**5.2 Silicon nitrate (Si3N4)**

The silicone nitrite is a material much industrially diffusing. In Table 5 the main characteristics of the Si3N4 are reported, according to the manufacturing process, for a temperature within 20°C and 1400°C. Data, relative to CVD operations, are not available, because for such material is only used to generate protecting films, not for solid pieces

Ultra Micro Gas Turbines 27

order of magnitude lower than the blade dimensions., and two orders of magnitude higher than the device accuracy, that evidently would lose its functionality with a crack "so large". Recent studies, aimed to improve the tenacity of the ceramic materials, thanks to the addition of some additive (Al, B and C), to clearly increase the KIC till values (for SiC) of 9. It can be assumed that the machine lifetime, subordinate to the maximum static stress (as previously calculated), is higher than to 104 hours if SiC is used (Figure 15), while is ~600 hours for the Si3N4 (Figure 16). In both cases the structure deformations, due to the sliding, are of little μm, therefore negligible because the design tolerances that are of about 10 μm.

The mechanism of complete structure failure the under a stationary cargo has had to the interaction between sliding and defects existence, to the speed of crack propagation. Both

In static conditions, the solicitation, where, superficial carvings or micro cavity between grains, are present, generates a crack advance along the grain edges, the material weaker point. Once reached the critical length, the structure fails and this happens in a determinate time, defined Time to failure; a stress σth of minimal threshold exists, necessary to prime the process of crack propagation. Under these conditions, it seems that the piece is capable to resist for an indeterminate time. For silicon carbide it has been extrapolated (Figure 17): σth = 165 MPa to traction to 1400°C. It can be noticed that for values higher than the threshold one,

Fig. 15. Alumina SIC alloy creep curves at 1400°C [NIST]

Fig. 16. Si3N4 creep curves [NIST]

properties depending on the manufacturing process.


Table 5. Si3N4 proprieties

creation. From a data analysis, the properties of the Si3N4 are strongly variable, also presenting higher values than the SiC ones. In effects the silicon nitrite has optimal characteristics to low temperature, but it degrades quickly with the temperature increase. To high temperatures, also maintaining a good behaviour, does not reaches the SiC values. In this case, it can be noticed as the Reaction Bonding does not allow to obtain good property because of the achieved lower density than the theoretical one: the porosity is too much high.

### **5.3 Tenacity, fracture toughness, creep, time to failure**

The fragile behaviour of the ceramics focuses the study of the mechanical characteristics on the field of the mechanics of the elastic linear fracture. The design, in this case, is difficult because the microcrystalline structure of the ceramics introduces intrinsic imperfections in the mold preparation and edging processes, that render the material properties extremely variable. A greater limit of the ceramic materials is the low fracture toughness KIC and, consequently, the greater probability of structure collapse due to the crack propagation. The critical crack length "*lc"* represents the dimension which the phenomenon increase and becomes spontaneous and irreversible. This event is not correlated to the operational environment but linked to the produced energy during the inner material tensions displacement. This largeness represents the maximum tolerable dimension of a crack in operational conditions, and determines the structure lifetime. Beginning from the energetic criterion of Griffith [Frechette] the simplified formula can be written:

$$\mathbf{K}\_{\rm ic} = \sigma \sqrt{\boldsymbol{\pi} \cdot \mathbf{l}\_{\rm c}} \tag{24}$$

Once *σ* and KIC are known (Table 4 e 5) the SiC critical crack length can be calculated:

$$
\sigma = \text{SU}\_1 \, ^2 \rho\_{\text{m}} = 133.2 \text{ MPa} \quad \Rightarrow \, l\_{\text{c}} = 172 \text{ } \text{μm} \tag{25}
$$

for Si3N4:

$$
\sigma = \text{SU}\_1 \, ^2 \rho\_{\text{m}} = 137.6 \text{ MPa} \quad \Rightarrow l\_{\text{c}} = 420 \text{ } \text{μm} \tag{26}
$$

The silicon nitrite have a better tenacity, but of a lower value (140 MPa, Table 5) of the maximum permissible stress to traction at high temperature, value that appears insufficient to assure adequate safety margins. It can be noticed as the critical length, at this scale, is an

creation. From a data analysis, the properties of the Si3N4 are strongly variable, also presenting higher values than the SiC ones. In effects the silicon nitrite has optimal characteristics to low temperature, but it degrades quickly with the temperature increase. To high temperatures, also maintaining a good behaviour, does not reaches the SiC values. In this case, it can be noticed as the Reaction Bonding does not allow to obtain good property because

The fragile behaviour of the ceramics focuses the study of the mechanical characteristics on the field of the mechanics of the elastic linear fracture. The design, in this case, is difficult because the microcrystalline structure of the ceramics introduces intrinsic imperfections in the mold preparation and edging processes, that render the material properties extremely variable. A greater limit of the ceramic materials is the low fracture toughness KIC and, consequently, the greater probability of structure collapse due to the crack propagation. The critical crack length "*lc"* represents the dimension which the phenomenon increase and becomes spontaneous and irreversible. This event is not correlated to the operational environment but linked to the produced energy during the inner material tensions displacement. This largeness represents the maximum tolerable dimension of a crack in operational conditions, and determines the structure lifetime. Beginning from the energetic

> K l ic = ⋅ σ π

133.2 MPa

137.6 MPa

The silicon nitrite have a better tenacity, but of a lower value (140 MPa, Table 5) of the maximum permissible stress to traction at high temperature, value that appears insufficient to assure adequate safety margins. It can be noticed as the critical length, at this scale, is an

Once *σ* and KIC are known (Table 4 e 5) the SiC critical crack length can be calculated:

<sup>c</sup> (24)

 *lc =* 172 μm (25)

 *lc* = 420 μm (26)

of the achieved lower density than the theoretical one: the porosity is too much high.

**5.3 Tenacity, fracture toughness, creep, time to failure** 

criterion of Griffith [Frechette] the simplified formula can be written:

2 1 m

 ρ= = SU

> 2 1 m

 ρ= = SU

σ

σ

**Creep Rate exponent** 1.7 1.1 - 1.2 **Density [g/cm3]** 2.3-2.6 3.2-3.27 - 3.1-3.31 **Elastic Modulus [GPa]** 155-200 245-310 - 175-320 **Flexural Strength [MPa]** 190-338 70-703 - 146-930 **Fracture Toughness [MPa m1/2]** 2-3.6 4.3-6 - 3-8 **Hardness Vickers [GPa]** 10 14.8-15.7 - 13.9-15.9 **Max use Temperature °C** 1200-1500 1000-1500 - 1200-1500 **Tensile Strength [MPa]** 140-170 140-576 - 140-726 **Thermal Conductivity [W/m K]** 10-16 26-30 - 15-42 **Thermal Expansion From 0°C [ 10-6 K-1]** 2.9-3.3 3.1-3.5 - 2.7-4.3

**Reaction** 

**Bonding Sintering CVD Hot** 

**Pressing** 

**Si3N4** 

Table 5. Si3N4 proprieties

for Si3N4:

order of magnitude lower than the blade dimensions., and two orders of magnitude higher than the device accuracy, that evidently would lose its functionality with a crack "so large". Recent studies, aimed to improve the tenacity of the ceramic materials, thanks to the addition of some additive (Al, B and C), to clearly increase the KIC till values (for SiC) of 9. It can be assumed that the machine lifetime, subordinate to the maximum static stress (as previously calculated), is higher than to 104 hours if SiC is used (Figure 15), while is ~600 hours for the Si3N4 (Figure 16). In both cases the structure deformations, due to the sliding, are of little μm, therefore negligible because the design tolerances that are of about 10 μm.

Fig. 15. Alumina SIC alloy creep curves at 1400°C [NIST]

Fig. 16. Si3N4 creep curves [NIST]

The mechanism of complete structure failure the under a stationary cargo has had to the interaction between sliding and defects existence, to the speed of crack propagation. Both properties depending on the manufacturing process.

In static conditions, the solicitation, where, superficial carvings or micro cavity between grains, are present, generates a crack advance along the grain edges, the material weaker point. Once reached the critical length, the structure fails and this happens in a determinate time, defined Time to failure; a stress σth of minimal threshold exists, necessary to prime the process of crack propagation. Under these conditions, it seems that the piece is capable to resist for an indeterminate time. For silicon carbide it has been extrapolated (Figure 17): σth = 165 MPa to traction to 1400°C. It can be noticed that for values higher than the threshold one,

Ultra Micro Gas Turbines 29

For the ceramic materials, the exponent is much higher (m > 20) and it is enough a factor 2 to modify the he component life-cycles at least six orders of magnitude. It is possible but to take advantage, in the preliminary design phase, of the threshold value of the ΔKi, that defines the variation of the stress intensity factor, and consequently, the value of the stress under of which the fatigue is negligible. Such value is usually around 50% of the Kic; in the event of the SiC reinforced with Al, B, C the data are represented in Figure 19. Operating under this threshold value, it is possible to reduce the influence of the fatigue on the machine lifetime to a secondary parameter, even if, some factors which the corrosive atmosphere or the inner disposition of the micro cavities can limited the really usable an allowable ΔKi. The available data for the UMGTs, actually under investigation, unfortunately, are not sufficient to determine the influence of the fatigue on the machine.

The ceramic materials are interesting for structural applications as they are thermally stable and not so heavy. In fact, since between their atoms create covalent or ionic bond, such materials generally have a high chemical inertia, a high elastic modulus and a remarkable hardness, also to temperatures over 1000°C. The same chemical bonds that give them interesting characteristics are also responsible of their fragile behaviour. They do not allow to the crystalline plans to slide ones regarding the other, and do not allow the material plastic deformation. Consequently the ceramic material presents a typical fragile fracture: without some warning, with a highest crack propagation velocity. Such behaviour is

> KIC a

π

To render ceramic a reliable material (or better to increase its Weibull module) it is necessary or increase the value of its critical stresses intensification factor or decrease the inner defects dimensions. In the first hypothesis it needs to modify the microstructure by new insertion of "new phases" in the matrix, in the second needs to optimize composite "processing" of and

<sup>=</sup> (28)

σ

Fig. 19. Si3N4 Stress intensity range

described using the Griffith law:

to take care the superficial finishing.

**5.4 Ceramic materials** 

Fig. 17. SiC *Time to failure* at 1400°C [NIST]

the lifetime is maintained to 104 hours. For Si3N4 this value is lower: *σth* ≈ 150 MPa to traction at 1300°C; Figure 18 shows how this value rapidly decrease at the temperature increasing. Particularly interesting is the fatigue behaviour, that it is one of the main mechanisms of priming and lengthening of a crack, and in for ceramic materials represents the determining factor of the lifetime. In the fragile materials is distinguished between static fatigue and cyclical: the first one is related to the supported load, with variable conditions of temperature and in oxidating atmosphere, while the second, the most meaningful one, is determined by variable solicitations conditions. The fundamental law that regulates the material fatigue lifetime is famous as law of Paris, the expresses the crack propagation velocity in "N" number of cycles:

$$\frac{\text{da}}{\text{dN}} = \text{CAK}\_{\text{l}}^{\text{m}} \tag{27}$$

The constants C and "m" is closely correlated to the material, while the ΔKi represents the variation of the stresses intensity factor (That means it is correlated to the structure applied solicitation). In the metals the exponent is small (m between 2 and 4) and an increase, as an example of a factor 2, the Δσ applied to the machine reduces the component life-cycles of a order of magnitude, acceptable during design procedures.

Fig. 18. Si3N4 lifetime at varying of solicitations and temperature [NIST]

the lifetime is maintained to 104 hours. For Si3N4 this value is lower: *σth* ≈ 150 MPa to traction at 1300°C; Figure 18 shows how this value rapidly decrease at the temperature increasing. Particularly interesting is the fatigue behaviour, that it is one of the main mechanisms of priming and lengthening of a crack, and in for ceramic materials represents the determining factor of the lifetime. In the fragile materials is distinguished between static fatigue and cyclical: the first one is related to the supported load, with variable conditions of temperature and in oxidating atmosphere, while the second, the most meaningful one, is determined by variable solicitations conditions. The fundamental law that regulates the material fatigue lifetime is famous as law of Paris, the expresses the crack propagation

> m i

= Δ (27)

da C K dN

The constants C and "m" is closely correlated to the material, while the ΔKi represents the variation of the stresses intensity factor (That means it is correlated to the structure applied solicitation). In the metals the exponent is small (m between 2 and 4) and an increase, as an example of a factor 2, the Δσ applied to the machine reduces the component life-cycles of a

Fig. 17. SiC *Time to failure* at 1400°C [NIST]

velocity in "N" number of cycles:

order of magnitude, acceptable during design procedures.

Fig. 18. Si3N4 lifetime at varying of solicitations and temperature [NIST]

For the ceramic materials, the exponent is much higher (m > 20) and it is enough a factor 2 to modify the he component life-cycles at least six orders of magnitude. It is possible but to take advantage, in the preliminary design phase, of the threshold value of the ΔKi, that defines the variation of the stress intensity factor, and consequently, the value of the stress under of which the fatigue is negligible. Such value is usually around 50% of the Kic; in the event of the SiC reinforced with Al, B, C the data are represented in Figure 19. Operating under this threshold value, it is possible to reduce the influence of the fatigue on the machine lifetime to a secondary parameter, even if, some factors which the corrosive atmosphere or the inner disposition of the micro cavities can limited the really usable an allowable ΔKi. The available data for the UMGTs, actually under investigation, unfortunately, are not sufficient to determine the influence of the fatigue on the machine.

Fig. 19. Si3N4 Stress intensity range

### **5.4 Ceramic materials**

The ceramic materials are interesting for structural applications as they are thermally stable and not so heavy. In fact, since between their atoms create covalent or ionic bond, such materials generally have a high chemical inertia, a high elastic modulus and a remarkable hardness, also to temperatures over 1000°C. The same chemical bonds that give them interesting characteristics are also responsible of their fragile behaviour. They do not allow to the crystalline plans to slide ones regarding the other, and do not allow the material plastic deformation. Consequently the ceramic material presents a typical fragile fracture: without some warning, with a highest crack propagation velocity. Such behaviour is described using the Griffith law:

$$
\sigma = \frac{\mathbf{K}\_{\text{IC}}}{\sqrt{\pi \mathbf{a}}} \tag{28}
$$

To render ceramic a reliable material (or better to increase its Weibull module) it is necessary or increase the value of its critical stresses intensification factor or decrease the inner defects dimensions. In the first hypothesis it needs to modify the microstructure by new insertion of "new phases" in the matrix, in the second needs to optimize composite "processing" of and to take care the superficial finishing.

Ultra Micro Gas Turbines 31

β σ

 σσ

The monolithic ceramic materials, that is without reinforced fibres are not adapt for applications to high temperature, due to the low resistance to the thermal shocks and for fragile behaviour. Since than ten years the research is being focused on ceramic materials that are constituted by ceramic reinforced matrices with ceramic fibres. The composites present a better tenacity and fracture toughness. We can notice that, also having chosen a matrix and a phase to increase its tenacity, to put together these elements and to create a composite with sufficiently low defects is not so simple. For composites with polymeric and metallic matrix, the problem is not banal: the matrix can be, in fact, brought to the liquid state, and consequently during the cross-linking and the cooling processes, the amount and the dimensions of the vacancies are rather small. Different is the case of ceramic composites. The matrix cannot be melt, because (moreover the technological difficulties linked to the manipulation of the liquid phase at temperature over 2000°C) or it is decomposed before melting or its fusion temperature are much high to react with the tenacity phase. The only method to increase the matrix density, is the sintering process, that can be defined schematically as a succession of hot transformations of the material structure that take advantage of mechanisms of gaps and species gaseous diffusion: in such a way a gas expulsion contained in green ceramic material is provoked, eliminating the excessive

P () <sup>V</sup> p( ) <sup>e</sup>

σ

σ

r

**5.5 Monolithic materials and composites** 

porosity and increasing the material compactness.

**(a)** 

**p**

Fig. 20. β (a) and σ (β) distribution at varying of probability density

**-** β **= 8 -** β **= 3 -** β **= 1** 

The model of the contact spheres elaborated by Frenkel and Kuczynski in 40s, explains metals and glasses densification process (the light violet sphere indicate the glass phase increase). This model is extended by Kingery to the sintering for the solid state diffusion for the ceramic materials. This process starts from the ceramic powders, to which has to be added a second phase, often constituted by particles with dimensions of some micron and lengthened shape. All it must then be heated to high temperature to prime the sintering process. It is opportune that the particles dimensions of the two phases can be comparable, to avoid that the larger particles stop or delay the process, working as "rigid inclusion" and producing a low density material with great vacancies amount, with poor mechanical properties, even if the KIC has been improved by the presence of the new phase. Generally, to produce ceramic composites an "oxidic" matrix can be used, like the alumina, the zirconium, ecc. Moreover some matrix with essentially covalent bond can be used, as an example the silicone nitrite, boron nitrite or aluminum, the silicon carbide and others. Between

σ

**p**

σ

<sup>1</sup> <sup>V</sup> r,V

<sup>−</sup> <sup>−</sup> <sup>∂</sup> = = <sup>∂</sup>

0 0

β

0

(33)

**(b)** σ

σ0 = 1 σ0 = 2 σ0 = 3

σ β

σ

### **5.4.1 Weibull statistic**

The design of ceramic components are based on three types of approach:


Weibull (1939) was the first one to introduce, through an statistics analysis, the concept of breach probability. In its model the member is considered as "a chain" constituted from N meshes: the failure of this chain when the destructive breakdown of a single mesh occurs, that weaker one. Such event is independent by the other possible events (failures). In statistical terms, the reliability of the chain is calculated as the product of the reliability of each mesh. The concept is perfectly suitable to the examination of a ceramic volume. To such purpose the experimental observation indicates that the Failure Probability Pf,u is given by:

$$P\_{t,u}(\sigma) = 1 - \mathbf{e}^{-\left(\frac{\sigma}{\sigma\_0}\right)^{\beta}} \tag{29}$$

in which σ0 and β are material constants. According to this model the probability is zero for null tension and unitary for tension sufficiently elevated. The Au reliability of the of volume element, equal to the complement to 1 of the probability, is:

$$\mathbf{A}\_u(\sigma) = \mathbf{e}^{-\left(\frac{\sigma}{\sigma\_0}\right)\rho} \tag{30}$$

According to the "chain" model, the AV(σ) reliability, of a component of volume V subject to a uniform stress σ, is equal to the product of the reliabilities of the unitary elements that compose it, that is:

$$\mathbf{A}\_{\rm V}(\sigma) = \mathbf{e}^{-\mathbf{v}\left(\frac{\sigma}{\sigma\_0}\right)\boldsymbol{\rho}} \tag{31}$$

So failure probability is equal to:

$$\mathbf{P}\_{\mathbf{f},\mathbf{V}} = \mathbf{1} - \mathbf{e} \,\mathrm{e}^{-\mathrm{V}\left(\frac{\sigma}{\sigma\_0}\right)\rho} \,\tag{32}$$

To this the function corresponds to the probability density of failure, expressed by the relation (32). The defined formula is indicated as 2 parameters Wiebull distribution. The parameter β is called "Weibull modulus" while the parameter σ0 is a scaling parameter. If the tensional state is not uniform, the reliability of the component of volume V is given by the product of the single constituent unit reliabilities of the total volume. Finally, it can be noticed that β modulus expresses a "simple probability" of the ceramic material behaviour.

• an *empiricist* approach, based on the iterative tests execution of that finish when the member satisfies the properties demanded. Sometimes, if the modelling and the

• a *determinist* approach, in which it is attempted , by mathematical models, to preview the material resistance behaviour. This approach is correlated to the FEM analysis, and satisfied with the metals but sometimes it is inadequate for the ceramic ones, especially

• a *probabilistic* approach: it is assumed that a data volume of ceramic material loaded by uniform stress breaks for effect of the defect of greater entity (approach of Weibull) Weibull (1939) was the first one to introduce, through an statistics analysis, the concept of breach probability. In its model the member is considered as "a chain" constituted from N meshes: the failure of this chain when the destructive breakdown of a single mesh occurs, that weaker one. Such event is independent by the other possible events (failures). In statistical terms, the reliability of the chain is calculated as the product of the reliability of each mesh. The concept is perfectly suitable to the examination of a ceramic volume. To such purpose the experimental observation indicates that the Failure Probability Pf,u is given by:

<sup>0</sup> P() 1 e f,u

<sup>0</sup> A( ) e <sup>u</sup>

According to the "chain" model, the AV(σ) reliability, of a component of volume V subject to a uniform stress σ, is equal to the product of the reliabilities of the unitary elements that

σ

A( ) e <sup>V</sup>

P 1e f,V

To this the function corresponds to the probability density of failure, expressed by the relation (32). The defined formula is indicated as 2 parameters Wiebull distribution. The parameter β is called "Weibull modulus" while the parameter σ0 is a scaling parameter. If the tensional state is not uniform, the reliability of the component of volume V is given by the product of the single constituent unit reliabilities of the total volume. Finally, it can be noticed that β modulus expresses a "simple probability" of the ceramic material behaviour.

σ

in which σ0 and β are material constants. According to this model the probability is zero for null tension and unitary for tension sufficiently elevated. The Au reliability of the of volume

σ

σ β σ

σ β σ

0 V

0 V

σ β σ

 <sup>−</sup> 

σ β σ

 <sup>−</sup> 

 − 

= − (29)

= (30)

= (31)

= − (32)

 − 

The design of ceramic components are based on three types of approach:

**5.4.1 Weibull statistic** 

compose it, that is:

So failure probability is equal to:

previewing, this is the only solution;

in the design loaded by critical stresses;

element, equal to the complement to 1 of the probability, is:

$$\mathbf{p}\_r(\sigma) = \frac{\partial \mathbf{P}\_{r, \mathbf{V}}(\sigma)}{\partial \sigma} = \frac{\beta \mathbf{V}}{\sigma\_0} \left(\frac{\sigma}{\sigma\_0}\right)^{\beta - 1} \mathbf{e}^{-\mathbf{V}\left(\frac{\sigma}{\sigma\_0}\right)\theta} \tag{33}$$

### **5.5 Monolithic materials and composites**

The monolithic ceramic materials, that is without reinforced fibres are not adapt for applications to high temperature, due to the low resistance to the thermal shocks and for fragile behaviour. Since than ten years the research is being focused on ceramic materials that are constituted by ceramic reinforced matrices with ceramic fibres. The composites present a better tenacity and fracture toughness. We can notice that, also having chosen a matrix and a phase to increase its tenacity, to put together these elements and to create a composite with sufficiently low defects is not so simple. For composites with polymeric and metallic matrix, the problem is not banal: the matrix can be, in fact, brought to the liquid state, and consequently during the cross-linking and the cooling processes, the amount and the dimensions of the vacancies are rather small. Different is the case of ceramic composites. The matrix cannot be melt, because (moreover the technological difficulties linked to the manipulation of the liquid phase at temperature over 2000°C) or it is decomposed before melting or its fusion temperature are much high to react with the tenacity phase. The only method to increase the matrix density, is the sintering process, that can be defined schematically as a succession of hot transformations of the material structure that take advantage of mechanisms of gaps and species gaseous diffusion: in such a way a gas expulsion contained in green ceramic material is provoked, eliminating the excessive porosity and increasing the material compactness.

Fig. 20. β (a) and σ (β) distribution at varying of probability density

The model of the contact spheres elaborated by Frenkel and Kuczynski in 40s, explains metals and glasses densification process (the light violet sphere indicate the glass phase increase). This model is extended by Kingery to the sintering for the solid state diffusion for the ceramic materials. This process starts from the ceramic powders, to which has to be added a second phase, often constituted by particles with dimensions of some micron and lengthened shape. All it must then be heated to high temperature to prime the sintering process. It is opportune that the particles dimensions of the two phases can be comparable, to avoid that the larger particles stop or delay the process, working as "rigid inclusion" and producing a low density material with great vacancies amount, with poor mechanical properties, even if the KIC has been improved by the presence of the new phase. Generally, to produce ceramic composites an "oxidic" matrix can be used, like the alumina, the zirconium, ecc. Moreover some matrix with essentially covalent bond can be used, as an example the silicone nitrite, boron nitrite or aluminum, the silicon carbide and others. Between

Ultra Micro Gas Turbines 33

many applications is necessary not to exceed tensions of the order of 102 MPa (typically 150 MPa) to safety reasons. No ceramic materials shown in figure seem able to support this tension to approximately 1600 °C; consequently the composites materials reinforced with fibre are the only ones that allow reaching such design specifications. The titanium boride they seem to be of the possible candidates to reinforce of oxidic matrix, having excellent resistances

Also the pure silicon carbide introduces an adapted resistance in the temperature range of interest, but the structural SiC and its fibres are typically lacking the necessary purity to obtain high levels of resistance, and consequently, present meaningful proprieties losses to 1200°C. A better quality in the realization of silicon carbide fibres is being obtained with the new formation processes to high temperature. The oxidic ceramic materials, on the other hand, do not present the necessary resistance in high temperature atmospheres. Meaningful improvements have been obtained through the increase of the hardness of the solution or the control of the precipitate (above all zirconium), but the allowable stress have been always maintained lower than 150MPa. The sapphire (mono crystalline alumina) shows the necessary degree of resistance if oriented in opportune way during its cooling, but the more amazing result have been obtained using a two-phase material apt to receive ulterior oxidic phases: the eutectic system Al2O3/YAG, is capable to support stress of about 250 MPa to 1650°C. Studying this material, it appears clearly, that in the ceramic the crystals orientation

is most important and, therefore, the direction of solidification of the green ceramic.

Figure 24 illustrates that creep is the dominant dynamic process to the high temperature, as well as that it is assumed as design criterion in any structural application. The creep rates must be of the order of 10-8/s or lower for long term applications; to obtain these resistant levels, a creep resistance fibre must be deposited into a less resistant matrix. It is obvious that the polycrystalline ceramic fibres are not able to supply an adequate creep resistance for such matrix. The oxidic and monocrystalline fibres analyzed by Corman seem to be more promising. As an example, it can be noticed the interesting behaviour of the mono

to the high temperatures, but highly oxidable even if they are included in the matrix.

Fig. 21. Oxidation curve

**5.5.1.3 Creep** 

the oxides based matrices, the alumina is most used. It has good mechanical properties, but its main propriety is the resistance to the usury and to the oxidation; less good are its creep resistance. The tenacity and the heat conductivity are lower. Other materials can be remembered, thanks of their wide use, like the yttrium, zirconium, and various carbides and nitrides. Both monolithic and composites materials, even if characterized by elevated stability, are subject to several forms of structural decay if loaded at high temperature.
