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Evaluating the reinforcement content and elastic properties of Mg-based composites using dual-mode ultrasonic velocities
Ultrasonics 81 (2017) 167–173
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Evaluating the reinforcement content and elastic properties of Mg-based composites using dual-mode ultrasonic velocities Yu Liu a, Yongfeng Song a, Xiongbing Li a,⇑, Chao Chen b,⇑, Kechao Zhou b a b
School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China
a r t i c l e
i n f o
Article history: Received 12 April 2017 Received in revised form 29 June 2017 Accepted 3 July 2017 Available online 4 July 2017 Keywords: Mg-based composites Reinforcement content Nondestructive characterization Dual-mode ultrasonic velocities Immersive scan Elastic properties
a b s t r a c t Based on the wave-mode-converted principle, an immersion-focused transducer is employed to determine the longitudinal wave and shear wave velocities. The experimental condition is then investigated to obtain the converted shear wave, which is used to analyze the relationship between the reinforcement content and the dual-mode ultrasonic velocities. In addition, the elastic modulus is calculated. Magnesium-based composite samples with different reinforcement contents are manufactured to conduct an ultrasonic experiment, wherein the dual-mode velocities vary with the change in the reinforcement content; the correlation coefficient is 99.17%. An ultrasonic dual-mode velocity model is developed to analyze the distribution of the reinforcement content. By employing the measured values obtained from the destructive method, the largest errors in the reinforcement content and elastic modulus evaluated using the proposed method are found to be 5.76% and 5.85%, respectively. The shear wave velocity determined using a normal-incidence shear-wave transducer reveals the accuracy with which the errors are measured. This method provides an effective tool to nondestructively evaluate the microstructure and elastic properties of Mg-based composites. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Magnesium-based metal matrix composites (MMCs) have a good potential to be applied in aircraft, electronic, and automobile industries owing to their excellent properties such as low weight and good abrasive and creep resistances [1–3]. The reinforcement content is an important parameter significantly affecting the mechanical properties of Mg-based MMCs. Among various reinforcements, SiC is one of the most widely used dispersoids in Mg-based composites. The elastic properties of the materials can be significantly improved by increasing the reinforcement content [4,5]. Krishnadev et al. [6] demonstrated that the elastic properties increase by 48% with the increase in the reinforcement content from 10% to 30%. Hence, it is necessary to determine the reinforcement content and elastic modulus. Generally, microstructural analyses are performed based on metallography, whereas mechanical properties are determined by conducting mechanical tests. The X-ray diffraction (XRD) and X-ray energy dispersive spectroscopy (EDS) methods can be used to visually measure the reinforcement content. However, the process is time consuming; requires high cost; and has low efficiency ⇑ Corresponding authors. E-mail addresses: [email protected] (X. Li), [email protected] (C. Chen). http://dx.doi.org/10.1016/j.ultras.2017.07.001 0041-624X/Ó 2017 Elsevier B.V. All rights reserved.
[7]. The static tension method can be used to determine the elastic modulus by employing the stretching and twisting loads to deform the materials [8]. Thus, the nondestructive testing is an important method for evaluating material properties as it can help in accurately and effectively ensuring the product quality, serviceability, and safety. Based on the changes in the ultrasonic velocities induced by the microstructure, the ultrasonic velocity method can be used to evaluate the reinforcement content, grain size, porosity contents, etc. [9–12]. El-Daly et al. [13] evaluated the reinforcement content of Al-based MMCs using the ultrasonic velocity method. The results indicated that the longitudinal wave and shear wave velocities increased with an increase in the reinforcement content. Based on these velocities, the Poisson’s ratio and Young’s, bulk, and shear moduli were effectively calculated. The longitudinal wave and normal-incidence shear-wave transducers are respectively used to measure the corresponding velocities. Clearly, the two types of ultrasonic velocities cannot be determined simultaneously using only a single ultrasonic transducer. The normal-incidence shearwave transducers are contact-type transducers, requiring indispensable coupling with the material using a strong couplant. Moreover, the scanning image of the shear wave velocity at each point cannot be obtained; thus, the entire material cannot be analyzed [14]. Li et al. [15] proposed a method for measuring the
Y. Liu et al. / Ultrasonics 81 (2017) 167–173
longitudinal and shear wave velocities simultaneously using a focused transducer based on the wave-mode-converted principle. However, the measured velocity of the shear wave is higher because they considered only the longitudinal wave generated from the edge of a transducer can be converted into a shear wave. In addition, the value of the incidence angle is observed depending on experimental result instead of theoretical calculation First, a modified method is investigated based on a method given elsewhere [15]. The formula used to determine the incidence angle is developed by the geometric acoustics. Moreover, the experimental condition is presented for obtaining the converted shear wave. Next, the longitudinal and shear wave velocities are determined using the modified method. The scanning images of the dual-mode velocities are then obtained for the entire sample. Finally, the reinforcement content and elastic modulus of the Mg-based MMC are evaluated.
a
P1
H
C
Fcf 2fa
ð1Þ
L2
P3
T2
T1
D
zf
Q
P2
When ultrasonic longitudinal waves are obliquely incident on a hetero-interface with an angle less than the second critical angle, the converted shear-longitudinal wave (TL wave) and converted shear wave (TT wave) are observed between the first back-wall echo and the second back-wall echo [16,17], as shown in Fig. 1. The TT wave will most likely appear as long as the TL wave exists. Thus, the water path should be optimized to measure the dual-mode ultrasonic velocities. Fig. 2 shows the wave-mode conversion of the TT wave. Suppose L1 is the obliquely incident longitudinal wave with an incident angle of a, the point of incidence is P1 . Accordingly, T 1 is the shear wave with a refractive angle of b; T 2 is the shear wave whose reflective point is P 2 ; and L2 is the longitudinal wave whose refractive point is P3 . When the water path is beyond the maximum, the transducer cannot receive L2 , i.e., the TT wave is absent. In Fig. 2, when the water path reaches the critical value, the points P 2 and D and points P4 and B would overlap. Points P1 and P 3 would be symmetrical about the point C. To calculate the maximum water path, suppose the transducer is focused in the water. The ultrasonic beams transmitted from the focused transducer do not exactly converge at a point, but forms a circular spot in the focal plane. The beam diameter is expressed elsewhere [18]
P4 B
r L1
2. Methods
d ¼ 1:02
O
A
Water
F
168
Sample
Water
Focal Point
d Fig. 2. Schematic of wave-mode-conversion of TT wave.
where a is the transducer radius, F is the focal length, f is the input frequency, and cf is the velocity of water. The radius of curvature of the transducer is given as follows.
r¼
1
cf F ct
ð2Þ
where ct is the velocity of the acoustic lens. Therefore, the incident angle can be written as follows.
a ¼ arctan
a d=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F þ r r 2 a2
ð3Þ
According to the Snell’s law, the refractive angle is expressed as follows.
b ¼ arcsin
cT sin a cf
ð4Þ
where cT is the estimated value of the shear wave velocity in the is given as follows. sample. The maximum water path zmax f
zmax ¼r f
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a H tan b pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðF þ r r 2 a2 Þ r2 a2 þ a d=2
ð5Þ
where H is the thickness of the sample. When the water path is so short that the second front-wall echo appears before the second back-wall echo, the TT wave would also be absent. Thus, the minimum water path zmin is given as follows. f
zmin ¼ 2H f
cf cL
ð6Þ
where cL is the estimated value of the longitudinal wave velocity in the sample. As cL and cT are the estimated values, we select the water path þ zmin Þ=2. as zf ¼ ðzmax f f
Fig. 1. Schematic of ultrasonic A-wave signal.
To avoid the overlap of any two echoes, such as the first backwall echo and TL wave, TL wave and TT wave, and TT wave and second back-wall echo, it is important to obtain an accurate time interval. Hence, the waveform duration D must meet the following conditions:
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Y. Liu et al. / Ultrasonics 81 (2017) 167–173
Fig. 5. Longitudinal and shear velocities of No. 1–No. 5 samples. Fig. 3. XRD patterns of: (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, and (e) No. 5.
where s1 and s2 are the time intervals of the waves until the two adjacent echoes overlap each other. s1 and s2 are determined when the cross-correlation values y1 and y2 reach the maximum [19].
8 2zf 2zf 2H D H H D > > > cf þ cL þ 2 6 cf þ cL þ cT 2 > > < 2zf 2z þ cH þ cH þ D2 6 c f þ 2H D2 cf cT f L T > > > 2z > > : f þ 2H þ D 6 2zf þ 4H D c c c 2 c 2 f
f
T
(
ð7Þ
L
H H 4H 2H ; cT cL cL cT
ð8Þ
From Eq. (8), we can conclude that bandwidth of the transducer must be controlled strictly. Finally, using the cross-correlation analysis, the longitudinal wave velocity cL and shear wave velocity cT can be obtained as follows.
ð10Þ
1
The waveform duration is subject to the following condition:
D 6 min
R 1 max y1 ¼ 1 B1 ðtÞB2 ðt s1 Þdt R 1 B1 ðtÞB3 ðt s2 Þdt max y2 ¼
cL ¼ 2H=s1
ð9Þ
cT ¼ 2H=s2
Motion control card
where B1 , B2 and B3 are the first front-wall echo, the first back-wall echo and TT wave respectively. Finally, the mean velocities cL and cT are used to develop a model to evaluate the final dual-mode ultrasonic velocities based on the multivariate linear regression equation.
V ¼ b0 þ b1 cT þ b2 cL
ð11Þ
where b0 , b1 , and b2 are the regression coefficients. V is the reinforcement content. Thus, the reinforcement content of each point on the sample can be evaluated using Eq. (11). For an isotropic solid, many studies [13,14,19] have developed empirical relationships to relate the Poisson’s ratio, Young’s, and shear moduli.
Industrial computer
Main control circuit
PCIe-9852 Digital acquisition card
6-DOF motion platform GAIN 30 dB
Probe holder
Transducer Water
Sample
Fig. 4. Schematic diagram of the ultrasonic signal acquisition system.
Olympus 5072R ultrasonic pulse generator/receive
170
m¼
Y. Liu et al. / Ultrasonics 81 (2017) 167–173
1 2ðcT =cL Þ2
ð12Þ
2 2ðcT =cL Þ2
E ¼ qc2L
G ¼ qc2T
ð1 þ mÞð1 2mÞ 1m
3. Experiments and results 3.1. XRD analysis
ð13Þ ð14Þ
where m is the Poisson’s ratio, E is the Young’s modulus, G is the shear modulus and q is the density of the sample. The density is measured using the Archimedes principle.
The samples were manufactured using the conventional stircasting technique [20]. The matrix was AZ91D magnesium alloy reinforced with SiC particles with an average size of 20 lm. The chemical composition of the matrix was (in wt.%): Al: 9.3, Zn: 0.7, Mn: 0.23, Si: 0.02, Cu: 0.001, Ni: 0.001, Fe: 0.002, Be: 0.0015, Mg: balance. The six types of investigated samples correspond to six different design fractions of SiC (in vol.%):10, 15, 20, 25, 28,
Fig. 6. Reinforcement content images of (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, and (e) No. 5.
Fig. 7. Young’s modulus images of (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, and (e) No. 5.
Y. Liu et al. / Ultrasonics 81 (2017) 167–173
171
Fig. 8. Shear modulus images of (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, and (e) No. 5.
3.2. Ultrasonic measurement First, to eliminate the effects of interference such as oxide layers or roughness, each sample was sanded to make the upper surface parallel to the lower surface. Second, an experimental set-up, shown in Fig. 4, was used to obtain the ultrasonic signal. An Olympus 5072PR ultrasonic pulse generator/receiver was employed to drive a V313-SU-F1.5 water immersion-focused transducer with a center frequency f = 15 MHz, radius a = 6.35 mm, and focal length F = 38.1 mm. [21] A high-velocity data acquisition card ADLINK PCIe-9852 was employed to obtain the C-scan data, whose sample frequency is 200 MHz. The water path was controlled accurately using the DMC2610 PCI bus six axes motion control card, and a six-degrees-of-freedom motion platform were used to ensure that the transducer is perpendicular to the sample surface. The transducer was moving at the velocity of 4 mm/s with a scanning step of 0.2 mm.Based on Eqs. (5)–(8), zmax = 28.86 mm, f = 3.50 mm, and D = 0.71 lm Hence, the water path was set zmin f þ zmin Þ=2 = 16.18 mm for the experiment. The waveas zf ¼ ðzmax f f
Fig. 9. The error of calculated sound path.
Table 1 Analysis of shear-wave velocity obtained using different methods. Sample no.
vT
1 2 3 4 5
3160.1 3323.3 3408.8 3593.0 3738.2
(m/s)
cT (m/s)
eT /%
3145.6 3240.5 3518.7 3690.5 3860.6
3.51 2.49 3.22 4.75 3.27
and 30. The samples are marked as No. 1, No. 2, No. 3, No. 4, T1 and No. 5, respectively. The samples were obtained via wire cutting with overall dimensions of 15 15 6 mm. The XRD quantitative phase analysis of the samples confirmed the content of the SiC phases. Fig. 3 shows that the samples have only Mg and SiC phases. The volume fractions of SiC (in vol.%) are 10, 14, 17, 25, and 29.
form duration of the transducer is 0:33 lm with a gain of 30 dB, which met the experimental requirements. Fig. 5 shows the average longitudinal and shear wave velocities. The SiC affects the stressed state of the material. Hence, the increase in the SiC reinforcement should considerably modify the ultrasonic wave velocity [13]. Both the velocities increased with an increase in the volumetric fraction of SiC from 10 to 29. Eventually, V, cT , and cL were fitted to obtain the model for evaluating the dual-mode ultrasonic velocities as follows.
V ¼ 112:90 þ 0:0080cT þ 0:017cL
ð15Þ
This model was then used to obtain the C-scanning images of the reinforcement content, as shown in Fig. 6. Fig. 6 shows that the SiC particles were distributed evenly in the samples. The Poisson’s ratio varied between 0.2864 (Mg/10SiC) and 0.2325 (Mg/29SiC), where it slightly decreased with the increasing volume fraction of SiC in MMCs. This implied that the Poisson’s ratios serve to describe the redistribution of electrons along with the bonding process. [22] The Young’s and shear moduli were
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Y. Liu et al. / Ultrasonics 81 (2017) 167–173
Fig. 10. (a) Longitudinal velocity–reinforcement content graph of No. 1–No. 5 and (b) shear velocity–reinforcement content graph of No. 1–No. 5.
Table 2 Analysis of reinforcement content obtained using different methods. Sample no.
V e (vol.%)
V m (vol.%)
eV /%
1 2 3 4 5
10.54 ± 2.31 13.33 ± 2.55 17.80 ± 1.99 23.56 ± 2.99 29.77 ± 1.92
10 14 17 25 29
5.40 4.79 4.71 5.76 2.66
calculated using Eqs. (12)–(14), wherein the densities of No. 1–No. 5 samples were 1.92, 1.93, 2.05, 2.12, and 2.26 g/cm3, respectively. Figs. 7 and 8 show the images of the Young’s and shear moduli. The elastic modulus in each sample was clearly different, implying that the SiC particles helped in strengthening the matrix significantly. This is because the addition of the reinforcement not only helps in increasing the interfacial areas but also helps in refining the matrix grain size [23].
Fig. 11. Images of T1 (a) reinforcement content image, (b) SEM image, (c) Young’s modulus and (d) shear modulus.
Y. Liu et al. / Ultrasonics 81 (2017) 167–173
173
3.3. Effectiveness analysis
Acknowledgements
Because of the effect of the incident angle, the calculated sound path is smaller than the real sound path, which directly results in the error of ultrasonic velocity. Fig. 9 shows the relationship between the transducer radius and the error in the sound path. The error significantly decreases as the transducer radius decreases. The error in the ultrasonic velocity is controlled within 5.35% under the worst condition, wherein the ultrasonic signal comprises the echo generated from the edge of the transducer, and the incident angle reaches the maximum. To validate the present model, the traditional method was used to measure the shear velocity using an Olympus V155-RB transducer. Table 1 lists the shear wave velocity v T . The largest error was only 4.75%. Fig. 10 shows the relationship between the reinforcement content and the velocities, wherein the correlation coefficient of the shear wave velocity is larger than that of the longitudinal wave velocity. It states that the shear wave velocity is more sensitive to the SiC reinforcement than the longitudinal wave velocity, which is in good agreement with the results presented in other studies [13,14]. However, a single ultrasonic velocity evaluation model is inferior to the dual-mode ultrasonic velocity evaluation model, whose correlation coefficient is 0.9917. Table 2 lists the reinforcement contents obtained using different methods. V e is the evaluation result; V m is the result measured using the XRD method regarded as the true values. The maximum error is 5.76%. By comparing the evaluation and true values of the elastic property, it is found that the maximum relative error of the Young’s and shear moduli are 5.84% and 5.85%, respectively. The reinforcement content and Young’s and shear moduli of the sample T1 determined using the destructive method are 27%, 75.2 GPa, and 29.9 GPa, respectively. Fig. 11 shows that the evaluation values are 26.04%, 78.3, and 31.7 GPa, respectively. The results of the evaluation model are closer to the true value and are more stable.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51575541, 5161101582) and State Key Laboratory of Powder Metallurgy, Central South University. The authors would like to express their gratitude to Prof. Kun Yu for providing samples.
4. Conclusion (1) The experimental conditions including the water path and duration time were investigated for an immersion-focused transducer to obtain the longitudinal wave and shear wave velocities simultaneously. A regression equation was developed to relate the reinforcement content of the Mg-based composite with dual-mode ultrasonic velocities. This relationship was used to calculate the Young’s and shear moduli. (2) The ultrasonic experimental results show that both the longitudinal wave and shear wave velocities increased with the increase in the reinforcement content. The shear wave has better sensitivity to the reinforcement content than the longitudinal wave. (3) The shear wave velocity measured using a normal-incidence shear-wave transducer and elastic modulus determined using the destructive method reveal the effectiveness of the proposed method.
References [1] S. Kudela, Magnesium-lithium matrix composites – an overview, Int. J. Mater. Prod. Technol. 18 (2003) 91–115. [2] J.W. Kaczmar, K. Pietrzak, W. Włosin´ski, The production and application of metal matrix composite materials, J. Mater. Process. Technol. 106 (2000) 58–67. [3] C.Y.H. Lim, S.C. Lim, M. Gupta, Wear behaviour of SiC p-reinforced magnesium matrix composites, Wear 255 (2003) 629–637. [4] D.J. Lloyd, Particle reinforced aluminium and magnesium matrix composites, Int. Mater. Rev. 39 (1994) 1–23. [5] X.J. Wang, K. Wu, W.X. Huang, et al., Study on fracture behavior of particulate reinforced magnesium matrix composite using in situ SEM, Compos. Sci. Technol. 67 (2007) 2253–2260. [6] M.R. Krishnadev, R. Angers, C.G.K. Nair, et al., The structure and properties of magnesium-matrix composites, JOM 45 (1993) 52–54. [7] E.W. Nuffield, X-ray diffraction methods, 7(1966) [8] J.J. Wortman, R.A. Evans, Young’s modulus, shear modulus, and Poisson’s ratio in silicon and germanium, J. Appl. Phys. 36 (1965) 153–156. [9] R. Ünal, I.H. Sarpün, H.A. Yalım, et al., The mean grain size determination of boron carbide (B4C)–aluminium (Al) and boron carbide (B4C)–nickel (Ni) composites by ultrasonic velocity technique, Mater. Charact. 56 (2006) 241– 244. [10] P. Palanichamy, A. Joseph, T. Jayakumar, et al., Ultrasonic velocity measurements for estimation of grain size in austenitic stainless steel, NDT and E Int. 28 (1995) 179–185. [11] E. Eren, S. Kurama, I. Solodov, Characterization of porosity and defect imaging in ceramic tile using ultrasonic inspections, Ceram. Int. 38 (2012) 2145–2151. [12] W. Piekarczyk, D. Kata, Methodology for determining material constants of anisotropic materials belonging to the transversely isotropic system by ultrasound method, Ultrasonics 71 (2016) 199–204. [13] A.A. El-Daly, M. Abdelhameed, M. Hashish, et al., Synthesis of Al/SiC nanocomposite and evaluation of its mechanical properties using pulse echo overlap method, J. Alloys Compd. 542 (2012) 51–58. [14] S.S. Kumar, V.S. Bai, K.V. Rajkumar, et al., Elastic modulus of Al–Si/SiC metal matrix composites as a function of volume fraction, J. Phys. D Appl. Phys. 42 (2009) 175504. [15] G.K. Li, M.L. Zhu, L.H. Hao, et al., Method of measuring elastic modulus of material based on water immersion point focusing probe, J. Test Measure. Technol. 28 (2014) 277–281. [16] E. Drescher-Krasicka, J.R. Willis, Mapping stress with ultrasound, Nature 384 (1996) 52. [17] P. Hu, C.M. Kube, L.W. Koester, et al., Mode-converted diffuse ultrasonic backscatter, J. Acoust. Soc. Am. 134 (2013) 982–990. [18] G. Ghoshal, J.A. Turner, B.M. Wilson, Correlation of ultrasonic inspection of bearing components with bearing fatigue life, in: ASME/IEEE/ASCE Joint Rail Conference, vol. 2008, 2008. [19] V.L. de Araújo Freitas, V.H.C. de Albuquerque, E. de Macedo Silva, et al., Nondestructive characterization of microstructures and determination of elastic properties in plain carbon steel using ultrasonic measurements, Mater. Sci. Eng., A 527 (2010) 4431–4437. [20] R.A. Saravanan, M.K. Surappa, Fabrication and characterisation of pure magnesium-30 vol.% SiC P particle composite, Mater. Sci. Eng., A 276 (2000) 108–116. [21] S.Z. Zhang, X.B. Li, H. Jeong, S. Cho, H.W. Hu, Theoretical and experimental investigation of the pulse-echo nonlinearity acoustic sound fields of focused transducers, Appl. Acoust. 117 (2017) 145–149. [22] X. Peng, N. Hu, H. Zheng, et al., Evaluation of mechanical properties of particulate composites with a combined self-consistent and Mori-Tanaka approach, Mech. Mater. 41 (2009) 1288–1297. [23] W.S. Miller, F.J. Humphreys, Strengthening mechanisms in particulate metal matrix composites, Scripta Metall. Mater. 25 (1991) 33–38.
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Evaluating the reinforcement content and elastic properties of Mg-based composites using dual-mode ultrasonic velocities Yu Liu a, Yongfeng Song a, Xiongbing Li a,⇑, Chao Chen b,⇑, Kechao Zhou b a b
School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China
a r t i c l e
i n f o
Article history: Received 12 April 2017 Received in revised form 29 June 2017 Accepted 3 July 2017 Available online 4 July 2017 Keywords: Mg-based composites Reinforcement content Nondestructive characterization Dual-mode ultrasonic velocities Immersive scan Elastic properties
a b s t r a c t Based on the wave-mode-converted principle, an immersion-focused transducer is employed to determine the longitudinal wave and shear wave velocities. The experimental condition is then investigated to obtain the converted shear wave, which is used to analyze the relationship between the reinforcement content and the dual-mode ultrasonic velocities. In addition, the elastic modulus is calculated. Magnesium-based composite samples with different reinforcement contents are manufactured to conduct an ultrasonic experiment, wherein the dual-mode velocities vary with the change in the reinforcement content; the correlation coefficient is 99.17%. An ultrasonic dual-mode velocity model is developed to analyze the distribution of the reinforcement content. By employing the measured values obtained from the destructive method, the largest errors in the reinforcement content and elastic modulus evaluated using the proposed method are found to be 5.76% and 5.85%, respectively. The shear wave velocity determined using a normal-incidence shear-wave transducer reveals the accuracy with which the errors are measured. This method provides an effective tool to nondestructively evaluate the microstructure and elastic properties of Mg-based composites. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Magnesium-based metal matrix composites (MMCs) have a good potential to be applied in aircraft, electronic, and automobile industries owing to their excellent properties such as low weight and good abrasive and creep resistances [1–3]. The reinforcement content is an important parameter significantly affecting the mechanical properties of Mg-based MMCs. Among various reinforcements, SiC is one of the most widely used dispersoids in Mg-based composites. The elastic properties of the materials can be significantly improved by increasing the reinforcement content [4,5]. Krishnadev et al. [6] demonstrated that the elastic properties increase by 48% with the increase in the reinforcement content from 10% to 30%. Hence, it is necessary to determine the reinforcement content and elastic modulus. Generally, microstructural analyses are performed based on metallography, whereas mechanical properties are determined by conducting mechanical tests. The X-ray diffraction (XRD) and X-ray energy dispersive spectroscopy (EDS) methods can be used to visually measure the reinforcement content. However, the process is time consuming; requires high cost; and has low efficiency ⇑ Corresponding authors. E-mail addresses: [email protected] (X. Li), [email protected] (C. Chen). http://dx.doi.org/10.1016/j.ultras.2017.07.001 0041-624X/Ó 2017 Elsevier B.V. All rights reserved.
[7]. The static tension method can be used to determine the elastic modulus by employing the stretching and twisting loads to deform the materials [8]. Thus, the nondestructive testing is an important method for evaluating material properties as it can help in accurately and effectively ensuring the product quality, serviceability, and safety. Based on the changes in the ultrasonic velocities induced by the microstructure, the ultrasonic velocity method can be used to evaluate the reinforcement content, grain size, porosity contents, etc. [9–12]. El-Daly et al. [13] evaluated the reinforcement content of Al-based MMCs using the ultrasonic velocity method. The results indicated that the longitudinal wave and shear wave velocities increased with an increase in the reinforcement content. Based on these velocities, the Poisson’s ratio and Young’s, bulk, and shear moduli were effectively calculated. The longitudinal wave and normal-incidence shear-wave transducers are respectively used to measure the corresponding velocities. Clearly, the two types of ultrasonic velocities cannot be determined simultaneously using only a single ultrasonic transducer. The normal-incidence shearwave transducers are contact-type transducers, requiring indispensable coupling with the material using a strong couplant. Moreover, the scanning image of the shear wave velocity at each point cannot be obtained; thus, the entire material cannot be analyzed [14]. Li et al. [15] proposed a method for measuring the
Y. Liu et al. / Ultrasonics 81 (2017) 167–173
longitudinal and shear wave velocities simultaneously using a focused transducer based on the wave-mode-converted principle. However, the measured velocity of the shear wave is higher because they considered only the longitudinal wave generated from the edge of a transducer can be converted into a shear wave. In addition, the value of the incidence angle is observed depending on experimental result instead of theoretical calculation First, a modified method is investigated based on a method given elsewhere [15]. The formula used to determine the incidence angle is developed by the geometric acoustics. Moreover, the experimental condition is presented for obtaining the converted shear wave. Next, the longitudinal and shear wave velocities are determined using the modified method. The scanning images of the dual-mode velocities are then obtained for the entire sample. Finally, the reinforcement content and elastic modulus of the Mg-based MMC are evaluated.
a
P1
H
C
Fcf 2fa
ð1Þ
L2
P3
T2
T1
D
zf
Q
P2
When ultrasonic longitudinal waves are obliquely incident on a hetero-interface with an angle less than the second critical angle, the converted shear-longitudinal wave (TL wave) and converted shear wave (TT wave) are observed between the first back-wall echo and the second back-wall echo [16,17], as shown in Fig. 1. The TT wave will most likely appear as long as the TL wave exists. Thus, the water path should be optimized to measure the dual-mode ultrasonic velocities. Fig. 2 shows the wave-mode conversion of the TT wave. Suppose L1 is the obliquely incident longitudinal wave with an incident angle of a, the point of incidence is P1 . Accordingly, T 1 is the shear wave with a refractive angle of b; T 2 is the shear wave whose reflective point is P 2 ; and L2 is the longitudinal wave whose refractive point is P3 . When the water path is beyond the maximum, the transducer cannot receive L2 , i.e., the TT wave is absent. In Fig. 2, when the water path reaches the critical value, the points P 2 and D and points P4 and B would overlap. Points P1 and P 3 would be symmetrical about the point C. To calculate the maximum water path, suppose the transducer is focused in the water. The ultrasonic beams transmitted from the focused transducer do not exactly converge at a point, but forms a circular spot in the focal plane. The beam diameter is expressed elsewhere [18]
P4 B
r L1
2. Methods
d ¼ 1:02
O
A
Water
F
168
Sample
Water
Focal Point
d Fig. 2. Schematic of wave-mode-conversion of TT wave.
where a is the transducer radius, F is the focal length, f is the input frequency, and cf is the velocity of water. The radius of curvature of the transducer is given as follows.
r¼
1
cf F ct
ð2Þ
where ct is the velocity of the acoustic lens. Therefore, the incident angle can be written as follows.
a ¼ arctan
a d=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F þ r r 2 a2
ð3Þ
According to the Snell’s law, the refractive angle is expressed as follows.
b ¼ arcsin
cT sin a cf
ð4Þ
where cT is the estimated value of the shear wave velocity in the is given as follows. sample. The maximum water path zmax f
zmax ¼r f
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a H tan b pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðF þ r r 2 a2 Þ r2 a2 þ a d=2
ð5Þ
where H is the thickness of the sample. When the water path is so short that the second front-wall echo appears before the second back-wall echo, the TT wave would also be absent. Thus, the minimum water path zmin is given as follows. f
zmin ¼ 2H f
cf cL
ð6Þ
where cL is the estimated value of the longitudinal wave velocity in the sample. As cL and cT are the estimated values, we select the water path þ zmin Þ=2. as zf ¼ ðzmax f f
Fig. 1. Schematic of ultrasonic A-wave signal.
To avoid the overlap of any two echoes, such as the first backwall echo and TL wave, TL wave and TT wave, and TT wave and second back-wall echo, it is important to obtain an accurate time interval. Hence, the waveform duration D must meet the following conditions:
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Fig. 5. Longitudinal and shear velocities of No. 1–No. 5 samples. Fig. 3. XRD patterns of: (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, and (e) No. 5.
where s1 and s2 are the time intervals of the waves until the two adjacent echoes overlap each other. s1 and s2 are determined when the cross-correlation values y1 and y2 reach the maximum [19].
8 2zf 2zf 2H D H H D > > > cf þ cL þ 2 6 cf þ cL þ cT 2 > > < 2zf 2z þ cH þ cH þ D2 6 c f þ 2H D2 cf cT f L T > > > 2z > > : f þ 2H þ D 6 2zf þ 4H D c c c 2 c 2 f
f
T
(
ð7Þ
L
H H 4H 2H ; cT cL cL cT
ð8Þ
From Eq. (8), we can conclude that bandwidth of the transducer must be controlled strictly. Finally, using the cross-correlation analysis, the longitudinal wave velocity cL and shear wave velocity cT can be obtained as follows.
ð10Þ
1
The waveform duration is subject to the following condition:
D 6 min
R 1 max y1 ¼ 1 B1 ðtÞB2 ðt s1 Þdt R 1 B1 ðtÞB3 ðt s2 Þdt max y2 ¼
cL ¼ 2H=s1
ð9Þ
cT ¼ 2H=s2
Motion control card
where B1 , B2 and B3 are the first front-wall echo, the first back-wall echo and TT wave respectively. Finally, the mean velocities cL and cT are used to develop a model to evaluate the final dual-mode ultrasonic velocities based on the multivariate linear regression equation.
V ¼ b0 þ b1 cT þ b2 cL
ð11Þ
where b0 , b1 , and b2 are the regression coefficients. V is the reinforcement content. Thus, the reinforcement content of each point on the sample can be evaluated using Eq. (11). For an isotropic solid, many studies [13,14,19] have developed empirical relationships to relate the Poisson’s ratio, Young’s, and shear moduli.
Industrial computer
Main control circuit
PCIe-9852 Digital acquisition card
6-DOF motion platform GAIN 30 dB
Probe holder
Transducer Water
Sample
Fig. 4. Schematic diagram of the ultrasonic signal acquisition system.
Olympus 5072R ultrasonic pulse generator/receive
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1 2ðcT =cL Þ2
ð12Þ
2 2ðcT =cL Þ2
E ¼ qc2L
G ¼ qc2T
ð1 þ mÞð1 2mÞ 1m
3. Experiments and results 3.1. XRD analysis
ð13Þ ð14Þ
where m is the Poisson’s ratio, E is the Young’s modulus, G is the shear modulus and q is the density of the sample. The density is measured using the Archimedes principle.
The samples were manufactured using the conventional stircasting technique [20]. The matrix was AZ91D magnesium alloy reinforced with SiC particles with an average size of 20 lm. The chemical composition of the matrix was (in wt.%): Al: 9.3, Zn: 0.7, Mn: 0.23, Si: 0.02, Cu: 0.001, Ni: 0.001, Fe: 0.002, Be: 0.0015, Mg: balance. The six types of investigated samples correspond to six different design fractions of SiC (in vol.%):10, 15, 20, 25, 28,
Fig. 6. Reinforcement content images of (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, and (e) No. 5.
Fig. 7. Young’s modulus images of (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, and (e) No. 5.
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Fig. 8. Shear modulus images of (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, and (e) No. 5.
3.2. Ultrasonic measurement First, to eliminate the effects of interference such as oxide layers or roughness, each sample was sanded to make the upper surface parallel to the lower surface. Second, an experimental set-up, shown in Fig. 4, was used to obtain the ultrasonic signal. An Olympus 5072PR ultrasonic pulse generator/receiver was employed to drive a V313-SU-F1.5 water immersion-focused transducer with a center frequency f = 15 MHz, radius a = 6.35 mm, and focal length F = 38.1 mm. [21] A high-velocity data acquisition card ADLINK PCIe-9852 was employed to obtain the C-scan data, whose sample frequency is 200 MHz. The water path was controlled accurately using the DMC2610 PCI bus six axes motion control card, and a six-degrees-of-freedom motion platform were used to ensure that the transducer is perpendicular to the sample surface. The transducer was moving at the velocity of 4 mm/s with a scanning step of 0.2 mm.Based on Eqs. (5)–(8), zmax = 28.86 mm, f = 3.50 mm, and D = 0.71 lm Hence, the water path was set zmin f þ zmin Þ=2 = 16.18 mm for the experiment. The waveas zf ¼ ðzmax f f
Fig. 9. The error of calculated sound path.
Table 1 Analysis of shear-wave velocity obtained using different methods. Sample no.
vT
1 2 3 4 5
3160.1 3323.3 3408.8 3593.0 3738.2
(m/s)
cT (m/s)
eT /%
3145.6 3240.5 3518.7 3690.5 3860.6
3.51 2.49 3.22 4.75 3.27
and 30. The samples are marked as No. 1, No. 2, No. 3, No. 4, T1 and No. 5, respectively. The samples were obtained via wire cutting with overall dimensions of 15 15 6 mm. The XRD quantitative phase analysis of the samples confirmed the content of the SiC phases. Fig. 3 shows that the samples have only Mg and SiC phases. The volume fractions of SiC (in vol.%) are 10, 14, 17, 25, and 29.
form duration of the transducer is 0:33 lm with a gain of 30 dB, which met the experimental requirements. Fig. 5 shows the average longitudinal and shear wave velocities. The SiC affects the stressed state of the material. Hence, the increase in the SiC reinforcement should considerably modify the ultrasonic wave velocity [13]. Both the velocities increased with an increase in the volumetric fraction of SiC from 10 to 29. Eventually, V, cT , and cL were fitted to obtain the model for evaluating the dual-mode ultrasonic velocities as follows.
V ¼ 112:90 þ 0:0080cT þ 0:017cL
ð15Þ
This model was then used to obtain the C-scanning images of the reinforcement content, as shown in Fig. 6. Fig. 6 shows that the SiC particles were distributed evenly in the samples. The Poisson’s ratio varied between 0.2864 (Mg/10SiC) and 0.2325 (Mg/29SiC), where it slightly decreased with the increasing volume fraction of SiC in MMCs. This implied that the Poisson’s ratios serve to describe the redistribution of electrons along with the bonding process. [22] The Young’s and shear moduli were
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Fig. 10. (a) Longitudinal velocity–reinforcement content graph of No. 1–No. 5 and (b) shear velocity–reinforcement content graph of No. 1–No. 5.
Table 2 Analysis of reinforcement content obtained using different methods. Sample no.
V e (vol.%)
V m (vol.%)
eV /%
1 2 3 4 5
10.54 ± 2.31 13.33 ± 2.55 17.80 ± 1.99 23.56 ± 2.99 29.77 ± 1.92
10 14 17 25 29
5.40 4.79 4.71 5.76 2.66
calculated using Eqs. (12)–(14), wherein the densities of No. 1–No. 5 samples were 1.92, 1.93, 2.05, 2.12, and 2.26 g/cm3, respectively. Figs. 7 and 8 show the images of the Young’s and shear moduli. The elastic modulus in each sample was clearly different, implying that the SiC particles helped in strengthening the matrix significantly. This is because the addition of the reinforcement not only helps in increasing the interfacial areas but also helps in refining the matrix grain size [23].
Fig. 11. Images of T1 (a) reinforcement content image, (b) SEM image, (c) Young’s modulus and (d) shear modulus.
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3.3. Effectiveness analysis
Acknowledgements
Because of the effect of the incident angle, the calculated sound path is smaller than the real sound path, which directly results in the error of ultrasonic velocity. Fig. 9 shows the relationship between the transducer radius and the error in the sound path. The error significantly decreases as the transducer radius decreases. The error in the ultrasonic velocity is controlled within 5.35% under the worst condition, wherein the ultrasonic signal comprises the echo generated from the edge of the transducer, and the incident angle reaches the maximum. To validate the present model, the traditional method was used to measure the shear velocity using an Olympus V155-RB transducer. Table 1 lists the shear wave velocity v T . The largest error was only 4.75%. Fig. 10 shows the relationship between the reinforcement content and the velocities, wherein the correlation coefficient of the shear wave velocity is larger than that of the longitudinal wave velocity. It states that the shear wave velocity is more sensitive to the SiC reinforcement than the longitudinal wave velocity, which is in good agreement with the results presented in other studies [13,14]. However, a single ultrasonic velocity evaluation model is inferior to the dual-mode ultrasonic velocity evaluation model, whose correlation coefficient is 0.9917. Table 2 lists the reinforcement contents obtained using different methods. V e is the evaluation result; V m is the result measured using the XRD method regarded as the true values. The maximum error is 5.76%. By comparing the evaluation and true values of the elastic property, it is found that the maximum relative error of the Young’s and shear moduli are 5.84% and 5.85%, respectively. The reinforcement content and Young’s and shear moduli of the sample T1 determined using the destructive method are 27%, 75.2 GPa, and 29.9 GPa, respectively. Fig. 11 shows that the evaluation values are 26.04%, 78.3, and 31.7 GPa, respectively. The results of the evaluation model are closer to the true value and are more stable.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51575541, 5161101582) and State Key Laboratory of Powder Metallurgy, Central South University. The authors would like to express their gratitude to Prof. Kun Yu for providing samples.
4. Conclusion (1) The experimental conditions including the water path and duration time were investigated for an immersion-focused transducer to obtain the longitudinal wave and shear wave velocities simultaneously. A regression equation was developed to relate the reinforcement content of the Mg-based composite with dual-mode ultrasonic velocities. This relationship was used to calculate the Young’s and shear moduli. (2) The ultrasonic experimental results show that both the longitudinal wave and shear wave velocities increased with the increase in the reinforcement content. The shear wave has better sensitivity to the reinforcement content than the longitudinal wave. (3) The shear wave velocity measured using a normal-incidence shear-wave transducer and elastic modulus determined using the destructive method reveal the effectiveness of the proposed method.
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