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Mechanical properties of silica aerogels
Journal of Non-Crystalline Solids 223 Ž1998. 179–189
Mechanical properties of silica aerogels Kelly E. Parmenter, Frederick Milstein
)
Departments of Mechanical Engineering and Materials, UniÕersity of California, Santa Barbara, CA 93106, USA Received 4 November 1996; revised 26 August 1997
Abstract Aerogels are extremely low density solids that are characterized by a high porosity and pore sizes in the order of nanometers. The mechanical behavior of silica aerogel was investigated with hardness, compression, tension and shear tests. The influences of testing conditions, storage environment and age were examined, with particular attention paid to the effects of processing parameters, including fiber-reinforcement. Good correlation was found between hardness and compressive strength over a wide range of processing parameters. Increasing fiber reinforcement generally retarded shrinkage during fabrication and yielded smaller matrix densities for a given target density. For a given fiber content, hardness, compressive strength and elastic moduli increased and strain at fracture decreased with increasing matrix density. In the lower ranges of matrix density, fiber reinforcement increased strain at fracture and elastic moduli. The mechanical response was also sensitive to environment and storage history. With age, the compressive strength and elastic moduli increased while the strain at fracture decreased. Tension and shear results indicate that shear strength of aerogels exceeds tensile strength which is consistent with brittle materials response. q 1998 Elsevier Science B.V.
1. Introduction Silica aerogels are high porosity, extremely low density solids composed of interconnected particles that form an open nanostructure. As a result of the low thermal conductivity of silica and nanometer pore sizes the thermal conductivity of silica aerogel is very low. Low thermal conductivity and optical properties make silica aerogels desirable for insulating applications such as cover layers for windows and solar collectors and as replacements for chlorofluoro carbon foams in cryo-vessels w1x. The properties of aerogels that make them such good insulators also make them inherently fragile and brittle. Thus, their use in load-bearing applications presents )
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a challenge. Currently, attention is being placed on improving the mechanical properties of aerogels without sacrificing other unique properties. Relatively few experiments to determine the mechanical properties of aerogels have been carried out to date. No results for fiber-reinforced silica aerogels have been found in the literature. Experiments most applicable to the present work include work on unreinforced silica aerogels by Arvidson and Scull who measured compressive properties of unreinforced silica aerogel at 295, 76 and 20 K w2x. Gronauer et al. measured Young’s modulus using sound velocity measurements w3x. Woignier and Phalippou measured Young’s modulus and the fracture strength with a three point flexural technique, and the toughness with a single edge notched beam in three point bending w4x. Ultrasonic and static compression experiments have been undertaken to
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 Ž 9 7 . 0 0 4 3 0 - 4
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K.E. Parmenter, F. Milsteinr Journal of Non-Crystalline Solids 223 (1998) 179–189
determine the elastic moduli w5–7x. LeMay et al. w8x and Pekala et al. w9x measured the compressive moduli of silica aerogels as a function of density and pH of the precurser gel Žalcogel.. They found that the compressive modulus can be described by a simple scaling law, and that changes in the pH of the alcogel significantly affect the aerogel morphology. Silica aerogel data were also compared with compressive moduli of organic materials. This work investigates the mechanical behavior of fiber-reinforced and unreinforced silica aerogels. Two processing parameters, the mass percentage of fiber reinforcements and the target density, were altered to obtain aerogels with differing physical characteristics. The target density is a readily controllable processing variable, based on the mass of the aerogel phase and the volume of the original mold. The mechanical behavior of the aerogels was studied by hardness, compression, tension and modifications thereof. Particular attention was paid to the effects of processing parameters, testing conditions, storage environment and age on the mechanical behavior of aerogels.
2. Experimental procedures The source of silica for the aerogels that were tested in this study was tetraethylorthosilicate ŽTEOS.. The aerogels were manufactured by first dissolving TEOS ŽSiŽOCH 2 CH 3 .4 . in ethanol. The mixture was next hydrolyzed with water at room temperature, and a cross-linked silica network was produced. The fiber reinforcements were then mixed into the solution, while it was being stirred at a constant rate. The mass percentage of reinforcements was varied from 0 to 25% and the target density was varied from 40 to 80 kgrm3. The reinforced aerogels contained a mixture of 68% silica fibers, 20% alumina fibers and 12% aluminaborosilicate fibers, with diameters of 3, 2–4 and 8 mm, respectively. All fibers had lengths of 1.27 cm. The solution was base-catalyzed with ammonia and ammonium fluoride until it reached a pH of 6.5 and then it was poured into molds. The molds were rectangular, with dimensions of 1 = 2 = 4 inch. The target density is the mass of the aerogel phase divided by the mold volume Žtarget density does not
include the mass of the fibers.. Gelation occurred within 30 min, after which the gels further solidified overnight in the molds. The samples were aged for three days in ethanol before they were supercritically dried. Gels were supercritically dried by placing them in an autoclave in an ethanol bath, and liquid carbon dioxide was introduced to displace the ethanol. The autoclave was then heated to above critical temperature to vaporize the solvent while eliminating its saturated vapor phase. The vapor was then evacuated and the aerogels were cooled. In the preparation of these materials, the autoclave was pressurized to 600 psi and then the temperature was increased to 358C causing the pressure to rise to 1200 psi. Final aerogelrfiber composite densities are significantly larger than the target densities owing to shrinkage during processing and to the additional mass of fiber reinforcements. The final density is taken to be the final mass Žincluding the fibers. divided by the final volume. Additionally, the final matrix density Žwhich is simply called the matrix density. was calculated by subtracting the mass of the fibers and neglecting their volume Ži.e. by assuming that the final volume of the matrix is approximately equal to the final volume of the composite.. These silica aerogels were found to be physically destroyed by water Žhydrophilic. and other liquids. In addition, it was observed that perspiration from fingers and hands caused micro-cracks to form on surfaces that were handled without gloves. To prevent this from occurring, all test specimens were handled with gloves. Moreover, special care was taken to degrease and dry all equipment that came in contact with the specimens. Hardness testing is widely used because of its non-destructive nature, and for many materials relations exist between hardness and strength. Correlations between hardness and compressive strength have been established in ‘non-traditional’ materials, such as polymer concretes w10x. Here we show that the compressive strength and hardness of fiber-reinforced silica aerogels are also well correlated. We would therefore expect good correlation between compressive strength and hardness in silica aerogels. Fiber contents and densities of the samples subjected to hardness and compression testing are listed in Table 1.
15.0"2.1 22.3"3.1 0.79"0.02 15
0.077"0.010
14.1"0.6 18.3"3.2 33.9"2.5 6.1"0.9 18.0"0.7 31.8"3.2 5.3"0.5 16.4"1.8 20.4"3.2 36.0"3.4 8.1"1.6 23.4"1.4 30.4"4.4 8.6"0.7 0.100"0.009 0.071"0.010 0.053"0.004 0.069"0.007 0.067"0.004 0.051"0.003 0.142"0.015 1.01"0.03 1.00"0.08 1.45"0.18 0.34"0.03 1.01"0.05 1.27"0.14 0.55"0.03 3 3 4 6 9 15 16
5.37"0.47 2.20" 0.26 5.67" 1.84 0.97" 0.04 3.71" 0.55 5.37" 2.71 1.54" 0.06 2.02"0.24 2.11"0.21 12 10 6 7 6 12 14 24 10 240 247 304 171 207 297 143 150 180 – 40 80 40 50 80 40 50 80 0 5 5 10 10 10 25 25 25
240 260 320 190 230 330 190 200 240
Secant modulus at 50% of S ŽMPa. Strain at fracture, ´ f Žmmrmm. Compressive strength, S ŽMpa. No. of compression tests Mean hardness ŽMPa. No. of hardness indents Matrix density Žkgrm3 . Final density Žkgrm3 . Target density Žkgrm3 .
H s LrA. Ž 2.2 . The bulk of the hardness tests were carried out with a maximum load of approximately 14 N, a crosshead speed of 0.102 mmrmin and no time delay at maximum load. ŽFor the aerogel manufactured with a target density of 40 kgrm3 and a fiber percentage of 10%, the maximum load was lowered to 10.2 N because of the extreme softness of the material.. The
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Fiber percentage Žmass %.
A s p Dd . Ž 2.1 . The hardness, H, was defined as the maximum load, L, divided by the indent surface area:
Table 1 Summary of hardness and compression results. The numerical values following the ‘" signs’ are standard deviations
Attempts were made to determine hardness by Vickers and Knoop tests; however, these methods failed to work on the silica aerogel specimens. At very small loads Ž; 0.25 N., the indentation pressure was too large for these fragile materials and resulted in cracks and surface cave-ins as shown in Figs. 1 and 2. In addition, because the aerogels absorb and transmit light more readily than they reflect it, it was difficult to obtain enough contrast in the magnified images of the indents to make accurate measurements of indent size. This was particularly true for very low loads, and for the more opaque Žfiber-reinforced. aerogels. Attempts to use dyes to improve the contrast of the magnified images were unsuccessful because the dyes caused cracks on the surfaces of the aerogels. Vickers and Knoop hardness tests demonstrated the need to reduce indentation pressure substantially in order to deform the aerogels without cracking. In an alternative approach, the indents were made with a 19.05 mm diameter steel ball, at loads of 18.2 N and smaller. A ball and socket fixture was secured to the crosshead of a displacement-controlled Instron 1123 testing machine. The load was measured with a compression load cell and the crosshead displacement was measured with a linear variable differential transformer ŽLVDT.. All tests were conducted under ambient conditions. An initial preload of 2.0 N was applied to minimize surface effects. The load was subsequently applied to the ‘full-loading’ value and then reduced to the preload value where the depth, d , was determined. A representative load–displacement curve for an unreinforced aerogel specimen is shown in Fig. 3. The indent surface area, A, was approximated from the measured value of d and ball diameter, D, with the relationship
Secant modulus at 90% of S ŽMPa.
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maximum load was varied to determine whether the hardness tests were ‘load sensitive’. The peak loads ranged from 10.2 to 18.3 N. In this range, the hardness was not sensitive to load, within the scatter due to material inhomogeneities. Loads higher than 18.3 N tended to crack the specimens and loads smaller than 10.2 N tended to yield indiscernible results. Compression tests were performed with the same machine used for hardness tests. Compression specimens with 2:1 height:width ratios were cut from raw material into rectangular blocks, with nominal dimensions of 0.3 = 0.3 = 0.6 inch. The aerogels could be readily cut with a diamond, slitting saw. The more difficult part of specimen preparation was gripping the specimens, not the actual cutting. The gripping problem was solved with a vacuum chuck. The specimens were placed, one at a time, between the top and bottom portions of a compression fixture and were loaded at a rate of 0.102 mmrmin by lowering the top portion of the fixture Žwhich was secured to the crosshead. until they fractured macroscopically. The bottom portion of the compression fixture was a stationary flat plate, whereas the top portion consisted of a ‘frictionless’ hemisphere secured into a socket with vacuum grease. The top
portion was thus self-aligning. The load was measured with the compression load cell and the crosshead displacement was measured with a LVDT. The majority of tests were conducted under ambient conditions. The load–displacement curves were converted to stress–strain curves by dividing the loads by the original cross-sectional areas of the specimens, and the displacements by the original heights of the specimens. The compressive strength, the strain at fracture, ´ f , and secant moduli, E50% and E90% , were determined from the stress–strain data. The compressive strength is defined as the maximum stress carried by the specimens during a test, and the strain at fracture is the strain at which macroscopic failure of the specimen occurred. Each secant modulus was determined by measuring the slope between two points on the stress–strain curves. For E50 % , the slope was calculated between the point of stress equal to 0.040 MPa and the point where the stress is 50% of the compressive strength. For E90 % , the slope was calculated between the point of stress equal to 0.040 MPa and the point where the stress is 90% of the compressive strength. The slopes are referenced to the 0.040 MPa value to reduce or eliminate possible effects of surface irregularities.
Fig. 1. Vickers indentation at 1 N load.
K.E. Parmenter, F. Milsteinr Journal of Non-Crystalline Solids 223 (1998) 179–189
The influences of age and storage environment on aerogel compression results were quantified by comparing stress–strain curves for aerogels that had different storage histories. Two types of aerogels were
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investigated in this manner. The fiber contents, densities and histories of these materials are summarized in Table 2. The first type of aerogel was manufactured with a target density of 50 kgrm3 and a fiber
Fig. 2. Knoop indentation at 2 N load.
K.E. Parmenter, F. Milsteinr Journal of Non-Crystalline Solids 223 (1998) 179–189
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Fig. 3. Load versus displacement for unreinforced silica aerogel during a hardness measurement. The relative displacement d at the ‘preload value’ of 2 N is used to compute the hardness in Eqs. Ž2.1. and Ž2.2..
percentage of 10%. Tests were performed on compression specimens machined from two different batches of bulk material. Specimens from one batch were tested within one week of being machined, and specimens from the other batch were stored in an air environment, under ambient conditions, for 2 months before being tested. The second type was manufactured with a target density of 80 kgrm3 and a fiber percentage of 25%. For this type of aerogel, all tests were done on specimens machined from the same batch of bulk material. Some compression specimens were tested within a week of being machined, some were tested after being stored in an air environment, under ambient conditions, for approximately 2
months, and the remaining were tested after being stored in the same air environment for 2 months and then in a desiccator at ambient temperature for 10 days. Tensile, shear and hardness-creep tests were performed on an exploratory basis. Tensile tests were performed with the testing machine described previously using aerogel specimens cut from bulk material into ‘dog-bone’ shapes. Specimens were held with pins between the top and bottom portions of a tension fixture, and loaded by raising the top portion at a rate of 0.102 mmrmin until fracture. Crosshead displacement was determined from machine displacement. All tensile tests were conducted under ambient conditions. Shear tests were conducted with notched beam Iosipescu specimens in antisymmetric four point bending w11x. The load was measured with a compression load cell and the displacement was determined from machine displacement. The crosshead speed was 0.102 mmrmin and experiments were conducted under ambient conditions. Samples tested in this way will have virtually pure shear in the notch-root axis section w11x. Since brittle materials typically fail in tension, this type of test can yield a lower bound of shear strength. Diagrams depicting Iosipescu specimens failing by pure shear and by tension are provided in Fig. 4. A specimen failing by pure shear will exhibit cracking across the notch-root axis, as in Fig. 4a, whereas a specimen failing by tension will exhibit two areas of cracking outside of the notch-root axis in the pattern shown in Fig. 4b. During hardness testing, the time at maximum displacement was varied to determine if the aerogels were prone to stress relaxation or creep. Specimens
Table 2 Summary of compression results for specimens freshly machined, aged in air for 2 months, and aged in air for 2 months and then desiccated for 10 days Fiber percent Ž%.
Target density Žkgrm3 .
Final density Žkgrm3 .
Matrix density Žkgrm3 .
Storage
No. of specimens
Compressive strength, S ŽMPa.
Strain at fracture, ´ f Žmmrmm.
Modulus at 50% of S ŽMPa.
Modulus at 90% of S ŽMPa.
10 10 25 25 25
50 50 80 80 80
230 250 240 250 240
207 225 180 188 180
fresh aged fresh aged desiccated
9 2 3 3 4
1.01 " 0.05 1.07 " 0.05 0.77 " 0.02 0.77 " 0.09 0.90 " 0.05
0.067 " 0.004 0.045 " 0.002 0.073 " 0.007 0.045 " 0.004 0.047 " 0.004
23.4 " 1.4 34.2 " 0.2 23.9 " 1.4 28.9 " 5.9 30.6 " 2.1
18.0 " 0.7 28.4 " 0.1 16.1 " 0.8 25.1 " 3.8 26.9 " 1.5
K.E. Parmenter, F. Milsteinr Journal of Non-Crystalline Solids 223 (1998) 179–189
Fig. 4. Diagrams of Ža. an Iosipescu specimen failing by pure shear and Žb. an Iosipescu specimen failing by tension.
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Fig. 5. Representative stress–strain curves for aerogels under compressive loading. Degree of fiber reinforcement Žmass %. and target density Žkgrm3 . are shown in the legend.
were loaded at a rate of 0.102 mmrmin to approximately 14 N and displacement was held constant for a time before load was reduced. The time at maximum displacement ranged from 0 to 60 min.
3. Results 3.1. Hardness and compression tests Fig. 5 contains representative stress–strain curves for various aerogel specimens under compressive loading. Hardness and compressive strength are plotted in Fig. 6 as a function of fiber percentage. Lines in this figure connect data points for samples with the same target density. Data in Fig. 6 represent mean average values of the properties listed on the ordinate axes; the number of tests, mean values and standard deviations are listed in Table 1. Fig. 7 shows the matrix density versus the target density for these samples and Figs. 8–10 show the hardness, compressive strength, strain at fracture and secant moduli as functions of matrix density. Lines in Figs. 7–10 connect data points for samples with the same fiber percentages and the data points in Figs. 8–10 represent mean averages of the ordinate-scale properties, the numerical values of which are also listed in Table 1. Fig. 11 shows the relationship between hardness and compressive strength. Compression re-
Fig. 6. Hardness H and compressive strength S versus fiber reinforcement Žmass %. with target density Žkgrm3 . as a parameter.
Fig. 7. Target density Žkgrm3 . versus matrix density Žkgrm3 . with fiber reinforcement Žmass %. as a parameter.
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K.E. Parmenter, F. Milsteinr Journal of Non-Crystalline Solids 223 (1998) 179–189
Fig. 8. Hardness H and compressive strength S versus matrix density Žkgrm3 . with fiber reinforcements Žmass %. as a parameter.
Fig. 11. Average compressive strength S versus average hardness H of silica aerogels; the fiber contents Žmass %. and target densities Žin kgrm3 . are also indicated.
sults in Table 1 and Figs. 5 and 6 and 8–11 are from samples that were tested within one week of being machined. Results from experiments to determine the influences of age and storage environment on aerogel compressive behavior tabulated in Table 2 are shown in Figs. 12 and 13. Fig. 12 compares the compressive responses of specimens Ž10% fibers, target density s 50 kgrm3 . aged for 2 months in air with those tested within a week of being machined. Fig. 13 is a comparison of compressive responses of specimens Ž25% fibers, target densitys 80 kgrm3 . aged for 2 months in air, with specimens aged for 2 Fig. 9. Strain at fracture ´ f versus matrix density Žkgrm3 . with fiber reinforcement Žmass %. as a parameter.
Fig. 10. Secant moduli, E50 % and E90% , versus matrix density Žkgrm3 . with fiber reinforcements Žmass %. as a parameter.
Fig. 12. Comparison of stress–strain curves for freshly machined specimens and specimens aged in air for 2 months. Target density s 50 kgrm3 and fiber percentages10% Žby mass..
K.E. Parmenter, F. Milsteinr Journal of Non-Crystalline Solids 223 (1998) 179–189
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approximately 23 MPa. The ultimate tensile strength of this specimen is 0.25 MPa. Shear tests were attempted on six Iosipescu specimens. Five specimens had a target density of 80 kgrm3 and 10% fibers and one specimen had a target density of 80 kgrm3 and 25% fibers. Four specimens failed in tension while one failed under mixed-mode conditions. A lower bound of shear strength, equal to approximately 0.1 MPa for both types of material, was obtained. The results of hardness creep tests are shown in Fig. 12. Here the hardness versus time data are plotted. A line has been drawn to show the trend of the data.
Fig. 13. Comparison of stress–strain curves for freshly machined specimens, specimens aged in air for 2 months and specimens aged in air for 2 months and desiccated for 10 days. Target density s80 kgrm3 and fiber percentages 25% Žby mass..
months in air and then stored in a desiccator for 10 days, and with those tested within a week of being machined. 3.2. Other mechanical tests Tensile tests proved to be very challenging owing to practical difficulties machining and handling specimens with small cross-sectional areas within the ‘gage length’. As a result, only three of ten specimens machined remained intact for testing. Two specimens tested consisted of 25% fibers, and had a target density of 80 kgrm3 , while one specimen consisted of 5% fibers with a target density of 80 kgrm3. The tensile stress–strain responses Žnot depicted. show a significant discrepancy between the two specimens manufactured with 25% fibers and a target density of 80 kgrm3. Their initial slopes Ži.e. apparent Young’s moduli. agree well, with value approximately 13 MPa, but diverge at a strain of approximately 0.005 mmrmm. The ultimate tensile strength of the weaker specimen Ž0.18 MPa. is 44% less than that of the stronger specimen Ž0.32 MPa.. The apparent Young modulus of the 5%, 80 kgrm3 specimen is significantly larger, with a value of
4. Discussion Table 1 and Figs. 5 and 6 indicate that hardness, compressive strength, strain at fracture and secant moduli all vary with target density and fiber percentage. Both the hardness and the compressive strength tend to decrease with an increase in fiber percentage for a given target density and to increase with an increase in target density for a given fiber percentage. The strain at fracture tends to decrease with an increase in target density for a given fiber percentage, but does not follow a discernible trend with fiber percentage, when target density is the considered parameter. Secant moduli increase with target density for a given fiber percentage and mostly decrease with an increase in fiber percentage for a given target density. In order to gain greater insight into the mechanical response of the aerogels and its dependency on fiber content and density, it is of interest to distinguish between the target density and the final matrix density, particularly since the matrix density after supercritical drying is considerably greater than the target density. Fig. 7 shows that, for a given fiber content, the matrix density increases with target density, as expected; additionally, for a given target density, a higher fiber content yields a lower matrix density, suggesting that the fibers retard shrinkage. For a given fiber content, Fig. 8 shows that the hardness and compressive strength increase with matrix density, while Fig. 9 shows that the strain at
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K.E. Parmenter, F. Milsteinr Journal of Non-Crystalline Solids 223 (1998) 179–189
fracture decreases with matrix density. This inverse relationship between strength and strain at failure is typical of many material systems. Fig. 9 also indicates that, in the higher ranges of matrix density, the strain at fracture decreases with increasing fiber content, whereas in the lower ranges it appears that increasing fiber content may increase strain at fracture. This may in part be a consequence of fibers reducing shrinkage during processing; however, at 25% fiber content, the fibers also seem to yield enhanced strain at fracture. That is, in the range of matrix densities less than about 180 kgrm3, apparently the strain at fracture for the aerogels containing 25% fibers significantly exceeds that of the composites with 10% fiber content. Such enhancement of strain at fracture is generally what is sought from the fabrication of composite materials. Fig. 10 shows that the secant moduli also increase with matrix density, for a given fiber content and, in the lower matrix density range Žless than about 250 kgrm3 ., secant moduli increase with fiber percentage for a given matrix density, thus indicating that the fibers can act to stiffen aerogels. The stress–strain behavior shown in Fig. 5 is qualitatively similar to that reported for unreinforced silica aerogels at low strains in Ref. w2x. However, at large strains, there are divergences between the present results and those of Ref. w2x, in that the latter exhibit a region where the stress–strain curves become upwardly-concave at large strains, whereas in the present tests, fracture occurred before such behavior was encountered. Since hardness is a measure of the resistance to localized, compression in the neighborhood of the indenter, it is reasonable to expect a relationship between hardness and compressive strength. Such a relationship is useful because hardness determination is less destructive than traditional compression testing. Fig. 11 shows the average compressive strength of the specimens plotted against the average hardness. A line has been drawn in to show the trend of the data. Considering the wide range of processing parameters investigated, there is reasonably good correlation between compressive strength and hardness. Also, as mentioned above, the hardness and compressive strength tend to decrease with an increase in fiber percentage for a given target density. One exception to this trend was found with speci-
mens of target density equal to 40 kgrm3 ; for these specimens, the hardness and compressive strength of the 25% fiber-reinforced material are greater than the hardness and compressive strength of 10% fiber-reinforced material, but are smaller than that of the 5% material. It is significant that hardness testing, alone, would have ‘uncovered’ the anomalous behavior of the compressive strengths of these samples. Table 2 and Figs. 12 and 13 indicate that the aging process tends to increase secant moduli, while decreasing the strain at fracture, and not significantly affecting the compressive strength, for both types of materials. Therefore, the toughness decreases and specimens become more brittle with age. This may in part be a consequence of a density increase with aging. However, the strains at fracture of the aged 10% and 25% fiber reinforced specimens Ži.e. 0.045 " 0.002 and 0.045 " 0.004, respectively. are much lower than what would be expected for freshly machined specimens with the respective matrix densities of 225 and 188 kgrm3, that were observed following aging. This conclusion is made evident by comparing these values of failure strain with those of similar fiber contents and matrix densities in Fig. 9. Furthermore, even though the density decreases noticeably after desiccation, the mechanical responses of the desiccated specimens are similar to those of the specimens aged in air. Results also indicate a slight increase in strength during desiccation. Comparison of tensile with compression results indicates that the mechanical responses of the samples are clearly superior in compression; e.g. in compression ´ f is about four or five times greater than in tension, and the ultimate tensile strength in compression is at least double that in tension. Four of five Iosipescu specimens failed in tension rather than in shear which is consistent with brittle material behavior. Time-dependent hardness results in Fig. 14 indicate that, with an increase in time at maximum displacement, load relaxed, indentation depth increased and apparent hardness decreased. Relaxation was initially rapid and then gradually approached a constant value. A plot of inverse hardness versus time exhibits behavior that is typical of a plot of strain versus time for creep, i.e. there is an initial or primary Žtransient, non-linear. region for times approximately less than or equal to a half hour and for
K.E. Parmenter, F. Milsteinr Journal of Non-Crystalline Solids 223 (1998) 179–189
Fig. 14. Indicated hardness versus the time that the specimen was held at the maximum displacement during the measurement procedure.
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less than about 250 kgrm3. The greater relative enhancement of mechanical properties, owing to fiber reinforcement, was found for the specimens with smaller matrix densities. Aerogels are sensitive to moisture absorption from handling and storage, tend to become more brittle with aging and may exhibit stress relaxation Žor creep. under certain conditions. Tensile and shear test results suggest that the aerogels have low tensile strengths relative to compressive and shear strengths, which is typical of brittle materials.
Acknowledgements greater times there exists a secondary Žsteady state, linear. region. This is readily understood from the consideration that hardness varies inversely with indent depth.
5. Conclusions Good correlation between hardness and compressive strength was found over a wide range of processing parameters for unreinforced and fiber-reinforced silica aerogels. Aerogels generally exhibited lower compressive strengths and decreased elastic moduli when reinforced with fibers. This is largely due to the greater matrix densities observed for unreinforced and slightly reinforced aerogels relative to highly reinforced aerogels. During supercritical drying, fibers support the matrix, reducing shrinkage. Without fibers, or with smaller numbers of fibers, the matrix shrinks more. Hardness, compressive strength and secant moduli increase, while the strain at fracture decreases as the matrix density increases. For specimens in the lower range of matrix density Žless than approximately 180 kgrm3 ., high fiber reinforcement had a beneficial effect on strain at fracture. The hardness and compressive strength did not show discernible trends with fiber percentage for a given matrix density. However, the secant moduli increased with an increase in fiber percentage for a given matrix density in the range of matrix densities
This work was supported by the National Aeronautics and Space Administration, Grant No. NAG 2-930. The authors wish to thank Daniel Rasky and Susan White of NASA, particularly for providing the samples and a description of sample preparation, and Kirk Fields and Greg Carver of UCSB for helping to implement the experiments and machining the specimens.
References w1x J. Fricke, J. Non-Cryst. Solids 147&148 Ž1992. 356. w2x J.M. Arvidson, L.L. Scull, Adv. Cryogenic Eng. Mater. 32 Ž1986. 243. w3x M. Gronauer, A. Kadur, J. Fricke, in: J. Fricke ŽEd.., Aerogels, Springer, Berlin, 1986, p. 6. w4x T. Woignier, J. Phalippou, Rev. Phys. Appl. C4-4 24 Ž1989. 179. w5x J. Cross, R. Goswin, R. Gerlach, J. Fricke, Rev. Phys. Appl. C4-4 24 Ž1989. 185. w6x J. Gross, J. Fricke, J. Non-Cryst. Solids 145 Ž1992. 217. w7x J. Gross, J. Fricke, R.W. Pekala, L.W. Hrubesh, Phys. Rev. B 45 Ž22. Ž1992. 12774. w8x J.D. LeMay, T.M. Tillotson, L.W. Hrubesh, R.W. Pekala, Mater. Res. Soc. Symp. Proc. 180 Ž1990. 321. w9x R.W. Pekala, L.W. Hrubesh, T.M. Tillotson, C.T. Alviso, J.F. Poco, J.D. LeMay, Mater. Res. Soc. Symp. Proc. 207 Ž1991. 197. w10x K. Kim, F. Milstein, Construct. Building Mater. 1 Ž1987. 209. w11x N. Iosipescu, Rev. Mec. Appl. 1 Ž1963. 147.
Mechanical properties of silica aerogels Kelly E. Parmenter, Frederick Milstein
)
Departments of Mechanical Engineering and Materials, UniÕersity of California, Santa Barbara, CA 93106, USA Received 4 November 1996; revised 26 August 1997
Abstract Aerogels are extremely low density solids that are characterized by a high porosity and pore sizes in the order of nanometers. The mechanical behavior of silica aerogel was investigated with hardness, compression, tension and shear tests. The influences of testing conditions, storage environment and age were examined, with particular attention paid to the effects of processing parameters, including fiber-reinforcement. Good correlation was found between hardness and compressive strength over a wide range of processing parameters. Increasing fiber reinforcement generally retarded shrinkage during fabrication and yielded smaller matrix densities for a given target density. For a given fiber content, hardness, compressive strength and elastic moduli increased and strain at fracture decreased with increasing matrix density. In the lower ranges of matrix density, fiber reinforcement increased strain at fracture and elastic moduli. The mechanical response was also sensitive to environment and storage history. With age, the compressive strength and elastic moduli increased while the strain at fracture decreased. Tension and shear results indicate that shear strength of aerogels exceeds tensile strength which is consistent with brittle materials response. q 1998 Elsevier Science B.V.
1. Introduction Silica aerogels are high porosity, extremely low density solids composed of interconnected particles that form an open nanostructure. As a result of the low thermal conductivity of silica and nanometer pore sizes the thermal conductivity of silica aerogel is very low. Low thermal conductivity and optical properties make silica aerogels desirable for insulating applications such as cover layers for windows and solar collectors and as replacements for chlorofluoro carbon foams in cryo-vessels w1x. The properties of aerogels that make them such good insulators also make them inherently fragile and brittle. Thus, their use in load-bearing applications presents )
Corresponding author. Tel.: q1-805-8933037; fax: q1-8058938651; e-mail: [email protected].
a challenge. Currently, attention is being placed on improving the mechanical properties of aerogels without sacrificing other unique properties. Relatively few experiments to determine the mechanical properties of aerogels have been carried out to date. No results for fiber-reinforced silica aerogels have been found in the literature. Experiments most applicable to the present work include work on unreinforced silica aerogels by Arvidson and Scull who measured compressive properties of unreinforced silica aerogel at 295, 76 and 20 K w2x. Gronauer et al. measured Young’s modulus using sound velocity measurements w3x. Woignier and Phalippou measured Young’s modulus and the fracture strength with a three point flexural technique, and the toughness with a single edge notched beam in three point bending w4x. Ultrasonic and static compression experiments have been undertaken to
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 Ž 9 7 . 0 0 4 3 0 - 4
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determine the elastic moduli w5–7x. LeMay et al. w8x and Pekala et al. w9x measured the compressive moduli of silica aerogels as a function of density and pH of the precurser gel Žalcogel.. They found that the compressive modulus can be described by a simple scaling law, and that changes in the pH of the alcogel significantly affect the aerogel morphology. Silica aerogel data were also compared with compressive moduli of organic materials. This work investigates the mechanical behavior of fiber-reinforced and unreinforced silica aerogels. Two processing parameters, the mass percentage of fiber reinforcements and the target density, were altered to obtain aerogels with differing physical characteristics. The target density is a readily controllable processing variable, based on the mass of the aerogel phase and the volume of the original mold. The mechanical behavior of the aerogels was studied by hardness, compression, tension and modifications thereof. Particular attention was paid to the effects of processing parameters, testing conditions, storage environment and age on the mechanical behavior of aerogels.
2. Experimental procedures The source of silica for the aerogels that were tested in this study was tetraethylorthosilicate ŽTEOS.. The aerogels were manufactured by first dissolving TEOS ŽSiŽOCH 2 CH 3 .4 . in ethanol. The mixture was next hydrolyzed with water at room temperature, and a cross-linked silica network was produced. The fiber reinforcements were then mixed into the solution, while it was being stirred at a constant rate. The mass percentage of reinforcements was varied from 0 to 25% and the target density was varied from 40 to 80 kgrm3. The reinforced aerogels contained a mixture of 68% silica fibers, 20% alumina fibers and 12% aluminaborosilicate fibers, with diameters of 3, 2–4 and 8 mm, respectively. All fibers had lengths of 1.27 cm. The solution was base-catalyzed with ammonia and ammonium fluoride until it reached a pH of 6.5 and then it was poured into molds. The molds were rectangular, with dimensions of 1 = 2 = 4 inch. The target density is the mass of the aerogel phase divided by the mold volume Žtarget density does not
include the mass of the fibers.. Gelation occurred within 30 min, after which the gels further solidified overnight in the molds. The samples were aged for three days in ethanol before they were supercritically dried. Gels were supercritically dried by placing them in an autoclave in an ethanol bath, and liquid carbon dioxide was introduced to displace the ethanol. The autoclave was then heated to above critical temperature to vaporize the solvent while eliminating its saturated vapor phase. The vapor was then evacuated and the aerogels were cooled. In the preparation of these materials, the autoclave was pressurized to 600 psi and then the temperature was increased to 358C causing the pressure to rise to 1200 psi. Final aerogelrfiber composite densities are significantly larger than the target densities owing to shrinkage during processing and to the additional mass of fiber reinforcements. The final density is taken to be the final mass Žincluding the fibers. divided by the final volume. Additionally, the final matrix density Žwhich is simply called the matrix density. was calculated by subtracting the mass of the fibers and neglecting their volume Ži.e. by assuming that the final volume of the matrix is approximately equal to the final volume of the composite.. These silica aerogels were found to be physically destroyed by water Žhydrophilic. and other liquids. In addition, it was observed that perspiration from fingers and hands caused micro-cracks to form on surfaces that were handled without gloves. To prevent this from occurring, all test specimens were handled with gloves. Moreover, special care was taken to degrease and dry all equipment that came in contact with the specimens. Hardness testing is widely used because of its non-destructive nature, and for many materials relations exist between hardness and strength. Correlations between hardness and compressive strength have been established in ‘non-traditional’ materials, such as polymer concretes w10x. Here we show that the compressive strength and hardness of fiber-reinforced silica aerogels are also well correlated. We would therefore expect good correlation between compressive strength and hardness in silica aerogels. Fiber contents and densities of the samples subjected to hardness and compression testing are listed in Table 1.
15.0"2.1 22.3"3.1 0.79"0.02 15
0.077"0.010
14.1"0.6 18.3"3.2 33.9"2.5 6.1"0.9 18.0"0.7 31.8"3.2 5.3"0.5 16.4"1.8 20.4"3.2 36.0"3.4 8.1"1.6 23.4"1.4 30.4"4.4 8.6"0.7 0.100"0.009 0.071"0.010 0.053"0.004 0.069"0.007 0.067"0.004 0.051"0.003 0.142"0.015 1.01"0.03 1.00"0.08 1.45"0.18 0.34"0.03 1.01"0.05 1.27"0.14 0.55"0.03 3 3 4 6 9 15 16
5.37"0.47 2.20" 0.26 5.67" 1.84 0.97" 0.04 3.71" 0.55 5.37" 2.71 1.54" 0.06 2.02"0.24 2.11"0.21 12 10 6 7 6 12 14 24 10 240 247 304 171 207 297 143 150 180 – 40 80 40 50 80 40 50 80 0 5 5 10 10 10 25 25 25
240 260 320 190 230 330 190 200 240
Secant modulus at 50% of S ŽMPa. Strain at fracture, ´ f Žmmrmm. Compressive strength, S ŽMpa. No. of compression tests Mean hardness ŽMPa. No. of hardness indents Matrix density Žkgrm3 . Final density Žkgrm3 . Target density Žkgrm3 .
H s LrA. Ž 2.2 . The bulk of the hardness tests were carried out with a maximum load of approximately 14 N, a crosshead speed of 0.102 mmrmin and no time delay at maximum load. ŽFor the aerogel manufactured with a target density of 40 kgrm3 and a fiber percentage of 10%, the maximum load was lowered to 10.2 N because of the extreme softness of the material.. The
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Fiber percentage Žmass %.
A s p Dd . Ž 2.1 . The hardness, H, was defined as the maximum load, L, divided by the indent surface area:
Table 1 Summary of hardness and compression results. The numerical values following the ‘" signs’ are standard deviations
Attempts were made to determine hardness by Vickers and Knoop tests; however, these methods failed to work on the silica aerogel specimens. At very small loads Ž; 0.25 N., the indentation pressure was too large for these fragile materials and resulted in cracks and surface cave-ins as shown in Figs. 1 and 2. In addition, because the aerogels absorb and transmit light more readily than they reflect it, it was difficult to obtain enough contrast in the magnified images of the indents to make accurate measurements of indent size. This was particularly true for very low loads, and for the more opaque Žfiber-reinforced. aerogels. Attempts to use dyes to improve the contrast of the magnified images were unsuccessful because the dyes caused cracks on the surfaces of the aerogels. Vickers and Knoop hardness tests demonstrated the need to reduce indentation pressure substantially in order to deform the aerogels without cracking. In an alternative approach, the indents were made with a 19.05 mm diameter steel ball, at loads of 18.2 N and smaller. A ball and socket fixture was secured to the crosshead of a displacement-controlled Instron 1123 testing machine. The load was measured with a compression load cell and the crosshead displacement was measured with a linear variable differential transformer ŽLVDT.. All tests were conducted under ambient conditions. An initial preload of 2.0 N was applied to minimize surface effects. The load was subsequently applied to the ‘full-loading’ value and then reduced to the preload value where the depth, d , was determined. A representative load–displacement curve for an unreinforced aerogel specimen is shown in Fig. 3. The indent surface area, A, was approximated from the measured value of d and ball diameter, D, with the relationship
Secant modulus at 90% of S ŽMPa.
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maximum load was varied to determine whether the hardness tests were ‘load sensitive’. The peak loads ranged from 10.2 to 18.3 N. In this range, the hardness was not sensitive to load, within the scatter due to material inhomogeneities. Loads higher than 18.3 N tended to crack the specimens and loads smaller than 10.2 N tended to yield indiscernible results. Compression tests were performed with the same machine used for hardness tests. Compression specimens with 2:1 height:width ratios were cut from raw material into rectangular blocks, with nominal dimensions of 0.3 = 0.3 = 0.6 inch. The aerogels could be readily cut with a diamond, slitting saw. The more difficult part of specimen preparation was gripping the specimens, not the actual cutting. The gripping problem was solved with a vacuum chuck. The specimens were placed, one at a time, between the top and bottom portions of a compression fixture and were loaded at a rate of 0.102 mmrmin by lowering the top portion of the fixture Žwhich was secured to the crosshead. until they fractured macroscopically. The bottom portion of the compression fixture was a stationary flat plate, whereas the top portion consisted of a ‘frictionless’ hemisphere secured into a socket with vacuum grease. The top
portion was thus self-aligning. The load was measured with the compression load cell and the crosshead displacement was measured with a LVDT. The majority of tests were conducted under ambient conditions. The load–displacement curves were converted to stress–strain curves by dividing the loads by the original cross-sectional areas of the specimens, and the displacements by the original heights of the specimens. The compressive strength, the strain at fracture, ´ f , and secant moduli, E50% and E90% , were determined from the stress–strain data. The compressive strength is defined as the maximum stress carried by the specimens during a test, and the strain at fracture is the strain at which macroscopic failure of the specimen occurred. Each secant modulus was determined by measuring the slope between two points on the stress–strain curves. For E50 % , the slope was calculated between the point of stress equal to 0.040 MPa and the point where the stress is 50% of the compressive strength. For E90 % , the slope was calculated between the point of stress equal to 0.040 MPa and the point where the stress is 90% of the compressive strength. The slopes are referenced to the 0.040 MPa value to reduce or eliminate possible effects of surface irregularities.
Fig. 1. Vickers indentation at 1 N load.
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The influences of age and storage environment on aerogel compression results were quantified by comparing stress–strain curves for aerogels that had different storage histories. Two types of aerogels were
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investigated in this manner. The fiber contents, densities and histories of these materials are summarized in Table 2. The first type of aerogel was manufactured with a target density of 50 kgrm3 and a fiber
Fig. 2. Knoop indentation at 2 N load.
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Fig. 3. Load versus displacement for unreinforced silica aerogel during a hardness measurement. The relative displacement d at the ‘preload value’ of 2 N is used to compute the hardness in Eqs. Ž2.1. and Ž2.2..
percentage of 10%. Tests were performed on compression specimens machined from two different batches of bulk material. Specimens from one batch were tested within one week of being machined, and specimens from the other batch were stored in an air environment, under ambient conditions, for 2 months before being tested. The second type was manufactured with a target density of 80 kgrm3 and a fiber percentage of 25%. For this type of aerogel, all tests were done on specimens machined from the same batch of bulk material. Some compression specimens were tested within a week of being machined, some were tested after being stored in an air environment, under ambient conditions, for approximately 2
months, and the remaining were tested after being stored in the same air environment for 2 months and then in a desiccator at ambient temperature for 10 days. Tensile, shear and hardness-creep tests were performed on an exploratory basis. Tensile tests were performed with the testing machine described previously using aerogel specimens cut from bulk material into ‘dog-bone’ shapes. Specimens were held with pins between the top and bottom portions of a tension fixture, and loaded by raising the top portion at a rate of 0.102 mmrmin until fracture. Crosshead displacement was determined from machine displacement. All tensile tests were conducted under ambient conditions. Shear tests were conducted with notched beam Iosipescu specimens in antisymmetric four point bending w11x. The load was measured with a compression load cell and the displacement was determined from machine displacement. The crosshead speed was 0.102 mmrmin and experiments were conducted under ambient conditions. Samples tested in this way will have virtually pure shear in the notch-root axis section w11x. Since brittle materials typically fail in tension, this type of test can yield a lower bound of shear strength. Diagrams depicting Iosipescu specimens failing by pure shear and by tension are provided in Fig. 4. A specimen failing by pure shear will exhibit cracking across the notch-root axis, as in Fig. 4a, whereas a specimen failing by tension will exhibit two areas of cracking outside of the notch-root axis in the pattern shown in Fig. 4b. During hardness testing, the time at maximum displacement was varied to determine if the aerogels were prone to stress relaxation or creep. Specimens
Table 2 Summary of compression results for specimens freshly machined, aged in air for 2 months, and aged in air for 2 months and then desiccated for 10 days Fiber percent Ž%.
Target density Žkgrm3 .
Final density Žkgrm3 .
Matrix density Žkgrm3 .
Storage
No. of specimens
Compressive strength, S ŽMPa.
Strain at fracture, ´ f Žmmrmm.
Modulus at 50% of S ŽMPa.
Modulus at 90% of S ŽMPa.
10 10 25 25 25
50 50 80 80 80
230 250 240 250 240
207 225 180 188 180
fresh aged fresh aged desiccated
9 2 3 3 4
1.01 " 0.05 1.07 " 0.05 0.77 " 0.02 0.77 " 0.09 0.90 " 0.05
0.067 " 0.004 0.045 " 0.002 0.073 " 0.007 0.045 " 0.004 0.047 " 0.004
23.4 " 1.4 34.2 " 0.2 23.9 " 1.4 28.9 " 5.9 30.6 " 2.1
18.0 " 0.7 28.4 " 0.1 16.1 " 0.8 25.1 " 3.8 26.9 " 1.5
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Fig. 4. Diagrams of Ža. an Iosipescu specimen failing by pure shear and Žb. an Iosipescu specimen failing by tension.
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Fig. 5. Representative stress–strain curves for aerogels under compressive loading. Degree of fiber reinforcement Žmass %. and target density Žkgrm3 . are shown in the legend.
were loaded at a rate of 0.102 mmrmin to approximately 14 N and displacement was held constant for a time before load was reduced. The time at maximum displacement ranged from 0 to 60 min.
3. Results 3.1. Hardness and compression tests Fig. 5 contains representative stress–strain curves for various aerogel specimens under compressive loading. Hardness and compressive strength are plotted in Fig. 6 as a function of fiber percentage. Lines in this figure connect data points for samples with the same target density. Data in Fig. 6 represent mean average values of the properties listed on the ordinate axes; the number of tests, mean values and standard deviations are listed in Table 1. Fig. 7 shows the matrix density versus the target density for these samples and Figs. 8–10 show the hardness, compressive strength, strain at fracture and secant moduli as functions of matrix density. Lines in Figs. 7–10 connect data points for samples with the same fiber percentages and the data points in Figs. 8–10 represent mean averages of the ordinate-scale properties, the numerical values of which are also listed in Table 1. Fig. 11 shows the relationship between hardness and compressive strength. Compression re-
Fig. 6. Hardness H and compressive strength S versus fiber reinforcement Žmass %. with target density Žkgrm3 . as a parameter.
Fig. 7. Target density Žkgrm3 . versus matrix density Žkgrm3 . with fiber reinforcement Žmass %. as a parameter.
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Fig. 8. Hardness H and compressive strength S versus matrix density Žkgrm3 . with fiber reinforcements Žmass %. as a parameter.
Fig. 11. Average compressive strength S versus average hardness H of silica aerogels; the fiber contents Žmass %. and target densities Žin kgrm3 . are also indicated.
sults in Table 1 and Figs. 5 and 6 and 8–11 are from samples that were tested within one week of being machined. Results from experiments to determine the influences of age and storage environment on aerogel compressive behavior tabulated in Table 2 are shown in Figs. 12 and 13. Fig. 12 compares the compressive responses of specimens Ž10% fibers, target density s 50 kgrm3 . aged for 2 months in air with those tested within a week of being machined. Fig. 13 is a comparison of compressive responses of specimens Ž25% fibers, target densitys 80 kgrm3 . aged for 2 months in air, with specimens aged for 2 Fig. 9. Strain at fracture ´ f versus matrix density Žkgrm3 . with fiber reinforcement Žmass %. as a parameter.
Fig. 10. Secant moduli, E50 % and E90% , versus matrix density Žkgrm3 . with fiber reinforcements Žmass %. as a parameter.
Fig. 12. Comparison of stress–strain curves for freshly machined specimens and specimens aged in air for 2 months. Target density s 50 kgrm3 and fiber percentages10% Žby mass..
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approximately 23 MPa. The ultimate tensile strength of this specimen is 0.25 MPa. Shear tests were attempted on six Iosipescu specimens. Five specimens had a target density of 80 kgrm3 and 10% fibers and one specimen had a target density of 80 kgrm3 and 25% fibers. Four specimens failed in tension while one failed under mixed-mode conditions. A lower bound of shear strength, equal to approximately 0.1 MPa for both types of material, was obtained. The results of hardness creep tests are shown in Fig. 12. Here the hardness versus time data are plotted. A line has been drawn to show the trend of the data.
Fig. 13. Comparison of stress–strain curves for freshly machined specimens, specimens aged in air for 2 months and specimens aged in air for 2 months and desiccated for 10 days. Target density s80 kgrm3 and fiber percentages 25% Žby mass..
months in air and then stored in a desiccator for 10 days, and with those tested within a week of being machined. 3.2. Other mechanical tests Tensile tests proved to be very challenging owing to practical difficulties machining and handling specimens with small cross-sectional areas within the ‘gage length’. As a result, only three of ten specimens machined remained intact for testing. Two specimens tested consisted of 25% fibers, and had a target density of 80 kgrm3 , while one specimen consisted of 5% fibers with a target density of 80 kgrm3. The tensile stress–strain responses Žnot depicted. show a significant discrepancy between the two specimens manufactured with 25% fibers and a target density of 80 kgrm3. Their initial slopes Ži.e. apparent Young’s moduli. agree well, with value approximately 13 MPa, but diverge at a strain of approximately 0.005 mmrmm. The ultimate tensile strength of the weaker specimen Ž0.18 MPa. is 44% less than that of the stronger specimen Ž0.32 MPa.. The apparent Young modulus of the 5%, 80 kgrm3 specimen is significantly larger, with a value of
4. Discussion Table 1 and Figs. 5 and 6 indicate that hardness, compressive strength, strain at fracture and secant moduli all vary with target density and fiber percentage. Both the hardness and the compressive strength tend to decrease with an increase in fiber percentage for a given target density and to increase with an increase in target density for a given fiber percentage. The strain at fracture tends to decrease with an increase in target density for a given fiber percentage, but does not follow a discernible trend with fiber percentage, when target density is the considered parameter. Secant moduli increase with target density for a given fiber percentage and mostly decrease with an increase in fiber percentage for a given target density. In order to gain greater insight into the mechanical response of the aerogels and its dependency on fiber content and density, it is of interest to distinguish between the target density and the final matrix density, particularly since the matrix density after supercritical drying is considerably greater than the target density. Fig. 7 shows that, for a given fiber content, the matrix density increases with target density, as expected; additionally, for a given target density, a higher fiber content yields a lower matrix density, suggesting that the fibers retard shrinkage. For a given fiber content, Fig. 8 shows that the hardness and compressive strength increase with matrix density, while Fig. 9 shows that the strain at
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fracture decreases with matrix density. This inverse relationship between strength and strain at failure is typical of many material systems. Fig. 9 also indicates that, in the higher ranges of matrix density, the strain at fracture decreases with increasing fiber content, whereas in the lower ranges it appears that increasing fiber content may increase strain at fracture. This may in part be a consequence of fibers reducing shrinkage during processing; however, at 25% fiber content, the fibers also seem to yield enhanced strain at fracture. That is, in the range of matrix densities less than about 180 kgrm3, apparently the strain at fracture for the aerogels containing 25% fibers significantly exceeds that of the composites with 10% fiber content. Such enhancement of strain at fracture is generally what is sought from the fabrication of composite materials. Fig. 10 shows that the secant moduli also increase with matrix density, for a given fiber content and, in the lower matrix density range Žless than about 250 kgrm3 ., secant moduli increase with fiber percentage for a given matrix density, thus indicating that the fibers can act to stiffen aerogels. The stress–strain behavior shown in Fig. 5 is qualitatively similar to that reported for unreinforced silica aerogels at low strains in Ref. w2x. However, at large strains, there are divergences between the present results and those of Ref. w2x, in that the latter exhibit a region where the stress–strain curves become upwardly-concave at large strains, whereas in the present tests, fracture occurred before such behavior was encountered. Since hardness is a measure of the resistance to localized, compression in the neighborhood of the indenter, it is reasonable to expect a relationship between hardness and compressive strength. Such a relationship is useful because hardness determination is less destructive than traditional compression testing. Fig. 11 shows the average compressive strength of the specimens plotted against the average hardness. A line has been drawn in to show the trend of the data. Considering the wide range of processing parameters investigated, there is reasonably good correlation between compressive strength and hardness. Also, as mentioned above, the hardness and compressive strength tend to decrease with an increase in fiber percentage for a given target density. One exception to this trend was found with speci-
mens of target density equal to 40 kgrm3 ; for these specimens, the hardness and compressive strength of the 25% fiber-reinforced material are greater than the hardness and compressive strength of 10% fiber-reinforced material, but are smaller than that of the 5% material. It is significant that hardness testing, alone, would have ‘uncovered’ the anomalous behavior of the compressive strengths of these samples. Table 2 and Figs. 12 and 13 indicate that the aging process tends to increase secant moduli, while decreasing the strain at fracture, and not significantly affecting the compressive strength, for both types of materials. Therefore, the toughness decreases and specimens become more brittle with age. This may in part be a consequence of a density increase with aging. However, the strains at fracture of the aged 10% and 25% fiber reinforced specimens Ži.e. 0.045 " 0.002 and 0.045 " 0.004, respectively. are much lower than what would be expected for freshly machined specimens with the respective matrix densities of 225 and 188 kgrm3, that were observed following aging. This conclusion is made evident by comparing these values of failure strain with those of similar fiber contents and matrix densities in Fig. 9. Furthermore, even though the density decreases noticeably after desiccation, the mechanical responses of the desiccated specimens are similar to those of the specimens aged in air. Results also indicate a slight increase in strength during desiccation. Comparison of tensile with compression results indicates that the mechanical responses of the samples are clearly superior in compression; e.g. in compression ´ f is about four or five times greater than in tension, and the ultimate tensile strength in compression is at least double that in tension. Four of five Iosipescu specimens failed in tension rather than in shear which is consistent with brittle material behavior. Time-dependent hardness results in Fig. 14 indicate that, with an increase in time at maximum displacement, load relaxed, indentation depth increased and apparent hardness decreased. Relaxation was initially rapid and then gradually approached a constant value. A plot of inverse hardness versus time exhibits behavior that is typical of a plot of strain versus time for creep, i.e. there is an initial or primary Žtransient, non-linear. region for times approximately less than or equal to a half hour and for
K.E. Parmenter, F. Milsteinr Journal of Non-Crystalline Solids 223 (1998) 179–189
Fig. 14. Indicated hardness versus the time that the specimen was held at the maximum displacement during the measurement procedure.
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less than about 250 kgrm3. The greater relative enhancement of mechanical properties, owing to fiber reinforcement, was found for the specimens with smaller matrix densities. Aerogels are sensitive to moisture absorption from handling and storage, tend to become more brittle with aging and may exhibit stress relaxation Žor creep. under certain conditions. Tensile and shear test results suggest that the aerogels have low tensile strengths relative to compressive and shear strengths, which is typical of brittle materials.
Acknowledgements greater times there exists a secondary Žsteady state, linear. region. This is readily understood from the consideration that hardness varies inversely with indent depth.
5. Conclusions Good correlation between hardness and compressive strength was found over a wide range of processing parameters for unreinforced and fiber-reinforced silica aerogels. Aerogels generally exhibited lower compressive strengths and decreased elastic moduli when reinforced with fibers. This is largely due to the greater matrix densities observed for unreinforced and slightly reinforced aerogels relative to highly reinforced aerogels. During supercritical drying, fibers support the matrix, reducing shrinkage. Without fibers, or with smaller numbers of fibers, the matrix shrinks more. Hardness, compressive strength and secant moduli increase, while the strain at fracture decreases as the matrix density increases. For specimens in the lower range of matrix density Žless than approximately 180 kgrm3 ., high fiber reinforcement had a beneficial effect on strain at fracture. The hardness and compressive strength did not show discernible trends with fiber percentage for a given matrix density. However, the secant moduli increased with an increase in fiber percentage for a given matrix density in the range of matrix densities
This work was supported by the National Aeronautics and Space Administration, Grant No. NAG 2-930. The authors wish to thank Daniel Rasky and Susan White of NASA, particularly for providing the samples and a description of sample preparation, and Kirk Fields and Greg Carver of UCSB for helping to implement the experiments and machining the specimens.
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