Relation Between Strength, Fracture Toughness, and Critical Frontal Process Zone Size in Ceramics*1

Materials Transactions, Vol. 47, No. 6 (2006) pp. 1532 to 1539 #2006 The Japan Institute of Metals

Relation between Strength, Fracture Toughness, and Critical Frontal Process Zone Size in Ceramics*1

Hideo Awaji, Takuya Matsunaga*2 and Seong-Min Choi

Department of Materials Science and Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan

In order to improve the fracture toughness of inherently brittle ceramics, a new material design concept must be developed. One suitable concept involves the use of dislocation activities. Intra-type ceramic-based nanocomposites use dislocation activities to enhance strength and fracture toughness. The dislocations are generated by residual stresses induced during sintering process around the second-phase nanoparticles dispersed within the matrix grains. In this paper, ﬁrst, we proposed an indirect technique for estimating a critical frontal process zone (CFPZ) size for ceramics and clariﬁed the relation between the strength, fracture toughness, and CFPZ size. The fracture toughness of ceramics is closely related to the CFPZ size because ceramics with larger CFPZ size consume higher fracture energy during crack extension and consequently have higher fracture toughness. Second, we fabricated toughened alumina-nickel nanocomposites using a soaking method to construct an intra-type nanostructure, and found that the appropriate annealing conditions after sintering could achieve toughened nanocomposites. Finally, we discussed the relation between the experimentally obtained fracture toughness and the CFPZ size of monolithic alumina, as-sintered nanocomposites, and annealed nanocomposites. The results revealed that nanocomposites showed the largest CFPZ size and the highest fracture toughness after appropriate annealing: the sessile dislocations ahead of a crack tip in a nanocomposite are thought to serve as stress concentration, create many nanocracks in the CFPZ, and expand the CFPZ size. [doi:10.2320/matertrans.47.1532]

(Received January 20, 2006; Accepted April 25, 2006; Published June 15, 2006) Keywords: ceramics, strength, fracture toughness, frontal process zone, nanocomposites

1. Introduction that only lattice defects, such as dislocations, can be generated around the particles because nano-sized particles As high-temperature materials, ceramics possess several can only induce nanoscale residual stress distributions.7) superior properties, such as high thermal resistance, chemical Also, these dislocations become sessile dislocations at room durability, and fracture strength. However, ceramics inher- temperature and serve as origins of nanocrack nuclei in ently have low fracture toughness because of their ionic and highly stressed fields such as a main crack tip. Thus, these covalent bonding, and plastic deformation due to dislocation dislocations expand the CFPZ size and consequently enhance activities is extremely limited.1) For instance, the critical the fracture toughness of ceramics. This is the nanocomposite resolved shear stress of -alumina single crystal was toughening mechanism that we proposed.7) estimated by Lagerlo¨f et al.2) to be 4 GPa for prism-plane The toughening of ceramics is classified under three slip at room temperature, which is about ten times higher than mechanisms:5) the bending strength of polycrystalline alumina. Thus, (1) The frontal process zone expansion mechanism, which dislocations in -alumina are only generated at elevated increases the fracture energy consumed in the damaged temperatures except under compressive stress states, and the zone ahead of a crack tip and enhances the intrinsic critical frontal process zone (CFPZ) size of ceramics fracture toughness (Ki). becomes very small at room temperature, and is believed to (2) The crack surface bridging mechanism, which operates be composed of nanocracks, rather than the kind of in the process zone wake and increases the extrinsic 3,4) dislocations observed in metals. To overcome the inherent fracture toughness (KR). brittleness of ceramics, a new material design concept must (3) The crack deflection mechanism, in which the crack be developed. It is conceivable that expanding the CFPZ size deflection at a crack tip decreases the energy release may improve the fracture toughness of ceramics because the rate and apparently enhances the fracture toughness. CFPZ size of ceramics is quite small compared with that of Among these mechanisms, we concern ourselves with metals, and larger CFPZ sizes require higher fracture energy mechanism (1), which includes several mechanisms, such based on Griffith energy equilibirium.1,5) as phase transformation toughening by partially-stabilized The intra-type nanocomposites proposed by Niihara6) are zirconia and crack surface roughening in the particle- based on a newly developed material design concept and are dispersed or column-like crystal grown materials. These thought to have a CFPZ expansion mechanism.5) The intra- mechanisms increase the fracture energy and improve the type nanostructure constructed by dispersing nano-sized intrinsic fracture toughness. Our research aims at expanding second-phase particles within the matrix grains exhibits a the CFPZ size for fabricating highly toughened nanocompo- thermal expansion mismatch between the matrix and the sites using a new material design concept. dispersed particles, which generates dislocations around the There is the so-called HRR (Hutchinson,8) and Rice and particles due to the residual stresses. The important point is Rosengren9)) solution to express the stress field in the CFPZ of metals using the J-integral. However, it is not possible to 10) *1This Paper was Originally Published in Japanese in J. Japan Inst. Metals apply this solution to ceramics, since the CFPZ of ceramics 70 (2006) 59–66. is thought to be composed of nanocracks rather than *2Graduate Student, Nagoya Institute of Technology dislocations. Relation between Strength, Fracture Toughness, and Critical Frontal Process Zone Size in Ceramics 1533

In this paper, we propose an indirect technique for estimating the macroscopically defined CFPZ size for σ 11) σ y ceramics using a local fracture criterion and Griffith-Irwin fc σ = σ c fc Fc (r0 ) energy equilibrium1) under the assumption of the small scale yielding condition. We experimentally obtain the relation σ c σ (a + r) between the strength of the notched bending specimen and σ = fc e y 12) + 2 the notch depth for dense alumina, and show that the 2aer r critical condition of the crack extension satisfies the local fracture criterion. Then, we fabricate monolithic alumina and alumina-nickel nanocomposites, and estimate the strength, Irwin's expression fracture toughness, and CFPZ size of these materials.13) The r results show that materials with larger CFPZ size have higher 0 r0 2ae fracture toughness. In the present paper, the term ‘CFPZ size’ refers to a macroscopically defined CFPZ size, calculated from the macroscopically defined fracture toughness and strength. Fig. 2 Stress distribution ahead of a crack tip in an infinite plate with a 2. Theory short crack.

2.1 Criteria for crack extension For a crack in an infinite plate under mode I loading, the eq. (2), the following relation is derived at r0 exact solution of the stress on the r-axis (ahead of the crack K 14) IC plane) is expressed as c ¼ pffiffiffiffiffiffiffiffiffiffi ; ð3Þ 2r0 ða þ rÞ K 1 þ r=a f e ffiffiffiffiffiffiffiffiI e 1=2 y ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ p pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ f FcðrÞ; ð1Þ where K ¼ ða Þ , represents the critical value of 2 IC fc e fc 2aer þ r 2r 1 þ r=2ae the remote stress, and c is the critical local stress at r0. 11) where f represents the remote stress on the plate, ae is the The local fracture criterion states that the crack will 1=2 half crack length in an infinite plate, KI ¼ f ðaeÞ is the propagate when the stress at a characteristic distance from the stress intensity factor (SIF), and Fc is the non-dimensional crack tip reaches the critical local stress. If the characteristic stress distribution ahead of a crack tip. When the crack length distance is equal to the CFPZ size, we obtain the same is sufficiently long compared with the CFPZ size, r0, and in equation as eq. (3). Namely, the local fracture criterion and the range r0 r ae, the following Irwin’s expression is Griffith-Irwin criterion becomes the same for a long crack derived from eq. (1): problem in brittle materials. Next, we consider the short crack problem, where the crack KI y ¼ pffiffiffiffiffiffiffiffi : ð2Þ length is not sufficiently long compared with the CFPZ size. 2r The stress distribution ahead of the short crack tip is shown in Figure 1 shows the critical stress state in front of a long crack Fig. 2. In this case, the exact stress distribution and Irwin’s tip in an infinite plate, where KI reaches the fracture expression have different values at r0. So, we must use the toughness, KIC. The solid curve indicates the exact stress exact stress distribution to estimate the critical local stress. distribution of y expressed by eq. (1) and the dotted curve The critical local stress for the short crack problem can be represents Irwin’s expression indicated by eq. (2). From expressed from eq. (1) as

c ¼ fcFcðr0Þ: ð4Þ The strength of the infinite plate is then given by σ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ y 2 fc K 2a r þ r σ = IC e 0 0 c fc ¼ c : ð5Þ 2πr ae þ r σ 0 0 c Taking the limit as ae goes to zero in eq. (5), the following σ (a + r) σ = fc e relation is derived y + 2 2aer r lim fc ! c; ð6Þ ae!0

K which indicates that c is the strength of an infinite plate with σ = IC Irwin's expression y 2πr no artificial crack. The estimation of the c value obtained 0 r r from the bending strength will be explained later. 2a 0 e Munro and Freiman15) discussed the relation of fracture toughness and strength based on the following relation derived from linear fracture mechanics, pffiffiffi KIC ¼ Y fc a; ð7Þ Fig. 1 Stress distribution ahead of a crack tip in an infinite plate with a long crack. 1534 H. Awaji, T. Matsunaga and S.-M. Choi where a represents the critical flaw size. They derived the 103 linear relation between the fracture toughness, K , and the r (2a + r ) IC σ = σ 0 e 0 16) fc c strength, fc, in contrast of Swain’s trade-off relation. In σc a + r σ e 0 spite of the correct result, Munro’s error is that eq. (7) is only / MPa B fc applicable in the case of a long crack problem. The critical σ flaw size in materials which dominates the strength does not satisfy the small scale yielding condition. Therefore, there is 102 no direct relation between the strength and fracture toughness. The correct relation between them is derived from Alumina eq. (13) as17) pffiffiffiffiffiffiffiffiffiffi 1=2 KIC ¼ c 2r0 / B r0 : ð8Þ Fracture Strength 101 10-2 10-1 100 3. Experimental Results and Discussion Equivalent Crack Length a e / mm 3.1 Dense alumina Polycrystalline alumina of 99.5% purity with a minor Fig. 3 Experimental results of the bending strengths of the specimens with and without a notch, where B is a bending strength and c is a estimated dopant of MgO fabricated by Japan Fine Ceramics Center critical local stress. was used to explain the relation between the strength of a cracked specimen and the crack length.12) The mean grain size of the alumina was 2 mm with isotropic morphology and homogeneous microstructure. JIS type specimens 3 4 represents eq. (5) using the estimated critical local stress and 40 mm in size were machined out, chamfered, and finished by CFPZ size. Figure 3 shows that when the equivalent crack lapping. The three-point bending strength was 462 18:0 length is longer than about 100 mm, the bending strength of MPa for ten specimens, and the shape factor of the two- notched specimens lie on a straight line with a gradient of parameter Weibull distribution, m, was 28 and the scale 1=2, which means that linear fracture mechanics is factor, , was 471 MPa. The fracture toughness measured applicable in this region, where the fracture toughness was by the SEPB (singe-edge pre-cracked beam) method was estimated to be 3.72 MPam1=2 by curve fitting, which is 3:65 0:11 MPam1=2. almost the same as the value obtained by the SEPB method A three-point bending test with span = 30 mm was carried described previously. out on the specimens for various depths of a V-notch The strengths of the edge-cracked specimens lie on the machined using a sharp V-shaped diamond wheel,18) where dotted curve, not only in the long crack region but also in the the average root radius of the notch tip was about 20 mm. All short crack region, which suggests that these data satisfy the specimens had the same dimensions (H ¼ 3 mm (height) and local fracture criterion independent of the crack length, and B ¼ 4 mm (width)) to allow a comparison of the strength of the critical local stress, c, and the CFPZ size, r0, are constant specimens with and without the artificial notch. The nominal in the whole region of the edge crack. lengths of the V-notches were, 0.015, 0.02, 0.05, 0.1, 0.5, 1.0, Let us now explain how to estimate the critical local stress and 1.5 mm, and for each notch depth the strength was and the CFPZ size for ceramics. The relation between the estimated for five specimens. An equivalent crack length, i.e., critical local stress and the bending strength can be expressed the crack length in an infinite plate with the same SIF as the using Weibull statistics. The effective volume of the three- edge crack, is calculated assuming that the V-notch is an edge point bending specimen is expressed as1) crack. The SIF of the edge-cracked specimen was calculated V 19) using the following estimation by Wakai et al. VB ¼ ; ð11Þ 2ðm þ 1Þ2 K ¼ Y a1=2 I f where V ¼ B H S. The effective volume of the CFPZ ð9Þ 3PS ahead of a crack tip in ceramics is estimated as follows: The f ¼ ; 2BH2 CFPZ of ceramics consists of nanocracks, rather than where KI denotes the SIF of the edge cracked bending dislocations as in metals, and these nanocracks are mainly specimen, a is the crack length, Y is the shape factor shown in created by the maximum principal stress. Assuming that the Ref. 19, P is the load, S is the span. The equivalent crack stress inside the CFPZ is homogeneous, the shape of the length is defined as20) CFPZ can be approximated by the area enclosing in the contour of the maximum principal stress. Under the small Y2 a ¼ a: ð10Þ scale yielding condition, the stress distribution of the e maximum principal stress, 1, under mode I loading shown The experimental results are shown in Fig. 3, where the in Fig. 4 is expressed as21) double circles ( ) indicate the average strength of specimens KI with various depths of the V-shaped notch. The solid square ¼ pffiffiffiffiffiffiffiffi cos 1 þ sin : ð12Þ 1 2 2 ( ) indicates the average bending strength of the specimens 2r without a notch. The solid diamond ( ) shows the estimated The distance from the crack tip to the contour, r1, is then critical local stress, c, mentioned later, and the dotted curve given by Relation between Strength, Fracture Toughness, and Critical Frontal Process Zone Size in Ceramics 1535 σ Dislocation Nanocrack

Matrix grain Dispersed particle (r,θ) dA dθ r 1 θ Sub-grain boundary Main crack tip r0 FrontalFPZ Process Zone

Fig. 5 Schematic explanation of nano-crack formation in a frontal process zone. Fig. 4 Shape of the critical frontal process zone of ceramics.

from eq. (5) using the r and values, and is shown in Fig. 3 0 c 2 using the dotted curve. r ¼ r cos2 1 þ sin ; ð13Þ 1 0 2 2 3.2 Alumina/nickel nanocomposites where r0 represents r1 at ¼ 0 in eq. (13). The infinitesimal In order to enhance the fracture toughness of alumina, we area, dA, shown in Fig. 4, can be expressed as fabricate nanocomposites with an intra-type nanostructure, where the second phase nanoparticles are embedded within 1 2 dA ¼ r1d: ð14Þ the alumina matrix and generate dislocations around the 2 particles due to the thermal expansion mismatch.7) Thus, it is Thus, the area of the CFPZ is obtained: possible to disperse and reproduce dislocations by appro- Z 4 priate annealing. Since the dislocations of ceramics have a 2 4 1) A ¼ r0 cos 1 þ sin d: ð15Þ large lattice structure compared with that of metals, the 0 2 2 former have a relatively large tensile stress field with a The integral part in eq. (15) is numerically calculated to be compressive stress field and become sessile dislocations at 3.29. The effective volume of the CFPZ is then derived using room temperature. If the main crack tip approaches this area, the thickness of the specimen, B,as as shown in Fig. 5, these sessile dislocations act as nanocrack nuclei due to the interaction between the highly localized V ¼ 3:29r2B: ð16Þ FPZ 0 stress state at the main crack tip and the tensile stress around The CFPZ is in a biaxial stress state of the principal the dislocations, and create many nanocracks in the CFPZ. stresses 1 and 2. The strength ratio of the plates under These nanocracks expand the CFPZ, increase the fracture uniaxial and bi-axial stress states can be expressed statisti- energy, and thus enhance the fracture toughness.22) cally as1) The intra-type nanostructure is therefore essential in fabricating toughened ceramics. Ceramic-based nanocompo- S 1 1=m 2 ¼ ; ð17Þ sites have been fabricated using high-speed sintering tech- m S1 1 þ niques, such as pulse electric current sintering (PECS) or hot 22) where S1 and S2 denote the strengths of the specimens under pressing, but the second-phase particles tend to segregate uniaxial and biaxial states, respectively, and is the ratio of to the matrix boundaries. A soaking method13) was developed the biaxial stresses. We, however, omit the biaxial effect as a new technique for fabricating intra-type nanocomposites. because the ratio S2=S1 becomes almost 1 in this case. The present paper uses an alumina-nickel nanocomposite The ratio of the three-point bending strength and the system to explain the soaking method. Commercially critical local stress is expressed as1) available -alumina powder consists of column-like primary particles and has an agglomerated form with much nano- V 1=m S V 1=m c ¼ B 2 B : ð18Þ porosity. The -alumina powder is soaked in a nickel nitrate B VFPZ S1 VFPZ solution in vacuum, and filtered and dried, followed by Using this equation, the critical local stress, c, can be calcination to get nickel oxide particles in the pores of the estimated from the experimentally obtained bending -alumina powder. The calcinated powder was then reduced strength, B. under hydrogen atmosphere to obtain metallic nickel within For the dense alumina, c was calculated to be 561 MPa, the -alumina agglomerates. Upon sintering, we easily and r0 was obtained to be 7.0 mm from eq. (3). The strength obtained intra-type nanostructured alumina-nickel nanocom- of an infinite plate with an arbitrary crack length is estimated posites. 1536 H. Awaji, T. Matsunaga and S.-M. Choi

Because the experimental procedure of the soaking method With a seed was reported elsewhere,13) we describe it only brieﬂy here. Using the commercially available -alumina powder (AKP- G015, Sumitomo Chemical, Japan) and nickel nitrate (Osaka 4 Chemistry, Japan) solution, -alumina powder containing nano-sized nickel was prepared. To improve the sinterability, Alumina we added 10 mass% -alumina powder (TM-D, Taimei -3 3.8 Chemical Co., Japan) as a seed and 0.25 mass% MgO as a sintering additive. The mixtures were sintered by the PECS method at 1250, 1350, 1450, and 1550C under 30 MPa in 3.6 vacuum for 5 min. The volume fraction of nickel was about 3% in these nanocomposites. To disperse the dislocations generated around the nanoparticles into the alumina grains, 3.4 the sintered specimens were additionally annealed under Without a seed several conditions. Bulk densities / gcm Three-point bending specimens were 2 2 10 mm 3.2 (span ¼ 8 mm). The fracture toughness was measured on the same type of specimens, but with a sharp V-shaped notch, using the so-called SEVNB (single-edge V-notched beam) 14) 3 method. 1200 1300 1400 1500 1600 Figure 6 shows the bulk densities of the alumina-nickel nanocomposites with and without a seed, and the monolithic Sintering temperatures / °C alumina sintered under the same conditions as the nano- Fig. 6 Bulk densities of monolithic alumina and alumina-nickel nanocomposites. These materials sintered at above 1350 C show composites. high density except for the nanocomposites without a seed. Thus, we omit the data on the nanocomposites without a seed from our discussion. intergranular fracture mode. Figure 7 shows the SEM micrographs of the fracture Figure 8 shows the relation between the bending strength, surfaces of the nanocomposites with a seed, which indicates fracture toughness, and CFPZ size for the monolithic alumina that the grain size of the alumina matrix increases with and as-sintered nanocomposites. The mean strength and increasing temperature, and the fracture mode is almost fracture toughness were 470 MPa and 3.66 MPam1=2 for the transgranular fracture in all cases; a typical feature in intra- monolithic alumina, and 911 MPa and 4.61 MPam1=2 for the type nanocomposites, whereas monolithic alumina shows as-sintered nanocomposites, respectively. A comparison of

a) b)

11µµm 11µµm 1250°C 1350°C

c) d)

11µµm 11µµm

1450°C 1550°C

Fig. 7 SEM observations for fracture surfaces of seeded alumina-nickel nanocomposites sintered from 1250 to 1550C. Relation between Strength, Fracture Toughness, and Critical Frontal Process Zone Size in Ceramics 1537

1000 10 Strength 8.0 Toughness 1/2 800 Critical FPZ size Strength 8 m

Toughness µ 600 Critical FPZ size 6 1/2 7.0 400 4 Fracture strength / MPa 200 2 Fracture toughness / MPam Frontal process zone / 6.0 0 0 12501350 1450 1250 1350 1450 1550 Sintering temperature / °C Sintering temperature / °C before annealing (a) Monolithic alumina (b) As-sintered nanocomposites annealed at 800 annealed at 900 Fig. 8 Strength, fracture toughness, and critical frontal process zone size of 5.0 annealed at 1000 monolithic alumina and as-sintered nanocomposites.

Figs. 7 and 8 reveals that there is no apparent relation Fracture toughness / MPam between the strength and the grain size, despite well-known 4.0 Hall-Petch relation observed commonly in sintered materials. The typical features of these nanocomposites can be summa- rized as a high, grain-size-independent strength, and trans- 0 5 10 granular fracture mode.7) Figure 9 schematizes the fracture behavior of (a) mono- Annealing times / min lithic alumina and (b) nanocomposites. Monolithic alumina Fig. 10 Fracture toughness of as-sintered nanocomposites and annealed usually has sintering residual stresses in the grains, which are nanocomposites. in a self-equilibrium state in the specimen; namely, if a certain grain has a tensile residual stress, the neighboring grains are under compressive stress. Thus, it is conceivable the inherent size of the cavity, and the strength is signiﬁcantly that if there is a large cavity at the three-point grain boundary improved. Also, when a crack propagates from the cavity, and the grains around the cavity have tensile residual stresses, dislocations in the grains serve as nanocrack nuclei in the a crack can extend along the grain boundary due to the frontal process zone ahead of the crack tip, and the main interaction between the stress concentration of the cavity and crack propagates in the grains so as to connect these the tensile residual stresses. The crack then elongates to the nanocracks. Then, the fracture mode changes to transgranular grain size without external loading, and the elongated crack fracture. becomes the weakest defect in the specimen. Thus, the Let us consider annealing eﬀects on the nanocomposites. measured strength in the monolithic alumina largely falls Figure 8(b) shows that the highest fracture toughness was below the inherent value. 5.5 MPam1=2 for the as-sintered nanocomposites sintered at Figure 9(b) illustrates the fracture behavior of nanocom- 1350C. Thus, we annealed this specimen. The fracture posites. After sintering, dislocations are generated around the toughness of the annealed nanocomposites is shown in dispersed nanoparticles and release the sintering residual Fig. 10, where the empty circle ( ) indicates the fracture stresses in the grains. Then, the weakest defect size becomes toughness of the as-sintered nanocomposites sintered

Crack path Residual stress

Process zone wake Crack path Cavity The weakest crack

(a) Monolithic alumina (b) Nanocomposites

Fig. 9 Schematic explanation for strength of monolithic alumina and nanocomposites. 1538 H. Awaji, T. Matsunaga and S.-M. Choi

1000 10 1000 10

800 8 1/2 Strength m σ 1/2 Toughness µ 800 B 8 Critical FPZ size 600 6 m µ KIC 400 4 600 6 Strength Toughness Fracture strength / MPa Critical FPZ size 2

200 Frontal process zone / Fracture toughness / MPam 400 4 Strength / MPa 0 0 1250 1350 1450 1550 0 5 10 r0 Sintering temperature / Annealing time / min Critical FPZ size / (b) Annealed nanocomposites 200 2 (a) As-sintered nanocomposites Fracture toughness / MPam

Fig. 11 Strength, fracture toughness, and critical frontal process zone size of as-sintered and annealed nanocomposites. 0 0 A B C A: Monolithic, B: As-sintered, C: Annealed at 1350C, and the solid symbols ( , , and ) correspond to the fracture toughness of the specimens annealed at 800, Fig. 12 Comparison between the strength, fracture toughness, and critical 900, and 1000C, respectively. It is noted that the specimen frontal process zone size of monolithic alumina and as-sintered and annealed nanocomposites. annealed at 800C for 5 min has the maximum fracture toughness, 7.6 MPam1=2. However, annealing times of 10 min and annealing temperatures above 800C result in fracture higher than the measured value. Here, we assumed that the toughness that values are lower than the as-sintered value difference between the inherent strength and the measured ( ). This suggests that dislocations vanish from grains in strength was 260 MPa and we re-calculated the CFPZ size of specimens annealed for longer times or at higher temper- the monolithic alumina using the technique mentioned atures, and the fracture toughness reverts to the inherent previously. The modified relation between the average data value of the monolithic alumina. of the monolithic alumina, as-sintered nanocomposites, and Figure 11 shows the relation between the strength, fracture annealed nanocomposites are shown in Fig. 12, where the toughness, and CFPZ size of (a) as-sintered and (b) nano- data for 1550C for the as-sintered nanocomposites and composites annealed at 800C. Except in the case of the 10- 10 min for the annealed nanocomposites are omitted. In this min anneal, the strength did not change substantially between figure, for the monolithic alumina, the solid circle ( ) these materials, but both the fracture toughness and CFPZ indicates the measured strength and the empty circle ( ) size markedly increased upon annealing. Thus, specimens represents the assumed inherent strength, and the empty with larger CFPZ sizes showed higher fracture toughness. square ( ) indicates the re-calculated CFPZ size. It is known Figure 8 shows that monolithic alumina has a larger CFPZ that the strengths and fracture toughnesses of the nano- size than the as-sintered nanocomposites. However, we must composites are still higher than those of the monolithic consider that monolithic alumina has residual stresses after alumina, and that, of all materials studied, the annealed sintering, and the inherent strength of the alumina should be nanocomposites show the highest fracture toughness and

σ σ σ σ B - res Improved B Improved B

Cavity Cavity Larger FPZ Weakest crack

(a) Monolithic (b) As-sintered nanocomposites (c) Annealed nanocomposites alumina

Fig. 13 Schematic explanation of strength and critical frontal process zone size in monolithic alumina and as-sintered and annealed nanocomposites. Relation between Strength, Fracture Toughness, and Critical Frontal Process Zone Size in Ceramics 1539 larger CFPZ size, which indicates that annealing process REFERENCES disperses and reproduces dislocations in the matrix grains and improves the fracture toughness. 1) H. Awaji: Strength of Ceramic Materials, (Corona Pub., Tokyo, 2001). Figure 13 schematizes the mechanisms for improving 2) K. P. D. Lagerlo¨f, A. H. Heuer, J. Castaing, J. P. Rivie`re and T. E. Mitchell: J. Am. Ceram. Soc. 77 (1994) 385–397. strength and fracture toughness in the as-sintered and 3) R. G. Hoagland and J. D. Embury: J. Am. Ceram. Soc. 63 (1980) 404– annealed nanocomposites. Compared with the monolithic 410. alumina, the strength of the as-sintered nanocomposites was 4) A. G. Evans and K. T. Faber: J. Am. Ceram. Soc. 64 (1981) 394–398. markedly improved because of the small weakest defect size, 5) H. Awaji, S.-M. Choi and T. Ebisudani: J. Ceram. Soc. Japan 108 but the CFPZ size of the as-sintered nanocomposites did not (2000) 611–613. 6) K. Niihara: J. Ceram. Soc. Japan 99 (1991) 974–982. change substantially. Upon annealing, dislocations were 7) H. Awaji, S.-M. Choi and E. Yagi: Mech. of Mater. 34 (2002) 411–422. dispersed in the matrix grains, and the fracture toughness of 8) J. W. Hutchinson: J. Mech. Phys. Solids 16 (1968) 13–31. the annealed nanocomposites was signiﬁcantly improved due 9) J. R. Rice and G. F. Rosengren: J. Mech. Phys. Solids 16 (1968) 1–12. to enlargement of the CFPZ size. This is our new material 10) H. Okamura: Introduction to linear Fracture Mechanics, (Baifu-kan, design concept for improving the fracture toughness of Tokyo, 1976) p. 76. 11) J. Besson ed.: Local Approach to Fracture, (Les Presses de l’E´ cole des ceramics. Mines, Paris, 2004). 12) H. Awaji, S.-M. Choi and D. D. Jayaseelan: J. Ceram. Soc. Japan 109 4. Conclusions (2001) 591–595. 13) T. Matsunaga, U. Leela-adisorn, Y. Kobayashi, S.-M. Choi and H. We experimentally conﬁrmed the strengthening and Awaji: J. Ceram. Soc. Japan 113 (2005) 123–125. 14) H. Awaji, T. Watanabe and Y. Sakaida: Ceram. Int. 18 (1992) 11–17. toughening mechanisms of nanocomposites with an intra- 15) R. G. Munro and S. W. Freiman: J. Am. Ceram. Soc. 82 (1999) 2246– type nanostructure and a new material design concept for 2248. fabricating toughened ceramics based on dislocation activ- 16) M. V. Swain: Acta metal. 33 (1985) 2083–2091. ities. Highly toughened alumina-3 vol% Ni nanocomposites 17) H. Awaji, S.-M. Choi, C. H. Chen and N. Kishi: J. Soc. Mater. Sci. 53 were fabricated using the soaking method proposed previ- (2004) 1012–1018. 18) H. Awaji, T. Watanabe, T. Yamada, Y. Sakaida, H. Tamiya and H. ously. The results showed that the maximum fracture Nakagawa: Trans. Japan Soc. Mech. Engng. 525A (1990) 1148–1153. toughness of properly annealed nanocomposites was 19) F. Wakai, S. Sakaguchi and S. Matsuno: J. Ceram. Soc. Japan 93 (1985) 7.6 MPam1=2, which was twice that of monolithic alumina. 479–480. 20) S. Usami, H. Kimoto, I. Takahashi and S. Sida: Eng. Fract. Mech. 23 Acknowledgments (1986) 745–761. 21) H. Awaji and T. Kato: The Japan Institute. Metals 62 (1998) 735–741. 22) S.-M. Choi and H. Awaji: Sci. and Tech. of Advanced Mater. 6 (2005) st We received a grant from the NITECH 21 Century 2–10. COE Program ‘World Ceramics Center for Environmental Harmony’.