Superplasticity in fine grained ceramics and ceramic composites: current understanding and future prospects

Mawrials Science and Engineering, A 166 ( 1993 ) 119-133

I I t)

Superplasticity in fine grained ceramics and ceramic composites: current understanding and future prospects A t u l H. C h o k s h i l)epartment o['Applied Mechanics and Engineering Sciences, Universi O, of California, San Diego, La Jolla, ('14 92093-0411 (USA)

Abstract Superplasticity in ceramics has now been reported in a wide range of materials with elongations to failure of more than 100%. Although the experimental observations of large deformation are in some ways similar to those reported in numerous metallic alloys, there are significant differences in the mechanical properties and cavitation failure characteristics of superplastic ceramics. This paper provides an overview of superplastic defl)rmation and failure in ceramics, with specific emphasis on a 3 tool.% yttria stabilized zirconia and a zirconia-20wt.%alumina composite. It is demonstrated that there is a transition in the deformation behavior of zirconia which is dependent on the grain size and the impurity content of the material. Many of these materials fail by the nucleation, growth and interlinkage of cavities, so that the ductility is governed by the imposed stress and the grain size. Potential areas for additional research on superplastic ceramics are highlighted.

1. Introduction

The ability of some crystalline materials to exhibit very large elongations to failure, termed superplasticity, has been recognized in metallic materials for over 50 years. In a classic demonstration of this phenomenon, Pearson [1] illustrated the extraordinary capability of an Sn-Bi eutectic alloy to exhibit an elongation of more than 195(1% without failure. Currently, the largest elongation to failure reported in a metallic alloy is a value of approximately 8000% in a Cu-based alloy [2]. The major commercial interest in superplasticity arises from the possibility of utilizing the large uniform ductility associated with this phenomenon, in conjunction with the relatively low flow stresses, to form components with complex shapes. Although this possibility was recognized first by Backofen et al. [3] in 1964, it is only in the 1980s that there has been a significant commercial application of this phenomenon for forming complex-shaped aerospace components [4]. The various aspects of superplasticity in metallic alloys concerning their mechanical characteristics and fracture have been reviewed in considerable detail [5-10]. The mechanical behavior of superplastic materials can usually be represented as o = B g '''

(1)

where o is the steady state flow stress, g is the imposed strain rate, m is the strain rate sensitivity and B is a constant incorporating the temperature and micro0921-5093/93/$6.00

structural dependence of superplastic flow. Analytical models [11, 12] as well as experimental results [13] indicate that flow localization is retarded by an increase in m, and typically large elongations to failure of more than 400% are obtained when m >- 0.3. Superplasticity is generally observed in metallic materials with grain sizes of less than 10/~m tested at elevated temperatures, with m > 0.3. As noted elsewhere [14], the first observation of a large elongation to failure in a ceramic can be traced to the early work of Day and Stokes [15] on polycrystalline MgO. The mechanical data reported by Day and Stokes [15] are reproduced in Fig. 1 which shows the stress-strain curves for MgO as a function of temperature; an elongation of approximately 100% was reported at a temperature of 2073 K. These experimental results do not correspond to true conventional superplasticity because of the flow localization noted in this study, and the relatively coarse grain size of the material. Currently, the largest elongation to failure in a superplastic ceramic is a value of 1038% in a 2.5 mol% yttria stabilized zirconia containing 5 wt.% SiO~ reported recently by Kajihara et al. [16], as illustrateci in Fig. 2. Wang and Raj [17, 18] demonstrated the capability of a fl-spodumene glass ceramic to exhibit a large elongation to failure of more than 100% under optimum conditions. However, it is the more recent report by Wakai et al. [19] of an elongation to failure of more than 100% in a fine grained 3 mol.% yttria stabilized © 1993 - Elsevier Sequoia. All rights reserved

A. H. Chokshi

120

_O5 x

Day and S t o k e s (1966)

Superplasticity in ceramics

EIonqohon(%) !

a4

g ~3

c2 600°C 1700°C 700°C.~

been tabulated and examined in reviews on superplastic ceramics [38-47]. In order to keep this overview tractable, it will focus largely on a 3 mol.% yttria stabilized zirconia (3YTZ) and a zirconia-20%alumina composite (3Y20A), which have been studied extensively, to develop an understanding of the mechanical properties and cavitation failure characteristics of superplastic ceramics. Some limitations in the current understanding of superplasticity will be noted, and the future prospects of this phenomenon will be highlighted.

True stfOln Fig. I. The tensile stress-strain behavior of polycrystalline MgO over a range of temperature [15].

Fig. 2. The largest elongation to failure of 1038% in a superplastic zirconia-5%silica ceramic [16].

tetragonal zirconia (3YTZ) that is regarded as a pivotal publication on superplastic ceramics, and it has spurred experimental investigations on superplasticity in ceramics. Superplasticity has now been reported in a wide range of ceramics such as the 3 mol.% yttria stabilized zirconia [19, 20], alumina [21], a spinel [22], zirconia-alumina composites [23-25], barium titanate [26], silicon carbide [27], mullite-zirconia composites [28, 29], silicon nitride-silicon carbide composites [30-32], mullite [33], ZnS [34] and silicon nitride [35]. The brittle nature of most ceramics indicates that a capability to resist intergranular separation is an important additional requirement for superplastic ceramics. It is to be noted that some of the above investigations, as well as earlier reports on materials such as uranium oxide [36] and magnesium oxide [37], involved testing in compression, and these materials may not necessarily exhibit large tensile deformations. Many of the experimental studies up to 1990 have

2. Superplasticity in a 3 mol.% yttria stabilized zirconia

Following the initial report by Wakai et al. [19, 20], there have been numerous studies on the superplastic mechanical properties of the 3 mol.% yttria stabilized zirconia [48-81]. These experimental results are summarized in Table 1 which includes the names of the authors, the impurity content in wt. p.p.m., the source of the material, the absolute density p (and the relative value), the type of test (T = tension, C = compression, B = bending, I = indentation, S = sinter-forging), the independent test variable (o=stress, g=strain rate, with the subscripts e=engineering and t=true), the stress, strain rate, temperature, and grain size ranges respectively, and the stress exponent n, the inverse grain size exponent p, the activation energy Q and the maximum engineering strain. The inverse grain size dependence and the activation energy for superplastic flow are defined as follows:

where A is a dimensionless constant, G is the shear modulus, b is the Burgers vector, k is Boltzmann's constant, T is the absolute temperature, D is the diffusion coefficient, and p and n are constants. The diffusion coefficient may be expressed as D = D o e x p ( Q / R T ) , where D 0 is a frequency factor, Q is the activation energy and R is the gas constant. It follows from a comparison of eqns. (1) and (2) that n = l / m , so that superplasticity is usually obtained when n < 3. Inspection of all of the available data shown in Table 1 indicates that there is a wide range of values reported for n, p and Q: the values of n range from about 1 to 3, with typical values around either 2 or 3. The activation energies generally tend to lie in the range 500-600 kJ mol ]. There have been very few careful determinations of the inverse grain size exponent, and the values reported range from about 1.5 to 4. It is important to note also that there may be a significant difference in

10-60

g~

Nauer and Carry (1989) [62]

Hermansson et al. (1989) [61]

Nieh et al. (1989) [41]

g~, o~

T

(A) 920A1, 110Si, 50 Fe, 40 Na;(B) 920A1, 5110Si, 50 Fe, 40 Na; (C) 920A1, 25110Si, 50Fe, 40Na; (D) 24920A1, 24110Si, 50Fe, 40Na, Tosoh 5.97-6.07 (A) 650A1, 20Si, 30Fe, 70Na; (B) 50AI, 60Si, 100Fe, 80Na, Tosoh

7-3x10

~

4

~ 3 x 111-~'-1(t -3

4-60

= 5-40

g~,o~

g~., o t

T,C

C,T

= 10 ~'- 111- 3

10 ~ - 2 × 1 0

9-100

g~

T

5-150

10 5-10-4

3 x 10 ~'3xlO 4 5 x l O ~2x10 ~ = 10 ~'-10 ~

10 ~-111 3

=10

10 ~'-10 3

6 x 10 - ~ 1 x 10 -3 2 x 10 - s 2xlO 3

10 5-10 4

8.3 x 1(1 5_ 2x10 3 10 4-10 ~

15231723

15331693 15731723 15231773 1473 . 1773 149316/13 16231923 15231723

14531723 15331693 15231723

14931573 17231823 17231823 1723

13231773 14731773 16231723 1573

10 t~-10-3 10 7-10 ~

T(K)

g range (s 11

g~

C

5.98

10-50

g~

B,T

Ceramiques Techniques Desmarquest Nikkato

1-50

g~

B,C

I

Nieh and Wadsworth (1989)[59] Duclos et al. (1989) [60]

5-50

~1-40

g~., ot

o

B,C C,T

g~

T,B

E

Nikkato

6.04

Wakai et al. ( 19891 [58]

6.1,5.6 6.115

(A) 650A1, 20Si, 30Fe, 70Na; (B) 50A1, 60Si, 100Fe, 80Na, Tosoh Nikkato

Nikkato

( = 9698%) 6.08-6.12

Motohashi et al. (1989) [57] - -

Okamoto et al. (1989) [56]

Carry (1989)139]

H e r m a n n s o n et al. (1988) [54] Okamotoetal.(1988)[55]

Kellettetal.(1988)[53}

2-250

5-50

g~.

S

50AI, 60Si, 10(IFe, 80Na, Tosoh Tosoh

20-150

g

C

5.97 ( = 98%) ( = 75%100%)

Ceramiques Techniques Desmarquest 820A1, 30Si, 30Fe, 30Na, Tosoh Nikkato T

15-50

ot

C

6.08

Tosoh

Carry and Mocellin 119871 [49] Duclos and C r a m p o n (1987) [50] Panda and Raj (1988)[51]

Nieh et al. (1988) [52]

5-50

g~

C

--

Wakai et al. (1986) {48]

6.04

=3-70

g~,cr

T,C

Wakai etal. 11986)[211]

o/g orange control ~ (MPa)

3-70

6.04

Test type b

g~, o,

Nikkato

Wakaietal.(19861[19]

p (Mg m -~)

T

Impurity content ~' (ppm), and source

Reference

T A B L E 1. T h e mechanical properties of a superplastic 3 mol% yttria stabilized zirconia

=3

--

0.31.46

=11.3

-~0.3

=0.5

626 492

---

--

1.8-2, = 2 1.62.6

=1.92.4

523-581

600_+50, 380 + 50, 360-+75, 610+50

--

570+511

570

311-576

369__+8 537__+7 600

=580

--

--

--

560

--

380_+30

--

586_+40

O (kJ mol 1)

--

1.8

1.5-2

--

--

--

--

1.1__+ -0.1 =3 --

1.92.3 0.33- =2 0.7 =0.32.70.4 3.3, 2.2 0.3=2, 1.34 = 1 =0.3 ~-5 = 2.5 =11.31.8, 0.4 1.9 . . . .

3

=0.3

=0.3

3

--

1.52.7 1.1 --

1.8

--

--

p

2.1

=2

=1.9

n

=0.3

=0.5

0.30.4 0.32.3 0.23

=0.3

d (~m)

75

148,

800

45

150

330

147, 80

45

246

=350

>39

39

> 160 >78 >78

> 120

6 (o/,,)

Maximum

t~

2

',.e.

2~

--

50AI, 20Si, 20Fe, 30Na

50AI, 20Si, 20Fe, 30Na, Nikkato Nikkato

Nikkato

B

C C

( = 97%98%) [ ~ 100%1 T C

-( = 100%)

C

S

--

( = 100%)

4.27-5.42 S (71%-90%)

--

4.27-5.43 S (71%-90%) 6.08 C

o,, g~

ge

o t

at

g o'~

o ~

g

Ee

g~

g~, o~

t~t, ~e

o

gt

1 0 - 6 - 1 0 -3

2 x 10 -83 × 10 -3 2.7 x 10 - 5 2 × 10 -3 5 x 10 - 5 3 × 10 -3 3×10 -73 x 10 -4

3-500

10-80

3-200

2.8 x 10 - 5 2.8 x 10 -3 1 0 - 7 - 1 0 -2

1 0 - 7 - 1 0 -2

16-120 1 0 - 7 - 1 0 -3

16231723

13731573 16231723 1723

15231723 16731773 15231673 15131873 0.54 15231673 1723 1723

17231923 15131873 14731673

1623

~-0.3

16231923 1823

1.72, 2.12.9 --

1

1.7

2.6, 1.8 =3

--

-~3

3.2

~3,2

~2.2

0.41- = 3, 1.3 2

0.5

0.41

~'0.2

0.511.71.3 2.1 0.3, 1.50.42 2.7 0.21.7 0.45 0.5=2.2 1.2 ~2 -0.21.7 0.45 -2.5 0.41 3

0.9+ 4.3

0.5

0.31.8 0.4, 0.76 0.3

0.5

~-0.5

w

---4

~-3

--

560 + 150

560 + 150

540-596

660

660

515 + 20

400

720

523-606

D

461 455-603

Q (kJ mol 1)

d

(/~m)

1723

-2 1 5 2 3 1723

~5×10-8-10

2.8 x 10 - 5 2.8 x 10 -3 2 x 1 0 -52 x 10 -3 2.7 × 10 -5

r(K)

g range (s 1)

4 × 10 - 4 8 × 10 -3 1 5 - 3 0 0 3 x 10 -43 x 10 -3 30-80 5X10 -53 X 10 -3 1 0 - 7 - 1 0 -5 2-30 8-300 3X10 -43 X 10 -2 10-50 5 x l O - S - l O 3 1 0 - 7 - 1 0 -3 3-30 15-80

2-100

8-140

5-50

2-200

10-30

8-100

10-70

2-100

aA1 = A1203, Si = SiO2, Na = Na20, Fe = Fe203; e.g. 50A1 is 50wt ppm AI203. bC = compression, T = tension, B = bending, I = indentation, S = sinter-forging. CSubscript e is engineering, subscript t is true; e.g. ge is for constant engineering strain rate testing.

Owen and Chokshi (1993) [79] Ma and Langdon (1993) [80] Owen and Chokshi (1993) [81]

Akmoulin et al. ( 1991 ) [72]

T

T

6.07

Obninsk Scientific Production. Blandin et al. ( 1991 ) [73] Ceramiques Techniques Desmarquest Okamoto et al. (1991) [74] Nikkato Akmoulin et al. ( 1991 ) [75] Obninsk Scientific Production Matsuki et aL (1992) [76] -Owen and Chokshi (1992) Nikkato [77] Boutz et al. (1992) [78] --

[71]

Wakai and Nagano (1991) [701 Motohashi et al. (1991 )

o~

C

T

(99.9%)

(= 99%)

C

6.07

Badwal etaL (1990)[69]

T

--

et

g

T

--

ee

6.08 ± 0.01 C

T

--

Ma and Langdon (1990) [63] Nieh and Wadsworth (1990) [64] Nieh and Wadsworth (1990) [65] Nauer and Carry (1990) [66] Nieh and Wadsworth (1990) [67] Blandin et al. (1990) [68]

Ee, Oe

o/g orange controF (MPa)

50AI, 20Fe, 30Na, 20Si, Nikkato 50AI, 20Si, 20Fe, 30Na, Nikkmo 50A1,20Si, 20Fe, 30Na, Nikkato 50AI, 60Si, 80Na, 100Fe, Tosoh 50AI, 20Si, 20Fe, 30Na, Nikkato Ceramiques Techmques Desmarquest 300Na, 600Ca, 870Si, 30Fe, 920Ti, Dmichi KigensoKagakuKogyo Tosoh

T

(A) milled with A1203 balls, 6.07 (B) milled with Z r O 2 balls

Test type b

Wak~fi et al. (1989) [42]

p (Mg m 3)

Impurity contenP (ppm), and source

Reference

T A B L E 1 - (continued)

39

39

39

39

39

100

800

550, 150 45

355

~(%)

Maximum

5

g

A. H. Chokshi

/

Superplasticity in ceramics

the levels of impurities in material obtained from the same source; in addition Xo the impurities listed in Table 1, there was also a slight variation in the level of yttria content in the various investigations. Some of the discrepancies in the available data are examined in Section 2.1 in light of a recent detailed study on the superplastic zirconia and, following a description of the microstructural changes occurring during superplastic deformation (Section 2.2), the experimental data are evaluated critically in terms of dominant deformation mechanims (Section 2.3). 2.1. M e c h a n i c a l characteristics

The first two independent studies on superplastic zirconia yielded disparate values of the stress exponent [19, 52]. These results are shown in Fig. 3 as the variation in strain rate with stress. It is clear that while the data of Wakai et al. [19] follow n = 2, the results of Nieh et al. [52] follow n = 3 behavior. Both studies utilized nominally identical material from the same source. These differences have been attributed variously to differences in the testing atmosphere and differences in the testing procedure. Wakai et al. [19] tested specimens in air utilizing a stress change procedure under creep conditions, whereas Nieh et al. [52] used a vacuum atmosphere and tested a series of specimens individually over a range of strain rates. Wakai et al. [19] attributed their n ~ 2 to a mechanism based on some form of grain boundary sliding, whereas Nieh et al. [25] suggested that intragranular viscous glide of dislocations was the dominant deformation mechanism. Carry [39] has attributed the differences in the

-2 10

........

stress exponents to a variation in trace levels of impurity elements. Figure 4 illustrates another interesting observation on the mechanical behavior of the superplastic zirconia. Nauer and Carry [62] examined superplasticity in compression using material prepared from two different batches of 3YTZ powders. The specimens utilizing the lower purity powder exhibited n = 2 over over a range of grain size from 0.37 to 0.51 /~m. In contrast, specimens prepared from the higher purity powders exhibited a change in the stress exponent from a value of approximately 2.6 for d = 0.40/~m to n = 1.6 for d = 1.5 ~m, as shown in Fig. 4. These results are in contrast to the observations in superplastic metallic alloys where the stress exponent does not change with a change in grain size. It was suggested that a stress exponent of approximately 3 in the finer grained material arose from a significant contribution of intragranular dislocation creep in the material with a substantial number of boundaries without a glassy phase. In addition, the decrease in stress exponent with increasing grain size was attributed to the development of a more uniform coverage of a glassy phase at grain boundaries. A decrease in the stress exponent with an increase in the grain size has also been noted in 2 mol.%, 3 mol.% and 4 mol.% yttria stabilized zirconia by Wakai et al. [42]. It was demonstrated also that for a similar fine grain size of approximately 0.5 ffm, stress exponents of 2.9 and 2.0 were obtained for the higher purity and the lower purity material respectively. Langdon [45] analyzed data from several studies, and he attributed

10

i

-3 3YTZ

rl

[ ] Wakai O

et al. (`86)

2

Nieh et al. ('88) -4

3YTZ

-3

10

10

/

123

Nauer and Carry ('89)

T= 1 6 2 3 K d (/~rn)

n

o%~-

~.6

//

[] z~

1.8 1.6

( ~ /

0.76 1.5

r~ ~J

T= 1 7 2 3 K I (1") v

"cO -4 10

I

°cO

10 - 5

/1 n 1 10

-5

.

.

.

.

.

.

.

.

r

2

1

10

10

(7 ( M P a ) Fig. 3. Variation in strain rate with stress reported in two independent studies on the superplastic zirconia [19, 52].

10

- 6

. . . . . . . .

i . . . . . . . . .

1

10

10

2

o- ( M P a ) Fig. 4. Influence of grain size on the stress exponent in a superplastic zirconia [62].

A. H. Chokshi

124

/

Superplasticity in ceramics

the differences in the stress exponent between nominally high and low purity zirconias, as well as a decrease in the stress exponent with an increase in grain size, to an increase in the area fraction of grain boundaries covered by a glassy phase. Recently, a detailed study on the compression creep characteristics of a 3 mol.% yttria stabilized zirconia was completed over a wide range of experimental conditions [77, 79, 81]. Some of the experimental results obtained in this study are shown in Fig. 5 in the form of the variation in strain rate with stress for specimens tested with a grain size of 0.41 and 1.3/~m. It is interesting to note that there is a very well defined transition from n = 3 at low stresses to n = 2 at high stresses. In addition, inspection of the data indicates that with an increase in grain size there is a decrease in the stress at, at which the transition in stress exponents occurs; these results suggest that the inverse grain size exponent has different values in the high stress and the low stress regions. Careful experiments indicate that the low stress region may be characterized with n = 3 and p = 1 whereas the high stress region is associated with n = 2 and p = 3. It is possible to rationalize observations of a decrease in stress exponent with an increase in grain size based on the data shown in Fig. 5. Clearly, when experiments on 3YTZ are conducted over a limited range of stresses, the data will be obtained from regions that straddle the high stress and low stress behavior; consequently, n = 3 in the fine grained material, and n will approach a value of approximately 2 with an increase in grain size.

2.2. Microstructural changes Microstructural characterization of the deformed specimens generally reveals a lack of intragranular dis-1 10

. . . . . . .

3YTZ

i

. . . . . . . .

,

location activity. In addition, experiments conducted up to very large tensile true strains of up to 2.5, over a range of strain rates, indicate that there is no significant change in the aspect ratio of the grains, so that the grains essentially retain their equiaxed shapes [82, 83]. Deformation enhanced concurrent grain growth is observed over a wide range of experimental conditions; this is particularly important in experiments conducted at temperatures above 1723 K in specimens tested with a fine grain size of approximately 0.3/~m. Some of the experimental results on deformation enhanced grain growth in specimens tested to large strains are summarized in Fig. 6 as the variation in the average grain size with strain for a range of strain rates. The differences in grain sizes at zero strain, obtained from the undeformed grip sections of the tensile specimens, reflect the variation in static grain growth that occurs owing to differing times of exposure to elevated temperatures. It is clear that deformation enhanced grain growth is more important in specimens tested at lower strain rates, as depicted by an increase in the slope a. Measurements revealed that there was no significant difference in the changes in grain aspect ratio in the specimens tested in the high stress and the low stress regions of Fig. 5 [79, 81]. The measurements also indicated that there was very limited concurrent grain growth in the low stress region.

2.3. Deformation Mechanisms 2.3. I. Possible causes for the change in stress exponents Following the early study of Rai and Grant [84] on a superplastic A1-Cu eutectic alloy, it has been recognized that concurrent grain growth at low stresses may lead to spurious observations of an increase in the stress exponent at low stresses. This is caused by strain hardening that accompanies grain growth since ooc d", where the exponent c usually has a value close to unity.

T = 1723 K

-2

1o

-Lo qazn) [ ] 0.41

A

-3

10

-~

f

1.3

~

r

•N r

1 0- 4

1

3

~ is-ll

2

T

FI 1.7 x O 2.7 x

10- 3 10- 4

A 8.3 x

10- 5

V 2.7 X 10-- b

ct 0.0--'3 0.07

Y--TZP T = 1823 K

0.21 0.34

C -5

~ ~ _ _ _ I - - ~ g 1

2

10

-6

-~--~-

>

10

< 0.0

-7

1.0

2.0

10

2

10

100

200

o- 6vPa)

Fig. 5. Variation in strain rate with stress for the superplastic zirconia tested with.grain sizes of 0.41 and 1.3 # m [79, 81].

Local

True

3.0

Strain

Fig. 6. Variation in grain size with local strain in the superplastic zirconia tested over a range of strain rates [83].

A. H. Chokshi

/

Superplasticity in ceramics

However, the very limited concurrent grain growth noted at low stresses cannot account for the observed increase in the stress exponent at low stresses (Fig. 5). The presence of a threshold stress below which deformation cannot occur by a given mechanism can give rise to an increase in the stress exponent as the applied stress approaches the value of the threshold stress. However, careful analysis of the data in Fig. 5 indicates that it is not possible to rationalize the increase in stress exponent at low stresses in terms of a simple standard threshold stress concept. It is suggested that the change in stress exponent is related to the impurity content of the material and the level of segregation at grain boundaries. This suggestion can account for a decrease in o, with an increase in the grain size. For a material with a given level of residual trace impurities, it is anticipated that there will be an increase in the level of impurities at grain boundaries with a decrease in the total grain boundary area (caused by an increase in the grain size); such an increase in the level of impurities facilitates a transition to the n = 2 region at lower stresses. The above explanation can also rationalize the differences in the stress exponents reported in the earlier studies of Wakai et al. [19] and Nieh et al. [52]. The data reported by Wakai et al. [19] and Nieh et al. [52] on tensile specimens tested at 1723 K, in the asreceived conditions, are superimposed on the data obtained in a recent detailed compression study [79, 81], Fig. 7, in the form of the variation in strain rate with stress. It is clear that the data reported by Nieh et al. [52] are in good agreement with the present results for n = 3, and that the earlier data by Wakai et al. [19] fall on an extrapolation of the n = 2 region obtained in the present study. Thus, the value of ot appears to have been reduced in the earlier study of Wakai et al. [19]. As noted elsewhere by Carry [85], there is a continuous improvement in powder technology, which perhaps leads to powders with better quality and lesser residual impurities. Thus, the reduction in the o t value for the data obtained by Wakai et al. [19] can be rationalized by noting that they were obtained from an earlier batch of zirconia powders which contained a greater quantity of residual impurities. It has been well established in metallic alloys that there is a transition from the superplastic regime with n ~<3 to a non-superplastic region with n-> 3 at lower stresses. The transition stress is reduced with an increase in the purity of the material, and the low-stress region with n >~3 is eliminated in very pure metals [47]. It is important to note that although superplastic metallic alloys and ceramics appear to exhibit a similar transition from n < 3 at high stresses to n > 3 at low stresses, therre is a divergence in the causes for this behavior. In ceramics, the transition stress is increased

125

with an increase in the purity of the material, so that in very pure ceramics the high stress region may not be observed in experiments conducted over the standard limited range of stresses. 2.3.2. Dislocation and diffusion creep

In some of the early studies, a stress exponent of approximately 3 was attributed to some form of intragranular dislocation creep [51, 52, 62]. There are no data on dislocation creep in single-crystal tetragonal zirconia, but such data are available for single-crystal 9.4 mol.% yttria stabilized cubic zirconia [86]. The compressive creep characteristics of single-crystal cubic zirconia tested in the [] ] 2] orientation are shown in Fig. 8, in the form of the temperature compensated -1 10

ZrO2

T = 1723 K

(as-receive~

Tension

10-2

I--I Nieh and Wad@w(x'bh (lggO) 0 Wakai et al. (1986) Compression

-3 10

I v

~ '

__ 7

• Owen and Chokshi (1992)

10 -4

--5 10

--6 10

10

--7

,

,

,

i . . . . . . . . . . . . .

10 o" (MPa)

I

100 200

Fig. 7. Variation in strain rate with stress for the superplastic zirconia tested in the as-received condition [19, 52, 79].

Martgi~yc-Fernandez et aL (1990~ /

4 lO

single crystal [11-2]

/

To172~-l~2m3o, ~ 1 r ~

~

7

o

3

~ lO 0J .~

1°2

30

'

'

'

'

'

'

'J

10 2

10

3x10

2

cr (MPa)

Fig. 8. Variation in temperature compensated strain rate with stress for a 9.4 mol.%yttria stabilized cubic zirconia [86].

126

A. H. Chokshi

/

Superplasticity in ceramics

strain rate vs. stress. The strain rate was normalized for tests in the temperature range 1723-1823 K using the activation energy of 590 kJ mol-1. The data could be represented by a straight line with a stress exponent of approximately 4, and deformation was attributed to dislocation climb controlled intragranular dislocation creep [86]. There is not much information available on diffusion creep in tetragonal zirconia, in the absence of a glassy phase, but such data are available for a 25 mol.% yttria stabilized cubic zirconia. The experimental results of Dimos and Kohlstedt [87] are shown in Fig. 9 as grain size normalized strain rate vs. stress. The data were rationalized in terms of Nabarro-Herring diffusion creep with n = 1, p = 2.2 and Q = 550 kJ mol- 1. The above experimental results on dislocation and diffusion creep in cubic zirconia are superimposed in Fig. 10 on the experimental results on compression creep in the superplastic 3YTZ with a grain size of about 0.4 p m tested at 1723 K. It was not possible to extract all of the individual data for dislocation creep from the normalized plot shown in Fig. 8, and therefore Fig. 10 contains only the data that could be plotted in the current format. For diffusion creep, the data in Fig. 10 correspond to all experiments conducted at 1723 K, which were normalized to a grain size of 0.41 p m using p = 2.2. Inspection of Fig. 10 reveals clearly that it is not possible to rationalize the present experimental results for n = 3 using dislocation creep mechanisms: the strain rates for dislocation creep are several orders of magnitude lower than the experimental values in the 3YTZ. This is consistent with the transmission electron microscopy observations indicating a lack of intragranular dislocation activity and the lack of any grain elongation. An examination of Fig. 10 also suggests that diffusion creep does not contribute significantly to deformation in the n = 2 region of polycrystalline 3YTZ. The line corresponding to the diffusion creep data intersects the line corresponding to the n = 3 region for the 3YTZ, which suggests that diffusion creep may play a role in this low stress region. However, the stress exponent of approximately 3 and the lack of grain elongation indicates that this deformation cannot be attributed directly to diffusion creep. In this context it is important to note that grain elongation during diffusion and dislocation creep may with suitable spheroidization lead to observation of an equiaxed grain morphology; however, such an explanation cannot rationalize the strain rate dependence of deformation enhanced concurrent grain growth, as reflected in the varying values of a in Fig. 6. It is important to note that owing to the different values of p in the high and low stress regions, and the value of p = 2 for

25YCZ

Dimos and Kohlstedt (19871

d = 2 . 6 - 1 5 /.¢m p = 2.2

-4

lO

Q = 5 5 0 kJ mo1-1 []

7

d

T ~.~)

~ 10-5

lO_6

1

2 10

10

o- (MPa)

Fig. 9. Variation in grain size compensated strain rate with stress for a 25 mol.% yttria stabilized cubic zirconia [87].

lO-2

lo

-3

lO

Dg.4YCZ Mwtlnez--Femandez et al (lg90) 0 25YCZ Dirnos ~

Kohlstedt (1987)

• 3YTZ

f

T = 1723 K

-4

~-, lo

/

/

,tO

1°-5

I

/

1

-7

4.

10 -8 10

.

.

.

.

.

.

.

.

.

,

10

,"

.

.

.

102

.

2

3x10

~)

Fig. l 0. Comparison of experimental data on the superplastic zirconia [79] with the dislocation [86] and diffusion creep [87] data on cubic zirconia.

Nabarro-Herring diffusion creep, the relative position of the diffusion creep line will be shifted with a change in the grain size. Having ruled out intragranular dislocation creep, as well as significant contributions from diffusion creep, the observed superplastic deformation can be attributed to some form of grain boundary sliding and a grain rearrangement process of the type suggested originally for two dimensions by Ashby and Verall [88], and modified subsequently for three dimensions by Gifkins [89] and Langdon [90]. The model suggested by Langdon [90] allows for grain boundary sliding to

A. H. Chokshi

/ Superplasticityin ceramics 102

be the dominant process, and it accounts for grain rearrangement by enabling new grains to come to the surface. 2.4. Influence of alumina additions Wakai and Kato [23] demonstrated that a 3YTZ-20wt.% alumina composite (3Y20A) was capable of exhibiting large superplastic elongations of more than 200%. Most of the early studies on the 3Y20A composite were restricted to a narrow range of strain rates, and the results indicated n = 2. A recent study on tensile creep in the 3Y20A suggested that n = 3 and p = 2 over the strain rate range from around l(l s to 10 4 s ~[77]; the possibility of atransition to a lower stress exponent at higher strain rates could not be examined owing to the limitations of the experimental creep apparatus. Yoon and Chen [28] developed a micromechanical model for creep in composites, and it was demonstrated that the model was in reasonable agreement with the experimental results on mullite-zirconia composites; the comparison for the zirconia-alumina composites was not as satisfactory owing to the possibility of enhanced creep resistance in pure alumina doped with a small level of zirconia [44]. The correlation between the predictions of the model and the experimental observations are reproduced as Fig. 11 from the study by Chen and Xue [44]. It is important to note that p-- 2 in the 3Y20A, whereas p = 1 in the 3YTZ for the experimental conditions shown in Fig. 11, so that below a critical grain size the 3Y20A composite may not be stronger than the 3YTZ.

127

TZP/mullite (1350°C, 70 MPa)

"~ 10 4 _ .E_ TZP/alurrfina(1250°C, 40 MPa) "o ~ 10 s N "--

~'~""""~,~,~

-

Pure alumina

~

Alumma+1000 " ~ •

~

ppm zirconia~

Db" ~"

z

10~

d~,~=0 5 =" l~m

10a

0

"%~

I

I

I

I

20

40

60

80

1O0

Amount of mulliteor alumina (vol%) Fig. 11. Theoretical predictions and experimental observations on the influence of a second phase on creep behavior [44].

2500

10

3Y20A

Wakai and Kato ('88)

T=,723 K

&

8

/

q) q)

6

0 _J

t(1)

4

CO

2

4-., O~ C ~3

c-

0

a

0

10 - 5

10

-4

10

-3

(s -1)

Fig. 12. Variation with strain rate in the level of cavitation and

room temperature strength for a superplastic zirconia20wt.%alumina composite [23]. 3. Role of concurrent cavitation

It is well established in superplastic metallic alloys that an increase in the level of cavitation leads to a deterioration in the subsequent room temperature properties. Wakai and Kato [23] demonstrated that a similar observation is valid in superplastic ceramics. Their results are shown in Fig. 12 in the form of the variation with strain rate in both the level of cavitation and the room temperature strength. They tested a series of specimens over a range of strain rates to an elongation of 100%, determined the level of cavitation and then the room temperature strength of the deformed specimens. Inspection of Fig. 12 reveals clearly that the level of cavitation increases with increasing strain rate, and that there is a significant decrease in the room temperature strength of the composite with an increase in the level of cavitation. These results point clearly to the need for developing an understanding of concurrent cavitation in superplastic ceramics.

Processing plays a key role in the elimination of flaw sites for cavity nucleation. Flaws such as large agglomerated particles are preferential sites for cavity nucleation in superplastic ceramics, as illustrated elsewhere [14, 91 ]. In the absence of such flaws, cavities appear to nucleate at triple point junctions in both the 3YTZ and the 3Y20A composite. Figure 13 illustrates cavity nucleation at triple points in the 3YTZ [83]. A detailed microstructural investigation of cavitation at low strains in the 3Y20A composite revealed that cavities tend to grow by a crack-like process, which suggests that surface diffusion is controlling the diffusional cavity growth of the cavities [92]. In this composite, cavities tend to nucleate at triple point junctions associated with an alumina grain, and then they grow along a zirconia-zirconia interface that is perpendicular to the tensile axis; these processes are illustrated in Fig. 14. It is important to note that in a ceramic, surface diffusion controlled crack-like cavity

128

A. H. Chokshi

/ Superplasticity in ceramics ef = K'[g exp( Q / R T )/H] .r

Fig. 13. Scanning electron micrograph illustrating cavity nucleation at triple points in the superplastic zirconia [83].

Fig. 14. Scanning electron micrograph illustrating cavity nucleation at triple points and subsequent growth by a crack-like mechanism;the tensile axis is horizontal [92].

growth will be controlled by the surface diffusion of the slower diffusing ion. One of the remarkable features of superplastic ceramics is their capability of exhibiting very large elongations to failure in spite of significant concurrent cavitation; this observation is related to their resistance to transverse cavity interlinkage. Chen and Xue [44] examined the ductility of many superplastic ceramics, and they concluded that the elongation to failure is controlled by the flow stress of the material so that although a high strain rate sensitivity is necessary to preclude excessive external flow localization, failure is dominated by the accumulation of internal cavitation damage. Kim et al. [93] also examined failure in superplastic ceramics, and they showed that the elongation to failure in superplastic ceramics ef was given by the following expression:

(3)

where K' and H are constants, and the exponent f = - 0 . 3 3 . Since g e x p ( Q / R T ) is proportional to o, from eqn. (2), it is clear that the analyses of Chen and Xue [44] and Kim et al. [93] relate to stress controlled cavitation fracture in superplastic ceramics. It is generally well known that coarser grained ceramics with a grain size of greater than 1/~m tend to exhibit lower ductility; this may be related to the larger flow stresses for the coarser grained materials. However, a recent detailed microstructural investigation of concurrent cavitation in a superplastic 3Y20A tested under constant stress creep conditions indicated that the grain size may be an additional independent parameter controlling cavitation failure [92]. Based on observations of the type shown in Fig. 14, it is suggested that, once nucleated, cavities tend to grow quite rapidly along grain boundaries perpendicular to the tensile axis. Cavitation failure involves the formation of a macroscopic crack by the interlinkage of such transverse grain boundary facet cracks along grain boundaries that are inclined at an angle of about 15°-75 ° to the tensile axis. In a coarser grained material, there are fewer such inclined grain boundaries, and this facilitates the process of cavity interlinkage to reduce the elongation to failure. Evans [94] has examined theoretically the process of cavitation failure during creep in ceramics, and some of these concepts may be extended to cavitation failure in superplastic ceramics. Kim et al. [93] adopted a fracture-mechanics type approach to rationalize the grain size dependence of the ductility in superplastic ceramics. Recently, Yoshizawa and Sakuma [95] have discussed the role of grain size in terms of the relaxation of stress concentrations by localized Coble creep in the vicinity of triple points.

4. Possible techniques for enhancing superplasticity in ceramics There are two broad approaches to enhancing superplasticity in ceramics: (i) the introduction of a glassy grain boundary phase, and (ii) a reduction in grain size to the nanocrystalline range. Since superplasticity is a thermally activated process that depends on the grain size, the introduction of a glassy phase can lead to a reduction in the operating temperature for superplasticity by enhancing matter transport, whereas nanocrystalline grain sizes can lead to an increase in the superplastic deformation rate. 4.1. Influence of glassy grain boundary phases In an early study by Cannon [21] on creep in alumina doped with 2 mol.% Cu20 and TiO2, it was

A. H. Chokshi

/

Superplastici O' in ceramics

reported that the material exhibited superplastic-like characteristics with bending strains of more than 30%; although it was not clearly identified, it is likely that there was a eutectic phase with a low melting point at the grain boundaries in this material. Following the more recent studies by Wakai [96] and Yoshizawa and Sakuma [97] on the influence of an intentional addition of a glassy grain boundary phase on superplasticity in a 2.5 tool.% yttria stabilized zirconia, there have been several attempts to examine this effect [16, 42, 61, 98-101]. The experimental results from most of these studies indicate that the superplastic deformation rates are enhanced significantly by the addition of glass forming elements. There are several factors that may contribute to such an observation, including the viscosity of the glassy phase, the solubility of the matrix in the glassy phase, and the volume fraction of the glassy phase. It has not yet been possible to separate out these effects from the available experimental results. In addition, there is not much information available on the role of concurrent cavitation in such ceramics. Nevertheless, the presence of a glassy phase can have a significant beneficial effect on the ductility of superplastic ceramics, provided that the materials can be processed to full density prior to tensile testing. This was demonstrated by the phenomenal elongation of 1038% in a zirconia containing 5 wt.% SiOz [16]. There is clearly a need to evaluate carefully the influence of glassy phases on the deformation as well as the fracture characteristics of superplastic ceramics. 4.2. Nanocrystalline ceramics

An examination of superplasticity in a wide range of metallic alloys with varying grain sizes indicated that the optimum superplastic strain rate can be enhanced significantly from about 10 -4 to 10 s-~ by a decrease in the grain size from approximately 15 to 0.5/~, [47]. Recently, Higashi [102] has shown that the optimum superplastic strain rate can be increased to a value as high as about 103 s i by refining the grain size to the submicrometer range. Although the possibility of superplasticity in nanocrystalline ceramics has been recognized for quite some time [103, 104], this prospect has not yet been realized in practice owing to the difficulty in producing fully dense ceramics with nanocrystalline grain sizes [105, 106]. Gupta [107] demonstrated that there is considerable grain growth in the later stages of densification of submicrometer grained ceramics; the significant increase in grain size beyond a relative density of about 90% is related to the development of isolated pores. Data on nanocrystalline TiO 2 [108], ZrO z [109] and Y203 [110] replotted in the format utilized by Gupta [1071 indicate clearly that there is significant

129

grain growth during the later stages of densification beyond relative densities of about 95% [106]. Several different techniques for attaining full density while minimizing grain growth have been noted elsewhere [106, 111-113], and it is anticipated that it will soon be possible to produce large fully dense nanocrystalline ceramic compacts for subsequent evaluation of the deformation and fracture characteristics. In this context, it is interesting to consider the possibility of cavity nucleation and growth during the high temperature tensile deformation of such nanocrystalline materials. Following the procedure developed originally by Raj and Ashby [114] for cavity nucleation at grain boundaries, the critical stable cavity nucleus radii r c and the free energy change necessary to develop such a critical nucleus A G* are given by the following expressions: r c = 2y/o.

(4)

A G* = o,1 rc~f,

(5)

where y is the surface energy, o, is the normal stress at the grain boundary, f,, is a shape factor that depends on the dihedral angle 0, which is defined as c o s 0 = )'gb/2y and Ygbis the grain boundary energy. The left-hand side of Fig. 15 illustrates schematically the situation pertaining to cavity nucleation at grain boundaries in coarse grained materials, where the cavity nucleus is much smaller than the grain size. For typical values of o = 10 MPa and y = 1 J m -2 in eqn. (4), the value of a critical cavity nucleus is calculated to be 200 nm. This value is likely to be much larger than the anticipated grain size of fully dense nanocrystalline ceramics. The right-hand side of Fig. 15 illustrates schematically a situation where a cavity is larger than the grain size. It is necessary to modify the expressions for r~ and A G* to account for the increased amount of grain boundary area consumed during the nucleation of a cavity which is larger than the grain size. A simple analysis can be developed to model this process by assuming that the material consists of grains that are tetrakaidecahedron in shape. An isolated tetrakaidecahedron with an edge of length L consists of a total grain boundary area of 6(1 + 2,/3)L- and a volume of 8,/2L 3. Following Raj and Ashby [114], the change in

Fig. 15. Schematic illustration of cavity nucleation at grain boundaries for a cavity smaller than the grain size (left), and cavity larger than the grain size (right).

130

A. 11. Chokshi

/ Superplasticity in ceramics

free energy arising from the formation of a cavity is given as AG = - oo(volume of cavity) + y(surface area of cavity) - 7gb(grain boundary area consumed)

(6 )

The critical cavity radius is then obtained from the condition O(AG)/Or=O. Using tetrakaidecahedron grains, and the configuration on the right-hand side of Fig. 15, it can be shown that rc =

0.70, + (~gb/L)

AG*=r22yf'(O)

(7)

(8)

where f(0) and f'(0) are shape factors that depend on the dihedral angle. The expression for the change in free energy, eqn. (5), can be modified to incorporate additional contributions from triple points (corresponding to the 36 edges in an isolated tetrakaidecahedron) and quadrupole grain junctions (corresponding to the 24 corners of an isolated tetrakaidecahedron); these terms are not included in the present simple analysis. The above equation indicates that a decrease in the grain size L will lead to a decrease in the stable cavity nuclei, so that cavity nucleation will be facilitated by a corresponding decrease in the value of A G*. However, it is widely recognized that cavity nucleation generally occurs owing to the stress concentrations arising from an incomplete accommodation of grain boundary sliding. There is a possibility that in ultrafine grained materials, there will be a decrease in the stress concentration due to a reduction in the mean free path (triple point separation) associated with grain boundary sliding, and this may retard cavity nucleation. There is clearly a need for some experimental data as well as analytical modeling to evaluate cavity nucleation critically in nanocrystalline materials. In this context, it is interesting to note that there appears to be a decrease in the level of cavitation in superplastic metallic alloys with a decrease in grain size from approximately 15 to 0.5/~m [47]. It has been demonstrated both theoretically [115] and experimentally [116] that there is an increase in the diffusional cavity growth rate in fine grained superplastic alloys owing to an increase in the number of grain boundaries along which vacancies may diffuse into a large cavity with dimensions greater than the grain size. The models for enhanced diffusional cavity growth are also likely to apply to nanocrystalline materials, since cavities in these materials are likely to intersect multiple grain boundaries [105].

5. Closing comments Superplasticity is now a well established phenomenon in many structural ceramics and ceramic composites. However, the phenomenological aspects of superplasticity in ceramics have not yet been as firmly established as in metallic alloys. A detailed evaluation of the mechanical characteristics in the superplastic 3 mol.% yttria stabilized zirconia indicates that there is a transition from a region with n = 3 at low stresses to n = 2 at high stresses. The transition is sensitive to the impurity content of the material such that the transition stress is reduced with an increase in the grain size and impurity content. Concurrent cavitation is a serious problem that has a deleterious effect on the subsequent room temperature properties of superplastically deformed ceramics. Cavities tend to nucleate at triple point junction and then grow along two grain junctions that are perpendicular to the tensile axis. Although a high strain rate sensitivity is an important requirement, the available information suggests that failure in superplastic ceramics is controlled by the imposed stress, with the grain size playing an important additional role in the failure process. The role of impurities in deformation and failure has not yet been completely identified. In particular, although glassy grain boundary phases tend to enhance the superplastic strain rate, the details of the mechanisms are not known completely. Nanocrystalline materials offer the exciting possibility for superplasticity at higher strain rates and/or lower temperatures, and it is likely that further activity in this area will lead to a fulfilment of the potential.

Fig. 16. Various stages in the superplastic forming of a spherical dome in a 3Y20A composite [119].

A. H. Chokshi

/

Superplasticity in ceramics

Finally, it is important to note that superplasticity in ceramics will enable them to be formed into complex shapes. T h e r e have been several studies indicating that superplastic ceramics can be formed into useful shapes using some variant of punch forming [20, 117, 118]. Recently, Wadsworth and coworkers [119, 120] demonstrated that it is possible to use argon gas for forming a z i r c o n i a - 2 0 % alumina composite into the shape of a dome, in a manner similar to that used in the commercial forming of superplastic metallic alloys. Figure 16 illustrates the various stages in the formation of a spherical dome of the superplastic ceramic c o m p o site [119]. This forming technique can be adapted easily to superimpose a back pressure on the order of the flow stress to limit concurrent cavitation, which is a standard commercial practice in forming superplastic metallic alloys.

Acknowledgments This work was supported by the National Science Foundation under grant no. D M R - 9 0 2 3 6 9 9 .

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