**5.5.1 Property of the ceramic materials and high temperature behaviour**

The properties of the ceramic material at temperatures over 1600°C are analyzed here below. For the applications in study, they are:


### **5.5.1.1 Oxidation resistance**

Many structural applications to high temperature demand the exposure to highly oxidant atmosphere: the thermal stability and the oxidation resistance to the oxide materials become of fundamental interest. A comparison of parabolic rates of oxidation for not oxidic ceramic materials is introduced in Figure 21. In general, an acceptable rate of oxidation is attested around 10 μm2/h; this is equivalent to assert that the material produces 100 μm of oxidized slags in 1000 hours. As previously described, the great part of carbides, borides and nitrides, oxidize to rates that exceed of several orders of magnitude this threshold value, and consequently they can not be used in the long term structural applications to high temperature. Only the silicon nitride Si3N4 and carbide SiC are able to maintain the previously determinate value to the temperature of 1600 °C. Although the great part of the oxidic ceramic materials are considered stable in a full oxygen atmosphere, the phases interfaces can be oxidized in presence of an oxygen gradient; as an example, if stable ternary oxide, ABOx, are subject to an oxygen gradient and if the relative diffusion coefficients to the three elements are in the relationship DA> DB > > D0, the crystal will rich of AO on the side of the greater gradient.

### **5.5.1.2 Traction/Compression and shear structural resistance**

Many polycrystalline ceramic materials quickly lose their characteristics of structural resistance at high temperature. Hillig indicates that the resistance of fragile materials would have to decrease proportionally to the 3/2 of the T/Tmelt ratio (Tmelt is the melting temperature of the materials) and that the value would have decrease of the half approximately if the environment temperature is equal to 0.5 Tmelt. This behaviour is the result of the diffusion mechanism control of the particles that dominate the processes of deformation to the high temperature. A schematic diagram of the resistance limits correlated to the mechanisms of fracture and creep in the ceramics is shown in Figure 24. To high temperatures many materials show ductile behaviours; this involves that their properties of resistance immediately are controlled by creep phenomena. Consequently, the advance of the micro-crack in the material is regulated by the creep. In the table 6 and Figure 23 the resistance limits and the fields of application of several ceramic materials are shown s: for

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,

The properties of the ceramic material at temperatures over 1600°C are analyzed here below.

Many structural applications to high temperature demand the exposure to highly oxidant atmosphere: the thermal stability and the oxidation resistance to the oxide materials become of fundamental interest. A comparison of parabolic rates of oxidation for not oxidic ceramic materials is introduced in Figure 21. In general, an acceptable rate of oxidation is attested around 10 μm2/h; this is equivalent to assert that the material produces 100 μm of oxidized slags in 1000 hours. As previously described, the great part of carbides, borides and nitrides, oxidize to rates that exceed of several orders of magnitude this threshold value, and consequently they can not be used in the long term structural applications to high temperature. Only the silicon nitride Si3N4 and carbide SiC are able to maintain the previously determinate value to the temperature of 1600 °C. Although the great part of the oxidic ceramic materials are considered stable in a full oxygen atmosphere, the phases interfaces can be oxidized in presence of an oxygen gradient; as an example, if stable ternary oxide, ABOx, are subject to an oxygen gradient and if the relative diffusion coefficients to the three elements are in the relationship DA> DB > > D0, the crystal will rich of AO on the

Many polycrystalline ceramic materials quickly lose their characteristics of structural resistance at high temperature. Hillig indicates that the resistance of fragile materials would have to decrease proportionally to the 3/2 of the T/Tmelt ratio (Tmelt is the melting temperature of the materials) and that the value would have decrease of the half approximately if the environment temperature is equal to 0.5 Tmelt. This behaviour is the result of the diffusion mechanism control of the particles that dominate the processes of deformation to the high temperature. A schematic diagram of the resistance limits correlated to the mechanisms of fracture and creep in the ceramics is shown in Figure 24. To high temperatures many materials show ductile behaviours; this involves that their properties of resistance immediately are controlled by creep phenomena. Consequently, the advance of the micro-crack in the material is regulated by the creep. In the table 6 and Figure 23 the resistance limits and the fields of application of several ceramic materials are shown s: for

are subject to several forms of structural decay if loaded at high temperature.

**5.5.1 Property of the ceramic materials and high temperature behaviour** 

2. structural resistance to traction/compression and shear stresses;

**5.5.1.2 Traction/Compression and shear structural resistance** 

For the applications in study, they are:

1. oxidation resistance;

**5.5.1.1 Oxidation resistance** 

side of the greater gradient.

3. creep; 4. tenacity; 5. fatigue.

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

Fig. 21. Oxidation curve

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.

#### **5.5.1.3 Creep**

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

Ultra Micro Gas Turbines 35

It is not so easy, on the contrary, to preview the behaviour to creep of reinforced composite ceramic; a dominant parameter to take under control, in such composites, is fibre aspect ratio. The stationary creep phenomenon on formed ceramic materials is analogous to that one shown for the metallic ones, above all, in relation to the dependency by the module of applied stress. Cannon shows how the exponent (n) in the formula (36) varies within 3 to 5 in the "dislocation climb" and within 1 to 2 when the diffusion mechanisms are active. It is assumed here that the behaviour to creep of a ceramic fibre and its matrix can be described

<sup>n</sup> <sup>Q</sup> <sup>ε</sup> = A<sup>σ</sup> exp RT

where the composite deformation speed , and the σC stress, are weighed with the volume fraction of the two phases. The composed stress σC can be correlated to creep through the

ε ε

where, σfo, εfo, σmo, εfo, are obtained from material empiric relations, and "m" and "n" are the stress component for the matrix and fibres respectively. This equation allows calculating demand stresses to support a stationary creep speed in a continuous composite, being assumed that both fibres and matrix are sliding to the same speed and without distortions

Before using a fragile material in a structural application the resistance limit to thermal shock, damaging from impact and fast fracture for cracking advance must be indicated. As previously shown, the creep is the process of dominant deformation when the sliding tension is lower than the necessary one to prime unstable crack advancing. The intensity of

σ = +

c ε

1/n 1/m fo f c mo m c c 1/n 1/m fo mo σ V ε σ V ε

<sup>−</sup> (34)

(35)

from a common "power law" expression of the type:

following formula:

on the phase interfaces.

Fig. 24. Creep behaviour

**5.5.1.4 Tenacity** 

crystalline yttrium-alumina-garnet (Y3Al5O12): this fibre present an interesting creep resistance (in our application field), and, being to cubical material, its creep advancing rate is independent to the direction of its crystals; for this reason, the fibres having such structure, present a better resistance to complex stresses states.

Fig. 22. Stress/temperature diagram

Fig. 23. Application field


Table 6. Resistance characteristics

crystalline yttrium-alumina-garnet (Y3Al5O12): this fibre present an interesting creep resistance (in our application field), and, being to cubical material, its creep advancing rate is independent to the direction of its crystals; for this reason, the fibres having such

**Material Temperature(°C) Yield Stress(MPa)** 

Al2O3 - prismatic 1600 80-120 Al2O3 - pyramidal 1600 200-300 ZrO2 (4.5 mol% Y2O3) 1400 550 ZrO2 (9.4 mol% Y2O3) 1400 160 ZrO2 (9.4 mol% Y2O3) 1600 40 ZrO2 (18 mol% Y2O3) 1400 275

> TiB2 1600 > 800 TiB2 1900 500 SiC 1600 350 WC 1600 100

structure, present a better resistance to complex stresses states.

Fig. 22. Stress/temperature diagram

Fig. 23. Application field

Table 6. Resistance characteristics

It is not so easy, on the contrary, to preview the behaviour to creep of reinforced composite ceramic; a dominant parameter to take under control, in such composites, is fibre aspect ratio.

The stationary creep phenomenon on formed ceramic materials is analogous to that one shown for the metallic ones, above all, in relation to the dependency by the module of applied stress. Cannon shows how the exponent (n) in the formula (36) varies within 3 to 5 in the "dislocation climb" and within 1 to 2 when the diffusion mechanisms are active. It is assumed here that the behaviour to creep of a ceramic fibre and its matrix can be described from a common "power law" expression of the type:

$$
\dot{\varepsilon} = \mathbf{A} \sigma^n \exp\left(-\frac{\mathbf{Q}}{\mathbf{RT}}\right) \tag{34}
$$

where the composite deformation speed , and the σC stress, are weighed with the volume fraction of the two phases. The composed stress σC can be correlated to creep through the following formula: c ε

$$\sigma\_{\text{co}} = \frac{\sigma\_{\text{fo}} V\_{\text{f}} \dot{\varepsilon}\_{\text{c}}^{1/n}}{\dot{\varepsilon}\_{\text{fo}}^{1/n}} + \frac{\sigma\_{\text{mo}} V\_{\text{m}} \dot{\varepsilon}\_{\text{c}}^{1/m}}{\dot{\varepsilon}\_{\text{mo}}^{1/m}} \tag{35}$$

where, σfo, εfo, σmo, εfo, are obtained from material empiric relations, and "m" and "n" are the stress component for the matrix and fibres respectively. This equation allows calculating demand stresses to support a stationary creep speed in a continuous composite, being assumed that both fibres and matrix are sliding to the same speed and without distortions on the phase interfaces.

#### **5.5.1.4 Tenacity**

Before using a fragile material in a structural application the resistance limit to thermal shock, damaging from impact and fast fracture for cracking advance must be indicated. As previously shown, the creep is the process of dominant deformation when the sliding tension is lower than the necessary one to prime unstable crack advancing. The intensity of

Fig. 24. Creep behaviour

Ultra Micro Gas Turbines 37

an essential element in the design analysis. The *thermal fatigue* takes part on every material under re-heating and cooling cycles. The thermal shock is the effect and it is present every time that a material is not constantly heated or it is not held to a constant temperature. Naturally, when a material is heated in a furnace, above all if its heat conductivity is low, and is quickly heated, or vice versa, quickly cooled, it creates thermal gradient in the material. In these conditions every such material are characterized by embrittlement, thermal fatigue, micro fractures, crack, etc. that, in the long run, produces a thermo mechanical failure. These important considerations have to be mentioned, especially during the preliminary design phase. In fact it is not enough to consider the maximum temperature of resistance of a material or the mechanical resistance, but all the problem boundary conditions that indicates the better choice of the material to use. The *mechanical fatigue* is caused by "slow crack growth" (SCG) mechanisms that must be analyzed for nominal load conditions. In spite of the acquaintance of the mechanism, the device lifetime prevision is based on empiric correlations for the crack rate. Generally a "power law" is adopted, whose

> n I IC

<sup>−</sup> = = (37)

(36)

da <sup>K</sup> v A dt K = =

n

σ

where "v", "a" and "t" are the crack rate, its characteristic length and the time respectively. KI and KIC are the stress intensity factors (effective/critical). "a" and "n" are parameters depending on the material and the operational atmosphere. The lifetime (tf) depends

f IC t D D f(K ;A;n)

main advantage resides in the mathematical model simplicity:

essentially on the applied stress (assumed constant) and on the KIC:

Fig. 25. Ceramic materials Fatigue diagrams

the applied and localized stresses shows different increases in relation to the crack length; this produce a ductile behaviour in the material when the stress, Km, is lower than the limit stress, Kth. The tenacity is the result of the applied traction on the fracture of the matrix by same fibres behind the fracture line: the friction of the fibres to the sliding of broken fibres opposes resistance in the crack matrix. The table 7 reports the studied structural ceramic composite properties.


U = unknown

\* = 0.22mm crack after 50000 cycles @ 42 MPa in compression

Table 7. Ceramic material proprieties [NIST]

### **5.5.1.5 Fatigue**

The today's design strategies are based, first of all, on the tenacity and resistance of the material. The behaviour to cyclical fatigue, thermal and mechanical one, must be enclosed as

the applied and localized stresses shows different increases in relation to the crack length; this produce a ductile behaviour in the material when the stress, Km, is lower than the limit stress, Kth. The tenacity is the result of the applied traction on the fracture of the matrix by same fibres behind the fracture line: the friction of the fibres to the sliding of broken fibres opposes resistance in the crack matrix. The table 7 reports the studied structural ceramic

**@ 100 MPa s-1** 

*Reinforcements* **------------ ------------------- -------------------- -------------- ---------- -------------------- Carbon** 2000-4000 ≈2500 @ 2300°c 10-11 @ 1600°C U U Catastrophic **TiB2/TiB(C)** 670-1560 900@ 1000°C U U U Poor **Sic (CVD)** 3200 1200 @ 1400°C 3·10-9 @ 1600°C U U Good **SiC (polymer)** 1900 1050 @ 1400°C 5·10-9 @ 1400°C U U Good **C-axis Al2O3** 1400-3000 10-9 @ 1600°C U U Stable **C-axis BeO** U ≈40M @ 1000°C 10-9 @ 1750°C U U Stable **YAG** U U 5·10-10 @ 1600°C U U stable *Nonoxide/Nonoxide* **------------ ------------------- ------------------- -------------- ---------- ------------------- BNp/AlN-SiC** 28 @ 1530°C U U U Fair to 1600°C **SiC/SiC** 350-750 U U 18 U < 10�m2/h

**SiC/HfB2** 380 28 @ 1600°C 10-5 @ 1600°C U U 12�m (2000°C) **SiCp/HfB2-SiC** 1000 U U U 5% wt gain

**SiC/MoSi2** 310 20 @ 1400°C U ≈ 8 U < 10 m2/h

**ZrB2pl/ZrC(Zr)** 1800-1900 U U 18 U U **20vol% SiC/Si3N4** 500 U U 12 \* Good to 1600°C

**SiC/ZrB2-Y2O3** U 16 @ 1530°C U U U Poor **TiB2/ZrO2** U U U U U Poor **SiC/Al2O3** 600-800 U 10-5 @ 1525°C 5-9 U Poor **30vol% SiC/ZrO2** 650 40 @ 1000°C 12 U Poor > 1200°C *Oxide/oxide* **------------- ------------------- -------------------- -------------- ----------- ---------------------- Al2O3/mullite** ≈180 U U U Dissolution

**Al2O3/ZrO2** 500-900 U U U Stable **YAG/Al2O3** 373 198 @ 1650°C U 4 U Stable

The today's design strategies are based, first of all, on the tenacity and resistance of the material. The behaviour to cyclical fatigue, thermal and mechanical one, must be enclosed as

\* = 0.22mm crack after 50000 cycles @ 42 MPa in compression

Table 7. Ceramic material proprieties [NIST]

**resistance R.T. Elevated Temp.**

**R.T. Toughness MPa m-1/2**

**Fatigue Oxidation** 

(1600°C)

(1600°C)

(1600°C)

reaction

**Flexure or Bend Strength** 

**(MPA) Creep** 

composite properties.

**Composite reinforcement/ Matrix** 

*Nonoxide/oxide*

U = unknown

**5.5.1.5 Fatigue** 

an essential element in the design analysis. The *thermal fatigue* takes part on every material under re-heating and cooling cycles. The thermal shock is the effect and it is present every time that a material is not constantly heated or it is not held to a constant temperature. Naturally, when a material is heated in a furnace, above all if its heat conductivity is low, and is quickly heated, or vice versa, quickly cooled, it creates thermal gradient in the material. In these conditions every such material are characterized by embrittlement, thermal fatigue, micro fractures, crack, etc. that, in the long run, produces a thermo mechanical failure. These important considerations have to be mentioned, especially during the preliminary design phase. In fact it is not enough to consider the maximum temperature of resistance of a material or the mechanical resistance, but all the problem boundary conditions that indicates the better choice of the material to use. The *mechanical fatigue* is caused by "slow crack growth" (SCG) mechanisms that must be analyzed for nominal load conditions. In spite of the acquaintance of the mechanism, the device lifetime prevision is based on empiric correlations for the crack rate. Generally a "power law" is adopted, whose main advantage resides in the mathematical model simplicity:

$$\mathbf{v} = \frac{\mathbf{da}}{\mathbf{dt}} = \mathbf{A} \left(\frac{\mathbf{K}\_{\mathrm{l}}}{\mathbf{K}\_{\mathrm{l}\mathrm{C}}}\right)^{\mathrm{n}} \tag{36}$$

where "v", "a" and "t" are the crack rate, its characteristic length and the time respectively. KI and KIC are the stress intensity factors (effective/critical). "a" and "n" are parameters depending on the material and the operational atmosphere. The lifetime (tf) depends essentially on the applied stress (assumed constant) and on the KIC:

n f IC t D D f(K ;A;n) σ<sup>−</sup> = = (37)

Fig. 25. Ceramic materials Fatigue diagrams

Ultra Micro Gas Turbines 39

The refractory steels are used for those products whose main characteristic is the resistance to hot gases and residual of combustion, at higher temperature than 550 °C. In European

Melting point is approximately 1455 °C. The Ni, in steels alloy, reduces the grain dimensions, increases the depth of hardening and renders them less sensitive to the low temperatures fragile failure. The Ni can be bond with numerous metals (particularly with

• With low expansion coefficient or controlled expansion as the Invar; these alloys find applications in the fabrication of physical measurement device, bimetals and equipment

• alloy with constant elastic modulus used for clocks springs, frequency regulators; • alloy with special magnetic characteristics (non-magnetic, low and high constant

• Cu alloy, resistant to sea water and to many chemical compounds (Monel-Metal).

It is used in metallurgy with Fe, Ni, Mo, W and other metals for the production of refractory alloys, steels for tools and alloys for permanent magnets. It is a constituent of maraging

Ti is recently used in the industrial manufacturing but its utilization still is limited, due to the high fabrication cost. The main properties of this metal and its alloys are the oxidation resistance also to 400-450 °C and higher mechanical characteristics both cold and hot environment. Its low density (4,54), has as consequence an high σm/p.sp ratio. The melting point is 1672 °C. These characteristics of pure Ti and its alloys are a lot influenced by the inner contained gas and, in particular, by the H. The value does not have to exceed the 0,0125% to avoid a dangerous embrittlement. The Ti alloys find application in the fabrication of supersonic vehicles, the aerospace constructions and in particular in the

The UMGT design is strongly limited by the available technologies. The micro manufacturing introduces a several problems in the development of every single part of the device. All studies have bring to adopt as manufacturing techniques the DRIE (Deep Reactive Ion Etching) and the Wafer Bonding, diffuse and by now widely mature, add to Micro Reaction Sintering, a new process based on the HIP (Hot Isostatic Pressing), already experimented for the fabrication of micro turbines and capable to realize machines with an

accuracy of the order of the μm, in small series and with contained production costs.

code for these materials is EURONORM 95.

Fe, Cr, Cu). The Ni- Fe alloys can be:

for lowest temperatures;

• Magnetic resistance alloy, for transducers; • Cr or Co alloy, resistant to the heat;

**5.6.5 TITANIUM and TITANIUM alloy (Ti)** 

**6. Manufacturing technologies and process** 

permeability);

**5.6.4 COBALT alloy (Co)** 

steels.

missiles.

**5.6.3 NICHEL alloy (Ni)** 
