Geckeler K.E., Nishide H. (Eds.) Advanced Nanomaterials

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17.8 New Structural Integrity Method 579

Table 17.4 Weibull modulus ( m ) and shape parameter ( β ) of ball - grind

alumna composites containing 20 vol% of S i C whiskers.

Sample type Weibull modulus,

m (MPa)

Shape parameter

( β )

Machined specimen 6.69 549

Machined specimen healed at 1573 K for 1 h 6.70 796

Machined specimen healed at 1673 K for 10 h 11.5 1026

Healed (1573 K for 1 h) smooth specimen 8.15 1075

1673 K for more than 10 h is required to attain the complete strength recovery for

the machined alumina/20 vol% SiC whiskers composite. This behavior can be

clearly understood by the statistical analysis using the two - parameter Weibull

function given by Equation (17.5) . Table 17.4 shows the Weibull modulus and the

shape parameter evaluated from the analyses. The values of m and β of the

machined specimen healed at 1673 K for 10 h were 11.5 and 1026 MPa, respec-

tively. The values were almost equal to those of complete crack - healed specimen.

From this statistical and χ

analysis, it was found that the cracks introduced by

machining were completely healed by the crack healing process at 1673 K for 10 h.

On the other hand, the machined specimen healed at 1573 K for 1 h had lower

values of m and β than those of the smooth specimen healed; thus, it can be con-

cluded that this crack - healing condition is inadequate. Two approaches are con-

ﬁ rmed to be reasonable to explain this difference: (i) the difference in the state of

the subsurface residual stress associated with the different crack geometries and

(ii) the oxidation of SiC by the heat generation during the machining. The machin-

ing crack was closed by the action of the compressive residual stress resulting in

a redaction in the supply of oxygen to the crack walls. Moreover, before the crack -

healing treatment, if SiC particles were already covered with a thin oxidation layer,

by the grinding heat, this would lead to the decrease in the oxidation activity of

the SiC particles.

Furthermore, it was found that the various cracks initiated by machining into

various machined ﬁ gurations could be healed by crack - healing treatment at 1673 K

for 10 h, as shown in Figure 17.24 [53] .

17.8

New Structural Integrity Method

17.8.1

Outline

A combination of the crack healing and the proof testing ultimately guarantees

the structural integrity of the ceramic components. As mentioned above, by

580 17 Self-healing of Surface Cracks in Structural Ceramics

eliminating not only the cracks introduced during manufacturing but also the

cracks introduced during service, the crack healing can ensure perfectly against

risk of the fracture initiated from surface ﬂ aws. The proof testing, in which com-

ponents are over - stressed print to use, can determine the maximum critical size

of embedded ﬂ aws associated with fracture. Embedded ﬂ aws, such as voids, may

be present in a material as a result of the processing, and could not be generated

during service. Therefore, the minimum fracture stress caused by the embedded

ﬂ aws [55, 56] or probabilistic fatigue S – N curves [57 – 59] has been estimated from

the proof testing stress on the basis of the linear fracture mechanics.

However, two important points must be taken account of while using the

proof testing. First is to ensure that engineering ceramics show the nonlinear

fracture behavior [60, 61] . The other is that the evaluated minimum fracture

stress is valid only at the proof testing temperature. Therefore, if ceramic compo-

nents are used at high temperature, the proof testing must be conducted at

the operating temperature. Ando et al. [62] proposed a theory to evaluate the tem-

perature dependence of the guaranteed (minimum) fracture stress of a proof

tested sample based on nonlinear fracture mechanics. This approach allows the

ceramic components proof tested at room temperature to operate at the arbitrary

temperatures.

17.8.2

Theory

On the basis of the process zone size failure criterion, the minimum fracture stress

at high temperature can be guaranteed from the proof testing stress at room tem-

perature, The criterion proposed by Ando et al. [62] has been obtained by the size

of process zone, which is the plastic deformation region at the crack tip, well

Through hole

Square groove

f 2 mm

Width = 2 mm

Depth = 0.5 mm

Means nominal

fracture stress

Machined

458 MPa

Machined healed

728 MPa

Machined

250 MPa

Machined healed

728 MPa

Figure 17.24 Effect of crack - healing condition on strength

recoveries of various machined specimens.

17.8 New Structural Integrity Method 581

expressing the nonlinear fracture behavior of ceramics. From the criterion, the

process zone size at fracture D

, is given by the following equation:

⎛

⎝

⎞

⎠

⎛

⎝

⎞

⎠

−

{}

πσ

sec

(17.9)

where σ

and σ

are the fracture stress at the fracture caused by the ﬂ aws having

and the fracture strength of the plain specimen (intrinsic bending strength),

respectively. K

plane strain fracture toughness and a

, equivalent crack length,

which is given by the equation as

CC e

σπ

(17.10)

By expanding Equation 17.9 around a

, one can write the equivalent crack size

of the ﬂ aws associated with fracture as shown in the following equation:

IC C

⎛

⎝

⎞

⎠

⎛

⎝

⎞

⎠

−

{}

−

πσ

sec

(17.11)

Since K

and σ

is the function of temperature, the fracture strength associated

with a

needs to be also expressed as a function of temperature:

⎛

⎝

⎜

⎞

⎠

⎟

⎧

⎨

⎩

⎫

⎬

⎭

−

arccos (17.12)

where the superscript T is the value at elevated temperature.

The maximum size of the ﬂ aw. a

, that is able to present in the sample proof

tested under σ

, at room temperature can be given by

⎛

⎝

⎜

⎞

⎠

⎟

⎛

⎝

⎞

⎠

−

{}

−

πσ

sec (17.13)

where the superscript R is the value at room temperature. Assuming that the sizes

of the residual embedded ﬂ aws do not vary with change in the temperature, one

can determine the minimum fracture stress guaranteed of the proof tested sample,

, as the fracture strength associated with a

at arbitrary temperatures. Thus the

value of σ

can be expressed as

πσ

⎛

⎝

⎜

⎞

⎠

⎟

⎛

⎝

⎜

⎞

⎠

⎟

⎛

⎝

⎞

⎠

−

arccos sec

{{}

⎧

⎨

⎩

⎫

⎬

⎭

−

(17.14)

and can be evaluated from the data on the temperature dependences of K

and σ

582 17 Self-healing of Surface Cracks in Structural Ceramics

17.8.3

Temperature Dependence of the Minimum Fracture Stress Guaranteed

Using the above theory, one can estimate the minimum fracture stresses at

elevated temperatures for the sample proof tested at room temperature. Ono et al.

[49] (evaluated the temperature dependence of σ

for alumina/20 vol% SiC parti-

cles composite. Moreover, by comparing the evaluated σ

with the measured

fracture stress of the proof tested sample at elevated temperature, the validity of

this estimation was given by them. Their results and discussion are presented in

the following text.

Before discussing the temperature dependence of σ

, temperature dependences

of the plane strain fracture toughness, K

, and the intrinsic bending strength, σ

are noticed. Ono et al. [49] investigated these temperature dependences for

alumina/20 vol% SiC particles composite. The σ

, which is determined as the

average fracture stress of 5% of the highest strengths of the crack - healed speci-

mens at the temperatures, has large temperature dependence and the tendency is

almost linear and negative up to 1373 K. Moreover, the K

is almost constant

against temperature. The features affect the correlativeness between the fracture

stresses as a function of the equivalent crack length, a

, at room temperature and

at high temperature. The schematic is shown in Figure 17.25 .

The fracture stress associated with small ﬂ aw, that is, a

is low, is equal to the

, and varies considerably as temperature varies. On the other hand, the fracture

stress associated with large ﬂ aw, that is, a

, is high, is determined by linear fracture

mechanics as expressed by Equation (17.10) and changes scarcely with tempera-

ture change. Therefore, the negative temperature gradient of the σ

increases with

increasing the proof testing stress,

, as shown in Figure 17.26 . Since high

qualiﬁ es a

to be a low value, the negative temperature gradient of the σ

becomes

considerably high. Alternatively, since low

allows the large ﬂ aws to present

Legalism of

fracture stress

Legalism of equivalent

crack length, log (a

)

log s

log a

log (p

1/2

)

log (p

1/2

)

Room temperature

High temperature, T

Figure 17.25 Schematic illustration of proof - test theory and

the effect of equivalent crack on fracture strength at room

temperature and at high temperature.

17.8 New Structural Integrity Method 583

400 800 1200 1600

Temperature (K)

200

300

400

500

600

Evaluated minimum fracture

stress guaranteed, s

(MPa)

= 570 MPa

= 500 MPa

= 350 MPa

= 430 MPa

Figure 17.26 Temperature dependence of minimum fracture

stress guaranteed of the proof tested under several proof

testing stress for alumina containing 20 vol% SiC particles

composite.

in the proof tested specimen, the σ

is almost constant as a function of

temperature.

The values of the evaluated σ

have good agreements with the measured

minimum fracture stress of the proof tested specimens,

min

. Figure 17.27 shows

the data on the fracture stress of the crack - healed and the proof - tested specimens

as a function of temperature with the evaluated σ

for the crack - healed

alumina/20 vol% SiC particles composite when σ

= 435 MPa. Except the data at

1373 K, all specimens have higher strength than the σ

at all the temperature.

Measured fracture stress (MPa)

200

400

600

800

400 800 1200 1600

Temperature (K)

Evaluated minimum fracture

stress guaranteed, s

Fracture stress of the crack-healed

specimens proof tested under 435 MPa

Figure 17.27 Comparison between measured fracture stress

and the evaluated minimum fracture stress guaranteed for the

crack - heated alumina/20 vol% SiC particles composite proof

tested under 435 MPa.

584 17 Self-healing of Surface Cracks in Structural Ceramics

Also, the minimum values of the experimental fracture stress are almost equal

to the σ

at all temperatures. At 1373 K, the

min

is 6.8% less than σ

, but the

value exists in the dispersion evaluated from the K

and the σ

that have large

scatters. Moreover, in the case of σ

= 530 MPa, the evaluated σ

have good agree-

ments with the

min

as well as with all the proof - tested specimens fractured under

the tensile stress more than σ

. Therefore, the results well demonstrate the validity

of the guaranteed method.

Moreover, Ono et al. [49] and Ando et al. [62, 63] reported that the guaranteed

theory can be applied to different conditions and the different materials. The

obtained results can be seen in Figure 17.28 , where the measured

min

is plotted

as a function of the evaluated σ

. N in the ﬁ gure denotes the number of samples

used to obtain

min

. Four open diamonds indicate the data on the ceramic coil

spring made of silicon nitride. Also, a open square differs from the closed circles

in the crack healing condition, that is, the open square employs 1373 K for 50 h

and the closed circle employs 1573 K for 1 h. However, all

min

shows good agree-

ment with σ

. Therefore, using Equation (17.14) one can estimate the σ

at higher

temperatures of every material having the crack healing ability and every crack

healing condition.

On the other point of view, it is interesting whether this estimation is reversible

for temperatures, that is, the stress evaluated in Equation (17.14) can guarantee

the minimum fracture stress at room temperature of the specimen proof tested

at high temperature. For example, the σ

at room temperature of the

alumina/20 vol% SiC particles composite proof tested under 335 MPa (= σ

) at

1073 K is evaluated to be 435 MPa. Alternatively, the experimental minimum

fracture stress was 410 MPa. The σ

existed in the dispersion obtained from K

and σ

, which have large scatters.

200 400 600 800

200

400

600

800

Sintered Si

= 598 or 700 MPa)

Alumina/SiC composite

(

= 435 or 530 MPa)

Evaluated value, s

(MPa)

Measured value, s

min

(MPa)

coil spring

= 417 MPa)

Figure 17.28 Comparison between minimum fracture stresses

guaranteed and measured minimum fracture stress.

17.9 Advanced Self-crack Healing Ceramics 585

17.9

Advanced Self - crack Healing Ceramics

17.9.1

Multicomposite

Ceramic composite containing both SiC whiskers and SiC particles, called SiC

multicomposite , enhance fracture strength and toughness as well as endow the

ceramics with the good self - crack healing ability. As mentioned in Section 17.5 ,

the reinforcement by SiC whiskers can not only improve fracture toughness but

can also generate the self - crack healing ability. However, it is difﬁ cult to disperse

a large amount of SiC whiskers uniformly, and so the aggregated SiC whiskers

decreases the fracture strength. SiC multicomposits containing both whiskers

and particles improves the self - crack healing ability endowed by SiC whiskers

alone without adversely affecting the composite strength. Therefore, ceramic – SiC

multicomposites exhibit high strength, high fracture toughness, and excellent

self – crack - healing ability.

Especially, SiC multicomposites perform better than the mullite - based compos-

ites. Mullite and mullite - based composites have been expected to be advanced

ceramic spring because they exhibit the same low level elastic constant as metal

and excellent oxidation resistance. However, mullite has remarkably low fracture

toughness. Therefore, it is necessary to endow mullite with self – crack - healing

ability for actualizing mullite - based ceramic springs. The mechanical properties

of mullite/SiC composites [21, 46] and multicomposites [64] were investigated as

shown in Table 17.5 .

The fracture strength increases with SiC content increasing up to 20 vol%, above

which it remains almost constant. The fracture toughness increased with an

increase in SiC whiskers content. Clearly, it is conﬁ rmed that crack bridging and

pulling out due to SiC whiskers lead to increase in fracture toughness. All the

Table 17.5 Mullite/ S i C composites having self - crack healing ability.

Sample descriptions Content (vol%)

Mullite SiC particle

(diameter = 0.27 μ m)

SiC whisker

(diameter = 0.8 – 1.0 μ m,

length =30 – 100 μ m)

MSI5P 85 15 0

MS15W 85 0 15

MS20W 80 0 20

MS25W 75 0 25

MS15W5P 80 5 15

MS15W10P 75 10 15

586 17 Self-healing of Surface Cracks in Structural Ceramics

mullite/SiC composites, which are listed in Table 17.5 , can exhibit a large strength

recover by the crack healing. However, mullite/15 vol% SiC whiskers composite

(MS15W) [46] cannot attain the complete strength recovery despite the optimized

crack healing condition. Complete strength recovery of the crack - healed specimens

is deﬁ ned as the strength of the strength of the specimens, whose fracture initia-

tion is embedded ﬂ aw. This implies the complete elimination of surface cracks

that can be attained and the strength of the crack healed part is superior to that

of the base materials. The crack healed part in mullite/25 vol% SiC whiskers com-

posite (MS25W) holds higher strength than the base materials below 1273 K, as

shown in Figure 17.29 [64] . On the other hand, the crack healed part in

mullite/15 vol% SiC whiskers/10 vol% SiC particles composite (MS15W10P) holds

higher strength than the base materials at the whole of the experimental tempera-

ture region, as shown in Figure 17.29 .

Figure 17.30 [64] shows the maximum shear strains of the mullite/SiC multi-

composites as a function of SiC content. The maximum shear strain corresponds

to the deformation ability as spring. The value of the maximum shear strain

showed a maximum at a SiC content of 20 vol%, above which it slightly decreased

because Young ’ s modulus increased with an increase in SiC content, but the

fracture strengths were almost constant above SiC content of 20 vol%. MS15W10P

has the best potential as a material for the ceramic springs used at high tempera-

tures, because it has a shear deformation ability that was almost two times greater

than monolithic mullite as well as an adequate crack healing ability.

400

800

1000

Flexural strength (MPa)

400 800 1200 1600

Temperature (K)

600

200

MS15W10P

MS25W

Specimens fractured

from the crack-healed zone

Figure 17.29 Temperature dependence of the crack - healed

strength of mullite/25 vol% SiC whiskers composite (MS25W)

and mullite/15 vol% SiC whiskers/10 vol% SiC particles

composite (MS15W10P), in which the center lined symbols

indicate specimens fractured from the precrack healed.

17.9 Advanced Self-crack Healing Ceramics 587

17.9.2

SiC Nanoparticle Composites

Nanometer - sized SiC ﬁ ne particles enhance the self - crack healing rate because

it gives a large increment in the reactive area and makes the surface of SiC

particles active. This effect give a large beneﬁ t to the self - crack healing at

relatively low temperatures at which the self - crack healing is completed in more

than 100 h.

Reaction synthesis is a promising process for directly fabricating nanocompos-

ites which are difﬁ cult to obtain by the normal sintering of nanometer - sized start-

ing powder compacts. Reaction synthesis to fabricate alumina – SiC nanocomposites

[65 – 71] were reported. Using the reaction synthesis (17.15)

33 2 8 6 13 6

23 2 23

Al O SiO Al C Al O SiC

()

++= +

(17.15)

Zhang et al. [71] succeeded in fabricating alumina nanometer - sized SiC particles

nanocomposite, in which the formed SiC particles are mainly entrapped inside

the alumina grains. Employing the similar process to prepare alumina – SiC nano-

composite, Nakao et al. [72] investigated the effect of nanometer - sized SiC particle

on the crack - healing behavior, as shown in Figure 17.31 .

The result demonstrates that the nanometer - sized SiC with particle size of

20 nm can signiﬁ cantly increase the self - crack healing rate compared to the com-

mercial 270 nm SiC particles. Furthermore, the nano - SiC particles can attain the

complete strength recovery within 10 h at 1023 K, which is a 250 K lower tempera-

ture compared to the commercial SiC particles. Although nanometer - sized SiC

particles makes the crack - healing reaction activated at lower temperatures, it gives

same level of refractoriness as the alumina containing commercial SiC particles

10 20 30

0.1

0.2

0.3

0.4

0.5

SiC content (vol%)

Maximum shear strain (%)

MS15W

MS20W

MS15W5P

MS25W

MS15W10P

Maximum shear strain

of monolithic mullite

Figure 17.30 Maximum shear strains of mullite/SiC composites as a function of SiC content.

588 17 Self-healing of Surface Cracks in Structural Ceramics

composite. Therefore, it is noted that the use of SiC nanoparticles is a most valu-

able route to enhance the valid temperature region of the self crack healing.

17.10

Availability to Structural Components of the High Temperature Gas Turbine

The structural component of the high temperature gas turbine is one of the most

attractive applications for the self healing ceramics. The application requires high

temperature durability and high mechanical reliability because of its service condi-

tion consisting of high temperature and oxidizing atmosphere, which is valid

condition of the self - healing driven by the SiC oxidation. Actually the turbine

nozzle and blade of the 1500 ° C - class gas turbine are exposed in high temperatures

ranging from 1273 to 1773 K and oxygen partial pressures ranging from 8000 to

10 000 Pa. To discuss the availability of the self - healing driven by SiC oxidation to

the turbine blades and nozzles requires knowing the self healing kinetics as a

function of temperature and oxygen partial pressure, because the rate is sensitive

to temperature and oxygen partial pressure changes.

Osada et al. [39] proposed the kinetics model in which the rate of self - crack

healing, v

, is expressed as a function of both the healing temperature, T

, and

oxygen partial pressure, P

. Two assumptions of the kinetic model are that the

reaction order, n , is independent on temperature and that obeying Arrhenius ’ law,

the reaction constant, k , depends on only temperature. By using the kinetic model,

k is expressed as a following function of T

and P

;

Healing time (h)

2460

200

400

600

800

1000

Flexural strength (MPa)

*Center-lined symbols indicate the specimens fractured

from the precrack healed.

810

Alumina/18 vol% nanometer-

sized SiC particles composite

Alumina/15 vol% commercial

SiC particles composite

Figure 17.31 Crack - healing behavior at 1373 K on alumina

containing 18 vol% nanometer - sized SiC particles composite

and alumina containing 15 vol% commercial SiC particles

composite, in which center lined symbols indicate the

specimen fractured from the precrack healed.