2120-M-110-007. 300
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