J Mater Sci (2012) 47:2573–2582 DOI 10.1007/s10853-011-6080-9

Investigating the vibration damping behavior of barium titanate (BaTiO3) ceramics for use as a high damping reinforcement in metal matrix composites T. A. Asare • B. D. Poquette • J. P. Schultz S. L. Kampe

•

Received: 26 July 2011 / Accepted: 24 October 2011 / Published online: 19 November 2011 Ó Springer Science+Business Media, LLC 2011

Abstract We have examined factors that affect the vibration damping behavior of the ferroelectric ceramic barium titanate (BaTiO3) by measuring its low frequency (0.1–10 Hz) damping loss coefficient (tan d) using dynamic mechanical analysis. In monolithic BaTiO3, tan d was found to increase with temperature up its Curie temperature (TC), beyond which the damping capability exhibited a sharp drop. The abrupt drop as temperatures increase beyond TC has been attributed to the disappearance of ferroelastic domains as the crystallographic structure of BaTiO3 transforms from tetragonal to cubic. At temperatures below TC, the damping coefficient is further shown to increase with decreasing frequency of the imposed vibration, and in microstructures with a high degree of tetragonality and large domain densities. Data further indicate that tan d values tend to decrease with the number of cycles that are imposed; however, initial values can be restored if the material is allowed to age following loading.

T. A. Asare Special Metals Corporation, New Hartford, NY 13413, USA B. D. Poquette GE Healthcare, Milwaukee, WI 53219, USA J. P. Schultz Aeroprobe Corporation, Blacksburg, VA 24060, USA S. L. Kampe (&) Department of Materials Science & Engineering, Michigan Tech, Houghton, MI 49931, USA e-mail: [email protected]

Introduction A material that combines good mechanical properties and a high damping capacity is attractive for structural applications where the detrimental effects of unmitigated mechanical vibrations can lead to reduced service lifetimes. Structures subjected to uncontrolled cyclic stress may fail by premature fatigue at applied stresses far lower than the yield strength of the material. In response, several vibration control solutions have been devised to suppress mechanical vibrations and prolong the life of structures. These include selecting materials with high inherent vibration damping abilities or by the use of externally attached dampers. Unfortunately in the former regard, most structural alloys do not show appreciable levels of intrinsic vibration damping capability since the mechanisms and microstructural features responsible for favorable damping tend to scale inversely with mechanical stiffness, and by a common correlation, the strength characteristics of the material. This dilemma is visually reinforced in a table presented by Sugimoto [1] that maps specific damping index versus tensile strength for common structural metals, showing that increasing damping capacity is typically associated with decreasing tensile strength. As a consequence, structural damping has historically been addressed with strategies that tend to maintain an independence between features or approaches that provide good damping behavior from those strategies associated with improved mechanical performance. An extreme example of the independent approach is the use of external elastomeric dampers applied to structural-bearing metallic members for the sole purpose of vibration suppression. Obviously, such design-based solutions have large implications with respect to cost, weight, and system efficiency. Similarly, a microstructural-based equivalent might be that exemplified by

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gray cast iron, notoriously effective in applications requiring good damping characteristics. In this article, the damping benefit has been attributed to the presence of the graphitic flakes and the creation of interface associated with their presence with the iron matrix [2]. Unfortunately, however, the graphitic flakes are also responsible for inarguable compromises in material toughness and ductility relative to the iron or steel matrix alone. This necessitates similar compromises with respect to structural versus damping capabilities of the material system. Metal matrix composite (MMC) strategies offer an alternative opportunity to independently select multiple components or constituents to create a customized material system [3–5]. In doing so, it is possible to identify reinforcements and microstructures capable of providing benefits that simultaneously enhance both the structural and intrinsic (microstructural-based) vibrational suppression characteristics. However, traditional high-modulus structural ceramics typically incorporated as reinforcements within structurally capable MMCs are unlikely to provide significant direct damping benefit. These materials exhibit very low intrinsic vibration damping capacity and consequently contribute only marginally to the overall vibration attenuation of the composites beyond the indirect benefits associated with the creation and influence of interface. Alternatively, reinforcements comprised of functionally active materials, such as shape memory alloys, magnetostrictives, piezoelectrics, or ferroelectrics, may be capable of providing both damping and structural benefits, in the manner of a multifunctional material [6]. Ferroelectric ceramics such as barium titanate (BaTiO3) and lead zirconate titanate (PZT) exhibit highly favorable vibration damping capacity, attributable to an anelastic strain response of ferroelastic domains to externally applied stress [7–13]. Thus, if a ferroelasticcapable ceramic is used to reinforce a metal matrix, it is conceivably capable of providing both strengthening, via mechanisms attributable to discontinuous-reinforced or dispersion-strengthened composite strategies, and a direct passive damping benefit. Poquette and coworkers have evaluated the damping capabilities of particulate ferroelastic ceramic-reinforced metal matrix composites (FR-MMCs), and have verified and quantified the damping benefit for bronze-based metallic systems at increasing loadings of unpoled polycrystalline BaTiO3 [7]; these data are partially summarized in Fig. 1. Here, the high damping capacity observed in the FR-MMCs is attributed to load transfer from the matrix to the reinforcement that, in turn, stimulates ferroelastic domain reorientation in response to the applied stress. The degree to which domain reorientation occurred in these experiments, and was subsequently recovered when loading was removed, was quantitatively estimated using in situ neutron

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0.02 0.015 0.01 (Cu-Sn) + 45 v% BaTiO (Cu-Sn) + 30 v% BaTiO

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Fig. 1 Damping coefficient as a function of temperature for BaTiO3 reinforcement within Cu–10Sn (bearing bronze) matrices. Damping capability is shown to decrease as the temperature increases beyond the Curie temperature of the BaTiO3 reinforcement. 90% confidence intervals are indicated. Data from [7]; reprinted with permission

scattering experiments that monitored the crystallographic domain switching in the composite during cyclic loading. It is noted that the BaTiO3 reinforcements were not poled since doing so directly within the as-processed metallic composite matrix is not possible due to the metal’s inability to sustain an electric field, and since any poling before MMC fabrication is lost due to the temperatures experienced during processing. In this article, we provide further insight into the damping behavior and potential of unpoled polycrystalline BaTiO3 as a multifunctional reinforcement within structural metallic matrices. While the effectiveness of dispersing BaTiO3 within a metallic matrix as a means to suppress damping has been demonstrated, microstructural optimization with respect to its potential contribution towards enhancing structural-based property development remains a challenge. For example and as shown by several investigators, the ferroelastic behavior of BaTiO3 tends to diminish as its particle or grain size becomes dimensionally smaller [14–17]. Thus, the loss of ferroelasticity with decreasing particle size presents opposing benefit vectors when attempting to couple damping enhancements to strengthening improvements in the manner of a multifunctional material design strategy. Recognizing the strong influence of reinforcement size and microstructure on strengthening potency, we have characterized the damping dependencies of BaTiO3 in its monolithic form with respect to its particle or grain size, reversibility in cyclic loading, and to aging treatments that serve to restore microstructural changes that occur during loading. This information serves to not only provide additional characterization of the damping characteristics of BaTiO3, but also supports its eventual incorporation as an effective reinforcing entity within metallic or ceramic matrix composites in a form appropriate for multifunctional property development.

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Experimental procedure Summary of experimental approach In this study, the particle size dependency associated with ferroelastic behavior is examined for monolithic forms of BaTiO3 procured initially in both ‘‘coarse’’ and ‘‘fine’’ sizes. In the latter instance, characterization both prior to, and following, powder densification via sintering is performed. In the former, tetragonal BaTiO3, received initially in the form of relatively large (millimeters in size) pieces, was comminutively reduced in size, and the associated reduction in tetragonality with decreasing particle size monitored. In parallel, BaTiO3 procured in the form of fine powder (2 lm average diameter) was compacted and sintered to larger bulk sizes and the degree of tetragonality similarly monitored as a function of increasing grain or particle sizes. Damping characteristics of the resulting sintered BaTiO3 were evaluated using dynamic mechanical analysis (DMA) and correlated to the degree of BaTiO3 tetragonality, number of imposed cycles, and subsequent aging treatments conducted to evaluate the reversibility of the damping effects. Specific details of the procedure are given below. Sample preparation and characterization Two different variants of BaTiO3 material were procured (Sigma Aldrich, St. Louis, MO, USA) as starting materials for this study. The first consisted of relatively coarse pieces, nominally 99.99% pure, ranging in size from approximately 3–12 mm in largest dimension. The second variant was obtained as nominally 99.995% pure BaTiO3 powder of an average particulate diameter of 2 lm. A Perkin Elmer (Waltham, MA) DSC 7 differential scanning calorimeter was used to monitor phase changes of the as-received samples. Here, the presence of a phase transformation upon heating through the Curie temperature of BaTiO3 (approx. 125 °C) is indicative of the tetragonal to cubic equilibrium congruent transformation; similarly, lack of the transformation provides evidence that the metastable cubic form of BaTiO3 is the predominant crystal form in the as-received form and at ambient temperatures [16]. Based on these observations and measurements, it was confirmed that the coarse variant was delivered in the equilibrium tetragonal phase form, and the fine powder as a metastable cubic—the latter presumably consistent with the observed particle size effects noted previously. The particle size dependency on the ferroelastic capability of BaTiO3 was quantified by evaluating the tetragonality of the BaTiO3 as the particle size of the coarse variant decreased, and as the particle size of the fine variant increased as a consequence of the sintering treatment. For

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the former, the coarse 3–12 mm pieces were processed by crushing in a glass mortar, mixed with ethanol, and wet sieved into size distributions associated with ?50/-120, -120/?200, -200/?325, -325/?500, and -500 mesh sizes. The sieved fractions were each dried in an oven at 105 °C for 24 h and the particle size distribution determined using a HORIBA Instruments (Ann Arbor, MI) LA-700 laser scattering particle size distribution analyzer. X-ray diffraction (XRD) patterns of samples taken from the sieved powder and sintered disks were collected on a Panalytical powder diffractometer using Cu-Ka radiation source with nickel filter and Xpert Data (Oldenzaal, Netherlands) collection software which was used to filter out the Cu-Ka 2 diffraction peaks. Diffraction patterns for BaTiO3 were collected at 2h angles from 20° to 85°, at room temperature. For each size distribution established, {002} and {200} diffraction peaks were quantified by fitting to a Lorentz function. From this fit, the c/a ratio was estimated as the ratio of planar spacing as obtained from the ratio resulting Bragg diffraction angles: c df002g sin hf200g ¼ ¼ a df200g sin hf200g

ð1Þ

The 2 lm powder was processed into bulk form by dispersing in isopropyl alcohol in a plastic bottle and milling for 24 h using zirconia grinding media. The slurry was subsequently dried in an oven at 80 °C for 24 h. The dried powder was then used to prepare green BaTiO3 disks by 2-stage compaction using a uniaxial press at 100 MPa and cold isostatic press at 207 MPa. Final consolidation of the disks was achieved by sintering in air at temperatures of 1000, 1250, and 1450 °C, each for 2 h, to obtain BaTiO3 monoliths with different grain sizes and morphologies. A sintered disk was approximately 25 mm in diameter and 3-mm thick. The degree of tetragonality was similarly evaluated using the method described above using Eq. 1, and evaluated as a function of sintering temperature. The microstructure of polished samples sectioned from the sintered disks was examined using a LEO (Carl Zeiss, Inc., Thornwood, NY) field emission scanning electron microscope (SEM). The samples were metallographically prepared by grinding using silicon carbide papers of grit size 240, 400, and 600, respectively, followed by a final polishing step using 0.05 lm colloidal silica, and then etched using an acid mixture consisting of 95% HCl and 5% HF.

DMA Prismatic-beam samples with respective length, height, and base dimensions of 25 9 3 9 1 mm were machined from

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sintered BaTiO3 disks. The damping loss coefficient, tan d, was determined using a TA Instruments (Wilmington, DE) DMA model Q800 loaded in three point bending mode with a beam span of 20 mm. The strain at yield was initially determined in preliminary testing, and all subsequent damping capacity measurements were then performed at maximum strain values below the determined yield strain. Based upon these initial measurements, a mean outer (maximum) mid-span strain of 0.01% with a cyclic strain amplitude of 0.008% was imposed in displacement-control mode. Tan d was measured as a function of temperature (ambient through 200 °C), vibration frequency (0.1, 1, and 10 Hz), and number of imposed cycles (up to approximately 36,000).

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Results Microstructure of the BaTiO3 The differential scanning calorimeter (DSC) profiles of the as-received BaTiO3 samples are shown in Fig. 2. These data indicate a strong room temperature presence of tetragonal BaTiO3 for the coarse, 3–12 mm particles, as evident by the distinct tetragonal (ferroelastic) to cubic (paraelectric) endotherm that occurs at the Curie temperature, TC—at approximately 126 °C in the present case. The 2 lm powder, on the other hand, does not exhibit evidence of a phase transformation over the temperature range examined. The latter confirms that the equilibrium tetragonal form of BaTiO3 is not present, or present only to a marginal degree [16], in the fine powder form, qualitatively consistent with previous studies that have documented the size influence on its crystallographic stability. The standard Cu-Ka XRD pattern of tetragonal BaTiO3, provided in Fig. 3, shows a split peak representing the {002} and {200} peaks at an approximate 2h-angle of 45° (i.e., 44.85° and 45.38° [14]). The {200}/{002} doublet was used to calculate the c/a ratio, and is used as a quantitative measure to compare the tetragonality of BaTiO3 processed under differing conditions and resulting in differing sizes. Figure 4 shows and an example Lorentz fit of the doublet peaks; based on this fit, 2h information was obtained and the c/a ratio was determined in the manner of Eq. 1. XRD data for the 2 lm BaTiO3 powder that has been subsequently densified by sintering is shown in Fig. 5. These data indicate that increasing sintering temperatures lead to the presence of well-defined tetragonal doublet {200}/{002} peaks, especially for sintering temperatures of 1250 °C and above. The tetragonality is quantified in Fig. 6, showing the c/a ratio (computed in the manner of Eq. 1) as a function of sintering temperature. As indicated,

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Fig. 2 Differential scanning calorimetry (DSC) scans (relative energy per mass vs. temperature) for as-received BaTiO3 samples. Samples obtained as 3–12 mm coarse granules exhibited an endotherm at approximately 126 °C, indicative of the tetragonal to cubic transformation. BaTiO3 obtained in the form of fine powder did not show evidence of the transformation, indicating that the 2 lm powder was received in the form of a metastable cubic

Fig. 3 The standard Cu-Ka X-ray diffraction pattern of tetragonal BaTiO3

higher tetragonality values are associated with higher sintering temperatures, with a significant increase in the c/ a values for samples sintered at 1250 °C and above when compared to the as-received powder and samples sintered below 1200 °C. The reduced tetragonality at sintering temperatures of 1200 °C and lower reflect the lack of {002} tetragonal diffraction and is further indicative of a suppression of the equilibrium, tetragonal form of BaTiO3. Representative microstructures of three sintered variants are provided in Fig. 7. Shown are bulk microstructures after sintering at 1000, 1250, and 1450 °C, each for 2 h.

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1.011

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Fig. 6 Ambient temperature c/a ratio versus sintering temperature for material pressed and sintered from fine powder. Tetragonality values typical of the equilibrium room temperature form are re-established for larger grain size; these evolve as a consequence of higher sintering temperatures

Fig. 4 Lorentz fit of {002} and {200} diffraction peaks

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Fig. 5 A segment of the X-ray diffraction (XRD) trace, showing the evolution of the {200}/{002} tetragonal doublet peak for BaTiO3 in the form of fine powder in the as-received form, and following densification processing at the indicated sintering temperatures

an apparent reduced number of domains relative to the sample sintered at 1450 °C. The c/a ratio for the initially coarse BaTiO3, similarly computed using Eq. 1, which was subsequently reduced in size from its as-delivered size of 3–12 mm pieces, is shown in Fig. 8. As stated above, this material was procured in the tetragonal form, as confirmed by a c/a ratio approaching 1.010 in its as-received form. However, as its particle size is reduced via comminution, its tetragonality (c/a ratio) is reduced to a value approaching approximately 1.001 for particle sizes on the order of 1 lm. As shown, the decrease in tetragonality is gradual through a reduction in size to approximately 50 lm (-325 mesh), but decreases precipitously at sizes less than this value. These data, coupled with those in Figs. 5 and 6, serve to confirm that the tetragonality of BaTiO3 exhibits a first-order dependency on particle size. Mechanical damping of BaTiO3

For the 1000 °C sample, a largely inhomogeneous microstructure is revealed, with evidence of the original powder boundaries visibly retained. In this instance, the average grain size appears to be similar to the as-received particle size. The SEM image for the sample sintered at 1250 and 1450 °C show relatively large grains with well-defined domain structures, as revealed by the distinctive herringbone-patterns which occur within the boundaries of the grains. There is negligible difference between the grain sizes of these two samples, approximately 20 lm in each case. However, the sample sintered at 1250 °C shows an increased presence of regions of micro-porosity (the roughened texture on the micrographs) between grains, and

Figure 9 shows damping loss coefficient, tan d, as a function of temperature (measured at 1 Hz) for three bulk BaTiO3 variants produced by sintering the fine powder temperatures of 1200, 1250, and 1450 °C. As shown, tan d exhibits a maximum as the Curie temperature, TC, is approached, and then drops off abruptly as temperatures are increased beyond TC. Below TC, the tan d data are observed to be dependent on the temperature at which the BaTiO3 was sintered, with higher damping capabilities associated with higher sintering temperatures. The low tan d values above TC are attributed to the loss of ferroelastic damping and is coincident with the temperature associated

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Fig. 8 c/a ratio versus average BaTiO3 particle size, for material received in the form of large 3–12 mm granules and subsequently reduced by comminution to the average sizes shown

BaTiO3 samples below TC is dominated and distinguished by differences in domain morphology as it evolves during sintering, and as further influence by the temperature at which the sintering occurs. Tan d measured as a function of temperature at excitation vibrational frequencies of 0.1, 1, and 10 Hz is shown in Fig. 10, as obtained from samples sintered at 1350 °C. Within this frequency range, tan d decreases with increasing frequency below TC. Above the TC, there is no discernable dependence of tan d on frequency. Figure 11 shows the decay of tan d as the number of vibrational cycles for a BaTiO3 sample is increased, tested at 1 Hz and up to 36,000 cycles of excitation. Initially, there is a sharp decrease in tan d, especially during the first

Fig. 7 Microstructure of BaTiO3 sintered at a 1200 °C, b 1250 °C, and c 1450 °C

with the transformation from the ferroelastic-capable tetragonal form of BaTiO3 to the paraelectric cubic form, and the associated disappearance of the ferroelastic domain structure. In this temperature range (above TC), there are no significant differences in the tan d values resulting from the differing sintering temperatures utilized. From these observations, we conclude that the vibration damping in

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Damping loss coefficient, tan· δ

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Fig. 9 Damping loss coefficient (tan d) versus temperature, for BaTiO3 densified from fine powder by sintering at the indicated temperatures

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dielectric constant of BaTiO3, and permanent polarization observed if poled [12, 13, 18]. The loss in tan d can, however, be fully restored if the previously tested and/or aged BaTiO3 sample is heated above the TC.

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Fig. 10 Damping loss coefficient (tan d) versus imposed vibration frequency for BaTiO3 fine powder densified by sintering at 1350 °C

5,000 cycles of excitation. As cycling increases, the tan d appears to saturate at a value corresponding to approximately half of the initial value recorded. Figure 12 shows that the decay in tan d that occurs as a function of lifetime (i.e., number of cycles) can be restored by allowing the BaTiO3 to age. Shown in Fig. 12 are the tan d measurements as a function of number of cycles at 1 Hz from Fig. 11; included are data obtained from the same sample following 2 and 48 h of room temperature aging, and also following a thermal treatment conducted at temperatures in excess of the TC. The decrease in tan d that occurs during extended cycling is partially recovered when the BaTiO3 sample is evaluated following various time intervals after the initial test. The partial recovery in tan d is due to the gradual re-orientation (aging) of irreversible domains with time, which is identical to decrease in

Damping loss coefficient, tan· δ

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Fig. 11 Damping loss coefficient (tan d) versus number of cycles for BaTiO3 fine powder densified by sintering at 1350 °C

Figures 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 collectively confirm previous observations that BaTiO3 in its equilibrium tetragonal form provides superior damping capability relative to that observed if present in the metastable cubic structure. Figures 5, 6, 7, and 8 further indicate that the equilibrium tetragonal form of BaTiO3 will be suppressed at smaller particle (alt granule or powder) or grain sizes in preference to the cubic form. The particle size dependence has been explained by noting that the energy required for a BaTiO3 particle to achieve global charge neutrality (depolarize) via the creation of reoriented domains increases as the particle size decreases [14, 15]. Thus, below some critical particle size, depolarization is alternatively achieved through a crystallographic transformation to the metastable, non-polar cubic form. In dense polycrystalline BaTiO3, a similar effect is observed with respect to grain (i.e., crystallite) size, but with an additional destabilizing component attributable to misfit strains that occur that oppose the creation of charge-compensating domains [15]. A systematic evaluation of particle size versus unit cell tetragonality, in the manner of Figs. 6 and 8, quantifies and provides insight into the trade-off associated with the strength- versus damping-based size effect. In this study, tetragonality is shown to abruptly increase somewhere between 2 lm as-received particle size and the as-sintered 20 lm grain size, as per Fig. 8. Several researchers have quantified the critical particle size associated with the tetragonal to cubic destabilization and the associated loss of ferroelasticity. While there is generally little agreement among the specific values reported due likely to variabilities in processing methods utilized and exact composition, it is generally accepted that the transition occurs as particle size decreases below approximately 1 lm, with several studies reporting critical sizes less than 0.2 lm. Such sizes are within the range capable of providing effective strengthening for volume percentages typical of a composite (e.g., for percentages greater than 1%, for example) by way of dispersion-hardening and/or particulate strengthening mechanisms. Figure 9 shows that increasing sintering temperature results in higher damping capabilities. This behavior is explained by the fact that the microstructure of the samples sintered at higher temperatures (for example, at 1450 °C) consist of well-defined grains containing a relatively large number of domains relative to the samples sintered at

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Fig. 12 Damping loss coefficient (tan d) versus number of cycles following various aging scenarios. Data marked as ‘‘first run’’ correspond to the data given previously in Fig. 11. The data for (b) represents the same data as (a), but is provided to show higher resolution for the early cycles. Initial values of tan d increase, relative to final values obtained from the initial run, for 2-h and 48-h room temperature aging treatments. Full restoration of tan d occurs for thermal treatments that exceed the Curie temperature of the BaTiO3

temperatures of 1250 °C and below. Further, the 1250 °C sample exhibited porous regions that were devoid of any defined ferroelastic domains. Since the relative magnitude of tan d has been associated with domain activity, it is reasonable to deduce that dense large grain ferroelectric ceramics will show better damping behavior than porous and fine grain material. Figure 10 demonstrates that the damping benefit in BaTiO3 is frequency and temperature-dependent; specifically, showing that damping increases exponentially with increasing temperature up to the Curie temperature, and with decreasing activation frequency. Damping capability abruptly decreases and becomes temperature-invariant once the Curie temperature is exceeded, concurrent with the phase transition from tetragonal to cubic form and the associated extinction of the ferroelasticity domain structure. These data confirm that the value of the tan d is

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enhanced by the presence of the ferroelastic domains, specifically by their reversible crystallographic reorientation that occurs during cyclic loading. The data in Fig. 10 further suggests that the domain reorientation relies on a time-dependent, thermally activated rate process within the temperature range they are present, and/or that the reversibility of the domain reorientation is frequency dependent. In the former instance, the increasing tan d values with decreasing frequency reveals that the resonant frequency applicable to the operative thermally activated mobile defect is being approached [18, 19] (i.e., higher tan d values at frequencies less than 0.1 Hz), or that it exists somewhere between 1 and 0.1 Hz (i.e., the maximum tan d occurs between these frequencies). The uncertainty originates from the inability to resolve the exact frequency associated with the maximum tan d value from data generated only at the three frequencies utilized in Fig. 10. It is

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also conceivable, especially in the absence of a welldefined resonant frequency, that an extrinsic effect associated with the ability of the DMA unit to respond to the strain control set-points could be frequency dependent (e.g., at higher frequencies, actual maximum and/or minimum strain may either under- or over-shoot the set-point). Given the magnitude of the frequency effect on tan d shown in Fig. 10, however, it is unlikely that such testing artifacts represent more than a small portion of the effect observed, if present at all. In Fig. 11, the decrease in tan d with number of cycles could be explained by the relative presence of reversible and irreversible domain switching in the BaTiO3 ceramic. The initial drop in tan d can be attributed to the activation and subsequent exhaustion of irreversible ferroelastic domains. Saturation of the irreversible domain switching occurs at about 2,000 cycles, after which a steady state damping mainly due to reversible domain activity is reached. Irreversible domain switching of PZT and BaTiO3 has been observed and characterized in experiments conducted by Pojprapai et al. [8], Forrester et al. [10], and by Ma et al. [20]. Interestingly, a time-dependent recovery of the decrease in tan d was observed in this study when a sample previously subjected to long periods of vibration cycles was retested after 2 and 48 h, as shown in Fig. 12. Here, it is noted that some of the decay in tan d that occurs initially (after first run) is recovered when the sample was retested after 2 h. This is manifested by the higher starting value of tan d for the retest, relative to the saturated tan d value obtained during the first run. The recovery in tan d is even more significant when the same sample is allowed to age for 48 h before a retest. Further, retesting the sample after a heating excursion through the TC and cooling to room temperature results in a nearly full recovery of the initial tan d response. The mechanism responsible in the recovery of the drop in tan d with aging time is likely common to that which has been long observed as responsible for the degradation of certain properties of ferroelectric and piezoelectric ceramics over time. For instance, it is well established that the dielectric constant and permanent polarization of BaTiO3 is strongly time- and temperature-dependent [18]. The most common explanation for aging in ferroelectric ceramics is attributed to the gradual change in domain wall orientation over time as a means to reduce (via creep) residual stresses that initially develop as a consequence of space-constrained domain reorientation, and as a means to minimize polarization energy. Attempts to associate the rate at which aging occurs to a specific microstructural or lattice defect have suggested that diffusion of oxygen vacancies represents a likely rate-limiting phenomena in the ability of domain walls to reorient of move [18, 19] and/or creep. Such kinetic effects will likely affect a

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damping capacity measurement that relies on the presence and mobility of domain walls. In this regard, as the applied stress causes individual domains to switch orientations, internal residual stresses will likely result. The timedependent recovery in tan d can therefore be similarly attributed to the gradual domain wall motion to relieve the residual mechanical stress imposed on the sample during testing. Finally, it is noted that other types of functional materials, i.e., shape memory alloys [21] and magnetostrictive materials [22], are also capable of exhibiting high inherent damping capabilities [23, 24] and similarly offer potential as multifunctional composite reinforcement [25–35]. Mechanistically, the damping characteristics of these materials are similar in that energy dissipation accompanies stress-activated twinning (shape memory), or the activation of non-180° domain wall motion (magnetostrictive). In all instances, these events lead to a hysteretic inelastic strain resulting from a cyclic (forward–reverse) application of stress characteristic of the specific transformation, the magnitude of which establishes the damping benefit possible. The approximate magnitudes of the maximum inelastic strain in each instance may vary depending on material—but are on the order of 10-2 for shape memory alloys, 10-3 for ferroelectrics, and 10-4 for magnetostrictive alloys. Whether the full hysteresis effect is utilized in practice will rely on both the stress mean and amplitude applied. Thus, the potential for improved damping will rely on both the specific functionality of the reinforcement and on the details of the applied stress, e.g., the description of cyclic loading including the degree of reversibility, any prestressing present, and the presence of residual stresses that evolve during application. Moreover, the behavior of ferroelectric and magnetostrictive-reinforced MMCs will rely on contributions attributable to the electrical and/or magnetic environment provided by the matrix, i.e., whether they exist in an insulating or shortcircuit mode.

Conclusions Ferroelastic ceramics are promising high damping materials that can be used as reinforcement within metallic composite matrices to augment the damping capacity of structural materials. The results from this study have shown that the damping capacity is strongly dependent on the tetragonality of BaTiO3, which is also highly dependent on the microstructure and particle or grain dimension, and on temperature, frequency, and ability to age. The most challenging issue frustrating the potential use of a ferroelastic as a reinforcement in MMCs continues to be that the damping effect is maximized for large

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ferroelastic particle or grain sizes. Large reinforcement sizes capable of exhibiting significant ferroelastic-derived vibrational damping, such as sizes in excess of 2 lm diameter, would be predicted to contribute negligibly to strength at volume percentages typical of MMCs. Nonetheless and as demonstrated in this study, significant useful damping augmentation may be possible for applications conducive to the recoverability associated with ferroelastic aging, that is, low actuation frequencies, slightly elevated temperatures, fully reversed loading, and finite periods of loading inactivity. Acknowledgements The authors gratefully acknowledge the support of this study by the Army Research Office under Grant No. DAAD19-01-1-0714, Dr. William Mullins, ARO Contract Manager; and the Material Science and Engineering Department at Virginia Tech. The authors also gratefully acknowledge the comments and clarifications provided by Dr. Yongmei Jin, Assistant Professor of MSE at Michigan Tech.

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