Structure property Relationships in Polymer Composites with Micrometer and Submicrometer Graphite Platelets

Structure property Relationships in Polymer Composites with Micrometer and Submicrometer Graphite Platelets by I. Chasiotis, Q. Chen, G.M. Odegard and T.S. Gates ABSTRACT The objectives of this work were (a) to investigate the influence of micrometer and submicrometer scale graphite platelets of different aspect ratios and volume fractions on the effective and local quasi-static and dynamic properties of composites with micrometer and submicrometer scale reinforcement, and (b) to compare and evaluate mechanical property measurements of inhomogeneous materials via local (microscale) and bulk (macroscale) experimental methods. Small platelet volume fractions (0.5%) provided proportionally larger increase of the elastic and storage moduli compared to large volume fractions (3.0%). Randomly distributed 15 µm platelets provided marginally higher composite stiffness compared to 1 µm platelets while small volume fractions (0.5%) of 15 µm platelets had a pronounced effect on the effective Poisson s ratio. It was found that local property measurements of inhomogeneous materials conducted by nanoindentation are not representative of the bulk behavior even when the characteristic length of the inhomogeneity is an order of magnitude smaller than the indentation contact area. In this case, statistical averaging of data from a large number of indentations does not result in agreement with bulk measurements. On the other hand, for small aspect ratio platelets with dimensions two orders of magnitude smaller than the nanoindentation contact area, the nanoindenter-obtained properties agreed well with the effective material behavior. It was found that platelets residing at the specimen surface contribute the most to nanoindentation data, which implies that this technique is only valid for well-distributed nanoparticulate and microparticulate systems, and that nanoindentation cannot be used for depth profiling of microstructured composites. KEY WORDS Polymer composites, graphite platelets, mechanical properties, local properties, nanoindentation Introduction Composite materials are key to many performancecritical structural applications that range from automotive to aerospace transportation. In an effort to improve the man- I. Chasiotis (SEM member; chasioti@uiuc.edu) is an Assistant Professor and Q. Chen is a Graduate Student, Aerospace Engineering, University of Illinois at Urbana Champaign, Urbana, IL 61801, USA. G.M. Odegard (SEM member) is an Assistant Professor, Mechanical Engineering Engineering Mechanics, Michigan Technological University, Houghton, MI 49931, USA. T.S. Gates (SEM member) is a Senior Materials Research Engineer, Mechanics and Durability Branch, NASA Langley Research Center, Hampton, VA 23681, USA. Original manuscript submitted: November 5, 2004. Final manuscript received: September 6, 2005. DOI: 10.1177/0014485105059992 ufacturability and multifunctionality of composite structures, polymer microcomposites and nanocomposites have been developed. 1 3 They are characterized by refined microstructure which, when properly ordered, can result in increased performance; small quantities of hard inorganic particles 3 can control the deformation, failure, heat resistance, and thermal degradation properties of polymers. Concomitant to the development of microcomposite and nanocomposite structural materials is the ability to integrate different functionalities, such as electromagnetic shielding, health monitoring, or structural morphing. A challenge in designing load-carrying microstructured and nanostructured composites is establishing relationships between the structure and their macromechanical properties. To date, research conducted in this area has been largely empirical and has not yet resulted in efficient structure property models. The latter require multiscale experimental characterization to assess the effectiveness of the small-scale reinforcement and support our understanding of the interactions between the polymer matrix and the small-scale particles. The objective of this work was to investigate the relevancy of mechanical properties measured via local and bulk testing methods. The results of this study could be employed to validate and further develop existing micromechanics models by providing inputs for small-scale material behavior and reference values for macroscale properties. The approach followed in this work involved the quasi-static and dynamic mechanical characterization of an epoxy reinforced with micrometer and submicrometer size graphite platelets of different volume fractions. The experimental characterization was conducted with nanoindentation, dynamic mechanical analysis (DMA), and conventional tensile testing and was assisted by atomic force microscopy (AFM) surface measurements to draw connections between the material microstructure and the local and the effective quasi-static and dynamic mechanical behavior. In the following sections, the material fabrication and the experimental procedures are outlined. The discussion of the experimental results is divided into two parts: the dependence of the material properties on platelet size and volume fraction and the interpretation of data acquired via local and bulk property measurement techniques. The effect of microstructure on the quasi-static (Young s) modulus and dynamic (storage) modulus is presented and the validity of the application of nanoindentation to obtain macroscopically relevant (effective) material properties is evaluated. 2005 Society for Experimental Mechanics Experimental Mechanics 507

Materials and Experimental Procedures The composite samples prepared for this study allowed for control of the platelet volume fraction and size. Commonly employed mechanical testing techniques were selected so that the results and the conclusions could be readily adopted by other laboratories. Material Description Epoxy matrix composites with different micrometer and submicrometer size graphite platelets and volume fractions were fabricated for parametric studies of their quasi-static and dynamic elastic properties and for derivation of structure property relationships. The epoxy was Epon828/Jeffamine T403 (100/45 wt%). Optical images of the composites showed a mix of oblate and prolate spheroids with the former being most common. Details of the material fabrication and the characterization of the degree of graphitic exfoliation are provided in Fukushima and Drzal. 4 Table 1 provides a list of the nominal and the measured platelet sizes and volume fractions of the five different sets of samples that were fabricated. The nominal platelet size refers to the average effective radius of the graphite platelet plane as reported in Fukushima and Drzal. 4 The nominal platelet volume fraction was obtained from fabrication data based on the weight fraction of graphite platelets. The measured platelet volume fractions and thicknesses were derived from AFM surface images as described in the following section. Of the five different sample types, the first was the control epoxy (henceforth referred to as control) and the remaining four sets were composites containing graphite platelets. Two composites contained graphite platelets with 1 µm average size (henceforth referred to as D1) and the remaining two contained microplatelets with 15 µm average size (henceforth referred to as D15). The composites with the same platelet size had nominal platelet volume fractions of 0.5% (henceforth referred to as V0.5) and 3.0% (henceforth referred to as V3.0). The five different sets of samples allowed for analyzing the results based on platelet size (D1 and D15) and platelet volume fraction (control, V0.5, and V3.0.) In the following sections, each material is referred to according to the two abbreviations of nominal platelet size and volume fraction given in the first column of Table 1. Material Characterization The surface of finely polished samples prepared for nanoindentation (details are given in the respective section of this paper) was imaged by an AFM in intermittent contact mode using both topographic and phase contrast images. In the AFM topographic images in Figs. 1(a) (d), the bright features are the platelets embedded in the epoxy. More than 10 20 20 µm 2 and 50 50 µm 2 AFM images were obtained for each volume fraction of D1 and D15 composites. These images were used to confirm the estimate for the platelet volume fraction in each sample based on surface records. The surface analysis was conducted with the aid of commercial image processing software. As shown in Table 1, the measured platelet volume fractions were close to the nominal values that are used hereafter. According to Fig. 1, the graphite platelets were uniformly distributed and no agglomeration was observed via highresolution optical 5 or AFM surface imaging. Of the four different composites, only D15V3.0 was above the percolation threshold as assessed by electrical resistivity measurements. 4 Using AFM measurements, the average platelet thickness for D1 composites was found to be 0.35 µm while the average platelet thickness of D15 composites was 0.55 µm. Thus, the small platelets had an average aspect ratio of 3 while the large platelets had an average aspect ratio of almost 30. However, there was a broad distribution of aspect ratios with larger and smaller platelets varying by a factor of 3 from the average size. Experimental Methods and Procedures The elastic properties of the composites were assessed by quasi-static tension tests, and nanoindentation. Of the dynamic properties the storage modulus, a measure of the recoverable material deformation under dynamic loading, was recorded at the bulk and local scales by DMA and nanoindentation, respectively. These mechanical property tests required different material preparation procedures and sample dimensions as well as data analyses that are described in the following sections. Quasi-static Tension Tests Test specimens in the form of uniform cross-section rectangular beams with nominal dimensions of 50 12 5mm 3 were fabricated from each of the five samples, and were subjected to quasi-static tension in a servohydraulic test frame at 10 4 10 5 s 1 strain rates and room temperature. Three load displacement curves were obtained for each volume fraction and platelet size. The axial strain was measured with a laser extensometer while the transverse strain was recorded via strain gages. The uniform tensile stress was calculated from the load cell measurement of the applied force and the specimen cross-section. The isotropic material constants, Young s modulus and Poisson s ratio, were obtained from the stress strain curve and the axial and transverse strain measurements, respectively. TheYoung s modulus was computed from the initially linear segment of the stress strain plots. The Poisson s ratio was calculated using the axial and the transverse strain from the linear segment of the stress strain plot under the same load. Nanoindentation The microscale determination of Young s and storage moduli of the composites was conducted via instrumented nanoindentation using a commercial nanoindenter equipped with a Berkovich type diamond tip. Two nanoindenter modules capable of residual imprint areas that differed by a factor of 10 were used to investigate the adequacy of the indenter tip size in recording the effective properties of inhomogeneous materials with micrometer and submicrometer platelets. The first nanoindenter module, called the dynamic contact module (DCM), allowed for a maximum indentation depth of 2000 nm. The second module, called XP, provided a maximum indentation depth of 5000 nm. 6 The maximum indentation depth was a result of the force range of each indenter module and the sample stiffness. In this paper, the indentations conducted with the DCM module (2000 nm maximum indentation depth) are referred to as small indentations and those conducted with the XP module (5000 nm maximum indentation depth) are referred to as large indentations. The terminology small indentation and large indentation is 508 Vol. 45, No. 6, December 2005 2005 Society for Experimental Mechanics

TABLE 1 NOMINAL VERSUS MEASURED AVERAGE PLATELET DIMENSIONS AND VOLUME FRACTIONS Description Nominal Platelet Measured Platelet Average Platelet Measured Platelet Volume Fraction Volume Fraction Sample Length (µm) Thickness (µm) (%) (%) 1 Control N/A N/A N/A N/A 2 D1V0.5 1 0.35 0.5 0.72 3 D1V3.0 1 0.35 3.0 3.06 4 D15V0.5 15 0.55 0.5 0.58 5 D15V3.0 15 0.55 3.0 3.29 Fig. 1 AFM topographic images showing the graphite platelet distributions and sizes. The bright features are the platelets embedded in the matrix. For V0.5 and V3.0 the platelets were randomly oriented and well dispersed derived from the relative, and not absolute, size of the indents. For all indentations the rate at which the indenter tip approached the sample was 0.05 s 1. This rate was calculated by the instrument as the ratio of the tip velocity over the entire range of motion. Variation of this rate by a factor of 2 had no significant effect on the measured properties. However, very slow rates would result in considerable thermal drift. At tip approach rates similar to ours, literature reports on nanoindentation of blended carbon nanotube composites also indicated no appreciable rate effects. 7 The two indenter modules were used in continuous stiffness measurement (CSM) mode 6,8 where a 10 nm amplitude and high-frequency (50 Hz) oscillation was superposed on the global indenter motion as it descended into the sample. The effect of the frequency of the modulated tip on the measured properties was small for frequencies between 10 and 120 Hz. 2005 Society for Experimental Mechanics Experimental Mechanics 509

SAMPLE PREPARATION Nanoindentation tests require a high degree of surface flatness. Even low amplitude surface roughness can induce lateral forces on the indenter tip, thus affecting the measurement accuracy. Large samples of each composite were first sectioned and mounted on epoxy pucks appropriate for the nanoindenter specimen mounts. Then, the top surface of the puck was polished with a combination of 320 4000 sandpapers for 5 10 min at 150 rpm. Using AFM images of 50 50 µm 2 sample areas, the peak-to-valley surface roughness was calculated; it was 15 20 nm (RMS = 3 5 nm) in areas free of platelets, and 30 60 nm (RMS = 5 8 nm) where platelets were present. Data reported in the literature 9 have indicated a small or minimal effect of polishing on nanoindentation properties; unpolished samples resulted in larger data scatter which could be attributed to the generation of non-axial loads on the indenter tip due to surface roughness. The uniform volumetric platelet distribution ensured that the polished surface was representative of the bulk material. To obtain sufficient statistical distribution of the local surface properties, arrays of 36 64 indents, each spaced 50 200 µm apart, were created on each of the five samples. These indentations were accompanied by post-indentation AFM imaging that provided surface profiles and local platelet volume fractions to support the data analysis. A simple preliminary calculation suggested guidelines for the number of indentations required to probe a surface area that contains a number of platelets that corresponds to the platelet volume fraction of the composite. If the surface required to contain at least one platelet is A tot and the surface area of the platelet is A pl, then for a volume (or surface) fraction x pl : A pl = A tot x pl. For the projected platelet crosssections measured from Fig. 1, the number of indentations required for D15V0.5 is 36 compared to only one indentation required for D1V0.5. This estimate is still rudimentary as the volume of influence by the indentation is extended beyond that under the immediate indentation contact area and the platelets were assumed to be uniformly dispersed at the scale of the indenter. As will be shown later, this calculation holds for D1 composites only. NANOINDENTATION DATA REDUCTION Following the work of Oliver and Pharr, 10 the reduced elastic modulus, E r, was calculated from the initial slope of the unloading curve. The Young s modulus was calculated from ( [ ( )] E = 1 ν 2) 1 1 ν 2 1 d (1) E r E d where ν and ν d are the Poisson s ratios for the sample and the indenter tip, respectively, and E d is the Young s modulus of the nanoindenter tip. Since the stiffness of the diamond tip is approximately three orders of magnitude higher than that of the epoxy and the composites studied here, eq (1) can be simplified to E = E r (1 ν 2). (2) The Poisson s ratio, ν, for each sample was measured via uniaxial tension tests described previously. The nanoindenter Fig. 2 Loading-unloading nanoindentation curve. The dashed line indicates the initial slope of the unloading curve (contact stiffness S) measures the applied normal force, P, at different indentation depths, h. The unloading segment of the indentation data can be fit to a power law 10 P = α ( h h f ) m (3) where α is a factor that combines all unknown geometric and material parameters, h is the indentation depth at force level P, h f is the final unloading depth, and m is an indenter tip related factor. The initial slope of the unloading curve, shown in Fig. 2, is defined as the contact stiffness, S, which is related to the reduced modulus as S = 2β π AEr = ( dp dh ) h max,p max = αm ( h max h f ) m 1 where A is the projected tip contact area, β is a tip geometry related constant, which for a Berkovich indenter is equal to 1.034, and h max is the maximum indentation depth. The reduced modulus can be found if the projected area, A, and the contact stiffness, S, are known. The projected area has a known relationship with the indentation depth, which is calibrated using a sample with predetermined E and ν. Given the calibration data, the load displacement curve was recorded and from eqs (3) and (4) the initial unloading slope was calculated from the derivative of a power-law fit to the unloading force versus indentation depth curve. Then, the reduced modulus was obtained from the first part of eq (4). Instrumented nanoindentation was also used to obtain the storage modulus under dynamic loading. These measurements were conducted using the CSM method 6,8 described in a previous section. The response of a time-dependent material to such loading is not in phase with the indenter tip motion and the phase shift is measured via a lock-in amplifier. Then, the storage, E, and loss, E, moduli can be calculated at various indentation depths as E = S 2β π A, E = ωd s π 2β A (4) (5) 510 Vol. 45, No. 6, December 2005 2005 Society for Experimental Mechanics

where D s is the damping of contact, and ω is the harmonic frequency of the nanoindenter tip. The contact stiffness, S, for the dynamic measurements is calculated according to Odegard et al. 11 The advantage of this approach is that the dynamic properties are calculated continuously and at every indentation depth. The average value of the storage modulus is then computed from the storage modulus versus depth curves for depth values that the storage modulus assumed a constant value. In this paper we report and discuss only the values of storage modulus. All tests were conducted at room temperature and the loss modulus was very small and invariant for indenter tip modulation frequencies between 5 and 70 Hz. CALIBRATION OF NANOINDENTATION PARAMETERS A prior study 11 defined the optimum parameters to minimize the effects of laboratory noise and vibration on CSM measurements. The CSM frequency was 50 Hz, which was significantly higher than the frequency of the laboratory background noise. The amplitude of the nanoindenter tip harmonic oscillation was selected to be 10 nm; amplitudes as small as 1 2 nm resulted in considerable data scatter whereas large tip modulation amplitudes would result in pronounced viscoelastic effects (creep) and plastic deformation. For data reduction, the value for the tip shape function, defined by the final contact depth, and the depth over which the tip makes contact with the material versus the projected contact area are required. The tip shape function used for both the control epoxy and the four composites was computed with the aid of a calibration sample with dynamic and quasi-static properties similar to those of the samples under study. The calibration material, a modified bismaleimide polymer manufactured by BASF Corp., 12 was homogeneous and isotropic at the scale of the indenter contact area with storage modulus E = 4.3 GPa and Poisson s ratio ν = 0.38 determined via DMA and quasi-static tension tests, respectively. 11 Dynamic Mechanical Analysis DMA was conducted using samples with nominal dimensions 50 12 5 mm 3. The exact dimensions of each specimen were measured with 0.01 mm accuracy, as small thickness variations would result in significant data inconsistency. Three samples from each composite material were tested in three-point bending at room temperature. The DMA tests were frequency sweeps in the range of 0.01 140 Hz with 20 µm mid-specimen deflection. For each sample, three frequency sweeps were conducted and the resulting data were used to calculate the average storage modulus at each frequency. Results The experimental results are presented according to the property measured (Young s and storage moduli) and the experimental method (tension tests, DMA, and nanoindentation) employed to measure the mechanical behavior of the composite. Comparisons of the results from different methods are provided in the discussion section. Tensile Tests: Quasi-static Properties The elastic modulus was calculated from the initial slope of the stress strain curves as seen in Fig. 3. All tests were Fig. 3 Stress-strain curve from a uniform tension test of a D1V3.0 specimen run to approximately 1.0 1.2% strain. The initial component of the plot was linear followed by a non-linear segment. No systematic strength data were collected in this study. The elastic modulus and Poisson s ratio measured from the uniaxial tension tests are plotted in Figs. 4(a) and (b). For D1V3.0 specimens, the tests failed to produce viable results and hence are not presented here. As seen in Fig. 4(a), an increase of the graphite volume fraction resulted in an increase of the elastic modulus. For D15V3.0 composites, the elastic modulus increased on average by 32% compared to the control. Analogous was the change in Poisson s ratio: the value of Poisson s ratio, ν, decreased significantly (Fig. 4b) with increasing platelet size. For D15V3.0, ν dropped by as much as 33% compared to the control. At small filler volume fractions, the elastic modulus increased more with the addition of small rather than large platelets. In contrast, small volume fractions of small platelets had negligible effect on ν, but small volume fractions of large platelets were very effective in reducing ν. Nanoindentation Tests: Quasi-static Properties A typical force versus indentation depth curve for a 2000 nm deep indentation is shown in Fig. 2. The residual imprint was an equilateral triangle with 14 µm side length. The depth of the residual indentation averaged 630 nm for the control epoxy and 880 nm for D1V3.0 specimens. The residual imprint for the large indentations was an equilateral triangle with 36 µm side length at a maximum 5000 nm indentation depth. For these indentations, the residual depth averaged 1800 nm for D1V0.5 specimens and 2400 nm for D1V3.0 specimens. For both indentation sizes, the depth of the residual imprint was larger for specimens with larger platelet volume fractions. Furthermore, the ratios of the maximum indentation versus residual indent depth were similar for small and large indentations. The residual pile-up measured from post-indentation AFM images was at most 70 nm in height, and it was the same for both the calibration material and all test materials, thus ensuring that the tip-shape function was valid for all tests. Although the equations used to determine the elastic properties do not account for the change in contact area due to pile-up, the use of a polymer instead of fused silica as calibration material indirectly accounted for pile-up. Figure 5 provides a comparative chart of theyoung s moduli measured by uniaxial tension, small indentations, and 2005 Society for Experimental Mechanics Experimental Mechanics 511

(a) (b) Fig. 4 Effective (a) Young s modulus and (b) Poisson s ratio as a function of platelet volume fraction and size as obtained from uniform tension tests. The error bars are equal to one standard deviation Fig. 5 Elastic modulus measured from small and large indentations and quasi-static tension tests. The error bars are equal to one standard deviation large indentations. The elastic moduli from the small and large indentations were in good agreement for all platelet volume fractions and sizes, despite the fact that the two indentation contact surfaces differed by almost an order of magnitude. The elastic modulus derived from indentation data did not always agree with that measured by uniaxial tension tests. The moduli from bulk and local indentation measurements on the epoxy and the D1 composites were consistent. However, the modulus of the D15 composites, as measured from small and large indentations, was considerably lower than that measured from uniaxial tension tests; the average elastic modulus of D15 composites derived from small indentations (Fig. 5) was approximately equal to that of the control epoxy. Nanoindentation and DMA Tests: Dynamic Properties The nanoindentation values of storage modulus of the control converged to a constant value after a scatter in the initial 50 100 nm. This behavior was attributed to the material surface roughness that was of the same order of magnitude as the indentation depth at which the data scatter was observed. Possible surface hardening induced during surface polishing may also have an effect on data from small indentation depths. Figure 6 shows typical storage modulus versus indentation depth curves at three locations on the same D1V3.0 sample. Such variations in the local properties of the four composites were attributed to differences in platelet size, platelet distribution, and the number of platelets under the indenter tip at each depth. Indentation (a) corresponds to an indent with no platelets at the beginning of the indentation process and the material behavior at small indentation depths is, as expected, similar to that of the epoxy. On the other hand, the local maxima at 500 nm depth in curves (b) and (c) are associated with graphite platelets included in the initial phase of indentation. After this initial rise, E decreased and reached a plateau at about 1300 nm which implied uniform platelet dispersion after that depth and supported the argument that the surface platelet distribution provided a good representation of the platelet distribution in the bulk. The storage moduli reported from CSM tests were the average plateau values. The dynamic properties derived from indentations using the aforementioned approach are compared to DMA data in Fig. 7. The average moduli obtained by the two indenter modules were in agreement for all platelet sizes and volume fractions, pointing to the absence of an indenter size effect. As expected, the data scatter from small size indentations was larger than that from large size indentations. The storage modulus measured via indentation increased with increasing platelet volume fraction for small platelet size, while for large platelets it was virtually the same as that of the epoxy. As was the case for the elastic moduli in Fig. 5, for small platelet sizes the nanoindentation-derived dynamic properties agreed with those from DMA, while for large platelets they were similar to the control epoxy. The effective storage modulus increased for both 0.5 and 3.0%vol small and large platelets but not proportionally to the increase in volume fraction; small volume fractions of platelets had the most significant effect on property improvement in relation to the control. DMA data showed a marked increase in E, for 0.5%vol filler, with the average storage modulus increasing by 32% and 35% for D1V3.0 and D15V3.0 composites, respectively. For large platelets, the main increase in E was accomplished 512 Vol. 45, No. 6, December 2005 2005 Society for Experimental Mechanics

The microscale (indentation) and macroscale (DMA, quasi-static tension) tests yielded local and global values for the quasi-static and dynamic elastic properties that followed consistent trends. However, significant differences were also observed. They were associated with the platelet size distribution and the stress profile (i.e., measurement method) applied in each test. The differences between the local and bulk measurement techniques are discussed next by comparing the results of the mechanical property measurements. Fig. 6 Storage modulus versus indentation depth, E d, obtained by CSM from a D1V3.0 composite. All curves converged to a single value for E although the highest recorded E was different depending on the number of platelets located under the tip at various indentation depths. Curves (b) and (c) correspond to indentations that included platelets at the beginning of the indentation process while in (a) there were no platelets at the initial contact with the indenter tip Fig. 7 Storage modulus as measured by small and large area indentation and DMA. The error bars are equal to one standard deviation at 0.5%vol filler. In terms of sensitivity to frequency, the storage modulus demonstrated a small increase with frequency for frequencies between 1 and 140 Hz. The storage moduli presented here were measured at 50 Hz so that direct comparisons with the nanoindentation data could be drawn. Discussion Quasi-static and Dynamic Properties in Relation to Measurement Techniques The significant stiffness increase with the addition of graphite platelets as recorded in uniaxial tension tests was expected because of the large mismatch between the elastic properties of the filler and the matrix. Large platelets resulted in maximum load transfer from the matrix to the platelets, and thus considerable increase of Young s modulus and decrease of Poisson s ratio. For D1V0.5 and D1V3.0 samples, the local elastic modulus derived from instrumented nanoindentation and the effective elastic modulus recorded in uniform tension agreed quite well. However, for D15 specimens the two measurement methods did not provide matching values. For 1 µm platelets, the indenter-sample contact area was sufficiently large to capture a statistically representative number of platelets embedded in the matrix. This was not the case for the larger, 15 µm, microplatelets whose dimensions were of the same order of magnitude as the indentation area. The small and large nanoindentation quasi-static and dynamic properties of D15 composites were virtually the same as those of the control epoxy. This can be explained in stochastic terms, and be attributed to the ineffectiveness of the indenter tip to probe material volumes larger than a representative volume element (the smallest material volume whose effective mechanical response is the same as that of the bulk).although the number of indentations performed on each sample was as high as 64, the average values did not provide a direct measure of the bulk material behavior. Thus, a calculation of the representative indentation area similar to that in the Sample Preparation section does not suffice to obtain the effective elastic properties when the size of inhomogeneity is similar to that of the sample surface probed by the indenter. As a result, indentation tests are not appropriate for inhomogeneous materials when the characteristic length-scale of the inhomogeneity is of the same order of magnitude as the lateral dimensions of the indentation. In addition to inhomogeneity, the different stress fields imposed by each test method influence the experimental results. In uniform tension, an increase in platelet length resulted in an increase of the effective tensile elastic modulus. Thus, as expected, large platelets provided better reinforcement. In contrast, the indentation load was compressive and the transverse loads applied to large platelets resulted in bending of the platelets rather than axial loading. Their small bending stiffness resulted in small local stiffness of the composite. Thus, an important reason for the discrepancy between macroscale measurements and nanoindentation was the large aspect ratio of D15 platelets. Such disagreement between uniaxial tension tests and nanoindentation data has also been reported for polymer clay and carbon nanotube composites 7,9 and it was attributed to dissimilar material response in tension and compression that stems from the complex loading profile applied in indentation. It has also been shown 13 that the non-convergent powerlaw fit of the unloading indentation curve may result in 3 5% overestimate of the modulus computed from nanoindentation data. Additionally, material creep may affect the accurate 2005 Society for Experimental Mechanics Experimental Mechanics 513

determination of the tip-shape function requiring properly adapted viscoelastic models to extract the time-dependent material behavior and account for it in the elasticity-based interpretation of the force indentation depth curves. 13 15 Yet, these considerations cannot explain the very small moduli of D15 composites recorded by nanoindentation. Analogous were the trends in the dynamic material behavior. The storage moduli from nanoindentation were in very good agreement with those from DMA for the control and the D1 composites. However, in accordance to the trends in the elastic modulus measured from nanoindentation unloading curves, the local E values of D15 composites were small. In the case of dynamic properties, disagreement between DMA and CSM measurements may also stem from the mechanics of contact between the time-dependent matrix and the indenter tip that is not straightforward to account for. Influence of Local Microstructure on Nanoindentation Measurements To shed light into the interrelations between indentation data and material microstructure, it is useful to discuss selected storage modulus versus indentation depth curves, E d, in connection with the associated topographic information. As shown in Fig. 6, the details of the distribution of platelets in D1V3.0 specimens were important at indentation depths up to 1300 nm when all E d curves converged to the same E, similar to that measured by DMA. The same behavior was observed for both small and large indentations. At 1300 nm indentation depth the projection of the contact area was approximately 50 µm 2, which is a measure of the contact area required to establish macroscopically representative properties for D1 specimens. According to Table 1 the average platelet surface area for D1 composites was 0.35 µm 2. Thus, the indentation data provided effective modulus values when the surface area of the inhomogeneity was at least two orders of magnitude smaller than the indentation contact area. On the contrary, for D15 composites, the nanoindenter was in most cases only in partial contact with a large platelet. Figure 8(a) points to a characteristic case where all platelets were probed after 850 nm indentation depth and no plateau value for the storage modulus existed. The undulations in the E d curve in Fig. 8(a) correspond to the addition of platelets under the indenter tip, and can be directly traced to the four consecutive platelets that cross the indentation area in Fig. 8(b). Thus, the relative location of a platelet at the specimen surface with respect to the apex of the indenter tip fully determines the profile of E d curves. The same figure provides an estimate of the degree post-indentation AFM images represent the contact area at maximum indentation depth. The features included in the three regions marked on the indentation imprint correspond to individual events occurred in the three segments of the E d curve until the maximum indentation depth of 2000 nm. Using AFM images of the residual indentation imprint one can show that, contrary to D15 composites, D1 composites were adequately characterized by nanoindentation. When the fraction of specimen surface covered by small platelets was the same, the plateau of the E d curve was also same, which implies that platelets residing at the specimen surface contribute the most to nanoindentation measurements. Figure 9(a) shows storage modulus plots from a D1 composite and the corresponding indent images with the platelets marked in black. The local platelet surface fraction in the two indentations was almost the same and equal to 0.0585. For the same platelet surface coverage, the E d curves converged to equivalent values of E after the first 800 nm. In summary, nanoindentation data from inhomogeneous materials are directly translated into effective properties when the indentation area is at least two orders of magnitude larger than the surface of the inclusion. An additional constraint is that the inclusion must be a spheroid or an ellipsoid of small aspect ratio so that no local anisotropy is present. Because of the statistical nature of the composite microstructure, the indentation area must be sufficiently large compared to the microreinforcement so that all possible microstructural configurations are sampled to generate the effective mechanical behavior. It is also important to note that even for 5000 nm deep indentations, platelets located at the specimen surface had the most contribution to E d curves. Effectiveness of Large Platelet Volume Fractions The use of instrumented nanoindentation provides a distinctive capability over macroscale measurement methods: it allows for obtaining relative mechanical property estimates from very small material volumes, an advantage during the development of costly nanostructured materials. Furthermore, for many nanocomposites, uniform dispersion is not always attainable and local variations in the filler volume fraction can be utilized to assess the mechanical behavior of the composite for various volume fractions. This is especially valuable because, as shown in the previous section, the surface particles have the main contribution on the indentation properties. Thus, AFM surface images from samples with non-uniformly distributed particles can be used to obtain a rough estimate of the local particle volume fraction. Figure 10 shows three indentations on a D1 sample with non-uniformly distributed platelets.all E d curves reached a plateau at 1000 nm depth, which implies that the relative surface coverage with particles remained unchanged after that depth. While the high-density area (Fig. 10(b)) yielded an average storage modulus (Fig. 10a) almost twice as high as the control (Fig. 10(c)), the platelet volume fraction in that area exceeded 50%. A similar conclusion can be derived from a comparison of Figs. 10(c) and (d), which implies that this category of composites provides significant benefits at low platelet volume fractions while very large volume fractions result in marginal additional improvement in stiffness. Conclusions An investigation of the multiscale quasi-static and dynamic elastic mechanical behavior of polymer composites with micrometer and submicrometer graphite platelets was conducted by various mechanical property measurement methods. The results suggest that local nanoindentation measurements in inhomogeneous materials are not representative of the effective properties when the characteristic length of the inhomogeneity is of the same order of magnitude as the indentation contact area. In that event, statistical data cannot provide an accurate measure of the effective (macroscale) material behavior and a systematic study to determine the 514 Vol. 45, No. 6, December 2005 2005 Society for Experimental Mechanics

(a) (b) Fig. 8 (a) Storage modulus versus indentation depth, E d, for a D15V3.0 specimen. (b) AFM acquired topography of the indentation mark. All platelets were located at the edge of the indent resulting in a rising curve. The undulations in the curve correspond to individual platelets traversed by the nanoindenter tip (a) (b) Fig. 9 (a) Storage modulus versus indentation depth from a D1V3.0 specimen. (b) AFM images showing the different platelet distributions. The local platelet surface fraction was 0.0583 for test 6 and 0.0585 for test 18, while the average plateau indentation storage moduli were 3.63 GPa and 3.71 GPa, respectively representative volume element of the material is required. It was shown that indentation data are appropriate in obtaining effective elastic and storage moduli values when the surface area of the inhomogeneity is two orders of magnitude smaller than the indentation contact area, and the inclusions are small aspect ratio ellipsoids (here, <3.) Thus, for inhomogeneous polymeric materials, the indentation size must be related to the material microstructure so that the indenter size effect is accounted for, similarly to studies conducted in polycrystalline material systems. Finally, it was found that platelets residing at the specimen surface contribute the most to nanoindentation measurements, which implies that nanoindentation is only valid for well-distributed nanoparticulate and microparticulate 2005 Society for Experimental Mechanics Experimental Mechanics 515

Fig. 10 (a) E d curves obtained in CSM mode from a D1 composite with considerable variations in platelet volume fraction. (b) Sample surface with >50% platelet coverage, (c) surface of the control epoxy, and (d) sample surface with partial platelet coverage. All curves converge to a constant, although different, value for E. For >50% platelet coverage the storage modulus converged to 5.5 GPa, which is considerably smaller than the theoretically expected value systems, and it is not an effective means for depth profiling of microstructured composites. Acknowledgments The UIUC group gratefully acknowledges the support by the National Aeronautics and Space Administration (NASA) Langley group for this study under NASA/NIA grant UVA 03-01. References 1. Pinnavaia, T.J. and Beal, G.W., editors, Polymer Clay Nanocomposites, Wiley, New York (2001). 2. Nanocomposites 1999: Polymer Technology for the Next Century, Principia Partners, Exton, PA (1999). 3. Vaia, R.R. and Giannelis, E.P., Polymer Nanocomposites: Status and Opportunities, MRS Bulletin 26, (5), 394 401 (2001). 4. Fukushima, H. and Drzal, L.T., Graphite Nanoplatelets as Reinforcements for Polymers: Structural and Electrical Properties, Proceedings of the 16th Annual American Society of Composites Conference, Blacksburg, VA, September 10 12 (2001). 5. Chasiotis, I., Chen, Q., and Odegard, G., Multiscale Experiments of Polymer Nanocomposites, Proceedings of the Society for Experimental Mechanics, Costa Mesa, CA (2004). 6. Testworks 4 Software Manual for Nanoindentation Systems, Version 14, MTS System Corporation, Oak Ridge (2001). 7. Penumadu, D., Dutta, A., Pharr, G.M., and Files, B., Mechanical Properties of Blended Single-wall Carbon Nanotube Composites, Journal of Materials Research, 18, (8), 1849 1853 (2003). 8. Li, X. and Bhushan, B., A Review of Nanoindentation Continuous Stiffness Measurement Technique and its Applications, Materials Characterization, 48, 11 36 (2002). 9. Shen, L., Phang, I.Y., Chen, L., Liu, T., and Zeng, K., Nanoindentation and Morphological Studies on Nylon 66 Nanocomposites. I: Effect of Clay Loading, Polymer, 45, 3341 3349 (2004). 10. Oliver, W.C. and Pharr, G.M., An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments, Journal of Materials Research, 7 (6), 1564 1583 (1992). 11. Odegard, G.M., Gates, T.S., and Herring, H.M., Characterization of Viscoelastic Properties of Polymeric Materials Through Nanoindentation, Experimental Mechanics, 45 (2), 130 136 (2005). 12. Cano, R.J. and Dow, M.B., Properties of Five Toughened Composite Materials, NASA TP-3254, NASA LaRC (1992). 13. VanLandingham, M.R., Villarrubia, J.S., Guthrie, W.F., and Meyers, G.F., Nanoindentation of Polymers: An Overview, Macromolecular Symposia, 167, 15 43 (2001). 14. Cheng, L., Xia, X., Yu, W., Scriven, L.E., and Gerberich, W.W., Flatpunch Indentation of Viscoelastic Material, Journal of Polymer Science Part B: Polymer Physics, 38, (1), 10 22 (2000). 15. Lu, H., Wang, B., Ma, J., Huang, G., and Viswanathan, H., Measurement of Creep Compliance of Solid Polymers by Nanoindentation, Mechanics of Time-Dependent Materials, 7, (3 4), 189 207 (2003). 16. Liu, C., On the Minimum Size of Representative Volume Element, Proceedings of the Society for Experimental Mechanics, X International Congress, Costa Mesa, CA, June 7 10 (2004). 516 Vol. 45, No. 6, December 2005 2005 Society for Experimental Mechanics