Effect of SiC and graphite particulates on the damping behavior of metal matrix composites

Acta metall, mater. Vol. 42, No. 2, pp. 395-409, 1994 Printed in Great Britain

0956-7151/94 $6.00 + 0.00 Pergamon Press Ltd

E F F E C T OF SiC A N D G R A P H I T E P A R T I C U L A T E S O N THE D A M P I N G B E H A V I O R OF M E T A L M A T R I X COMPOSITES J. ZHANG, R. J. PEREZ and E. J. LAVERNIA Materials Science and Engineering, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92717, U.S.A. (Received 12 October 1992; in revised [brrn I6 July 1993)

Abstract--The effect of SiC and graphite (Gr) particulates on the resultant damping behavior of 606l AI metal matrix composites (MMCs) was investigated in an effort to develop a high damping material. The MMCs were processed by a spray atomization and deposition technique and the damping characterization was conducted on a dynamic mechanical thermal analyzer. The damping capacity, as well as the dynamic modulus, was measured at frequencies of 0.1, 1, 10 and 30 Hz over a 30 to 250°C temperature range. The microstructural analysis was performed using scanning electron microscopy, optical microscopy and image analysis. The damping capacity of the 6061 A1/SiC and 6061 A1/Gr MMCs, with two different volume fractions of reinforcements, were compared with that of as-received 6061-T6AI and spray deposited 6061 AI. It was shown that the damping capacity of 6061 AI could be significantly improved by the addition of either SiC or graphite particulates through spray deposition processing. Finally, the operative damping mechanisms were discussed in light of the data obtained from characterization of microstructure and damping capacity.

1. INTRODUCTION

SiC particulate reinforced AI-Cu alloy showed a damping peak at 1318 Hz which was 2.8 times greater than the unreinforced A1 Cu alloy at the same frequency. In related work, Hartman et al. [7] studied damping behavior in the frequency range of 20-200 kHz for SiC and A1203 particulate reinforced 6061 A1 processed by powder metallurgy. Wong and Holcomb [16] studied the damping behavior of SiC and A1203 particulate reinforced A356 and 6061 AI alloys that were fabricated by conventional casting. Rohatgi et al. [17] utilized flake graphite particulates to reinforce AI--Cu-Si alloys by gravity casting and their experimental results showed that the damping capacity of the MMCs was proportional to the volume fraction of graphite particulates. The utilization of graphite particulate in MMCs has been prompted by the high damping capacity of gray cast iron in which the precipitated graphite plays a dominant role [18 21]. However, the addition of graphite particulates to molten AI alloys, under the thermodynamic conditions that are normally present in common casting fabrication techniques often leads to severe reactivity between graphite and A1 [17, 22, 23]. One approach that has been utilized to circumvent this problem is to coat the surface of the graphite particulates with Cu or Ni, thereby avoiding the possibility of interfacial reactions. There are, however, some limitations to the use of this approach, such as the difficulty in coating very fine graphite particulates. Among the processing techniques that are used to fabricate AI/Gr MMCs, spray atomization and deposition processing has been shown to be a promising technology [24--27]. This approach involves spray

The application of high damping materials may eliminate the need for special energy absorbers or dampers to attenuate undesirable noise and mechanical vibration. However, most of the frequently used metals and alloys usually exhibit a low damping capacity and hence, are limited in their application and performance in dynamic structures. Accordingly, investigators have sought to improve the damping capacity of metals and alloys through the use of innovative material processing techniques. With the advent of metal matrix composite (MMC) technology it became possible to modify the damping behavior, as well as other physical and mechanical properties, of metals and alloys by combining them with nonmetallic phases. First, M M C processing provides the possibility of tailoring the resultant damping properties of MMCs by selecting high damping reinforcing materials and varying reinforcement volume fractions and geometries. Second, M M C processing may be effectively utilized to modify the microstructure of metals and alloys, thereby providing the opportunity of introducing sources to dissipate energy in the materials. While fiber reinforced MMCs have been demonstrated to exhibit a comparable damping capacity to their corresponding metal and alloy matrices [1-6], particulate reinforced MMCs have shown promising improvements in damping and other mechanical properties [7-15]. SiC and A1203 particulates, for example, have been used as secondary phases to improve the damping capacity of AI alloys [11-14] with the objective of developing high damping materials. Bhagat et al. [15] reported that a AMM 42/2 E

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ZHANG et aL: DAMPING BEHAVIOROF METAL MATRIX COMPOSITES

atomization of the molten metal, injection of reinforcing ceramic particulates, and deposition of the atomized metal droplets and injected reinforcing particulates. It has been shown that spray atomization and deposition processing possesses several advantages in fabricating MMCs, such as the minimization of deleterious interfacial reactions, the refinement of grain morphology, the increase in solid solubilities, the presence of non-equilibrium phases and the absence of macro-segregation [24-27]. The present investigation was undertaken with the objective of systematically studying the damping capacity and dynamic modulus of 6061 AI MMCs reinforced with SiC and graphite particulates. The MMCs were fabricated using spray atomization and deposition processing. The effects of SiC and graphite particulates on the resultant damping behavior of the MMCs were investigated on the basis of damping measurements conducted on a dynamic mechanical thermal analyzer. The experimental results of the spray deposited MMCs following hot extrusion were compared with those of the as-received commercial 6061-T6 and the spray deposited 6061 AI alloy. Finally, the intrinsic damping mechanisms in two types of MMCs were discussed in light of the microstructural characteristics and damping data. 2. EXPERIMENTAL

2.1. Materials synthesis

The metal matrix utilized in the present study was 6061-T6AI alloy of commercial grade supplied by Alcoa, Pittsburgh, Pa. Chemical analysis revealed that the nominal composition of the alloy is of 1.0% Mg, 0.6% Si, 0.2% Cr, 0.15% Mn, 0.70% Fe, 0.28% Cu, 0.25% Zn, 0.15% Ti and balance in A1 (in wt%). The selection of 6061 A1 as a metal matrix was prompted by the relatively well established understanding of its damping behavior [7, 12, 15= 17, 28]. The ceramic reinforcing particulates used in the present study were single crystal 1200 SiC (ct phase) particulates and 2935 crystalline flake graphite, provided by Superior Graphite Co., Chicago, Ill. Table 1 lists the relevant data of the matrix and reinforcements at ambient temperature. In this table, d denotes the average particulate size, p the density, E the modulus and q the loss factor (damping capacity). Both 6061 AI/SiC and 6061A1/Gr MMCs were synthesized using spray atomization and deposition conducted in an environmental chamber filled with a nitrogen atmosphere as shown in Fig. 1. Inside the chamber, the molten 6061 AI was energetically disin-

tegrated into micrometer-sized droplets by high velocity jets of inert gas (in this case, nitrogen). Simultaneously, the ceramic particulates, carried by a separate flow of nitrogen, were co-injected via two or four nozzles, perpendicular to the outline of the atomization cone. The reinforcing particulates and partially solidified droplets then continued to travel under the combined effects of gravity and drag forces until they impinged on a water-cooled copper substrate. A summary of the experimental variables used in this study is given in Table 2, and a detailed description of this synthesis methodology may be found elsewhere [24-27]. All of the spray atomized and deposited materials were then extruded at 400°C using an area reduction ratio of 16: I to close the micrometer sized pores that are normally associated with spray atomized and deposited materials [34]. Representative specimens for microstructural characterization, volume fraction of reinforcement, and damping measurements were removed by sectioning the deposited and extruded MMCs. The damping specimens are rectangular bars with the dimensions of 1 × 5 × 35 mm.

2.2. Mierostructural characterization

The morphology of both SiC and graphite particulates was examined using scanning electron microscopy (SEM). The SEM analysis was conducted on an AMRAY Model 1645 SEM located at the Westinghouse Science and Technology Center, Pittsburgh, Pa. The SEM samples were polished on PANW synthetic cloth with 1/tm diamond paste and oil lubricant. After polishing, the SEM samples were rinsed using pure ethanol (Fisher No. A407). Grain morphology and particulate distribution in spray deposited 6061 A1 and MMCs were microstructurally analyzed utilizing standard optical metallographic techniques. The samples of the 6061 A1 and MMCs were polished and etched for the grain morphological analysis. The etchant used consists of 2 parts Poulton's reagent, 1 part HNO3 and 2 parts H 20. The size distribution of reinforcing particulates was evaluated using optical microscopy and computerized image analysis on powder samples. The image analysis was accomplished using a Nikon Epiphot optical microscope, an image recorder and a Macintosh IIci computer using an Imageset software. The volume fraction of ceramic reinforcing particulates present in the spray deposited MMCs was determined using chemical dissolution. The dissolution samples were taken from several locations

Table 1. Material data used in the present study Material

d (,am)

p (g/cm3)

E (GPa)

q

Reference

6061 A1 1200 SiC 2935 Gr Graphite

Bulk 3 7 Bulk

2.73 3.20 2.00 2.00

70 300-400 270~90 10-11

0.004 0.001~),005 0.010-0.015 0.013

[29] [30, 31] [32, 33] This work

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DAMPING

BEHAVIOR OF METAL MATRIX COMPOSITES

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Induction coil Crucible Nozzle Atomizer

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Fig. 1. Schematic d i a g r a m s h o w i n g s p r a y a t o m i z a t i o n a n d d e p o s i t i o n processing.

within the deposit adjacent to the damping specimens. The chemical dissolution method involved measuring the mass of M M C samples, dissolving the samples in a solution of 36% HCI for 24 h, followed by filtering to separate ceramic particulates with distilled water and acetone. The mass changes were

Table 2. Processing variables used in spray atomization and deposition Atomization pressure Atomized droplet flight distance Pouring temperature Ratio of metal/gas mass flow rates Injector distance to atomizer Particulate injection angle Particulate injector pressure

1.21 MPa 40 cm 800~C 2.29 30 cm 90 ° 0.24 MPa

carefully recorded during the entire procedure. The volume fraction of the reinforcement was calculated according to the following equation

Vp -- \ P p / / \ P p

Pro/

(1)

where Vv, mp and pp denote volume fraction, mass and density of particulate reinforcement, respectively; m m and Pm are the mass and density of AI matrix, respectively. Three samples taken from areas adjacent to the tested damping specimen within each MMC deposit were used for volume fraction measurements. The volume fraction and size distribution of reinforcing particulates were also confirmed using image analysis.

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2.3. Damping measurements

Material damping is realized, either by the decay of vibration amplitude in free vibration, or by the suppression of resonant amplitude and the phase lag of deformation behind the applied load in forced vibration [2]. Commonly used measures to report damping capacity include loss angle (~b), loss tangent (tan ~b), loss factor (t/), inverse quality factor (Q-I), logarithmic decrement (6) and specific damping capacity (SDC, ~). They are interchangeable with a proper conversion for cases of relatively small damping capacity (tan q~ < 0.1) by the following equation [2, 3, 12, 35] ~b = tan q~ = q = Q - i = 6/n = ~b/21r.

(2)

In this study, the measure of damping capacity utilized is loss tangent, tan ~b. The loss tangent and the dynamic modulus were measured using a dynamic mechanical thermal analyzer (DMTA) from Polymer Laboratories Ltd (Loughborough, U.K.). The D M T A includes an analyzer, a temperature programmer, a Compaq 386 computer and a testing head. All data acquisition and processing were driven by Polymer Laboratories' V5.11 software. A damping specimen, properly installed in the D M T A testing head, was constrained at each end by a clamping bar arrangement, one end being fixed to a rigid frame and the other end being driven by an electromagnetic vibrator via a composite drive shaft. This arrangement caused the specimen to deflect in a fixed-guided cantilever beam configuration. During operation, the electromagnetic vibrator maintained a sinusoidal time-varying force to the driven end of the sample with the corresponding displacement being measured using a non-contact eddy current transducer. The specimen and adjacent hardware protruded into the hot zone of a resistance furnace capable of temperatures of up to 800°C. The resulting sinusoidal force and deflection data were recorded and analyzed by the D M T A to determine loss tangent and dynamic modulus. The calculation of the loss tangent and dynamic modulus by the D M T A is based on the following forced vibration equation [36]

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(3)

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tan ~b = q = k E "

(4)

Considering the dependence of the damping capacity of most metals and alloys on strain amplitude, temperature and frequency, certain experimental conditions were selected for the damping characterizations. In the present study, samples were displaced 64/~m peak to peak at the drive clamp, giving a corresponding maximum surface strain amplitude of 260 × 10 -6 at the fixed end of the D M T A specimen. The furnace temperature was increased at a rate of 2°C/min from 30 to 250°C and was monitored through a platinum resistor adjacent to the test specimen. During the temperature range, the sample was oscillated at four discrete frequencies of 0.1, 1, 10 and 30 Hz in sequence. Sample length measured between clamps was 19.18 mm, although the effective cantilever length was slightly longer due to flexure of the specimen within the clamps. The resulting low modulus readings were compensated with an end correction equation provided by Read et al. [36]. Similarly, damping values were corrected in order to compensate for aerodynamic damping effects on the vibrating samples. 3. RESULTS The 6061 AI/1200 SiC and 6061 A1/2935 Gr MMCs, as well as unreinforced 6061A1, were processed using spray atomization and deposition. Two spray deposited preforms for each of the MMCs were fabricated with two distinct volume fractions of reinforcement. The geometry of the spray processed preforms exhibited a Gaussian distribution with a peak height of 5.0-7.5 cm in the central portion and a diameter of approximately 18 cm for a 2 kg charge of melt. All of the structural characterization studies were performed on material removed from the central portion of the preforms. Table 3 lists the volume fraction and the size of the ceramic particulates for the M M C deposits as determined on the basis of chemical dissolution and image analysis. In this table, Vp denotes the volume fraction of ceramic particulates and d is the particulate size. The size distribution of the particulates, also provided by the suppliers, was confirmed by image analysis. 3.1. Microstructure

where M denotes the vibrating system mass; r/v is the viscous damping term, S ' and S" represent the complex stiffness of the suspension which serve as calibration terms for the system; k is the sample geometry factor; both E', storage or dynamic modulus, and E", loss modulus, refer to the real and imaginary parts of the complex modulus of specimen, respectively [2]; x is deflection at the driven end of the sample at which the external force, Fp sin cot, is applied. The D M T A gives rise to the solution to k E ' and kE". The

Figures 2 and 3 show SEM micrographs of 1200 SiC and 2935 graphite particulates, respectively. As seen Table 3. Volumefraction and size of reinforcingparticulates Deposit Materialsystem d (# m) Vp 1 6061 A1 -0.00 2 6061 AI/1200SiC 3 0.05 3 6061 AI/1200SiC 3 0.10 4 6061 A1/2935Gr 7 0.05 5 6061 A1/2935Gr 7 0.10

ZHANG et al.: DAMPING BEHAVIOR OF METAL MATRIX COMPOSITES

399

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L Fig. 2. SEM micrograph showing surface morphology for SiC particulates,

Fig. 4. SEM micrograph showing the presence of graphite particulates in 6061 A1/2935 Gr MMC.

in Figs 2 and 3, the SiC particulates display a sharply faceted geometry with a clean surface, but the graphite particulates show a more rounded overall geometry with a surface texture indicative of continuous exfoliation. Figure 4 shows SEM micrographs of the 6061 A1/2935Gr MMC with Vp=0.10. From this figure, it is seen that graphite particulates generally exhibit a close contact at the particulate/matrix interfaces with the exception of a small amount of porosity observed at some part of the interfaces. Figure 5 shows the grain morphology of the asdeposited 6061 A1/2935 Gr M M C with Vp=0.05. This figure reveals the presence of a refined equiaxed grain morphology. The average grain sizes for all of the samples studied were in the 8-20~tm range, depending primarily on the location of the sample within the spray deposited material. The grain sizes for 6061 AI/1200SiC and 6061 A1/2935Gr MMCs ranged from 20 to 25/~m. In comparison, the average grain size for the as-deposited 6061 AI was 34 ~tm, and 73/~m for the as-received commercial 6061-T6 alloy. The refined grain morphology characteristics of the spray atomized and deposited materials have also been reported by a number of investigators [24-27, 37]. Furthermore, it has been shown that the grain size of as-deposited MMCs decreases with increasing volume fraction of reinforcement [38].

Another microstructural characteristic associated with the spray deposited materials is the presence of micrometer-sized pores [34]. Density measurements conducted in this study revealed that porosity in the as-deposited MMCs ranged from 5 to 10% in volume. The pores were generally closed after hot extrusion. Figures 6 and 7 illustrate the distribution of SiC and graphite reinforcements in the spray deposited and extruded 6061 AI/1200 SiC and 6061 A1/2935 Gr MMCs with Vp=0.10, respectively. Inspection of Figs 6 and 7 confirms the absence of micrometersized pores in the microstructure of the hot extruded materials. Following hot extrusion, alignment or re-orientation of flake graphite particulates in 6061 A1/2935Gr MMC was evident and this phenomenon is clearly illustrated in Fig. 8. The lack of success in etching the extruded MMC specimens with Vp = 0.10 precluded the measurement of grain size in these materials. However, grain growth in these M M C specimens did not appear to be significant during hot extrusion which involved heating from 25 to 400:C in 30min. This observation is supported by results reported by Gupta et al. [37] and Wu et al. [38]. From the results reported by Wu et al. [38], spray atomized and deposited MMCs exhibited a partially recrystallized grain structure with welldefined subgrains after hot extrusion. Gupta et al.

Fig. 3. SEM micrograph showing surface morphology for graphite particulates.

Fig. 5. Grain morphology of as-deposited 6061 A1/2935 Gr MMC with Vp= 0.05.

400

ZHANG et al.: DAMPING BEHAVIOR OF METAL MATRIX COMPOSITES

Fig. 6. Optical micrograph showing the distribution of SiC particulates in the spray deposited and extruded 6061 Al/ 1200SIC MMC with Vp=0.10.

Fig. 8. Optical micrograph showing the distribution of re-oriented flake graphite particulate along the extrusion direction in the spray deposited and extruded 6061 AI/ 2935 Gr MMC with Vp= 0.10 after hot extrusion.

[37] reported that the grain growth in a spray deposited AI/SiC M M C was from 28 to 35/~m after the specimen had been heat treated 50 min at 400°C.

temperatures for 6061 A1/SiC MMCs and a slight deviation for 6061 A1/Gr MMCs. The damping behavior of the two types of MMCs exhibits an increased frequency dependency with increasing temperature. At temperatures below 100°C, the MMCs appear to be approximately frequency independent over the frequency range used in the present study. Above 100°C, the MMCs become temperature sensitive with the lowest frequency exhibiting the highest damping. In the temperature range of interest, no peak phenomena were observed for the M M C specimens tested.

3.2. Damping capacity

The damping capacity (tan q~) and dynamic modulus (E) data for the five MMCs, as determined by the DMTA, are summarized in Figs 9-12. In these figures, both damping capacity and dynamic modulus curves versus temperature for each frequency were recorded, with the light symbols denoting damping capacity, and the dark symbols denoting modulus for each of the four frequencies. The plots are scaled identically along the damping capacity axis in order to allow direct comparison. At least three samples for each of the materials were tested on the D M T A to verify repeatability. Strain amplitude was preset at e0 = 260 x 10 - 6 and frequencies were set up at 0.1, 1, l0 and 30 Hz. The experimental results reveal that the general trend of modulus with temperature is linear until 150°C for 6061 A1/SiC MMCs and 200°C for 6061 Al/Gr MMCs, followed by a significant deviation from the near-linear negative slope at high

Fig. 7. Optical micrograph showing the distribution of graphite particulates in the spray deposited and extruded 6061 A1/2935 Gr MMC with Vp= 0.1.

4. DISCUSSION Figure 13 shows a comparison of the damping capacity for the four spray deposited MMCs with that of the as-received 6061-T6AI and the spray deposited 6061 AI at 1 Hz over the 30-250°C temperature range. Table 4 lists typical values of damping capacity of the MMCs at 1 Hz and at 50 and 250°C. From Fig. 13 and Table 4, the damping capacity of the 6061 A1/SiC or 6061 AI/Gr MMCs in the spray deposited condition is shown to increase two to three fold over that of as-received 6061-T6 over the measured temperature range. The largest gains were made at high temperature and low frequency for the MMCs. Damping capacity of the MMCs was noted to depend on volume fraction of graphite reinforcement but was relatively independent of volume fraction of SiC particulates. The 6061 AI/Gr MMCs exhibited a much higher damping capacity than that of the 6061A1/SIC MMCs at temperatures below 200°C and have comparable damping capacity to the 6061 A1/SiC MMCs at 250°C. However, associated with the high damping of the 6061 AI/Gr MMCs is a loss in elastic modulus (Table 4). The improved damping capacity of the 6061 A1/Gr and 6061 AI/SiC MMCs is thought to result from the addition of the SiC or graphite particulate reinforcements and the accompanying modification of the

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&AA A

xX

ooO x xxx 6 A && _mMt~r A-e-~A&~xl~J a A6 && A OO{2DO~[:][:]Ol:]ooOOU " a a ~ e =a . X ~al:At~_oooDOOOO

0.01

j~'x x "x xx~"~ oooOoooOoOO 00000 0000 0000000 0 000 00000 000000 0000000 O0 0000000

.

.

.

.

5 '0

.

.

.

1 0' 0

.

.

.

.

.

1 5' 0

.

.

.

.

2 0' 0

.

.

.

.

2""so

T e m p e r a t u r e (°C)

Fig. 13. Comparison of 1 Hz damping capacity for spray deposited MMCs and unreinforced 6061 AI alloy.

graphic defects, such as: a high concentration of twins and refined mobile grain boundaries [39]; a high density of dislocations formed because of the thermal mismatch strains induced by the difference in coefficient of thermal expansion (CTE) between a ceramic reinforcement and a metallic matrix [7, 40-42]; and a large amount of interfaces created between reinforcement and matrix [1]. The intrinsic dissipation of strain energy in metal and alloys typically occurs through a combination of several mechanisms [2-5, 12,35,43]. Among the damping mechanisms that are important in metals and alloys, thermoelastic and microstructural effects (i.e. crystallographic defects) are thought to be the two primary contributors to damping behavior of metallic materials. Thermoelastic damping can be described by the irreversible thermal flow produced in metallic materials under mechanical vibration [4, 12]. Defect damping, according to defectology [44], may be ascribed to internal friction acting on reversible

intrinsic movement of the microstructural defects in crystalline materials under cyclic loading. The defects inside polycrystalline metals and alloys include point defects (vacancies and interstitials), line defects (dislocations), surface defects (grain boundaries and interfaces) and bulk defects (micro-pores and microcracks). Point defect damping is realized by energy dissipation in a region of elastic distortion surrounding a point defect in a crystal under an applied stress. The point defect damping is essentially small relative to other sources of defect damping and therefore it is excluded herein [3, 44]. The dislocations contribute to damping by the motion of vibrating dislocation lines [5], the grain boundaries by their viscous sliding [45], the interfaces by the mobility of the incoherent microstructure at the interfaces [46] and interface slip [47-50], and the micropores by the stress concentration and mode conversion around the pores [34]. The damping capacity in the M M C s is directly related to each of the aforementioned damping mech-

Table 4. Typical values of damping, and modulus of 6061 AI and MMCs at I Hz At 50°C At 250°C Materials As-Rec. 606I-T6 Deposited 6061 6061 AI/1200SiC 6061 AI/1200SiC 6061 A1/2935Gr 6061 AI/2935Gr

V~, --0.05 0.10 0.05 0.10

Tan ~b 0.004 0.008 0.008 0.007 0.010 0.020

E(GPa) 68 69 74 77 69 52

Tan ~ 0.007 0.013 0.039 0.040 0.027 0.040

E(GPa) 61 65 64 68 66 47

404

ZHANG et al.: DAMPING BEHAVIOR OF METAL MATRIX COMPOSITES

anisms in ceramic reinforcement and metal matrix. The following discussion will address the experimental results with particular attention given to the damping mechanisms operative in the microstructure.

4.1. Intrinsic damping of SiC and graphite particulates The resultant damping capacity in composite materials is directly related to the damping capacity of each of constituents. One simple approach that may be utilized to rationalize the resultant damping capacity in particulate reinforced MMCs with increasing volume fraction of reinforcing particulates is to apply the rule of mixtures. Accordingly, the overall damping capacity, qc, would be proportional to the individual damping capacities of the reinforcement, No, and the matrix, qm, multipled by their respective volume fractions, Vp and (1 - Vp), as given by r/~ = qp Vp + qm(l -- Vp).

(5)

SiC is essentially a low damping material with a loss factor in the 0.0012-0.005 range (Table 1). Using this value for SiC particulate and qm = 0.008 for the spray deposited and extruded 6061 A1 at 50°C (Table 4), the application of the rule of mixtures by equation (5) yields a value of 0.0077 for 6061 AI/SiC MMCs with Vp = 0.10. The predicted value is lower than the experimental data for the 6061 A1/SiC MMCs as shown in Table 4. At 250°C, the rule of mixtures also underestimates the resultant damping capacity of the 6061 AI/SiC MMC, suggesting that other damping mechanisms may'be operative for the resultant damping of the 6061 A1/SiC MMCs. It is worth noting that the damping capacity of SiC bulk material is independent of temperature [30]. Therefore, the high temperature damping of the 6061 A1/SiC MMCs is thought to be primarily attributed to the 6061 A1/SiC interfaces and the 6061 AI matrix; these will be discussed in more detail subsequently. Graphite is a relatively high damping material, with a room temperature loss tangent of 0.013 by the DMTA measurement, which is in good agreement with those generally reported in the 0.0104).015 range (Table 1). The damping characteristics of flake graphite are thought to be a factor of the relatively high damping capacity of the 6061 A1/ 2935 Gr MMC observed in the present study. The relatively high damping capacity of graphite has been rationalized in terms of the importance of shear deformation mechanisms in the bulk mechanical behavior of graphite, and the presence of a high density of glissile dislocations. The shear deformation in graphite is attributed to its strong crystalline anisotropy as a result of its hexagonal lattice structure. The anisotropy of graphite facilitates sliding between graphite basal planes which effectively dissipates strain energy during cyclic loading. The structure consists of parallel hexagonal net planes in an ABABA stacking sequence. The strong in-plane covalent bonding and weak Van Der Waals throughplane forces lead to the large degree of anisotropy. In

addition, the basal planes are easily displaced in the in-plane direction when subjected to shear forces. Under cyclic loading, this sliding induces friction losses attributed largely to the dislocation mechanism proposed by Granato and Liicke [5]. This mechanism, based upon the sweeping motion of dislocations from pinning points, is believed to occur in the high concentration of glissile basal plane dislocations found in graphite. For the spray deposited 6061 A1/2935 Gr MMC, using qp = 0.013 for 2935 graphite and qm = 0.008 for the spray deposited and extruded 6061 A1 at 50°C (Tables 1 and 4), equation (5) predicts a value of qc = 0.0085 for the overall damping capacity for 6061 A1/2935 Gr MMC with Vp =0.10. At 250°C, using r/m = 0.013 and qp = 0.013, the predicted overall damping capacity for 6061 A1/2935Gr MMC is 0.013. The predicted values are significantly lower than the experimental results as shown in Table 4. Therefore, the high intrinsic damping of graphite alone, may not be utilized to rationalize the experimental results, again suggesting that other damping mechanisms were also operative in the MMCs.

4.2. Thermoelastic damping This mechanism was originally proposed by Zener [4] based on the fact that energy is dissipated by the irreversible heat flow within a material caused by stress-induced thermal gradients. This thermoelastic coupling effect may become obvious when the material undergoes a heterogeneous deformation [12, 51]. Examples of heterogeneous deformation are bending in beams, such as the DMTA specimens used in the present work, and local stress concentration in heterogeneous materials, such as the particulate reinforced MMCs. In the case of bending loads in a beam, thermoelastic damping is characterized by losses incurred in the irreversible flow of heat from the compression side to the cooler tension side. The thermoelastic damping is related to the thermal relaxation constant, A, and relaxation time, z, by the following equation [4] tan ~b = A 1 + co2z~

(6)

Euct2T0 A- - -

(7)

where

C

and

Cvh: Z-

7r2k

(8)

where Eu is the unrelaxed Young's modulus, ct the coefficient of thermal expansion (CTE), To the absolute temperature, C Vthe specific heat per unit volume, co the angular frequency (co = 2zcf), h the beam thickness and k the thermal conductivity. The CTE, specific heat and thermal conductivity for particulate reinforced MMCs can be predicted using the

ZHANG et al.: DAMPING BEHAVIOR OF METAL MATRIX COMPOSITES equations given by Vaidya and Chawla [52] and Taya and Arsenault [53]. According to the equations in Refs [52] and [53], however, when the volume fraction of reinforcing particulate is low (say, below 0.1), the quantities for a particulate reinforced MMC are comparable to their counterparts of the matrix alloy. Using the relevant thermodynamic data for 6061 A1 (ct = 22 x 1 0 - 6 / ° C , C v ~-- 2.25 x 106 J/°C m 3, k = 222 J/sm°C), given by Bishop and Kinra [51], equation (6) yields tan tk in an order of 10 -5 at f = 1 Hz and over the 30-250°C temperature range for the DMTA specimens (E U = 7 0 G P a , h = 1 mm) used in this work. Thermoelastic damping may also be realized by heterogeneous media such as particulate reinforced MMCs in which local heterogeneous deformation exists because of local stress concentration around the ceramic particulates. Therefore it may be anticipated that thermal gradient induced thermoelastic damping is higher in the particulate MMCs than in the unreinforced alloys. Bishop and Kinra [51] calculated thermoelastic damping for A1 with various inclusion materials including graphite, SiC and A1203 spherical inclusions. They showed that the thermoelastic damping could reach a maximum of 0.024 (in tan ~b) at 2000 Hz for A1/SiC and 0.010 at 1300 Hz for A1/Gr. At frequencies below 100 Hz, however, the thermoelastic damping is small, less than 0.0016 for both materials. Therefore, for the MMC specimens investigated in the present work, where the testing frequencies are less than 30Hz, it is reasonable to assume that the thermoelastic damping in the MMCs due to material heterogeneity does not play a dominant role in the resultant damping of the MMCs. According to equation (6), the thermoelastic damping is frequency dependent and reaches a maximum (thermoelastic damping peak) when o)~ is equal to unity [4]. The peak frequency, i.e. Zener relaxation frequency [4], is determined by 1 f = 27z - 2~zr

(9)

where r is given by equation (8). Using the data for AI given by Bishop and Kinra [51], equation (8) yields = 0.001 s and thus the Zener relaxation frequency for the 6061 A1 MMCs is approximately equal to 160 Hz determined using equation (9). According to the Zener thermoelasticity theory [4], the thermoelastic damping increases with increasing frequency as long as the frequencies are less than the Zener relaxation frequency. However, the measured damping for the unreinforced and reinforced 6061 A1 alloys in this work decreases with increasing frequencies in the testing frequency range which are below the Zener frequency. It is therefore proposed that the frequency dependency of the damping for the 6061 A1 MMCs is not due to thermoelasticity.

405

4.3. Grain boundary damping

Damping associated with grain boundary relaxation, anelasticity or viscosity in polycrystalline metals has been described by K~ [45] and Zener [4]. In polycrystailine metals there exist grain boundaries that display viscous-like properties. The viscous flow at grain boundaries will convert mechanical energy produced under cyclic shear stress into thermal energy, as a result of internal friction. The thermal energy will then be dissipated by the conductivity of metal and heat exchange with the surroundings. The energy absorbed in grain boundaries is dependent on the magnitude of the shear stress and the grain boundary area per unit volume, i.e. grain size. K~ [45] reported that a polycrystalline A1 showed a higher damping than a single crystal A1. The difference of grain boundary damping between the polycrystalline AI and the single crystal A1 became manifest when the testing temperature exceeded 200°C. In the present study, the grain sizes of as-deposited MMCs generally ranged from 8 to 20 #m, compared to the grain size of 73/~m for as-received 6061-T6 AI. The fine grained microstructure may play a partial role in the dissipation of elastic strain energy. This is evident from Fig. 13 that the spray deposited and extruded 6061 AI exhibited a higher damping capacity than that of the as-received 6061-T6 AI at elevated temperatures because of the effects of the grain boundary damping. 4.4. Thermal mismatch and dislocation damping

The contribution of ceramic particulates to the overall MMC damping may also be related to the increase in dislocation density in the metallic matrix as a result of thermal strain mismatch between the ceramic particulates and 6061 A1 matrix during fabrication. Several studies [40, 41, 54] have shown that the dislocation density found in as-quenched, age-hardenable A1 alloys is low, typically less than 10~2m -', but the dislocation density in A1 matrices of ceramic particulate MMCs is on the order of 1013_1014m 2. These dislocations, generated to accommodate the residual thermal mismatch strains associated with the difference between the CTEs of the matrix and the reinforcements, are located primarily near the reinforcement-matrix interface and decrease with increasing distance from the interface [54]. The residual thermal mismatch strain is proportional to the difference between the CTEs of the reinforcement and matrix. The CTE for graphite ranges from - 1.4 to 27 (in units of 10-6°C 1) and 5.0 for SiC, whereas a value of 23 is generally reported for A1 [32]. The difference between the CTEs results in dislocations generated at the interfaces during cooling and solidification of MMCs. Consequently, these become a possible source of high internal friction because of the motion of the dislocations under cyclic loading. According to the Granato--Liicke dislocation theory [5], the internal friction of a material is pro-

406

ZHANG et al.: DAMPING BEHAVIOR OF METAL MATRIX COMPOSITES

portional to the dislocation density present. Material damping is related to dislocations by the following equation given by Granato and Lficke [5, 7, 42]

Q-l=Clexp(-C2~ E0

k

(I0)

E0/

where Q - 1 is the inverse quality factor that is equal to the loss factor (q) and loss tangent (tan 4)) as given in equation (2), and C~ and C2 are material constants and C1 is proportional to dislocation density in matrix. While the measurements of dislocation density for the 6061 AI MMCs are not available at the present time, both C1 and (72 were determined by Perez et al. [55, 56] for the 6061 A1/2935 Gr MMCs by plotting log(Q-IE0) vs l/E0 from equation (10). For the 6061 A1/2935 Gr MMC with Vp = 0.10, C1 and C2 were calculated to be 3.367 × 10 -s and 7.740 x 10 -4, respectively. Using these values along with equation (10), the dislocation damping component for the 6061 A1/2935 Gr MMC with Vp = 0.10 is estimated to be tan 4~ = Q - I = 0.0066 at E0= 260 x 10 -6, compared to the counterpart of 0.0012 for the unreinforced 6061 A1 processed by spray deposition and the hot extrusion.

4.5. Interface damping Interfaces may affect the damping behavior of composite materials because the interface is a twodimensional defect where the crystal structure of the metal matrix is distorted. Updike et al. [9], for example, reported that the presence of graphite fibers enhanced the damping behavior of AI matrix composites, particularly when there were no interfacial reactions at the AI/Gr interface. Furthermore, the work of Bhagat et aL [15] and Rawal and Misra [8] showed that the loss factor of graphite fiber reinforced MMCs increased with the volume fraction of graphite fibers, and in some cases, the damping level of the composites exceeded the damping capacity of both the Al matrix and the carbon fibers. In the case of short fiber reinforced MMCs, the effects of fiber/matrix interface on the overall damping capacity of the MMCs have been ascribed to interface slip at weakly bonded interfaces [47], and to an increased dislocation density in the matrix region near the interfaces due to the CTE mismatch [35]. For the case of particulate reinforced MMCs, the interfacial effects on the damping of the particulate reinforced MMCs may become more manifest due to the heterogeneity and stress concentration as a result of the presence of particulates in the metal matrix. 4.5.1. Interface damping in AI/SiC MMC. In 6061 Al/1200 SiC MMC, there is generally a wellbonded interface between the SiC particulates and the 6061 Al matrix [57]. The effect of the perfectly bonded interface on the damping of particulate reinforced MMCs may be rationalized on the basis of the Schoeck theory, which was originally developed to explain precipitate/matrix interface damping in alloys [46]. In this theory, precipitates are treated as ellip-

soid inclusions in the matrix and the interaction energy between the precipitates and the applied stress is determined on the basis of the Eshelby inclusion theory [58]. Accordingly, precipitates have been found to enhance internal friction when the precipitate/matrix interface is semi-coherent or incoherent. This is thought to be a possible mechanism responsible for internal friction corresponding to the relaxation of interphase boundaries. Based on the Schoeck theory, internal friction is increased by interface relaxation and anelastic strain induced by dislocations in the vicinity of the interface. The internal friction is proportional to changes in volume and shape of the precipitates, volume fraction of the precipitates, and the magnitude of local stress at the precipitate/matrix interface. By inspection of the equations that Schoeck used, the following equation may be used to predict the contribution of interfaces to high temperature damping in particulate reinforced MMCs Q-l

1 8(l-v)

ai(ffl3)i

1

(11)

where Q - I is the inverse quality factor, P13 is the external shear stress, v is the Poisson ratio of the matrix, V is the sample volume, ai is the radius of the oblate spheroid i, and (Pl3)i is the component of pl3 in the plane of the spheroid i which can be relaxed. As a rough approximation, a damping value may be obtained from this equation by assuming that all the spheroidal particulates have the same radius and experience the same shear stress at the interface with a stress concentration factor of 1.5 [59-62], resulting in the simplified expression 4.5(1 - v ) Q-1 _ ~2(2 _- ~ Vp

(12)

where 1 ~ 4~a L

.

(13)

Equation (12) suggests that damping is directly proportional to the particulate volume fraction (lip). For the case of 6061 A1/1200 SiC MMC, the well bonded A1/SiC interface behaves as an incoherent interface similar to that present between the precipitate and matrix in alloys. Accordingly, reversible atomic movement due to diffusion under the applied load is likely to occur in the vicinity of the interface thereby giving rise to an enhanced internal friction. At temperatures above 100°C, the interface effect may become more significant because the metal matrix becomes relatively soft relative to the ceramic particulates and a reversible movement at the interface is likely to occur. Therefore the internal friction at the interface is thought to be thermally activated, and interface damping becomes dominant at high temperatures for 6061 AI/SiC MMC. As a first attempt, equation (12) predicts a value of 0.018 for interface damping that is consistent with the observed

ZHANG et al.: DAMPING BEHAVIOR OF METAL MATRIX COMPOSITES increase in damping for 6061A1/SiC M M C at elevated temperatures. 4.5.2. Interface damping in AI/Gr M M C . The spray deposited 6061A1/2935Gr M M C basically possesses a weakly-bonded interface between flake graphite particulates and 6061 A1 matrix (Figs 2 and 4). The weakly bonded interface may be inferred not only from the graphite particulates showing a surface texture indicative of continuous exfoliation as illustrated in Fig. 2, but also from the presence of a small amount of porosity between the graphite particulates and 6061 AI matrix (Fig. 4). Even in regions of the graphite/A1 matrix interface where there is no porosity present, interfacial bonding is likely to be weak due to the layered surface structure that is present in the flake graphite particulates (Fig. 2). This is in agreement with the other reported observations on the A1/Gr interfaces in graphite particulate reinforced MMCs [63]. On the basis of these considerations, interfacial slip is likely to occur at the interfaces when the D M T A damping samples are in a non-uniform stress state under bending mode. The effect of weakly bonded interfaces on the overall damping capacity of particulate reinforced composites have been analyzed by Nelson and Hancock [47], Kishore et al. [49] and Lederman [50] using the interface slip model. In the interface slip model, interface damping is attributed to the frictional energy loss between particulate and metal matrix under cyclic loading. For the case of weak bonding at the interface, interfacial slip may occur when the magnitude of the shear stress at the interface is sufficient to overcome frictional loads. Hence, the frictional energy loss caused by sliding at the particulate/matrix interface may become a primary source of damping. An analytical treatment on interfacial damping in particulate reinforced MMCs was provided by Lederman [50]. Lederman's analysis on predicting interfacial slip damping in particulate reinforced MMCs was extended from Nelson and Hancock's interfacial slip damping theory for short fiber reinforced composites [47]. According to Lederman's analysis [50], an upper bound of the damping component, ~/i, due to interfacial slip is approximately given by

rh-

3n # a ~ ( E o - E~.t) 2 o 02/E~ Vp

(14)

where # is the coefficient of friction between the ceramic particulate and metal matrix; ¢rr the radial stress at the particulate/matrix interface under the applied stress amplitude a0; E0 the strain amplitude corresponding to a0; E~t the critical interface strain corresponding to the critical interface shear stress rc~t at which the friction energy dissipation begins; Ec the elastic modulus of the MMC; and Vp the volume fraction of the particulates. For a weakly bonded

407

interface, it is assumed that Ecntis much smaller than Eo and therefore, equation (14) is rewritten as 3n ]'/fir ~' = ~ - , ~ o

v~

(15)

or 3/~

rh = ~ - p k V p

(16)

where k is the coefficient of the radial stress concentration at the interface and equal to Gr

k = --.

(17)

(70

In fact, Lederman's model is based on the fact that the damping specimen undergoes residual thermal mismatch stresses or uniaxial stresses. For the case of the damping specimen under bending, the specimen experiences a non-uniform strain state. Hence, only in a section of the specimen can the strain level reach the critical value needed to initiate interface slip at the particulate/matrix interfaces. Accordingly, a correction factor, C, is introduced to equation (16) 3n th = --f C#kVp.

(18)

In order to estimate the effect of interface slip friction on the overall damping of the spray deposited 6061 A1/2935 Gr MMC, the magnitude of the variables used in equation (18) have been carefully selected. Considering the symmetry of the strain distribution inside the D M T A damping specimen, the constant (C) in equation (18) is taken to be 0.5 [43]. The stress concentration factor (k) ranges from 1.1 to 1.3 at the interface between a soft particulate and metal matrix [62, 64] and an average value of 1.2 for k is utilized herein. The friction coefficient (p) of graphite on an AI surface has generally been reported between 0.1 and 0.2 [65-67] and an average value of 0.15 is used herein. Substitution of these values into equation (18) provides an estimate of an interfacial slip damping of 0.0424 for the spray deposited 6061 A1/2935 Gr M M C with Vp = 0.10. This estimation may be used to partially explain the resulting damping of the 6061 A1/2935 Gr M M C with Vp = 0.10 at 250°C. At this temperature, the difference in damping capacity between the 6061 A1/2935Gr MMC with Vp = 0.10 and the unreinforced 6061 A1 alloy is approximately 0.027 (see Table 4). This difference may not be ascribed to the intrinsic damping capacity of graphite and SiC particulates because their contribution to the overall damping of the MMCs is relatively small and their intrinsic damping is temperature independent [30]; it is not contributed by grain boundary damping because both unreinforced and reinforced 6061 AI alloys have comparable grain sizes through spray deposition processing; it is also unlikely to result from thermoelastic damping because there is approximately a similar thermoelastic effect on the resultant damping behavior in

408

ZHANG et al.: DAMPING BEHAVIOR OF METAL MATRIX COMPOSITES

both unreinforced and reinforced 6061 A1 alloys; it is not due to dislocation damping since the CTE mismatch induced dislocation density is reduced at 250°C relative to that present at ambient temperature [42]. Therefore, it is proposed that the difference in damping capacity between the 6061A1/2935Gr M M C with Vp -- 0.10 and the unreinforced 6061 A1 alloy may be attributed to the particulate/matrix interfaces. It is noted that the interfacial slip model overestimates the overall damping capacity of the AI/Gr M M C at room temperature since it yields the same result at elevated temperatures using equation (18). It should be pointed out that the aforementioned interface damping models as given in equation (18) do not take into account the effects of temperature and frequency on damping; therefore, the results predicted by the model should be considered as approximate. 5. CONCLUSIONS The spray deposited 6061 A1/Gr and 6061 A1/SiC MMCs were found to exhibit significant damping gains when compared to as-received 606 l-T6 A1 alloy both at ambient temperatures and at elevated temperatures. Damping capacity of the MMCs was noted to depend on volume fraction of graphite reinforcement but was relatively independent of volume fraction of SiC particulates. The 6061 A1/Gr MMCs exhibited a much higher damping capacity than that of the 6061 A1/SiC MMCs at temperatures below 200°C and have comparable damping capacity to the 6061 A1/SiC MMCs at 250°C. The damping mechanisms associated with AI/Gr MMCs were ascribed to dislocation damping, interface damping and intrinsic damping of graphite particulate at low testing temperatures, and to dislocation damping, grain boundary damping and interface damping at high testing temperatures. The damping mechanisms associated with A1/SiC MMCs are attributed to dislocation damping, interface damping at low testing temperatures, and to grain boundary damping and interface damping at high testing temperatures. Finally, the A1/Gr MMCs exhibited a lower modulus than that of the AI/SiC MMCs. The overall damping of MMCs may be approximately expressed as a summation of the aforementioned damping mechanisms; they are the intrinsic damping of the metal matrix, the intrinsic damping of the reinforcing particulates, and the particulate/ matrix interface damping. Matrix damping is governed by dislocation damping and grain boundary damping. On the basis of the present analysis it is proposed that at relatively low temperatures, say below 200°C, the possible dominant damping mechanisms are intrinsic damping of the reinforcing particulate, matrix dislocation damping, and particulate/ matrix interface damping; on the other hand, at high temperatures, above 200°C, grain boundary gliding

and interface sliding are likely to be responsible for a large portion of the observed damping. Therefore, at ambient temperatures, the damping of 6061 A1/Gr MMCs results primarily from the dislocations, reinforcement/matrix interface and the graphite particulates, while the damping capacity of 6061 A1/SiC MMCs is attributed to dislocations and interfaces. At elevated temperatures, interface damping plays a dominant role in the overall damping of the MMCs studied herein.

Acknowledgements--The authors wish to thank the Office of Naval Research (Grant No. N00014-90-J-1923) for financial support. In addition, the authors would also like to express their gratitude to M. N. Gungor of the Westinghouse Science and Technology Center for providing the SEM micrographs, to L. T. Kabacoff of the Office of Naval Research and C. R. Wong of Naval Surface Warfare Center for their able technical assistance and valuable discussions, to Read W, Stewart of Superior Graphite Co. for providing quality graphite powders, to I. Sauer and Y. Wu of the University of California at Irvine for their assistance with the experimental part of this study.

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