strengthening mechanism of alumina ceramics prepared by precoarsening treatments

E L S E V I E R Materials Science and Engineering A215 (1996) 18-25

HATERIALS SCIEMCE &

EHGIHEERING

A

Strengthening mechanism of alumina ceramics prepared by precoarsening treatments

Byung-Nam Kim, Teruo Kishi Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-I Komaba, Meguro-ku, Tokyo 153, Japan

Received 1 February 1996

Abstract

Effects of precoarsening treatments on strength and on subcriticaI crack growth are examined for A120 3 ceramics. AI2Oa polycrystals sintered by conventional hot-pressing procedure yield a 4-point bending strength of 400-500 MPa, while the precoarsening treatments increase strengths up to 750 MPa. Fracture toughness remains at the value of 3.5 MPax/m regardless of the treatments andthekindof source powder. From observations of fracture origin, it is found that the precoarsening treatments suppress the subcritical growth of flaws during testing to give a relatively small flaw size. The grain boundary toughness is evaluated qualitatively by comparing the lengths of subcritically fractured regions, and quantitatively by measuring the percentage of transgranular fracture. It is concluded that the fracture toughness of the grain boundary is increased by the precoarsening, and the toughened grain boundary plays a major role in reducing the subcriticaI growth rate of sintering flaws, resulting in strengthening.

Keywords: Strengthening mechanisms; AIumina ceramics; Precoarsening treatments

1. Introduction

In many structural ceramics, fracture originates at pre-existing flaws generated during sintering and machining processes, and fracture strength depends on the flaw size following fracture mechanical predictions. The reduction of flaw size is essential, along with the toughening of materials itself, to enhance the fracture strength. However, despite the reduced flaw size, the occurrence of subcritical crack growth (SCG) by applied loading increases the flaw size, resulting in lower strength. The suppression of the SCG is also an impor- tant requisite for higher strength. The SCG is induced mainly by stress corrosion, and it has been reported that grain boundaries in polycrystals provide the pre- ferred crack path due to its lower fracture energy compared with that of the grain [1-4], while transgranular SCG was observed for large-grained polycrystals when the flaw exists within a grain [5,6].

One of the ways to suppress such subcritical flaw growth during tests is the adoption of a higher loading rate under inert conditions because the SCG is a time- dependent and environmentally assisted process [7,8]. An alternative way is the modification of the mi-

crostructure of the materials. A complex microstructure, such as a composite microstructure, may enhance the resistance against the SCG by reducing chemical diffusion into crack tip. A complex microstructure also plays a role in rising fracture resistance (R-curve) with crack extension by forming bridged zones on crack surfaces [9,10]. The R-curve behavior has been an im- portant subject in developing high-strength and high- performance materials, and dramatically increasing fracture toughness with crack extension was obtained for composites reinforced with long fibers. However, the remarkable increase of fracture resistance is observed in general when a bridging zone is fully formed after some extension of the crack, indicating a long crack. If a crack becomes long, strengthening would not be expected so much despite considerable R-curve behavior. In order to accomplish high strength by the R-curve effects, a microstructure resulting in both higher initial toughness and higher initial slope of the R-curve has to be obtained.

If the microstructure is invariable, the SCG would be influenced by the properties of grain boundaries such as a bonding energy. The bonding energy of grain boundaries depends mainly on the orientation of adja-

0921-5093/96l$15.00 © 1996 -- Elsevier Science S.A. All rights reserved

B.-N. Kim, T. Kishi / Materials Science and Enghwerhzg A215 (1996) 18-25 19

Table I Properties of sintered alumina

Specimen* Sintering condition Density (g cm -3) Strength (MPa) (Ar, 30 MPa)

Without precoarsening NAK i500 °C x 2 h 3.97

Fracture toughness (from strength test) (MPax/m)

389 3.69 3.39

464 3.45 3.47 465 3.51 3.47 495 3.79 3.62 410 3.52 3.63 508 3.77 3.46 708 - - 3.50 752 - - 3.54 650 - - 3.48 614 - - 3.64 655 - - 3.53 751 - - 3.67

With precoarsening

NAL 1450 °C x 1 h 3.95 NAM 1400 °C x 1 h 3.95 NAN 1450 °C × 2 h 3.98 NTA 1450 °C x 10 min 3.98 NTB 1400 °C x 2 h 3.98 PTE 1400 °C x 2 h 3.98 PTF 1500 °Cx 1 h 3.98 PTG I550 °Cx 1 h 3.98 PTH 1600 °C x 20 min 3.98 PTJ 1500 °C x 1 h 3.98 PTL 1500 °Cx 1 h 3.98

Fracture toughness (by CSF method) (MPax/m)

*Specimens of second letter 'A' were made from AKP-50 and those of 'T' from TM-DAR.

cent grains, when the grain boundaries are free from impurities and considerable amount of glassy phase. In addition, the bonding energy may be iiffluenced by the degree of sintering, as pointed out by Krell et al. [11] and by the authors [12]. It is well known that grain boundaries in nanocrystalline materials have an unusual nonequilibrium structure [13,14]. The grain boundaries prefer to be flat and parallel to the plane giving the lowest energy configuration by the supply of thermal energy [15]. During sintering processes, this tendency is expected to allow the boundaries to be more stable with longer time and higher temperature, resulting in higher fracture energy of the grain boundary. This is one of our purposes. In this study, strengthening is attempted by toughening the grain boundary and by suppressing the SCG.

As a method to toughen grain boundaries without additional grain growth, precoarsening treatments of powder may be effective. By precoarsening treatments prior to conventional sintering for alumina, it was reported that uniform microstructure is developed and the increased uniformity allows the system to stay in the open porosity state longer, delaying or inhibiting grain growth during the final stage of densification [16]. The uniform microstructure may result in the reduction of flaw sizes due to high densities, and the higher grain boundary toughness due to the proceeded degree of sintering, resulting in higher strength compared with those sintered without the precoarsening treatments. The role of precoarsening in suppressing the SCG and in enhanc- ing the fracture strength of alumina is evaluated in terms of the fracture toughness of grain boundary (FTGB).

2. Experimental procedure

2.1. S#Ttering of Al20s polycrystals

A1203 polycrystals were made by hot-pressing two kinds of commercially available alumina powder (TM- DAR, Taimei Chemicals, Nagano, Japan and AKP-50, Sumitomo Chemicals, Ehime, Japan) with high purity > 99.99%. Final sintering was accomplished at 1400- 1600 °C in Ar atmosphere of 1 atm. To obtain high strengths, it is necessary to achieve high density, small grain size, small flaw size as well as high FTGB [17- 20]. To achieve these, the sintering temperature, time, pressing rate and heating rate were changed in every sintering procedure after evaluation of the developed microstructure. Grain size was measured by scanning electron microscopy (SEM) observations on the surfaces etched thermally at 1400 °C for 3 h in air, and density by the Archimedes method. The evaluation of FTGB was carried out qualitatively by measuring the lengths of SCG regions and quantitatively by the percentage of transgranular fracture at crack propagation, which will be discussed later.

The sintering conditions are shown in Table 1, where the pressing and heating rate are slightly different from each other, even though the sintering temperature and time are the same. During the sintering of TM-DAR, the effects of precoarsening treatments were examined on the microstructure and on the strength. It was previously reported that precoarsening at about 800 °C for long times is effective in homogenizing the microstructure of A1203 [16]. In the present sintering, alumina powder was uniaxially compacted at 40 MPa for 5 rain and followed by heating at 4 °C min - 1 to the precoarsening temperature. Precoarsening was accomplished in the same die by heating at 1100-1200 °C for 10 h prior to the initiation of pressing process. When

20 B.-N. Kim, T. Kishi / Materials Science and Engineering A215 (I996) 18-25

the sintering was made without precoarsening, it was found that the rapid shrinkage of powder, probably sintering, initiates at 1250-1300 °C. In this study, in order to precoarsen at as high a temperature as possible before the initiation of sintering, the above temperature range was selected. Soon after the precoarsening, the powder was heated to the sintering temperature at 2-4 °C min-1 with stepwise pressing by 5 MPa up to 30 MPa. The properties of A1203 sintered with precoarsening treatments (called the precoarsened A1203 here) were compared with those sintered without (called the normal A1203 here).

2.2. Mechanical properties

Sintered bodies were cut into 3 mm x 4 mm x 40 mm bars and polished with 1 gm diamond slurry. Corners of tensile plane were rounded off to release stress concentration due to applied loading. Strength was measured by 4-point bending with 10/30 mm spans at a cross head speed of 0.1 mm min - 1. For each sintered body, five to eight specimens were tested. From fracture surfaces, fracture initiating site was identified and the size was measured by both SEM and optical microscope. In most cases, since the fracture origin was surrounded by the apparent fracture mirror, there was no difficulty in identifying it. Flaws that developed into unstable fracture could be divided into two types: surface and internal flaws. For surface flaws, the critical stress intensity factor K was calculated with semi-elliptical approximation by the following formula

K= F~rx/(~ra/Q) (1)

where cy is the bending stress, a is the crack depth and F, Q are a function of crack size, crack shape and specimen size, described in detail in [21]. In the case of the flaw located in the corner of specimen, called corner flaws as distinguished from surface flaws, fracture toughness was not calculated because there is no proposed formula for the complicated crack shape at a round corner. When fracture originated from internal flaws, cy was corrected by flaw depth from tensile surface and F in Eq. (1) has a different form.

Fracture toughness was measured by the controlled surface flaw (CSF) method [22] with a Knoop indentation of 98 N on the center of the tensile surface. Speci- mens were obtained as rectangular bars of 3 mm x 4 m m x 25 mm. Following the fractographic observation of the indented specimen, the depth of the Knoop-induced plastic zone was about 50 ~tm and the crack length was 400-500 gm. To eliminate residual stresses owing to the indentation, a layer 100-200 itm thick was removed from the tensile surface by grinding. Four specimens for each sintered body were broken in 3-point bending at a cross head speed of 0.01 mm min-t with a span of 20 ram, and stress intensity factor was

calculated from Eq. (1). All the tests were performed in air at room temperature.

3. Results and discussion

3. I. Microstructure

Dense A1203 polycrystals (> 99% relative density) were obtained regardless of the different sintering conditions, and a slight increase of density was found for the precoarsened A1203 as shown in Table 1. For the precoarsened A12Q, nearly 100% relative density was obtained, where the number of voids on the polished surfaces was smaller than in the normal AIzQ. How- ever, there was no remarkable change in the size of the voids. The maximum size of the voids observed on the polished surfaces was about 20 ~tm for both aluminas.

The grain size of the two altmainas showed the nearly same value (2-4 ~tm) within the experimental error, and the considerable effect of the kind of powder on grain size was also not observed. According to the Chu et al.'s work of precoarsening effects on MgO powder [16], a grain size during precoarsening is larger compared with that of conventionally sintering body. However, the growth rate of grain size of the precoarsened body becomes lower during final sintering process, and the final grain size becomes smaller than that of the normal one under the condition of the same density. Hence, the slightly increased density of the precoarsened AlzO3 in this study may result in the nearly same grain sizes for the two present aluminas.

3.2. Strength and ~'acture toughness

For the normal A12Q, a bending strength of 350- 500 MPa was obtained independent of sintering conditions. The dependence on the kind of source powder was not also significant. On the contrary, the precoarsened A1203 showed bending strengths over 600 MPa and sometimes over 700 MPa. When adequate heating schedules and sintering conditions were selected, for example, a heating rate of 3 °C min-1 and stepwise pressing with uniform intervals in the temperature range of 1200-1500 °C, average strengths of about 750 MPa were obtained as in the case of specimens TPF and TPL in Table 1. According to the Chu et al.'s work [16], the center-to-center pore spacing becomes smaller during the final sintering stage when the body was precoarsened before than in the case without precoarsening. This suggests a uniform distribution of fine pores and/or the reduction of final flaw sizes in the precoarsened bodies. The increased strength of the present precoarsened A1203 indicates that precoarsening is also effective in homogenizing the microstructure under the hot-pressed sintering environments.

B.-N. Kim, T. Kishi / Materials Science and Engineering A215 (1996) I8 -25 21

Fracture toughness by the CSF method was about 3.5 MPa,,/m independent of sintering conditions and of starting powder, and shows good agreement with the value obtained from the strength tests as shown in Table 1. For the precoarsened A1203, although many strength specimens were broken into three to eight pieces as a result of the high strengths, since the fracture origins have an intergranular characteristic and were surrounded by the apparent transgranular fracture mirror, there was no difficulty in finding and identifying it. However, most fracture origins were located in the corner of the specimen, and the probability of corner flaws developed into fracture origin increased with increasing fracture strength. Despite that the corners of the specimens were rounded off to release stress concentration, slight differences of specimen thickness in two sides and misalignments in specimen setting for tests may induce large stress concentration, especially in the case of ceramics of high elastic modulus and high strength. Even when specimens were broken into two pieces, most fracture origins were located in the corner. About 10% of the fracture origins of the precoarsened A1203 were internal or surface flaws, and were available to calculate the fracture toughness of the flaws, yielding a little higher value of 3.5-4.0 MPax/m. Hence, owing to the lack of enough data for the precoarsened A1203, the fracture toughnesses from strength and flaw size measurements are represented in Table 1 only for the case of the normal A1203. In Table 1, it is also found that fracture toughness is insensitive to density for highly dense A1203 polycrystals ( > 99.0% relative density).

In a fracture mechanical sense, the increased strength under constant fracture toughness indicates a reduction of flaw size. The effect of flaw size on fracture strength is often evaluated quantitatively by converting actual flaws into an equivalent crack of size a e. The various types of flaws, for example, surface and internal flaws, are represented as the equivalent crack of identical type having the same value of stress intensity factor. When a two-dimensional (2D) crack of length 2a e is under mode I state in an infinite plate, since the stress intensity factor (c~/rcao) is the same as that of Eq. (1), the equivalent crack size is obtained as

ae = a F 2 / Q (2)

Flaws from both strength and fracture toughness specimens in the two aluminas were converted into the equivalent crack. Fig. 1 represents the fracture strength plotted against the equivalent crack size, where most data are of the normal A1203 and a few of high strength are of the precoarsened one. The fracture toughnesses of both natural sintering flaws and artificial Knoop cracks show nearly the same vahie of 3.5 MPa,,/m, so that the fundamental nature of the two types of flaws is expected to be similar. By applied loading, Knoop

cracks propagate intergranularly at subcritical speeds, and before critical state, the crack plane near the tip exists on grain boundaries. Cracks of this type were called an intergranular crack in the crack deflection model [12]. Hence, sintering flaws are also expected to have an intergranular characteristic. Additional discussion will be provided later along with the SEM observations.

For ceramic potycrystals, a tendency of decreasing fracture toughness with decreasing flaw size was reported by several researchers [5,17-20]. Rice et aI. [5] showed that there occurs a transition of fracture toughness fiom the polycrystal to the single crystal toughness value, as the ratio of flaw size to grain size decreases. However, in the range of ae of this study, the decreasing tendency of fracture toughness is not observed with decreasing flaw size, and there is a possibility of higher strengths over 800 MPa for smaller flaws, as can be predicted in Fig. 1. Actually 3-point bending tests for some specimens of the precoarsened AI203 yielded a fracture strength of 1 GPa.

For the dependence of fracture strength or fracture toughness on flaw size, many models have been proposed [5,17-20]. One of the models is based on the fracture criterion of process zone [19]. According to the model, fracture occurs at which the size of process zone reaches a critical value. When the size of the process zone is smaller compared with the crack length, linear elastic fracture mechanics are applicable. With decreasing crack size, the relative size of the process zone becomes large and non-linear fracture mechanics be- come to prevail. Fracture toughness is corrected by taking into account the size of Dugdale's process zone. As a result, the value of 2.59-2.94 MPax/m is obtained at ae of 10 gtm for the present aluminas, not corre- sponding to the results of Fig. 1. In non-transforming ceramics, a process zone is mainly composed of microc- racks near crack tip. To generate the microcrack process zone prior to propagation of the main crack, it was

1000

r.13

• from strength tests • from toughness tests

- - Kc=3.5 MPav'm

100 . . . . . . . . , . . . . . . 10 100

Equivalent Flaw Size, ]¢m

1000

Fig. i . F rac tu re s t rength depend ing on flaw size. F rac tu re toughness

of the flaws is a b o u t 3.5 M P a v / m .

22 B,-N. K#n, T. Kishi / Materials Science and Eng#zeering A215 (1996) 18-25

Fig. 2. Surface flaw of the normal AI203 of AKP-50 (fracture strength: 458 MPa). The intergranular fracture region by SCG is surrounded by the transgranular one called a fracture mirror.

reported theoretically and experimentally that large grain sizes are required exceeding a critical value of 30-100 gm for AlaO3 polycrystals [23,24]. Considering the grain size of the present aluminas is 2-4 lam, it is expected that microcracking, that is, the formation of the process zone, would not occur or have no influence on the crack tip stress fields, and fracture mechanical predictions are available in the range of crack sizes of the present study. If ae becomes smaller below about 5 lam, there may occur a decrease of fracture toughness owing to the transition from polycrystalline fracture energy to single crystal or grain boundary value as suggested by Rice et al. [5], not owing to the formation of the process zone.

The generation of bridging grains in the wake zone, resulting in R-curve, is also dependent on grain sizes. The R-curve behavior may be useful in strengthening ceramic polycrystals, when the curve has both higher initial toughness and higher initial slope, as mentioned before. Suzuki et al. [20] simulated the dependence of fracture strength on crack size for polycrystals repre- senting R-curve behavior, and showed the similar results to that of the process zone model [19], a decreasing fracture toughness with decreasing flaw size. However, the effect of R-curve behavior decreases at smaller grains and is expected to have little influence for the present aluminas of 2-4 lam grain size. Specifi- cally, the invariant fracture toughness, within the range of crack sizes in Fig. 1, indicates that there is no considerable R-curve behavior.

3.3. Observation of fracture orig#z

As a fracture origin, surface flaws are representative for the normal A1203 as shown in Fig. 2, while corner

flaws are for the precoarsened one. In both cases, the regions of apparent transgranular fracture mirror were observed surrounding sintering flaws. As can be seen in Fig. 2, the critical flaw prior to unstable fracture represents an intergranular characteristic of the flaw plane. The intergranular characteristic of the surface and corner flaws appeared for all the tested specimens regardless of sintering conditions and starting powder. Owing to this reason, the fracture toughness of the flaws from strength tests is thought to be similar to that of the artificial Knoop cracks, as mentioned before.

Observing the region within the critical flaw, it is found that the flaw is not entirely a natural flaw but resulted from SCG during tests, because many grains represent an angled boundary facet. Sintering flaws are expected to have characteristics of voids and/or abnor- mally large grains. For most fracture origins, the exis- tence of sintering flaws was found as the initiating site of SCG. In the case that sintering flaws was not found within the critical flaw, the initiating flaw of SCG might be generated during machining processes, although it could not be identified clearly as in Fig. 2.

A typical sintering flaw is found from the internal flaw represented in Fig. 3, which is for the normal A1203 of AKP-50. In this case, the original sintering flaw is found in the central region of the critical flaw as a void, and can be distinguished from the SCG region by the difference of microstructural appearances, as described in Fig. 3(b). Within the sintering flaw, the grains of round shape and interval are observed frequently. The microstructural observations indicate that the SCG initiated from the sintering flaw explicitly. The SCG behavior from internal sintering flaw was also found for the normal A1203 of TM-DAR, as shown in Fig. 4(a). In the case of internal flaws growing near

B.-N. Kim, T. Kishi / Materials Science and Engineering A215 (1996) 18-25 23

specimen surface, the flaw type was sometimes changed into the surface flaws.

For the precoarsened A1203, however, the SCG from internal sintering flaws was not observed as shown in Fig. 4(b), while the SCG occurred from surface flaws. Internal sintering flaws in the precoarsened A1203 propagated unstably without intergranular SCG. Although the sintering flaw of Fig. 4(b) is the complicated one composed of the central void and the surrounding large grains, the critical flaw is thought to be the void only and the fracture of the large grains resulted in the unstable propagation of the flaw. In any way, the suppression of the SCG were induced by precoarsening treatments, and it resulted in the enhanced fracture strengths of A1203.

J . " ~ , " * 2 "

,~ ' - , "T.I ' "; " ' , " ' ' I ' ,

" i~

Fig. 3. Internal flaw of the normal A1203 of AKP-50 (fracture strength: 485 MPa). (a) Critical flaw surrounded by fracture mirror and (b) enlarged feature of the square of (a). The sintering flaw (SF) and the SCG region can be distinguished by the microstructural difference; the grains of round shape (R) and of intervals (i) are found frequently within the sintering flaw.

Fig. 4. (a) Internal flaw of the normal A1203 of TM-DAR (fracture strength: 405 MPa). The subcritical growth of the sintering flaw is observed. (b) Internal flaw of the precoarsened AI203 of TM-DAR (fracture strength: 785 MPa), which propagated unstably without subcritical growth.

3.4. Subcritical growth of internal flaws

During fracture of the alumina ceramics, the exten- sive SCG of internal flaws was not expected to occur owing to the lack of corrosive environments. Though some models of SCG in vacuum were proposed, based on the concept of thermal activation at crack tip [7,8,25,26], the different SCG rate for the two present aluminas cannot be explained by the thermal mechanism only. The internal sintering flaw of Fig. 3 grew by SCG about two times its original size within the specimen. In addition to the thermal activation for the SCG of internal flaws~ alternative explanations may be made by the introduction of the concept of the FTGB. For a subcritically propagating crack, higher fracture energy under the same stress level lowers its speed. Hence the high FTGB of the precoarsened A1203 may reduce or suppress the SCG during the fracture tests.

However, no available experimental methods were proposed up to now to measure the absolute value of FTGB, because of the difficulty of direct measurements. Although measurements of thermally grooved

24 B.-N. Kim, T. Kishi / Materials Science and Engineering A215 (1996) 18-25

dihedral angles from etched surfaces have been carried out extensively to estimate the surface energy of grain boundaries [27], it is also known that an equilibrium surface energy does not always correspond to a fracture energy, especially for a (0001) plane of A1203 single crystal [12,28], despite their deep relationships with each other. The same thing may be said for the case of grain boundaries and an alternative method to estimate the FTGB is required.

The fracture energy of grain boundaries was often taken as a constant for simplicity by many researchers, e.g., 50%-100% of the single crystal value [5,29]. How- ever, even though polycrystals are sintered with identical powder, the percentage of transgranular fracture (PTF) varies from body to body depending on sintering conditions [11,12]. Since grains in the polycrystal are expected to maintain the characteristics of a single crystal, the main parameter to determine the crack path is the properties of the grain boundaries, for example, fracture toughness and three-dimensional (3D) network in the polycrystal. At equilibrium state, the grain boundaries in AI203 are known to have a tendency to facet with the crystallographic plane of lower surface energy [15], as mentioned before, and the degree of faceting is expected to depend on sintering temperature and time to some extent. Hence, it is inferred that the surface energy and the FTGB are also dependent on the sintering conditions, and that the proceeded degree of sintering by precoarsening treatments may result in the more stabilized grain boundaries.

The first estimation of the absolute FTGB was con- ducted by Krell et aI. [11] by comparing the observed crack path with the analytical results. They proposed a simple model to estimate the FTGB by measuring the percentage of intergranular fracture for a crack propagated from Vickers indentation. According to the

On the contrary, the attthors analyzed the crack propagation behavior in 3D polycrystals with crack deflection mechanism [12]. In the crack deflection model, the crack path is determined by the value of FTGB, impinging angle on grain boundaries, and stress intensity factors. The constraint of crack path in the direction of specimen thickness was considered to pre- dict the fracture behavior, when cracks pass tlu'ough a triple or quadruple point. As a result, the PTF was calculated as a function of FTGB, and the predicted relationship is shown in Fig. 5 along with the Krell et al.'s results. The predicted relationship between PTF and FTGB showed a good agreement with that obtained by fracture mechanical simulation of crack path [31].

In Fig. 5, the measurements of PTF make it possible to estimate the value of FTGB. The PTF was measured by counting the number of steps of transgranular propagation, and by dividing by the number of all steps for cracks introduced by Vickers indentation of 196N. About 500 steps were counted totally for respective aluminas. In order to avoid the effects of both indentation-damaged zone and SCG in measuring the PTF, the counung was carried out witlfin the central region of the indentation-induced crack, distant from the two tips by about 20 btm. Almost same value of about 25% PTF was obtained for the normal AI_,O3 of the specimen TNA, while 36% PTF for the precoarsened AlaO3 of the specimen TPF. The values of the PTF nearly corre- sponds to the Krell et al.'s value of 33%-43% [1t]. Estimating from the analytical results of the 3D deflection model in Fig. 5, the FTGB of 1.16 MPa\ /m and of 1.25 M P a ~ m are obtained for the normal and for the precoarsened A120> respectively. In this case, the absolute FTGB was calculated by using the fracture toughness of A1,Q single crystal of 1.5 MPa, jm as the value

model, the fracture energy of grain boundaries is 2%- 20% of the single crystal value for A1203 polycrystals, the values of which are somewhat lower compared with the generally employed values. However, their analytical results are not thought to be valid, because the stress intensity factor at deflected crack tip is not cor- rect. Mode I stress intensity at deflected crack tip (/q) can be represented approximately by cos3(0/2)K~ as first order solutions [30], while k~ = cos2(0)K~ was employed in the model, where 0 is the deflected angle from a flat crack with infinitesimally small length and K~ is the stress intensity before deflection. The results of the model are shown in Fig. 5. At any values of FTGB, the crack has a probability to advance into grains. Accord- ing to the fracture criterion of energy release rate, the critical FTGB is about 0.5 times the value of grain toughness, below which only intergranular propagation occurs [31]. The Krell et al.'s results show large devia- tion from the expected crack propagation behavior.

~D

E-

100

~" 80

60

40

20

i '3D a'nalys'is [I2'] . . . . "Z analysis [31 ] ? J / 2D

- -O-- 2D simulation [31] .,',~J[ ......... 2D analysis [I I] .,"**;/l""

f / , **'* !

"*'*'*'""'" / ,

- - - O - - - - O - - - o - - . . O - -¢) 0.2 0.4 0.6 0.8

Grain Boundary Toughness, Kcb/Kcg

Fig. 5. Percentage of transgranular fracture depending on the fracture toughness of grain boundary (IQu), Keg is the fracture toughness of grain.

B.-N. Kim, T. Kishi / Materials Science and Engineerhzg A215 (I996) I8-25 25

of grain toughness [12]. It is uncertain whether just a little difference of FTGB yield such greatly different phenomenoloNcal fracture behavior or not, as described in Figs. 3 and 4. However, it is certain that the estimated value of PTF and FTGB are different from for the two present aluminas.

4. Conclusions

(1) The strength of A1203 ceramics can be increased up to 750 MPa by the precoarsening treatments at 1100-1200 °C for 10 h prior to conventional sintering. The strengthening by the precoarsening was accomplished by the reduced growth rate of sintering flaws during tests.

(2) The FTGB is expected to be different for the two present aluminas. From the measured value of PTF, the FTGB is estimated to be 1.16 MPa,,/m for the normal and 1.25 MPa~/m for the precoarsened Al:O3, respectively.

(3) When the grain size of A12Q is 2 -4 ~tm, the fracture toughness of sintering flaws is independent of its size, and the decreasing tendency of strength with decreasing flaw size is not found.

References

[1] K.R-. McKinney, J.J. Mecholsky and S.W. Freiman, 3. Am. Ceram. Soc., 62 (1979) 336.

[2] J.J. Mecholsky, d. Am. Ceram. Soc., 64 (1981) 563. [3] K. Zeng, K. Breder and D. Rowcliffe, Z Am. Ceram. Soe., 76

(1993) 1673. [4] R.K. Govila, K.R. Kinsman and P. Beardmore, 3. Mater. Sci.,

I4 (1979) 1095. [5] R.W. Rice, S.W. Freiman and J.J. Mecholsky, Jr., d. Am.

Ceram. Soc., 63 (1980) 129.

[6] H.P. Kirchner and R.M. Gruver, J. Am. Ceram. Soc., 63 (i980) 169.

[7] B.R. Lawn, J. Am. Ceram. Soe.. 66 (1983) 83. [8] T. Fett, I~t. d. Fractto'e, 54 (1992) 117. [9] R.W. Steinbrech, A. Reichl and W. Schaarwachter, J. Am.

Ceram. Soc., 73 (1990) 2009. [i0] H. Tsuda, M. Enoki and T. Kishi, J. Ceram. Soc. Jpn., I00

(1992) 998. [11] A. Krell, J. Woltersdorf, E. Pippel and D. Schulze, Philos. Mag.,

ASI (1985) 765. [12] B.-N. Kim and T. Kishi, Mater. Sci. Eng., A176 (1994) 371. [13] W. Wunderlich, Y. Ishida and R. Maurer, Scr. Meta/l. Mater.,

24 (I990) 403. [I4] A.A. Nazarov, A.E. Romanov and R.Z. Valiev, Acta Metal/.

Mater., 41 (I993) 1033. [15] K.J. Morrissey and C.B. Carter, d. Am. Ceram. Soc., 67 (1984)

292. [16] M.Y. Chu, L.C. De Jonghe, M.K.F. Lin and F.J.T. Lin, J. Am.

Ceram. Soe., 74 (1991) 2902. [17] J.P. Singh, A.V. Virkar, D.K. Shetty and R.S. Gordon, J. Am.

Ceram. Soc., 62 (1979) 179. [18] A.G. Evans, d. Am. Ceram. Sot., 63 (1980) II5. [19] M. Iwasa, K. Ando and N. Ogura, Trans. Jpn. Soc. Mech. Eng.,

A56 (1990) 2353. [20] K. Suzuki, K. Tanaka and H. Tanaka, Trans. Jpn. Soc. Mech.

Eng., A59 (1993) 1292. [21] J.C. Newman, Jr. and I.S. Raju, Eng. Fract. Mech., I5 (1987)

185. [22] J.J. Petrovic, L.A. Jacobson, P.K. Talty and A.K. Vasudevan, J.

Am. Ceram. Soe., 58 (1975) 113. [23] Y. Fu and A.G. Evans, Acta Metall., 35 (1985) 1515. [24] R.W. Rice and R.C. Pohanka: d. Am. Ceram. Soc., 62 (1979)

559. [25] E.R. Fuller, Jr. and R.M. Thomson, Fractm'e Mechanics of

Ceramics, Vol. 2, Plenum, New York, 1978, p. 507. [26] S.M. Wiederhorn, H. Johnson, A.M. Diness and A.H. Heuer, J.

Am. Ceram. Soc., 57 (1974) 336. [27] C.A. Handwerker, J.M. Dynys, R.M. Cannon and R.L. CoNe,

J. Am. Ceram. Soc., 75 (I990) 1365. [28] P.W. Tasker, Advances in Ceramics, Vol. 10, American Ceramic

Society, Ohio, I983, p. 176. [29] A.G. Evans, Acta Metall., 26 (I978) 1845. [30] B. Cotterell and J.R. Rice, Int. J. Fracture, I6 (1980) I55. [3i] B.-N. Kim, S. Wakayama and M. Kawahara, Int. J. Fracture, 75

(i996) 247.

strengthening mechanism of alumina ceramics prepared by precoarsening treatments

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