Mechanical Properties of Magnesia?Spinel Composites
Descripción
J. Am. Ceram. Soc., 90 [8] 2489–2496 (2007) DOI: 10.1111/j.1551-2916.2007.01733.x r 2007 The American Ceramic Society
Journal
Mechanical Properties of Magnesia–Spinel Composites Alan Atkinson,w,* Phillipe Bastid, and Qiuyun Liu Department of Materials, Imperial College, London SW7 2AZ, UK
composites using a variety of mechanical tests.6–8 The present study differs in that the composites have a higher spinel content and are porous.
The mechanical properties of magnesia–spinel composite ceramics, which are candidate materials for supporting solid oxide fuel cells, have been measured as a function of porosity (up to 30%) and temperature (up to 9001C). The theory for the ring-on-ring test has been re-examined to resolve an inconsistency in the literature. The Young’s modulus shows an exponential dependence on porosity that is in agreement with the expectation of minimum solid area models. Fracture toughness, fracture energy, and flexural strength are all approximately proportional to Young’s modulus. The mechanical properties are not greatly dependent on temperature, but there is a detectable increase in fracture toughness with temperature, which could be due to some limited plasticity.
II. Experimental Methods (1) Materials The fuel cell structural material is a two-phase ceramic of magnesium oxide and magnesium aluminate spinel. The composition studied here is nominally 58% by weight MgO and 42% MgAl2O4, which corresponds to approximately the same relative solid volumes. This composition was chosen because it has a suitable CTE to match to yttria-stabilized zirconia SOFC electrolytes. Because MgO and spinel have similar elastic moduli, the thermal expansion coefficient is a linear function of the volume fraction of each phase between the limits of approximately 8 ppm/K for spinel and 13 ppm/K for MgO.3 The average thermal expansion coefficient (from 251 to 10001C) of the composition in this work was measured by dilatometry to be 10.8 ppm/K, which is close to that of stabilized zirconia. The composite material is referred to in abbreviation as magnesia–magnesium– aluminate (MMA). The material was fabricated from the constituent ceramic powders by conventional ceramic shaping techniques and then sintering at 15001C. Coarser powders were used for the porous ceramics because for use as a fuel cell support, it must remain porous during sintering of the zirconia electrolyte to full density. The porous material was produced in the form of calendered plates approximately 4 or 2 mm in thickness. Porosity was in the range of 17%–28%. The specimens were produced in two batches: one with a porosity of approximately 19% and the other 25%. Circular disk specimens and rectangular bar specimens were cut from the porous sintered plates using a silicon carbide wheel and ground to uniform thickness. The ‘‘dense’’ MMA was formed as a monolithic block by isostatic pressing and sintering. Rectangular bar specimens were cut from the block by diamond machining. Specimen dimensions and other preparation procedures are given in the appropriate later sections. The total porosity of each mechanical test specimen was measured by comparing the bulk density (from mass and dimensions) with the theoretical density of each phase (3.579 g/cm3 for MgO and 3.619 for spinel) and the overall composition. Open porosity and pore size distribution were measured on representative specimens by mercury intrusion porosimetry (MIP). Microstructures were characterized by scanning electron microscopy (SEM) of polished sections and fracture surfaces after carbon coating.
I. Introduction
M
AGNESIA-SPINEL
composites are well-established refractory materials, noted for their good thermal shock resistance.1,2 Recently, the material has been considered to be a suitable inert substrate for some designs of solid oxide fuel cell (SOFC).3,4 An additional attraction for this application is that its coefficient of thermal expansion (CTE) can be varied by changing the relative amounts of the constituent phases and thereby adjusted to match that of other fuel cell ceramics (e.g., stabilized zirconia electrolyte). Because the two components of the composite are known to exhibit negligible departures from oxygen stoichiometry, their properties are not influenced by the variations in oxygen activity in the fuel cell environment as is the case with conventional Ni-based cermet support materials (e.g., Malzbender et al.5). In particular, they show no chemical expansion (dimensional changes as a function of oxygen activity). When used as an SOFC substrate, the material must be porous to allow access of gases to the fuel cell electrodes. Thus, the porous ceramic becomes a major structural component of the SOFC and its mechanical properties are particularly important. Because the thickness of the support must be minimized to allow good gas access to the SOFC electrodes, the grain size of the ceramic is smaller than normally used in refractories. For the same reason, the porosity must be maximized. Clearly, a compromise must be struck between mechanical strength and permeability to gases and this requires knowledge of how porosity influences the mechanical properties of the composite ceramic. The objective of the research reported here is to establish and understand the mechanical properties of magnesia–spinel composites, for potential use in SOFCs, as a function of porosity. The main properties of interest are elastic modulus, flexural strength, and fracture toughness. Aksel and co-workers have studied the mechanical properties of dense magnesia–spinel
(2) Measurement of Elastic Modulus Three different methods were used to measure elastic modulus: impulse excitation test; load-displacement in ring-on-ring geometry using disks; and load displacement in four-point bending using rectangular prisms. The load cells were calibrated using standard weights to an accuracy of one part in 1000. For loaddisplacement methods, the specimens were subjected to several loading–unloading cycles to permit ‘‘settling’’ at the loading points. It was generally found that the results of the first loading cycle gave lower apparent stiffness than subsequent cycles due to
D. Green—contributing editor
Manuscript No. 22622. Received December 23, 2006; approved March 26, 2007. This work was supported by the European Commission in the project ‘‘Multi-Functional Solid Oxide Fuel Cell (MF-SOFC).’’ *Member, American Ceramic Society w Author to whom correspondence should be addressed. e-mail: alan.atkinson@ imperial.ac.uk
2489
2490
Journal of the American Ceramic Society—Atkinson et al.
this ‘‘settling’’ process. All displacement data were corrected for machine stiffness, and the accuracy of modulus measurement was checked using aluminum standard specimens and, in the case of four-point bending, strain gauges. The results showed that the method was accurate to within the random errors of reproducibility, which were 73%. (A) Impulse Excitation Test (IET): The IET measures two natural vibrational modes of the specimen from which Young’s modulus, E, and Poisson’s ratio, n, can be determined.9 The measurements were made on disk specimens 50 mm in diameter and with a thickness between 1.23 and 2.45 mm using a resonance system (GrindoSonic MK5, J.W. Lemmens, Leuven, Belgium). The two vibration modes were a cruciformsupported flexure and a ring-supported membrane. (B) Ring-On-Ring Test: The ring-on-ring test measures the load–displacement relationship in biaxial flexure and gives Young’s modulus if a value is assumed for Poisson’s ratio (0.21 from IET measurement). The radius of the inner loading ring (r1) was 4.95 mm and that of the outer (r2) one was 19 mm. The displacement of the center of the disk with respect to the outer loading ring was measured using a linear displacement transducer at a cross-head speed of 0.01 mm/min. Specimen surfaces were ground on 1200-grit silicon carbide paper in order to minimize friction between the specimen and the loading rings due to the roughness of the surface. The value of Young’s modulus is often calculated from the load P and the deflection y (of the center of the specimen) using an equation from Schmitt et al.10: E¼
3ð1 n2 Þr21 P y 2pt3 " # 2 r2 r2 1 1 n r22 r21 r22 r21 1 2 ln þ r1 r1 2 1 þ n r23 r21
(1)
where r3 is the specimen radius and t its thickness. However, another equation has been proposed by Hoffman and Birringer11: 12ð1 n Þ P 3 þ n 2 1n 2 r2 ðr2 r21 Þ ðr2 r21 Þ 12 E¼ 3 16pt y 1þn 1þn r3 2 2 r r r r 1 2 2r22 1 þ 12 ln þ2r21 1 þ 22 ln r3 r3 r1 r2
(2)
This equation gives results for Young’s modulus that are about 40% higher than the values determined from Schmitt’s equation for the dimensions used in the present experiments. Furthermore, the calculation details given in Hoffman and Birringer are not clear. A re-analysis of the load–deflection relationship was therefore carried out based on Timoshenko’s theory of plates and shells12 in order to evaluate the validity of these equations. The equation that has been determined is: 2
E¼
Þr21
(C) Four-Point Bending: Four-point bending Young’s modulus from the load-deflection response: E¼
2Pd12 ðd1 þ 3d2 Þ ywh3
P 2nð1 nÞ r21 r1 4 ln 8 þ 2n r2 y 1 þ n r23
3ð1 n 8pt3 r1 2ð1 nÞ n r2 2 n n2 r22 ð1 þ Þ 12 4nþ ln 1þn 2 r3 r2 1 þ n r23 2 2 2 4 r 2ð1 nÞ r2 2 n n r2 (3) þ ð4 þ nÞ 22 þ 1 þ n r23 1 n r21 r23 r1
Although it appears very different, the results given by Eq. (3) were found to be very similar to the values determined by Schmitt’s equation (Eq. (1)). The difference is of the order of only 2%. We have therefore used Eq. (3) to analyze the results and conclude that Hoffman’s equation (Eq. (2)) is incorrect.
gives
(4)
where d1 is the distance between the inner and outer loading roller points (11 mm), d2 is the half distance between the inner rollers (also 11 mm), h is the height of the specimen, and w its width.9 The deflection in this case is the relative displacement of the upper and lower rollers and was measured by a linear displacement transducer connected between the upper and lower parts of the loading jig. The width of the porous specimens was 5 mm, or lower, and the height was equal to 2.4 mm. The width of the dense specimens was 4 mm and the height was equal to 3 mm. Young’s modulus was measured as the average from both loading and unloading slopes and from four loading/unloading cycles for each specimen. Friction was minimized by using free rollers located in grooves as the specimen support points. Measurements at above room temperature (up to 8801C) were carried out using a four-point loading rig of the same dimensions constructed from silicon nitride, and using the same procedure.
(3) Measurement of Flexural Strength The flexural strength was measured in four-point bending and ring-on-ring configuration using the same arrangements as described for the elastic modulus. The failure stress was taken to be the outer fiber stress at fracture and is given by sf ¼
3PðS1 S2 Þ 2h2 d
(5a)
for four-point bending and sf ¼
2
Vol. 90, No. 8
3ð1 nÞP r2 1 n r22 r21 þ 2 ln r1 4pt2 1þn r23
(5b)
for the ring-on-ring test.10 Here, S1 is the distance between the outer rollers and S2 between the inner rollers, and P is the total load applied to the specimen, i.e. the force measured by the load cell plus the dead weight of the upper part of the loading jig. The porous fourpoint specimens had a length of approximately 50 mm, a width of 4.5–5 mm and thickness from 1.7 to 2.3 mm. The ‘‘dense’’ specimens had the same dimensions as for modulus measurement. The edges of the ‘‘dense’’ specimens on the tensile face were lightly rounded using 1200-grit SiC paper to suppress premature failure initiation from edge-chipping defects introduced by specimen machining.
(4) Measurement of Fracture Toughness Fracture toughness, KIc, was measured on rectangular bar specimens in four-point bending using the same arrangement. The specimens were mostly single edge notched, but some specimens were tested with chevron notches. The porous test specimens were rectangular bars whose thickness was 4.5 mm and width was 2.4 mm. The edge notch was made using a silicon carbide cutting wheel and then finished with a razor blade and diamond paste, so that the radius at the crack tip was as small as possible. The notch length varied from 0.6 to 2.7 mm. The material at the chevron notch had an outer height of 4 mm and a central height of 1 mm in a bar of height 4.5 mm and width 3.5 mm. The fracture toughness was calculated from the following equation given by Munz and Fett13 for a single edge-notched beam of height W:
August 2007
2491
Mechanical Properties of Magnesia–Spinel Composites pffiffiffi 3Gm a
P S1 S2 KIC ¼ pffiffiffiffiffiffi W B W 2ð1 aÞ3=2
H¼
1:8544P 4a2
(8)
where a is the projected diagonal of the indentation. a with a ¼ W ;
b ¼ 1 a and pffiffiffi Gm ¼ 1:1215 p 5 5 1 3 a a þ a2 þ 5a2 b6 þ exp 6:1342 8 12 8 8 b (6)
For the chevron notch test,13 P KIC ¼ pffiffiffiffiffiffi Y B W
(7)
with
Y ¼ 3:08 þ 5:00a0 þ
8:33a20
rffiffiffiffiffiffiffiffiffiffi! S1 S2 a1 a0 1 þ 0:007 W 2 1 a0
S1 S2 ; W
where a0 5 A0/W, a1 5 A1/W, A0 is the height to the bottom of the chevron, and A1 is the height to the top. The notch dimensions of the edge-notched specimens were measured accurately by optical microscopy of the fracture face after testing.
(5) Measurement of Hardness The hardness of dense MMA was measured with a Vickers indenter using a Leitz Miniload apparatus (MeBtechnik GmbH, Wetzlar, Germany). The hardness was calculated using the equation
III. Results (1) Microstructure A polished section of a typical porous MMA specimen is shown in Fig. 1. The structure contains large solid ‘‘particles,’’ with a size up to 50 mm, and a mean size on section of 15 mm, and smaller porous regions, with a size of up to about 10 mm and a mean size on section of 5 mm. Quantitative image analysis gave a volume fraction of porosity in the range 20%–25% depending on the gray-level setting for distinguishing between solid and porous regions. The intermediate gray contrast is probably due to some rounding of solid particle edges during polishing. The Al elemental maps in Fig. 1 show the locations of the spinel component. The pore size distribution was measured by mercury intrusion porosimetry. The pore entry diameter had a narrow distribution and a mean value of approximately 2 mm. The microstructure of ‘‘dense’’ MMA is also illustrated in Fig. 1. There is some residual porosity (6% in this particular specimen) and the pores are now closed and have an average diameter below 10 mm. (2) Young’s Modulus The stress–strain relationship from load-displacement tests was linear to within experimental error and reproducible over repeated loading and unloading cycles. The accuracy of the measurements was checked using materials of similar dimensions and known Young’s modulus. The materials used were highpurity aluminium (for the porous MMA) and mild steel (for the dense MMA). The Young’s modulus of ‘‘dense’’ MMA at room temperature averaged over five specimens is 19277 GPa and corresponds to an average porosity of 6%. These and the results for porous specimens at room temperature are shown plotted as a
Fig. 1. Scanning electron microscopy micrographs and Al maps of polished sections of (a) porous and (b) ‘‘dense’’ magnesia–magnesium–aluminate.
2492
Vol. 90, No. 8
Journal of the American Ceramic Society—Atkinson et al.
350
90 80
300
70 60 E (GPa)
E (GPa)
250
200
50 40 30
150
20
RoR IET 4 point Calculated exp(-bP) (1-P)(1-P/0.684)
100
50
10 0 0
0 0
5
10
15
20
25
30
Porosity (%)
Fig. 2. Young’s modulus as a function of porosity at room temperature. The lines show fits to the literature models for the effect of porosity on E.
function of porosity in Fig. 2. The results from the different measurement methods are in good agreement and within the specimen-to-specimen variability. The theoretical value for zero porosity (286 GPa) was calculated using the rule of mixtures and data for the pure phases (300 GPa for MgO and 268 GPa14 for spinel). Because the Young’s moduli of the two components are so similar, the modulus of the composite is not sensitive to the model used for its estimation. The effect of temperature on the Young’s modulus of dense MMA is shown in Fig. 3 and, although there might be a slight increase with temperature, this is negligible in comparison with the specimen-to-specimen variability. The results of similar measurements for porous MMA specimens with a porosity of approximately 25% are shown in Fig. 4. In this case, there is evidence of a slight reduction with temperature, but again this is small in comparison with specimen-to-specimen variability.
(3) Flexural Strength The flexural strengths of all the specimens are shown as a function of porosity in Fig. 5. The results for porous material clearly show two groups corresponding to the two batches of material; one centered on an average porosity of 18.3% (where the porosity varies from 17.3% to 19.4%), and one on 24.5% (where the porosity varies from 21.9% to 27.1%). The biaxial strength
200
400 600 Temperature (°C)
800
1000
Fig. 4. Young’s modulus as a function of temperature for porous (approximately 25% porosity) magnesia–magnesium–aluminate.
is slightly higher than the four-point strength despite the fact that the biaxial stress is more likely to act on a defect in a favorable orientation. This is probably because the volume under stress is larger in the four-point test than in the ring-on-ring test. The bending strengths of the porous materials are similar in magnitude to that of 51 MPa reported for a typical Ni/YSZ cermet fuel cell support.15 Weibull plots for the four-point data of the two groups of porous MMA are shown in Fig. 6 according to the equation for failure probability (Pf) s m Pf ¼ 1 exp s0
(9)
where m is the Weibull modulus and s0 is the characteristic Weibull stress.16 The Weibull moduli are approximately 10 for each material set and are typical of a reasonably reliable ceramic. Examination of the fracture faces gave no clear indication of the site of fracture nucleation. A typical fracture surface of porous MMA (Fig. 7) shows trans-granular fracture through the large grains. The fracture surface of dense MMA (Fig. 7) shows a mixture of trans- and inter-granular fracture paths and a much finer grain size of approximately 5 mm. Data for flexural strength at 8801C are shown in Weibull plots in Fig. 8. The mean flexural strengths for both ‘‘dense’’ and porous materials are not significantly different from their roomtemperature values. There are apparent changes in the Weibull moduli, but these are probably an artifact caused by the smaller number of samples in the high-temperature measurements. 180
250
160 Flexural strength (MPa)
E (GPa)
200
150
100
50
140 120 100 80 4 point
60
RoR
40 20
0 0
200
400 600 Temperature (°C)
800
1000
Fig. 3. Young’s modulus as a function of temperature for ‘‘dense’’ (6% porosity) magnesia–magnesium–aluminate.
0 0
5
10
15 20 Porosity (%)
25
30
Fig. 5. Flexural strength at room temperature as a function of porosity.
August 2007 3
1
Porosity = 24.5% 2 y = 10.7x − 36.9
Porosity = 18.3% y = 9.3x − 37.1
"Dense" y = 10.8x − 54.5
1 0 −1
Porosity = 24.5% y = 6.1x −19.1
0.5
"Dense" y = 24.31x −124
0
Ln(-Ln(1-Pf))
Ln (-Ln(1-Pf))
2493
Mechanical Properties of Magnesia–Spinel Composites
−0.5 −1 −1.5 −2
−2
−2.5
−3
−3
−4 3
3.5
4 4.5 Ln (strength/MPa)
5
2
5.5
Fig. 6. Weibull plots of four-point flexural strength at room temperature.
(4) Fracture Toughness For ‘‘dense’’ MMA, the load–displacement curves were characteristic of simple brittle failure with a single well-defined maximum load. However, on porous MMA the chevron notch gives an initial ‘‘pop-in’’ of the crack, which then arrests and requires an increased load to propagate. This suggests increasing crack resistance with crack length in this material. For these specimens, the toughness was calculated using the second maximum load, which was typically 15% greater than the initial ‘‘pop-in’’ load. The results of the fracture toughness measurements are presented in Table I, and the toughness from the single edgenotched beam experiments as a function of notch depth in Fig. 9. The results show that toughness is independent of notch depth and the chevron notch and single-edge notch methods both give the same results to within experimental error for both
2.5
3
3.5
4
4.5
5
5.5
Ln (strength/MPa)
Fig. 8. Weibull plots of four-point flexural strength at 8801C.
the dense and porous materials. This indicates that the sharpness of the single notch is sufficient to nucleate a sharp crack. The results reveal a slight increase in toughness for both ‘‘dense’’ and porous material at the higher temperature.
(5) Hardness The hardness of ‘‘dense’’ MMA was measured using loads from 1 to 10 kg. There was no detectable dependence on load and the hardness was 6.370.3 GPa. Scanning electron microscopy of the indentations showed no evidence of corner cracking from the indentations even at the highest loads. IV. Discussion The results of all the measurements at room temperature are summarized in Table II and, for 8801C, in Table III. The fracture energy, Gc, is calculated from the relationship for plane strain KIc2 ¼
EGc 1 n2
(10)
(1) Comparison with MMA Refractories The most striking feature of the mechanical properties of these ceramics is how different they are from MgO–MgAl2O4 refractory materials studied previously. The values of E measured here in ‘‘dense’’ material (B200 GPa) and that extrapolated to fully dense material (260 GPa) are significantly greater than reported by Aksel et al.6 for hotpressed MMA composites. They found that E decreased with the spinel content, and for 30% spinel, they report values ranging from 70 to 150 GPa depending on the spinel particle size (the smallest particles yielding the highest modulus). They also found that the sonic modulus measurement method yielded higher values of E (180–210 GPa for 30% spinel) than did load–displacement or strain gauge methods.7 However, in the present study, we found no significant difference in the results Table I. Summary of Fracture Toughness Measurements Material
Fig. 7. Fracture faces after fracture at room temperature of (a) porous and (b) ‘‘dense’’ magnesia–magnesium–aluminate.
‘‘Dense’’ ‘‘Dense’’ ‘‘Dense’’ 19% porous 25% porous 25% porous 25% porous 25% porous
T (1C)
Method
Number of specimens
KIc (MPa m1/2)
25 25 880 25 25 25 880 880
SENB Chevron SENB SENB SENB Chevron SENB Chevron
4 3 5 14 21 3 4 2
2.070.2 2.2670.07 2.8670.05 1.2070.09 0.6470.09 0.6170.04 0.9070.05 0.8170.03
2494
Vol. 90, No. 8
Journal of the American Ceramic Society—Atkinson et al. Table II. Summary of Mechanical Properties of MMA at Room Temperature
Property
Units
Dense MMA (6% porosity)
Porous (18.3%)
Porous (24.5%)
Young’s modulus, E Poisson’s ratio, n Fracture toughness, KIc Fracture energy, Gc Mean flexural strength, sf Weibull’s stress, s0 Weibull modulus, m 2 c ffi KsIcf
GPa
19278
7077
MPa m1/2
2.170.2 22 151714 157 10.8
100710 0.21 1.270.09 14 5176 54 10.7
0.6370.08 5.3 3073 31.5 9.3
m
1.9 104
5.5 104
4.4 104
GPa
6.370.3
MPa MPa
Vickers hardness MMA, magnesia–magnesium–aluminate.
Table III. Summary of Mechanical Properties of MMA at 8801C Property
Units
Dense MMA (6% porosity)
(2) Effect of Porosity on Mechanical Properties The influence of porosity on the mechanical properties of ceramics is complex and has been studied widely.18 Minimum solid area (MSA) models predict the dependence of Young’s modulus on porosity of the form E ¼ expðbPÞ E0
(11)
where b is a constant that depends on pore geometry and P is the fractional pore volume. This is generally obeyed by porous ceramics, provided that P is not close to the solid percolation limit and there are no other high-compliance defects (e.g., microcracks). Young’s modulus data are shown compared with this expression in Fig. 2 and the best-fit line corresponds to values of 260 GPa for E0 and 5.1 for b. This value of E0 is slightly lower than the value calculated from the rule of mixtures. The value of b is similar to the values found for other partially sintered ceramics (e.g., b 5 4 for alumina).18,19 Recently, Pabst et al.20 proposed the relationship E ¼ ð1 PÞð1 P=0:684Þ E0
(12)
which they found fitted experimental data well for ceramics sintered with pore-forming materials. This relationship is compared with the present experimental data in Fig. 2. Even by lowering the value of E0 to 210 GPa, Eq. (12) does not fit the data. This is probably due to the very different microstructures
3 18.3% porosity 24.5% porosity
2.5
KIc (MPa m1/2)
between the sonic modulus and load–displacement methods. These differences between the two studies could be due to the different microstructures. They found evidence of micro-cracking at MgO grain boundaries, which they attributed to tensile residual hoop stresses generated by the lower thermal expansion coefficient spinel inclusions. These micro-cracks would reduce the elastic modulus of the composite, particularly in load–displacement and strain gauge measurements. However, our ‘‘dense’’ specimens show no evidence of micro-cracking and have a smaller grain size (Fig. 1). The smaller grain size is the result of processing at a lower temperature (15001C as opposed to 17001C) and inhibits micro-cracking because the stored elastic energy per particle is smaller for smaller particles and, below a critical size, is insufficient to propagate a crack in the surrounding matrix. Henderson et al.17 have reported markedly non-linear stress–strain curves in MMA refractories, of unspecified composition, which they also attributed to micro-cracking. We did not observe any obvious non-linearity in our measurements, which again could be due to the absence of micro-cracks. Aksel et al.6 measured the room-temperature fracture toughness of hot-pressed dense MMA refractories with 10%–30% spinel to be in the range 0.7–1.4 MPa m1/2, whereas the ‘‘dense’’ material in this study had a toughness of 2.170.2 MPa m1/2. This higher toughness is probably due to the absence of microcracks in the present material. It is notable that even the materials in this study with 19% and 25% porosity have toughness similar (Table II) to the hot-pressed refractories. This difference is also reflected in the room-temperature flexural strength, which was found to be 60–110 MPa for hot-pressed MMA (30% spinel), whereas the present ‘‘dense’’ material has a mean flexural strength of 151714 MPa. Thus, the materials in this study have significantly better mechanical properties than hot-pressed refractories of similar composition. This is probably because they are free of internal micro-cracks, which in turn is due to a finer grain size in the ‘‘dense’’ material and the ability of free surfaces to relax internal thermal expansion mismatch stresses in the porous materials.
"dense"
2
1.5
1
Porous (24.5%)
0.5
Young’s modulus, E GPa 216715 54711 Fracture toughness, KIc MPam1/2 2.8570.05 0.8770.06 35 13 Fracture energy, Gc MPa 16078 2678 Mean flexural strength, sf MPa 163 23.2 Weibull stress, s0 Weibull modulus, m 24 6.1 MMA, magnesia–magnesium–aluminate.
0 0
0.2
0.4
0.6
0.8
α (=a/W) Fig. 9. Fracture toughness, from SENB experiments at room temperature, as a function of notch length, a, relative to specimen thickness, W.
YK Ic
40
(a) 30 25 20 15 10 5 0 0
50
100
150 E (GPa)
200
150
200
250
180
(b)
160
25 C 880 C
140
(13)
1 c2
25 C 880 C
35
Gc (J m−2)
found in porous materials formed by partial sintering of powders as opposed to those using pore formers. In partially sintered ceramics, the properties of the inter-particle necks dominate at intermediate porosity, whereas those produced with pore formers have relatively large pores in a well-sintered skeletal matrix. In the simplest analysis, fracture energy is expected to be proportional to Young’s modulus.18 The data for both ‘‘dense’’ and porous material at 251 and 8801C are shown in Fig. 10, from which it can be seen that the expected correlation is approximately valid. The fracture energies at 8801C are somewhat greater than the correlation for 251C, which could be due to some increased plasticity near the advancing crack tip at the higher temperature. The effect of porosity on fracture energy of ceramics has recently been discussed by Vandeperre et al.21 Their experiments show that the fracture energy varies as (1P) for various porous aluminas (made with pore formers or by partial sintering) that are claimed to have the same alumina grain size. This relationship does not hold for the materials in this study, presumably because the solid microstructure is different in the materials of differing porosity. In Fig. 10, the flexural strength is also plotted as a function of Young’s modulus and the two are seen to be approximately proportional. In an otherwise homogeneous material containing a single fracture-initiating flaw, the far-field tensile failure stress is given by
sf ¼
2495
Mechanical Properties of Magnesia–Spinel Composites
Strength (MPa)
August 2007
120 100 80 60 40
where c is the characteristic size of the defect and Y a numerical factor that depends on its shape and is close to unity. The approximate proportionality between Gc and E in Fig. 10 means that KIc is also approximately proportional to E through Eq. (10). Therefore, strength and Young’s modulus would be expected to be proportional only if the critical defects are of constant size. Because this is unlikely to be true for bulk defects in materials with such different microstructures, it is suggested that the failure-inducing flaws are from the surface machining process (which was the same for all specimens). Putting YD1 in Eq. (13) and using the average values of sf and KIc from Table II, the approximate critical flaw size, c, is shown in Table II. This is approximately 0.5 mm for the porous materials and 0.2 mm for the ‘‘dense.’’
20 0 0
100
250
E (GPa)
Fig. 10. (a) Fracture energy and (b) mean flexural strength as a function of Young’s modulus for both ‘‘dense’’ and porous magnesia–magnesium–aluminate at 251 and 8801C.
Acknowledgments The authors are grateful to Rolls-Royce Fuel Cell Systems Ltd., for the provision of materials, and to R. Travis and S. Pyke for useful discussions.
References
V. Conclusions 1
Magnesia–spinel composite ceramics have good mechanical properties in both dense and porous forms that make them suitable for application as substrates and structural components in SOFCs. The materials studied here show properties (Young’s modulus, fracture toughness and flexural strength) that are superior to those reported for refractories of similar composition and display no evidence of internal micro-cracking that degrades these properties in refractories. It is suggested that this is due to the finer grain size that suppresses crack nucleation and (in porous materials) relief of internal stresses by relaxation at internal surfaces. The Young’s modulus shows an exponential dependence in porosity that is similar to that reported for partially sintered alumina and is in agreement with the expectation of minimum solid area models. Fracture toughness, fracture energy, and flexural strength are all approximately proportional to Young’s modulus. The mechanical properties are not considerably different at 9001C from those at 251C. However, there is a detectable increase in fracture toughness (and fracture energy) at the higher temperature, which could be due to some limited additional plasticity.
50
G. R. Eusner and D. H. Hubble, ‘‘Technology of Spinel-Bonded Periclase Brick,’’ J. Am. Ceram. Soc., 43 [6] 292–7 (1960). 2 C. Aksel, B. Rand, F. L. Riley, and P. D. Warren, ‘‘Thermal Shock Behaviour of Magnesia–Spinel Composites,’’ J. Eur. Ceram. Soc., 24 [9] 2839–45 (2004). 3 T. Ogiwara, H. Yakabe, M. Hishinuma, and I. Yasuda, ‘‘Assessment of Mechanical Reliability of Planar SOFCs in View of Selection of Materials and Operating Conditions’’; pp. 193–202 in Proceedings of Fourth European Solid Oxide Fuel Cell Forum, Edited by A. J. McEvoy. European Fuel Cell Forum, Oberrohrdorf, Switzerland, 2000. 4 F. J. Gardner, M. J. Day, N. P. Brandon, M. N. Pashley, and M. Cassidy, ‘‘SOFC Technology Development at Rolls-Royce,’’ J. Power Sourc., 86 [1–2] 122– 9 (2000). 5 J. Malzbender, E. Wessel, and R. W. Steinbrech, ‘‘Reduction and Re-Oxidation of Anodes for Solid Oxide Fuel Cells,’’ Solid State Ionics, 176 [29–30] 2201–3 (2005). 6 C. Aksel, B. Rand, F. L. Riley, and P. D. Warren, ‘‘Mechanical Properties of Magnesia–Spinel Composites,’’ J. Eur. Ceram. Soc., 22 [5] 745–54 (2002). 7 C. Aksel and F. L. Riley, ‘‘Young’s Modulus Measurements of Magnesia-Spinel Composites Using Load-Deflection Curves, Sonic Modulus, Strain Gauges and Rayleigh Waves,’’ J. Eur. Ceram. Soc., 23 [16] 3089–96 (2003). 8 C. Aksel, P. D. Warren, and F. L. Riley, ‘‘Magnesia–Spinel Microcomposites,’’ J. Eur. Ceram. Soc., 24 [10–11] 3119–28 (2004). 9 ‘‘Advanced Technical Ceramics—Mechanical Properties of Monolithic Ceramics at Room Temperature—Part 2: Determination of Young’s Modulus, Shear Modulus and Poisson’s Ratio,’’ British Standard BS EN 843–2: 2006.
2496 10
Journal of the American Ceramic Society—Atkinson et al.
R. W. Schmitt, K. Blank, and G. Schonbrunn, ‘‘Experimentelle Spannunganalyse zum Doppelringverfahren,’’ Sprechsaal, 116 [5] 397–405 (1983). 11 M. Hoffmann and R. Birringer, ‘‘Quantitative Measurements of Young’s Modulus Using the Miniaturized Disk-Bend Test,’’ Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process., 202 [1–2] 18–25 (1995). 12 S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd edition, McGraw-Hill Book Co, New York, 1959. 13 D. Munz and T. Fett, Ceramics: Mechanical Properties, Failure Behaviour, Materials Selection. Springer-Verlag, Berlin, 1999. 14 NIST structural ceramics database. 15 M. Radovic and E. Lara-Curzio, ‘‘Mechanical Properties of Tape Cast NickelBased Anode Materials For Solid Oxide Fuel Cells Before and After Reduction in Hydrogen,’’ Acta Mater., 52 [20] 5747–56 (2004).
16
Vol. 90, No. 8
W. Weibull, ‘‘A Statistical Theory of the Strength of Materials,’’ Proc. R. Swed. Inst. Eng. Res., 151, 1–45 (1939). 17 R. J. Henderson, H. W. Chandler, and I. Strawbridge, ‘‘A Model For Non-Linear Mechanical Behaviour of Refractories,’’ Bri. Ceram. Trans., 96 [3] 85–91 (1997). 18 R. W. Rice, Porosity of Ceramics. Marcel Dekker, New York, 1998. 19 J. C. Wang, ‘‘Young’s Modulus of Porous Materials. 1. Theoretical Derivation of Modulus–Porosity Correlation,’’ J. Mater. Sci., 19 [3] 801–8 (1984). 20 W. Pabst, E. Gregorova, and G. Ticha, ‘‘Elasticity of Porous Ceramics—a Critical Study of Modulus–Porosity Relations,’’ J. Eur. Ceram. Soc., 26 [7] 1085– 97 (2006). 21 L. J. Vandeperre, J. Wang, and W. J. Clegg, ‘‘Effects of Porosity on the Measured Fracture Energy of Brittle Materials,’’ Phil. Mag., 84 [34] 3689–704 (2004). &
Lihat lebih banyak...
Comentarios
