MECHANICS MATERIALS ELSEVIER Mechanics of Materials 30(1998)111-123 Toughening mechanisms of nano-composite ceramics lai Tan, Wei Yang Department of Engineering Mechanics, Tsinghua Unicersity, Beijing 100084, China Received 9 October 1997: received in revised form 3 March 1998 abstract Recent experiments showed that nano-composite ceramics with particles distributed within the matrix gras g s along the grain boundaries can acquire high toughening. The toughening of alumina ceramics with dispersed silicon carbide nano-particles are studied in the present paper. Three toughening mechanisms are identified: switching from the intergranular cracking to the transgranular one by nano-particles along the grain boundaries, fracture surface roughening by zigzag crack path perturbed by the internal stresses of nano-particles within the grains, and shielding by clinched rough surfaces near the crack tip. For different volume fractions of nano-particles, the estimated gross toughening agrees with the experiments. o 1998 Elsevier Science Ltd. All rights reserved Keywords: Toughening mechanisms; Fracture; Ceramics; Nano-particles 1. Introduction stresses in the material. The residual stresses in fluence the path of crack propagation. Levin et al. Many attempts have been made to improve the (1994)measured the average distribution and inherently brittle ceramics. Recent experiments by fluctuation of micro-strain in the matrix of Al O3/ Izaki et al.(1988) and Niihara and coworke nano-SiC composites by X-ray diffraction method (Niihara, 1991; Niihara and Nakahira, 1990: Nil- While the matrix toughness remains unchange ha aL, 1993, 1994; Sawaguchi in nano-composite ceramics(Zhao et al., 1993) Sasaki et al., 1992) showed that fracture toughness other toughening mechanisms exist. One approach of nano-composite ceramics, in which nanometer is to steer the crack to propagate along the path of sized second particles are dispersed within the ce- higher toughness. For ceramics, the toughness of ramic matrix, can be greatly enhanced grain boundaries is lower than that within the The substantial toughening of nano-composite grains. Thus the fracture pattern in conventional tes many related studies. Sawa- ceramics are mainly intergranular. Fo or nano- guchi et al. (1991) discovered an inter/intra type of composite ceramics, nano-particles along the grain nano-composite ceramics that induces transgran- boundaries tend to switch the intergranular frac ular fracture. Thermal mismatch between the ture to the transgranular one, and consequently nano-particles and the matrix generates residual toughen the composites. The other approach is to gain gross toughening by local weakening. The residual stresses generated by nano-particles pro- mote crack curving in ceramics, thus the crack du.cn grows along a wavy path. The global toughness is 0167-663698/S-see front matter c 1998 Elsevier Science Ltd. All rights reserved PI:S0167-6636(98)00027
Toughening mechanisms of nano-composite ceramics Honglai Tan, Wei Yang * Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China Received 9 October 1997; received in revised form 3 March 1998 Abstract Recent experiments showed that nano-composite ceramics with particles distributed within the matrix grains and along the grain boundaries can acquire high toughening. The toughening of alumina ceramics with dispersed silicon carbide nano-particles are studied in the present paper. Three toughening mechanisms are identi®ed: switching from the intergranular cracking to the transgranular one by nano-particles along the grain boundaries, fracture surface roughening by zigzag crack path perturbed by the internal stresses of nano-particles within the grains, and shielding by clinched rough surfaces near the crack tip. For dierent volume fractions of nano-particles, the estimated gross toughening agrees with the experiments. Ó 1998 Elsevier Science Ltd. All rights reserved. Keywords: Toughening mechanisms; Fracture; Ceramics; Nano-particles 1. Introduction Many attempts have been made to improve the inherently brittle ceramics. Recent experiments by Izaki et al. (1988) and Niihara and coworkers (Niihara, 1991; Niihara and Nakahira, 1990; Niihara et al., 1993, 1994; Sawaguchi et al., 1991; Sasaki et al., 1992) showed that fracture toughness of nano-composite ceramics, in which nanometer sized second particles are dispersed within the ceramic matrix, can be greatly enhanced. The substantial toughening of nano-composite ceramics stimulates many related studies. Sawaguchi et al. (1991) discovered an inter/intra type of nano-composite ceramics that induces transgranular fracture. Thermal mismatch between the nano-particles and the matrix generates residual stresses in the material. The residual stresses in- ¯uence the path of crack propagation. Levin et al. (1994) measured the average distribution and ¯uctuation of micro-strain in the matrix of Al2O3/ nano-SiC composites by X-ray diraction method. While the matrix toughness remains unchanged in nano-composite ceramics (Zhao et al., 1993), other toughening mechanisms exist. One approach is to steer the crack to propagate along the path of higher toughness. For ceramics, the toughness of grain boundaries is lower than that within the grains. Thus the fracture pattern in conventional ceramics are mainly intergranular. For nanocomposite ceramics, nano-particles along the grain boundaries tend to switch the intergranular fracture to the transgranular one, and consequently toughen the composites. The other approach is to gain gross toughening by local weakening. The residual stresses generated by nano-particles promote crack curving in ceramics, thus the crack grows along a wavy path. The global toughness is Mechanics of Materials 30 (1998) 111±123 * Corresponding author. E-mail: yw-dem@mail.tsinghua.edu.cn. 0167-6636/98/$ ± see front matter Ó 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 6 3 6 ( 9 8 ) 0 0 0 2 7 - 1
H. Tan, H. Yang Mechanics of Materials 30(1998)111-123 improved by the increasing of fracture surfaces and by the shielding of the clinched rough crack O--experimental point calculated curve 2. Fracture toughness 1.5 1.0 AlO3 /nano-SiC ceramics are fabricated by di ect coagulation casting technology( Gauckler and Graule. 1992). The sintering temp ratures are 1650°C,1650°C,1700°C,1750°C,and1750C when the nano-particles have volume contents of %. 5%6.10%. 15% and 20%. The relative densities of the specimens all exceed 99%. The average size of matrix grains and nano-particles is 2 um and 80 nm, respectively. Representative mechanical Fig. l. Toughening effect of the nano-composite ceramics with respect to the volume fraction of the dispersed nano-particles properties are listed in Table 1. For comparison, pure AlO3 ceramics are made with the same ma- trix grain size. Denote as Gcm and Gc the critical energy release rates of the nano-composite ce- 3. Microscopy observations ramics and the comparison Al,O3 ceramics. The latter is measured as Go=33. 8 J The frac- 3.1. Fractography observations ture toughness is measured by three-point-bending specimens, with length 24 mm, height 6.0 mm and The fracture surface of a three-point be thickness 4.0 mm specimen is examined under a field emission The toughening factor a is defined as scanning electronic microscope. Fig. 2 compares x=C/C-1, the fracture surface of nano-composite ceramics and that of the pure AlO3 ceramics. Fig. 2(A) which varies with the volume fraction of nano- shows that the fracture surface of Al,O3 ceramics particles, Vr. The experimental o versus Vr curve is consists of many smooth facets of grain size. shown in the cycles of Fig. I for AlO3/nano-Sic Fig. 2(B)shows that the fracture surface of nano- composites. The curve peaks at a critical volume composite ceramics is zigzag within the matrix fraction of added nano-particles. Volume fractions grains, due to the residual stress fields of the nar higher or lower than this critical value will reduce particles within the grain. From Fig. 2(B), few the toughening effect. For AlO3/nano-Sic ce- debonded nano-particles or holes can be found ramics, the highest toughening occurs at about along the crack surface, indicating strong cohesion between the nano-particles and the matrix anical parameters of matrix and nano-particles AlO,(matrix) Thermal expansion coefficient x=843×10-K oung's modulus Em=402 GPa Ep=450 GPa V=0.2
improved by the increasing of fracture surfaces and by the shielding of the clinched rough crack surfaces. 2. Fracture toughness Al2O3/nano-SiC ceramics are fabricated by direct coagulation casting technology (Gauckler and Graule, 1992). The sintering temperatures are 1650°C, 1650°C, 1700°C, 1750°C, and 1750°C when the nano-particles have volume contents of 0%, 5%, 10%, 15% and 20%. The relative densities of the specimens all exceed 99%. The average size of matrix grains and nano-particles is 2 lm and 80 nm, respectively. Representative mechanical properties are listed in Table 1. For comparison, pure Al2O3 ceramics are made with the same matrix grain size. Denote as Gnm C and Glm C the critical energy release rates of the nano-composite ceramics and the comparison Al2O3 ceramics. The latter is measured as Glm C 33.8 J mÿ2. The fracture toughness is measured by three-point-bending specimens, with length 24 mm, height 6.0 mm and thickness 4.0 mm. The toughening factor a is de®ned as a Gnm C =Glm C ÿ 1; 1 which varies with the volume fraction of nanoparticles, Vf. The experimental a versus Vf curve is shown in the cycles of Fig. 1 for Al2O3/nano-SiC composites. The curve peaks at a critical volume fraction of added nano-particles. Volume fractions higher or lower than this critical value will reduce the toughening eect. For Al2O3/nano-SiC ceramics, the highest toughening occurs at about Vf 10%. 3. Microscopy observations 3.1. Fractography observations The fracture surface of a three-point bending specimen is examined under a ®eld emission scanning electronic microscope. Fig. 2 compares the fracture surface of nano-composite ceramics and that of the pure Al2O3 ceramics. Fig. 2(A) shows that the fracture surface of Al2O3 ceramics consists of many smooth facets of grain size. Fig. 2(B) shows that the fracture surface of nanocomposite ceramics is zigzag within the matrix grains, due to the residual stress ®elds of the nanoparticles within the grain. From Fig. 2(B), few debonded nano-particles or holes can be found along the crack surface, indicating strong cohesion between the nano-particles and the matrix. Table 1 Mechanical parameters of matrix and nano-particles Al2O3 (matrix) SiC (nano-particle) Thermal expansion coecient am 8:43 10ÿ6K-1 ap 4:45 10ÿ6K-1 Young's modulus Em 402 GPa Ep 450 GPa Poission's ratio mm 0:23 mp 0:17 Fig. 1. Toughening eect of the nano-composite ceramics with respect to the volume fraction of the dispersed nano-particles. 112 H. Tan, W. Yang / Mechanics of Materials 30 (1998) 111±123
H. Tan, W. Yang/ Mechanics of Materials 30(1998)111-123 1日.日kU AMRAY 8日13 (A) Ceramics without added particles 16.8 kV AMRAY (B)Nano-composite ceramics Fig. 2. Comparison of the fracture surface: (A) ceramics without added particles: (B)nano-composite ceramic 3. 2. SEM image of the crack path pecimen by an alloy string stained with Sic par- ticles. The specimen ligament is comparable to the Cracks formed in a brittle material usually specimen thickness. The two edges of the sp ause a catastrophic failure. In order to get stable are slightly tilted: one side is higher and the other cracks in ceramics specimen for in situ electron side is lower. During the in situ test, compressing nicroscopies, a double side-cracked specimen is force is applied to the top and the bottom edges of devised. As shown in Fig 3, two sharp cracks of the specimen. The tilted edges cause a bending the same length are sawed into the two sides of the moment, the higher side is compressed and the
3.2. SEM image of the crack path Cracks formed in a brittle material usually cause a catastrophic failure. In order to get stable cracks in ceramics specimen for in situ electron microscopies, a double side-cracked specimen is devised. As shown in Fig. 3, two sharp cracks of the same length are sawed into the two sides of the specimen by an alloy string stained with SiC particles. The specimen ligament is comparable to the specimen thickness. The two edges of the specimen are slightly tilted: one side is higher and the other side is lower. During the in situ test, compressing force is applied to the top and the bottom edges of the specimen. The tilted edges cause a bending moment, the higher side is compressed and the Fig. 2. Comparison of the fracture surface: (A) ceramics without added particles; (B) nano-composite ceramics. H. Tan, W. Yang / Mechanics of Materials 30 (1998) 111±123 113
l14 H. Tan, H. Yang Mechanics of Materials 30(1998)111-123 3.3. Distribution of nano-particles in the matrix Nano-particles may be distributed in three 0.8mm patterns: the intra-type with nano-particles dis- persed within the matrix grains, the inter-type with nano-particles dispersed along the grain bound aries, and the intra/inter-type with nano-particles 6mm dispersed both along the grain boundaries and within the matrix grains. Experimental results showed that the intra/inter-type possesses the highest toughness and the intra-type the lowest (Sawaguchi et al., 1991). The analysis in Section 4 Fig 3 Double side-cracked specimen for SEM observation will explain these experiments: the nano-particles along the grain boundaries steer the crack to propagate into the matrix grains, while the nano- particles within the grains may lead the trans- wer ed. The crack normal to the lower granular crack to take a wavy path. Transgranular side grows under a local tensile stress. The initial fracture is unlikely to be induced by the intra-type crack should be sharp so that a small compressing ceramics, so the nano-particles inside the grain force by the loading stage in SEM can drive it. As have little effect on the fracture event along the the gap between the specimen edges and the folder grain boundaries. For the inter-type and the intra/ narrows, the crack driving force declines. The inter-type ceramics, transgranular fracture is in- stress intensity factor decreases with the propaga tion of the crack, and stable crack growth in the duced by the nano-particles along the boundary. The intra/inter-type ceramic lower side of the specimen is obtained toughens by the nano-particles within the grains theg. 4 shows the clinched crack surfaces near he tip. The crack propagates in a wavy path by 3.4. In 3.4. Influence of nano-particles on the crack path influence of the nano-particles. The stress field at the zigzag crack tip is inherently mixed mode, ig. 5 shows the TEM image(H-800)of a crack though the specimen is loaded externally by pure path under the influence of nano-particles. The mode I. The partial locking of the crack surfaces crack in the thin film specimen is obtained by provides shielding to the crack tip field ig. 4. Clinched rough surface near the crack Fig. 5. TEM image reveals the influence of the ceramics sustains a remote mode i loading on the crack path
lower side is lifted. The crack normal to the lower side grows under a local tensile stress. The initial crack should be sharp so that a small compressing force by the loading stage in SEM can drive it. As the gap between the specimen edges and the folder narrows, the crack driving force declines. The stress intensity factor decreases with the propagation of the crack, and stable crack growth in the lower side of the specimen is obtained. Fig. 4 shows the clinched crack surfaces near the tip. The crack propagates in a wavy path by the in¯uence of the nano-particles. The stress ®eld at the zigzag crack tip is inherently mixed mode, though the specimen is loaded externally by pure mode I. The partial locking of the crack surfaces provides shielding to the crack tip ®eld. 3.3. Distribution of nano-particles in the matrix Nano-particles may be distributed in three patterns: the intra-type with nano-particles dispersed within the matrix grains, the inter-type with nano-particles dispersed along the grain boundaries, and the intra/inter-type with nano-particles dispersed both along the grain boundaries and within the matrix grains. Experimental results showed that the intra/inter-type possesses the highest toughness and the intra-type the lowest (Sawaguchi et al., 1991). The analysis in Section 4 will explain these experiments: the nano-particles along the grain boundaries steer the crack to propagate into the matrix grains, while the nanoparticles within the grains may lead the transgranular crack to take a wavy path. Transgranular fracture is unlikely to be induced by the intra-type ceramics, so the nano-particles inside the grain have little eect on the fracture event along the grain boundaries. For the inter-type and the intra/ inter-type ceramics, transgranular fracture is induced by the nano-particles along the grain boundary. The intra/inter-type ceramic further toughens by the nano-particles within the grains. 3.4. In¯uence of nano-particles on the crack path Fig. 5 shows the TEM image (H-800) of a crack path under the in¯uence of nano-particles. The crack in the thin ®lm specimen is obtained by Fig. 3. Double side-cracked specimen for SEM observation. Fig. 4. Clinched rough surface near the crack tip when the nano-composite ceramics sustains a remote mode I loading. Fig. 5. TEM image reveals the in¯uence of the nano-particles on the crack path. 114 H. Tan, W. Yang / Mechanics of Materials 30 (1998) 111±123
H. Tan, W. Yang/ Mechanics of Materials 30(1998)111-123 l15 pressing a needle lightly on the film. The induced direction. The local mode I and II stress intensity crack path clearly follows the scattering of nano- factors, denoted as Ki and Ki, can be written as particles. The residual stresses generated by the (Cotterell and Rice, 1980; Sumi et aL., 1983, 1985) nano-particles alter the crack direction for slightly tilted crack k(0)=cos3(0/2)K1-3sin(0/2)cos2(0/2)K KI(O= sin(0/2)cos (0/2)KI+ cos(0/2) 4. Toughening mechanisms In 4.1. Mechanism 1: Transgranular fracture induced by The error of the above formulas is less than 5% provided闭≤40°. For the special case of mode I We first analyze the toughening by increasing remote loading, the 5% error can be retained even the extent of transgranular fracture. For the se- if 10 <90, which is larger than the maximum lection of crack paths, our development here is tilting angle for intergranular fracture (58.5%),as similar to the discussion of Sumi (1989, 1992)on will be shown by the analysis in the sequel. The he kinked fracture along the degraded zone of an energy release rate for the tilt crack to advance imhomogeneous material. Denote as GEb and Ga along 0 angle, G, can be expressed as the fracture energy of the grain boundary and the fracture energy of the lattice(without the influence of nano-particles). Usually GC is considerably less than Ga. Under mode I loading, a crack will The competition between intergrana (5) penetrate into the grain and grow transgranularly transgranular fracture relies on the relative values if it is approximately normal to the grain boun- of G/Gc and Ge/Gl. For the case of remote dary. Thus, a portion of the fracture path would mode I loading, as can be compared with the ex perimental results listed in the previous sections, particles. For the Al, O, ceramics with a density of one can define a characteristic angle that the fraction of intergranular fracture, hence- o =2 arccos(Ga/da) 99.5%. a detailed fra forth denoted as f, is about 65%(McColm, 1990) and thisf value is insensitive to grain sizes Intergranular fracture occurs when Bo E 0, o]and transgranular fracture occurs when Bo E 0o, T/2 The overall toughness G for the Al,O3 ce For a random grain boundary orientation, the ramics can be estimated by a surface average of the definition of leads fracture energy f=26/兀 ⑦=f鹦+(1-fc Then we have Take the coordinate xI along the macroscopic crack direction. Denote the mode i and ii stress cos intensity factors for the main crack as Ki and Ku f +f cos!(fr/4) The energy release rate for a crack to extend along the xi direction is I-f+f cos!(r/4) (K2+K) (3) Accordingly, the value of Ga and G can be duced from the measurable values Gc and f. where E and v are the Youngs modulus and the Numeric calculation gives gc=270 J m- and Poisson's ratio, respectively. Suppose the grain GC=465J m-2 boundary ahead of the crack tip forms an angle 0 Nano-particles along the grain boundaries may with the x, direction For intergranular fracture to steer the crack into the matrix grains. Fig. 6(A) occur, the crack will tilt an angle of 0 with the xI shows the case when nano-particles are absent
pressing a needle lightly on the ®lm. The induced crack path clearly follows the scattering of nanoparticles. The residual stresses generated by the nano-particles alter the crack direction. 4. Toughening mechanisms 4.1. Mechanism 1: Transgranular fracture induced by nano-particles We ®rst analyze the toughening by increasing the extent of transgranular fracture. For the selection of crack paths, our development here is similar to the discussion of Sumi (1989, 1992) on the kinked fracture along the degraded zone of an imhomogeneous material. Denote as Ggb C and Gla C the fracture energy of the grain boundary and the fracture energy of the lattice (without the in¯uence of nano-particles). Usually Ggb C is considerably less than Gla C. Under mode I loading, a crack will penetrate into the grain and grow transgranularly if it is approximately normal to the grain boundary. Thus, a portion of the fracture path would be transgranular even for ceramics without nanoparticles. For the Al2O3 ceramics with a density of 99.5%, a detailed fracture path analysis indicated that the fraction of intergranular fracture, henceforth denoted as f, is about 65% (McColm, 1990), and this f value is insensitive to grain sizes. The overall toughness Glm C for the Al2O3 ceramics can be estimated by a surface average of the fracture energy: Glm C fGgb C 1 ÿ f Gla C: 2 Take the coordinate x1 along the macroscopic crack direction. Denote the mode I and II stress intensity factors for the main crack as KI and KII. The energy release rate for a crack to extend along the x1 direction is G 1 ÿ m2 E K2 I K2 II; 3 where E and m are the Young's modulus and the Poisson's ratio, respectively. Suppose the grain boundary ahead of the crack tip forms an angle h with the x1 direction. For intergranular fracture to occur, the crack will tilt an angle of h with the x1 direction. The local mode I and II stress intensity factors, denoted as Kh I and Kh II, can be written as (Cotterell and Rice, 1980; Sumi et al., 1983, 1985) for slightly tilted crack, Kh I h cos3 h=2KI ÿ 3sin h=2 cos2 h=2KII; Kh II h sin h=2 cos2 h=2KI cos h=2 1 ÿ 3sin2 h=2KII: 4 The error of the above formulas is less than 5% provided |h| 6 40°. For the special case of mode I remote loading, the 5% error can be retained even if |h| 6 90°, which is larger than the maximum tilting angle for intergranular fracture (58.5°), as will be shown by the analysis in the sequel. The energy release rate for the tilt crack to advance along h angle, Gh, can be expressed as Gh 1 ÿ m2 E Kh2 I Kh2 II : 5 The competition between intergranular and transgranular fracture relies on the relative values of Gh=Ggb C and Gh=Gla C. For the case of remote mode I loading, as can be compared with the experimental results listed in the previous sections, one can de®ne a characteristic angle h0 2 arccos Ggb C =Gla C 1=4 : 6 Intergranular fracture occurs when h0 2 0; h0 and transgranular fracture occurs when h0 2 h0; p=2. For a random grain boundary orientation, the de®nition of f leads to f 2h0=p: 7 Then we have Ggb C cos4 f p=4 1 ÿ f f cos4 f p=4 Glm C ; Gla C 1 1 ÿ f f cos4 f p=4 Glm C : 8 Accordingly, the value of Gla C and Ggb C can be deduced from the measurable values Glm C and f. Numeric calculation gives Ggb C 27.0 J mÿ2 and Gla C 46.5 J mÿ2. Nano-particles along the grain boundaries may steer the crack into the matrix grains. Fig. 6(A) shows the case when nano-particles are absent. H. Tan, W. Yang / Mechanics of Materials 30 (1998) 111±123 115