Jianguo WuDepartment of Industrial and

Systems Engineering,

University of Wisconsin-Madison,

3255 Mechanical Engineering,

1513 University Avenue,

Madison, WI 53706

e-mail: wu45@wisc.edu

Shiyu Zhou1

Department of Industrial and

Systems Engineering,

University of Wisconsin-Madison,

3270 Mechanical Engineering,

1513 University Avenue,

Madison, WI 53706

e-mail: szhou@engr.wisc.edu

Xiaochun LiDepartment of Mechanical and

Aerospace Engineering,

University of California, Los Angeles,

48-121G Eng IV,

Los Angeles, CA 90095

e-mail: xcli@seas.ucla.edu

Ultrasonic Attenuation BasedInspection Method for Scale-upProduction of A206–Al2O3 MetalMatrix NanocompositesA206–Al2O3 metal matrix nanocomposite (MMNC) is a promising high performance ma-terial with potential applications in various industries, such as automotive, aerospace,and defense. Al2O3 nanoparticles dispersed into molten Al using ultrasonic cavitationtechnique can enhance the nucleation of primary Al phase to reduce its grain size andmodify the secondary intermetallic phases. To enable a scale-up production, an effectiveyet easy-to-implement quality inspection technique is needed to effectively evaluate theresultant microstructure of the MMNCs. At present the standard inspection technique isbased on the microscopic images, which are costly and time-consuming to obtain. Thispaper investigates the relationship between the ultrasonic attenuation and the micro-structures of pure A206 and Al2O3 reinforced MMNCs with/without ultrasonic disper-sion. A hypothesis test based on an estimated attenuation variance was developed and itcould accurately differentiate poor samples from good ones. This study provides usefulguidelines to establish a new quality inspection technique for A206–Al2O3 nanocompo-sites using ultrasonic nondestructive testing method. [DOI: 10.1115/1.4028128]

1 Introduction

Recently, there has been a growing market for high perform-ance lightweight materials, especially in the automotive, aero-space, and defense industries. Aluminum–copper alloy A206 hasa chemical composition of Al (93.5–95.3%), Cu (4.2–5.0%), Fe(�0.1%), Mg (0.15–0.35%), Mn (0.2–0.5%), and Ti (0.15–0.3%).It offers superior mechanical properties with excellent highstrength at both room and elevated temperature and long fatiguelife [1]. However, due to its long solidification range and the for-mation of a long continuous intermetallic phase, A206 alloy isextremely susceptible to hot tearing in the casting process, whichlimits its widespread applications [1,2].

A206–Al2O3 MMNCs provide a promising solution to improvehot tearing resistance [1]. The A206–Al2O3 MMNCs are fabri-cated by dispersing nanosized Al2O3 particles into the A206 metalmatrix using the ultrasonic cavitation method during the liquidphase and then casting into required solid shape [3–7]. The well-dispersed Al2O3 nanoparticles in A206 work have heterogeneousnucleation agents which could significantly reduce the grain sizeof a-Al and refine the h-Al2Cu network, thus reducing the hottearing susceptibility and enhance the mechanical properties, e.g.,strength and ductility [8].

The amount and distribution of Al2O3 in A206 play a signifi-cant role in grain refinement and eutectic morphology modifica-tion [1,9]. Due to their high surface energy, large surface-to-volume ratio, and poor wettability in liquid, Al2O3 nanoparticlestend to agglomerate and cluster together in the fabrication process[5,9–11], which may limit their effectiveness. The microscopicimages, e.g., the scanning electron microscope (SEM) images, aretypically used to analyze the distribution of Al2O3 particles andthe grain refinement of A206. However, the microscopic imagesare very expensive and time-consuming to obtain. As a result, theinspection of microstructure based on microscopic images cannotsatisfy the quality control needs for the scale-up production of

A206–Al2O3 MMNCs. It is highly desirable to develop a simplerand more economical method for the quality control of the fabri-cation process of A206–Al2O3 MMNCs.

In this paper, we investigate the feasibility of relating the ultra-sonic attenuation with the microstructure of A206–Al2O3

MMNCs for the purpose of quality control. Ultrasonic techniqueshave been widely used for material characterization [12–17]. Inthese techniques, ultrasonic velocity and attenuation are two typi-cal indicators used to evaluate microstructures and material prop-erties, such as density, porosity, elastic constant, and grain size.The variation of ultrasonic velocity with frequency is typicallyvery small in solid (<1%) [18]. Therefore, ultrasonic attenuationis used more frequently than the velocity measurement in charac-terizing solids since it allows a better characterization of themicrostructure [19].

Acoustic attenuation is the decaying rate of the acoustic waveas it propagates through materials. It arises from two loss mecha-nisms: material absorption and scattering. Material absorption isthe conversion of the mechanical energy of the acoustic wave intothermal energy and it usually dominates the acoustic attenuationat low frequencies. Material absorption involves various kinds ofmechanisms [18], including hysteresis absorption, thermoelasticlosses, and thermal conduction. Hysteresis absorption is caused byphysical relaxation mechanism and it typically occurs in singlecrystals, amorphous solids, and especially polymers [20]. It isobserved to be proportional to the frequency [20,21]. Thermoelas-tic absorption is defined as coupling of the thermal and elasticfields created by the propagation of acoustic wave and is presentin almost all materials [18]. The acoustic scattering arises at theboundaries between materials, grains, and inclusions with differ-ent acoustic properties. The total attenuation coefficient is the sumof the acoustic absorption coefficient and scattering coefficient. Inthe low frequency range, the absorption losses dominate theattenuation while at high frequencies, the absorption losses arenegligible and the attenuation is mainly caused by the scatteringlosses.

Although considerable work has been done on the relationshipbetween ultrasonic attenuation and material microstructures, mostof the studies are focused on the single-phase materials where thescattering is mainly caused by the grains with different

1Corresponding author.Contributed by the Manufacturing Engineering Division of ASME for publication

in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript receivedJanuary 29, 2014; final manuscript received July 23, 2014; published onlineNovember 26, 2014. Assoc. Editor: Robert Gao.

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orientations. The attenuation of two-phase systems has also beenstudied where each phase is often modeled as a continuum and thescattering only occurs at the boundary of different phases[19,22–26]. These models match well with experimental resultsfor solid or liquid particles in the liquid continuum. While in thetwo-phase system with both phases are solid, the scattering effectsin the grain boundaries of the same phase may dominate in thetotal attenuation, which makes these models inaccurate. ForA206–Al2O3 MMNCs, the attenuation is much more complexsince there are three phases, the a-Al base phase, h-Al2Cu inter-metallic phase and Al2O3 clusters.

In this research, the relationship between the ultrasonic attenua-tion and the microstructure of A206–Al2O3 MMNCs is investi-gated through experiments and statistical analysis, which providesa useful guideline for the quality control in the manufacturing ofA206–Al2O3 MMNCs. The paper is organized as follows. In Sec.2, the fabrication of the samples and the ultrasonic attenuationmeasurement are introduced. Section 3 first presents the micro-structures of A206 and its nanocomposites and the morphologymodification mechanisms of Al2O3. Then the relationship betweenthe ultrasonic attenuation and microstructures are discussed indetails. The conclusions are presented in Sec. 4.

2 Experimental Procedure

2.1 Sample Preparation. Figure 1 shows the experimentalsetup for ultrasonic processing before casting of A206–Al2O3

MMNCs. It consists of a resistance heating furnace, an ultrasoniccavitation based processing system (Misonic Sonicator 3000) witha niobium probe of 12.7 mm in diameter and 92 mm in length, atemperature control system and a gas protection system. A graph-ite crucible with an inner diameter of 88.9 mm and a height of101.6 mm was used for melting. The ultrasonic probe vibrateswith the operating frequency of 20 KHz and power of 4.0 KW.Due to their low density and poor wettability with A206, Al2O3

particles tend to float on the surface of A206 melt. Therefore, thedouble-capsulate feeding method [8] is used where the Al2O3 par-ticles are wrapped by ultrathin aluminum foils and discharged intothe melt.

About 500 g A206 alloy was first melted in the graphite crucibleunder the protection of argon gas and the temperature was con-trolled to be at 700 �C. Then the ultrasonic cavitation system wasturned on and the c-Al2O3 nanoparticles with a diameter of 50 nmwere added into the molten melt. After all Al2O3 nanoparticleswere added, the ultrasonic cavitation continued for 15 min andthen the ultrasonic probe was lifted out of the melt. After that, themolten melt was heated up to 740 �C and then poured into a steelpermanent mold with a preheated temperature of 400 �C. Total

five samples were fabricated, as shown in Table 1. The castedsamples were cut and polished to 8.5 cm� 8.5 cm� 1.6 cmblocks, as shown in Fig. 2. Note for sample 4, only mechanicalstirring was applied to disperse Al2O3 nanoparticles.

2.2 Attenuation Measurement. Figure 3 illustrates the ultra-sonic attenuation measurement process using the spectral ratioanalysis technique [27–29]. The attenuations were measured usingthe Olympus Epoch 1000 series NDT device with two dual ele-ment transducers working in pulse-echo mode: transducer D785-RP with diameter of 6 mm and nominal central frequency of 2.25MHz, and transducer MTD705 with diameter of 3.8 mm and nom-inal central frequency of 5 MHz. The transducer was coupled tothe largest surface of samples (thickness 1.6 cm) using couplantglycerin with acoustic impedance of 2.42� 105 g/(cm2�s). The firstand the second back wall echoes S1ðtÞ and S2ðtÞwere extractedfrom the measured signals using a rectangular window. Note thatin Fig. 3 there is a time shift for S1 tð Þ and S2ðtÞ.

The frequency spectra were obtained by performing the fastFourier transform on the extracted echoes. The spectra S fð Þ canbe expressed as [27,30,31]

S1 fð Þ ¼ RbottomD f ; 2dð ÞS0ðf Þ exp �2a fð Þdð Þ exp i 2pft� 2dk fð Þð Þð ÞS2 fð Þ ¼ RtopR2

bottomD f ; 4dð ÞS0ðf Þ exp �4a fð Þdð Þ� exp i 2pft� 4dk fð Þð Þð Þ (1)

where a fð Þ is the attenuation coefficient, S0ðf Þ is the source spec-trum, Rtop and Rbottom are the acoustic reflection coefficients forthe top surface and bottom surface, respectively, k is the wavenumber, t is the traveling time, d is the thickness of the sample,and Dðf ; zÞ is the diffraction coefficient [32]. Dðf ; zÞ is given as

D f ; zð Þ ¼ 1� exp � i2ps

� �J0

2ps

� �þ iJ1

2ps

� �� �(2)

where J0 and J1 are the cylindrical Bessel functions ands ¼ 2pz=kr2 with r being the radius of the transducer.

Fig. 1 The experimental setup for ultrasonic processing

Table 1 Details of fabricated samples

Sample ID Sample Al2O3 (wt.%) Ultrasound (min)

1 A206 pure 0 02 A206 pure 0 153 A206–Al2O3 1% 154 A206–Al2O3 5% 05 A206–Al2O3 5% 15

Fig. 2 A representative casted sample

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The compressive wave velocity (6320 m/s) for Al material is usedto calculate the wave number.

The attenuation can be calculated using Eq. (1) as

a fð Þ ¼ 1

2dln

S1

S2

��������� ln

D f ; 2dð ÞD f ; 4dð Þ

��������þ ln RtopRbottom

�� ��� �(3)

Note that the unit of the calculated attenuation is Nepers/mmusing Eq. (3), which equals 8.686 dB/mm. The reflection coeffi-cient Rbottom � 1 and Rtop can be approximated using the formula[12]

Rtop ¼Z2 � Z1

Z2 þ Z1

(4)

where Z1¼ 2.42� 105 g/(cm2 � s) and Z2¼ 17.1� 105 g/(cm2 � s)are the acoustic impedances of glycerin and aluminum, respec-tively. Since the spectrum with large deviation from the centralfrequency has low accuracy, about �6 dB bandwidth is selectedsuch that only the center 50% of the frequency range is used tocalculate the attenuation.

3 Experimental Results and Analysis

3.1 Microstructures and Morphology ModificationMechanism. Figure 4 shows the micrographs of the pure A206alloy and A206–1 wt.%Al2O3 nanocomposite in as-cast formtaken at random positions of the samples. For the pure A206 alloy,there are large dendritic primary a-Al phases surrounded by con-tinuous h-Al2Cu intermetallic phases. These h-Al2Cu phases accu-mulate along the grain boundaries of the primary a-Al phases withthe morphology of long continuous network. For theA206–1 wt.% Al2O3 nanocomposites, the morphology of the pri-mary a-Al phases is changed from the large dendritic structures tosmall equiaxed crystals. Besides, the h-Al2Cu phases becomethinner and much less continuous. It should be noted that the

ultrasonic processing for the pure A206 has almost no influenceon the microstructure. Choi et al. [1] found that the average grainsize for pure A206 with ultrasonic processing is slightly reducedcompared with pure A206 without ultrasonic processing.

The polarized-light micrographs of the pure A206 alloy andA206–1 wt.%Al2O3 MMNCs are shown in Fig. 5. The averagegrain size for the primary a-Al phases of the pure A206 is about160 lm measured using the linear intercept method. Comparedwith pure A206, the average grain size for A206–1 wt.%Al2O3 issignificantly reduced by almost 50%. It indicates that the Al2O3

nanoparticles work as heterogeneous nucleation agents and thuscould noticeably reduce the grain size of a-Al and refine theh-Al2Cu network.

The mechanisms for the formation of continuous network ofthe eutectic h-Al2Cu phase in the pure A206 and the morphologymodification by Al2O3 in A206–Al2O3 nanocomposites are wellstudied [1,3,8,33]. For the pure A206 alloys, the primary a-Alphases will first nucleate and grow to large dendritic structure inthe solidification process. Due to the high supercooling of the h-Al2Cu phase nucleation, the Cu solute will be pushed out of a-Alphases into the remaining liquid phase and accumulates betweendendrite arms and adjacent dendrites. When the Cu contentincreases to the eutectic composition (33%Cu), the h-Al2Cu phasestarts to nucleate and grow into a long continuous eutectic micro-structure in-between the a-Al dendrites.

For the A206–Al2O3 nanocomposites, the formation mecha-nism of the eutectic phase is modified with the existence of Al2O3

nanoparticles. Similarly, the Cu solute and the Al2O3 particles arepushed to the remaining liquid in the formation of the primary a-Al phases. The concentrated Al2O3 particles have good nucleantpotency and could serve as effective nucleation sites for h-Al2Cuto nucleate and grow before the remaining liquid reaches theeutectic composition. The depletion of Cu due to the formation ofh-Al2Cu will, on the other hand, enrich the content of Al aroundthe h-Al2Cu phases and thus form a-Al phases to block the growthof long h-Al2Cu phases. Therefore, the Al2O3 nanoparticles caneffectively refine both a-Al phases and h-Al2Cu phases, and thus

Fig. 3 Illustration of the attenuation measurement using spectral ratio technique

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reduce the hot tearing susceptibility and enhance the materialstrength and ductility.

3.2 Relationship Between the Acoustic Attenuationand Microstructures

3.2.1 Non-uniformity of Acoustic Attenuation. Figure 6 showsthe ultrasonic attenuations as functions of frequency measured at25 randomly selected locations using the transducer D785-RP of2.25 MHz as nominal frequency for each casted sample. Note thatzero-padding is used as a frequency interpolation method in the

discrete Fourier transform to increase the number of observationswithin the selected bandwidth. From this figure we can clearly seethat there are large variations for the measured attenuation at eachfrequency for the first four samples while for sample 5A206–5%Al2O3 the variation is much lower. Figure 7 shows theultrasonic attenuation measured at 25 randomly selected locationsusing the transducer MTD705. Similarly, the variations of theattenuation among different locations are very large for the firstfour samples, especially the sample A206–5%Al2O3 without ultra-sonic processing. While for the sample A206–5%Al2O3 withultrasonic treatment (UT), the attenuation is quite uniform.

Fig. 4 Optical micrographs of as-cast pure A206 and A206–1 wt.%Al2O3 MMNCs with 15 minultrasonic processing

Fig. 5 Polarized light micrographs of as-cast pure A206 and A206–1 wt.%Al2O3 MMNCs with 15 min ultrasonicprocessing

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There are three types of inherited uncertainties in the ultrasonicmeasurement system itself that may lead to large variation,namely, the couplant thickness between the sample and trans-ducer, the reflection or transmission coefficient due to differentcoupling conditions, and the electronic noises. To determine ifthese factors are significant in our experiments, we measured theattenuation of sample 2 at 10 randomly selected locations witheach location measured 10 times. The results are shown in Fig. 8.From the results we can clearly see that the variation of the attenu-ation at the same location is negligible compared with the varia-tion across different measurement locations. It indicates that thelarge nonuniformity of the attenuation is mainly due to the varia-tion in microstructures of the samples.

This nonuniformity of ultrasonic attenuation is quite similar tothe phenomenon of large anisotropies of the acoustic backscatter-ing found in titanium alloys [34–37]. In these alloys (e.g., Ti6242,Ti–6Al–4V [38–40]), there exist microtextures or colonies ofcrystallites sharing a common crystallographic orientation over along range. The formation of long microtextures due to the prefer-ence of certain orientations directly results in the plastic anisot-ropy and thus large inhomogeneities of the backscattering orultrasonic attenuation along different acoustic paths. For example,Mukhopadhyay et al. [36] measured the nonlinear ultrasonic(NLU) parameters at different locations of b heat treated near atitanium alloys under different cooling rates. The slow cooling ratetends to produce microtexture structures while fast cooling rateresults in fine acicular a structure with random orientation in theprimary b phase. Their results showed that the variance of NLUparameter was significant for the specimen with slowest coolingrate and the variance decreased with increasing cooling rate.

The nonuniformity of the acoustic attenuation in A206/A206–Al2O3 can be explained in a similar way. Three main sour-ces may cause the nonuniformity of attenuation: the primary a-Al

phase, the h-Al2Cu phase, and the cluster of Al2O3 nanoparticlesin the A206–Al2O3 MMNCs. In the pure A206 with/without ultra-sonic processing, the primary a-Al phase exhibits large dendriticstructures with grain size up to several hundred micrometers, asshown in Figs. 4 and 5. Typically the orientations of these dendritesare not randomly distributed due to the preference of certain crys-talline orientations, e.g., the heat flow direction, in different loca-tions. Besides, the h-Al2Cu phase along the grain boundaries existsin the morphology of long continuous network. The interfacesbetween the a-Al phase and the h-Al2Cu phase are quite anisotropicalong different acoustic paths. Since the difference of acousticproperties between a-Al and h-Al2Cu are much more significantthan that between a-Al grains with different orientations, the acous-tic nonuniformity is mainly caused by the h-Al2Cu network.

For the A206–5%Al2O3 nanocomposites with ultrasonic proc-essing, due to the enhanced nucleation by evenly distributedAl2O3 nanoparticles, both the grain size of the primary phase andthe long continuous h-Al2Cu phase are significantly reduced,which makes the material much more isotropic. Figure 9 showsthe optical micrographs of the A206–5 wt.%Al2O3 nanocompo-sites with ultrasonic processing, from which we can clearly seethat the h-Al2Cu network is totally broken and the boundaries ofthe primary phase are much more difficult to recognize.

For the A206–5 wt.% Al2O3 nanocomposites without ultrasonicprocessing, the Al2O3 particles agglomerate together and form bigclusters (Fig. 10), which could significantly reduce their effective-ness in refining grain sizes. Besides, without ultrasonic process-ing, the Al2O3 nanoparticles or clusters may not be evenlydistributed in the nanocomposites, which may make the materialeven more anisotropic. For the A206–1%Al2O3 nanocomposites,there still exists long h-Al2Cu phase, though less continuous andthinner. Therefore the nonuniformity is still notable comparedwith A206–5 wt.% Al2O3 nanocomposites.

Fig. 6 Ultrasonic attenuation as function of frequency measured at multiple random locations using transducerwith nominal central frequency 2.25 MHz: (a) sample 1, pure A206 without ultrasonic processing; (b) sample 2, pureA206 with ultrasonic processing; (c) sample 3, A206 1 1%Al2O3 1 ultrasonic processing; (d) sample 4,A206 1 5%Al2O3, no ultrasonic processing; (e) sample 5, A206 1 5%Al2O3 1 ultrasonic processing

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3.2.2 Quantification of the Nonuniformity in UltrasonicAttenuation. To quantitatively describe the nonuniformity, we usethe variance in the ultrasonic attenuation and build a model toestimate it as follows. Denote aij as the attenuation of the jth loca-tion under the frequency fi and it is given as

aij ¼ li þ �ij (5)

where li is the mean attenuation at frequency fi and �ij is theattenuation bias for the jth location at frequency fi. Assume that �ij

follows independent and identically distributed (i.i.d.) normal dis-tribution. �ij � iid Nð0;r2Þ. It is reasonable to assume i.i.d. nor-mal distribution since at different measuring locations theattenuation at a specific frequency is random and at a specificlocation, the attenuation at different frequencies is somehow inde-pendent in many cases when the frequency increment is large.The unbiased estimator for the mean li and variance r2 can becalculated as

l̂i ¼1

m

Xm

j¼1

aij (6)

br2 ¼ S2 ¼

Xn

i¼1

Xm

j¼1

aij � l̂i

� �2

nðm� 1Þ (7)

where n and m are the number of frequencies (no zero-padding)and number of measuring locations at each frequency,respectively.

Figure 11 shows the estimated variance of the ultrasonic attenu-ation measured using these two transducers. It clearly shows thatsample 4 (A206þ 5%Al2O3, no ultrasonic processing) has thehighest variances while sample 5 (A206þ 5%Al2O3, ultrasonicprocessing) has the lowest variances for both transducers. Sample3 has the second lowest variance of the attenuation. It is consistentwith the discussion above that sample 5 has the most uniformstructure and it is followed by sample 3. For sample 4, due to the

Fig. 8 Ultrasonic attenuation of the pure A206 with ultrasonicprocessing (sample 2) measured at 10 random locations witheach location measuring 10 times using the transducer D785-RP

Fig. 7 Ultrasonic attenuation as function of frequency measured at multiple random locations using transducerwith nominal central frequency 5 MHz: (a) sample 1, pure A206 without ultrasonic processing; (b) sample 2, pureA206 with ultrasonic processing; (c) sample 3, A206 1 1%Al2O3 1 ultrasonic processing; (d) sample 4,A206 1 5%Al2O3, no ultrasonic processing; (e) sample 5, A206 1 5%Al2O3 1 ultrasonic processing

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unevenly distributed Al2O3 particles and formation of large Al2O3

clusters, the microstructure becomes the most inhomogeneous. Inaddition, the variances for the first three samples in Fig. 11(a) aremuch lower than in Fig. 11(b), indicating that at low frequencies,the ultrasonic attenuation is more isotropic. This result is similarto Han’s theoretical result [35] that at high frequencies, the

backscattering is much more anisotropic. For sample 1 and sample2, there is almost no difference in the variance in Fig. 11(a) andthe former is a little lower than the latter in Fig. 11(b).

From the discussion above we know that the nonuniformity ofthe acoustic attenuation can provide insight on the microstructuresof A206/A206–Al2O3 nanocomposites. When there exist longcontinuous intermetallic phase and large dendrites, the variance issignificant. Therefore, in the scale-up production, the estimatedvariance can be used as an indicator to inspect the quality ofA206–Al2O3 nanocomposites.

Specifically, suppose we have a good sample with evenly dis-tributed Al2O3 and well refined microstructures, and a target sam-ple to be inspected. We can construct a hypothesis test based onthe estimated variances as follows. The null hypothesis (H0) andthe alternative hypothesis (H1) are defined as

H0 : r22 � r2

1

H1 : r22 > r2

1

where r21 and r2

2 are the attenuation variances for the good sampleand the target sample, respectively. If the null hypothesis isaccepted, then the target sample can be determined as a good sam-ple. On the other hand, if the null hypothesis is rejected and thealternative is accepted, then the target sample is deemed as a poorsample. The estimated variances for the good sample and the tar-get sample are S2

1 and S22, respectively. Then we have

Fig. 9 Optical micrographs of A206–5 wt.% Al2O3 nanocomposites with ultrasonic processing treatment

Fig. 10 SEM image of A206–Al2O3 nanocomposites showingbig Al2O3 clusters

Fig. 11 The estimated variance of the acoustic attenuation measured using (a) transducerwith nominal central frequency 2.25 MHz; (b) transducer with nominal central frequency5 MHz

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S22=r

22

S21=r

21

� F n2 m2 � 1ð Þ; n1 m1 � 1ð Þð Þ (8)

where ni and mi are the number of frequencies and number ofmeasuring locations for good sample (i¼ 1) and the target sample(i¼ 2). The test statistic is defined as

R ¼ S22

S21

(9)

The critical value for the test with significance level a0 (upperbound of type I error, typically select 0.05) is given asF1�a0 n2 m2 � 1ð Þ; n1 m1 � 1ð Þð Þ, namely, the ð1� a0Þ-th quantilefor the F distribution with freedom n2 m2 � 1ð Þ and n1 m1 � 1ð Þ.The null hypothesis H0 can be rejected if

R > F1�a0 n2 m2 � 1ð Þ; n1 m1 � 1ð Þð Þ (10)

In practice, 1 wt.% Al2O3 nanoparticles are sufficient toimprove the A206–Al2O3 nanocomposites to reach the desiredmaterial properties [1,8]. Suppose we select sample 3 as the refer-ence sample with acceptable properties. n1 ¼ n2 ¼ 3 andm1 ¼ m2 ¼ 25 in the frequency range 2.0–2.5 MHz. The criticalvalue with a0 ¼ 0:05 is 1.4656. Then if S2

2 > 1:4656S21 ¼ 0:0023,

the null hypothesis can be rejected. From Fig. 11(a) we can seethat samples 1, 2, and 4 have variance larger than 0.0023. In thequality inspection we can treat them as poor samples. The testingresults are the same if we use the attenuation data in the frequencyrange 4.5–6 MHz. Note that the critical value in Eq. (10) is specifi-cally related to the selected frequency range and the number ofmeasuring locations.

3.2.3 Frequency Dependency of Acoustic Attenuation.Besides the attenuation variance, the mean attenuation also highlydepends on the microstructures and it is also used to characterizethe microstructures. In this section, the frequency dependency ofthe attenuation for both absorption and scattering mechanisms wasfirst introduced and then used to interpret the experimental results.

As mentioned in Sec. 1, the attenuation can be split into twoparts, the absorption loss and the scattering loss. The main absorp-tion mechanisms include the thermoelastic losses and thermal con-duction. For the thermoelastic losses can be classified into twotypes: interparticle and intraparticle thermoelastic absorption. Theintraparticle thermoelastic absorption ate1 can be expressed as [18]

ate1 �2p ES � ETð Þ

ES

f f01

f 2 þ f 201

(11)

where ES and ET are the elastic moduli under adiabatic and iso-thermal conditions, respectively, f is the acoustic frequency andf01 is the frequency of the maximum attenuation given as

f01 �p2

va2CV

(12)

where v is the thermal conductivity of the particle and a is the par-ticle size or grain size and CV is the specific heat at constant vol-ume. The interparticle thermoelastic absorption ate2 is given as [18]

ate2 �Ra CP � CVð Þ

CV

f f02

f 2 þ f 202

(13)

where Ra is the anisotropy factor, CP and CV are specific heat atconstant pressure and volume. Here f02 is given as

f02 �3p2

va2CV

(14)

The thermal conduction absorption atc has similar dependence onf and can be given as [18]

atc ¼ pV2

V20

� �MS �MY

MT

� �f f03

f 2 þ f 203

(15)

where V is the acoustic velocity at the current frequency, V0 is thevelocity at zero frequency, MS and MT are the combinations of theelastic constants under adiabatic and isothermal conditions, andf03 is the frequency where atc reaches maximum and it is given as

f03 ¼1

2pCVV2

v

� �MS

MT

(16)

The scattering coefficient as depends on the ratio of the grain orinclusion size a to the wavelength k and the functional depend-ence of scattering losses on frequency can be expressed as [14,41]

as /

a3 � f 4; Rayleighregion2pa

k 1

a � f 2; Stochasticregion2pa

k� 1

1

a; Diffusiveregion

2pa

k 1

8>>>>>><>>>>>>:

(17)

Typically the scattering is of the Rayleigh type when k > 8 � 10a[18]. Based on the absorption and scattering equations above, theidealized attenuation coefficient may have the shape shown inFig. 12, where there are three regions: the increasing regioncaused by the absorption loss before f0 (denoted as region I), thedecreasing region after f0 (region II), and the increasing regiondominated by the scattering loss (region III). It will be used toexplain the attenuation results of the A206/A206–Al2O3 nano-composites as follows.

Figure 13 shows the average ultrasonic attenuations of thesefive samples measured using these two selected transducers. In thefrequency range of 2–2.5 MHz, the attenuation of the pure A206with/without UT decreases with increasing frequency, which cor-responds to region II in Fig. 12 and indicates that the absorptionlosses dominate the attenuation in this low frequency range. Simi-lar decreasing trend of attenuation has also been reported on thecement-based materials in the low frequency range [22]. As forthe scattering loss, since the wavelength is about 2.5 mm–3.16 mm(wave speed 6320 m/s), there may exist both Rayleigh scatteringand stochastic scattering.

Fig. 12 Idealized attenuation coefficient identifying absorptionand scattering dominant regions based on theoretical models

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For both A206–1%Al2O3 and A206–5%Al2O3 nanocompositeswith UT, the attenuation increases with frequency. One possiblereason is that as the grain size decreases, f0 increases sincef0 / ð1=a2Þ as described in Eqs. (12) and (14). The frequencyrange lies in the region I of Fig. 12 and the absorption increaseswith the increasing of frequency. The attenuation ofA206–1%Al2O3 is higher than A206–5%Al2O3 with UT. The pos-sible reason is that a large amount of Al2O3 particles increases theabsorption losses. For these two samples, the Rayleigh scatteringdominates due to the significant reduction of grain sizes. ForA206–5%Al2O3 without UT, the attenuation is much more com-plex due to the clusters of nanoparticles and the attenuation isessentially flat.

In the frequency range of 4.5–6 MHz, the attenuation for allsamples increases with increasing frequencies, as shown in Fig.13(b). In this frequency range, the attenuation is dominated by thescattering losses (region III in Fig. 12) and the absorption lossesmay be negligible. The A206–5%Al2O3 with UT has the lowestattenuations while the pure A206 w/o UT have the largest attenua-tions in the high frequency range. The attenuations ofA206–1%Al2O3 with UT and A206–5%Al2O3 without UT liebetween the two extreme cases. The results are consistent withwhat we expected since the attenuations are dominated by thescattering along the grain boundaries at high frequency range andincreasing the grain size could increase the scattering effects.

4 Conclusions and Discussions

In this research, we proposed a new method to evaluate themicrostructures of MMNCs using ultrasonic nondestructive detec-tion methods. We have two main findings in this paper: (1) due tothe large primary dendrites, long continuous intermetallic phaseand unevenly distributed Al2O3 nanoparticles, the acoustic attenu-ations will be nonuniform at different locations of the same sam-ple of A206–Al2O3 MMNC. As a result, the variance of theacoustic attenuation could be used as an indicator of the micro-structure of MMNCs. A statistical hypothesis test based on theestimated variance is constructed and through this test, we can tellthe quality of microstructure refinement of the A206–Al2O3

MMNCs. (2) The functional form of the average attenuation atdifferent frequencies is also highly related with the microstruc-tures of MMNCs. For the pure A206, the attenuation functiondecreases with increasing frequencies at low frequency rangewhere the absorption mechanism dominates the attenuation losses.

For the A206–Al2O3 nanocomposites, the average attenuationincreases with frequencies in the low frequency range. In the highfrequency range, the attenuation curves for all samples haveincreasing trend and the samples with smaller grain sizes havelower attenuations due to the reduced scattering losses. Theseresults provide useful insight and promising tools on using ultra-sonic nondestructive testing techniques to examine the quality ofA206–Al2O3 nanocomposites.

There are still some open issues with this research direction.First, the measuring accuracy can be improved by using trans-ducers with wider bandwidth and using immersion method. Inaddition, the relationship between the ultrasonic attenuation andthe grain size can be quantitatively constructed using transducerswith higher frequencies. At higher frequencies, the absorptionlosses could be neglected and the frequency dependence of theultrasonic attenuation could be mainly determined by Eq. (17).Second, in the analysis method used in this paper, a summary sta-tistic, the variance, of the attenuation is used to differentiate themicrostructure of the MMNCs. Although proven to be effective,the specific functional form of the attenuation function withrespect to frequencies contains more information and may providemore quantitative insights to the microstructure of the materials.We will investigate this problem using functional data analysistechniques in the future.

Acknowledgment

We are very thankful to Jiaquan Xu, Yi Sun, and Dr. LianyiChen for kind help in the sample fabrication and taking micro-scopic images. We also appreciate the financial support from theNational Science Foundation (grant number 0926084) and theTechnology Innovation Program from National Institute of Stand-ards and Technology.

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