Materials Science and Engineering A 494(2008)203-216 Contents lists available at science direct Materials Science and Engineering A ELSEVIER urnalhomepagewww.elsevier.com/locate/msea Mechanical property and r-curve behavior of the b4c/BN ceramics composites Tao Jiang*, Zhihao Jin, Jianfeng Yang, Guanjun Qiao State Key laboratory for Mechanical Behavior of materials, Xi'an iaotong University, Xi an 710049, People's Republic of china ARTICLE INFO A BSTRACT The Ba C/BN ceramics composites were fabricated by the hot-pressing process. In this paper, the mechan- Received 7 January 2008 cal property and R-curves behavior of the B4C/BN composites were investigated. The fracture strength eceived in revised form 7 April 2008 Accepted 21 April 2008 and fracture toughness of the B4C/BN microcomposites and the ba C/Bn nanocomposites decreased grad- ually with the increasing content of h-BN. The fracture strength and fracture toughness of the B4C/BN age resistance and R-curves behavior of the BaC monolith and the B4C/BN composites were evaluated by the indentation-strength in bending technique(ISB). The fracture strength of the Bac monolith, the composites decreased gradually with the increase of the dentation load. The B4 C/BN nanocomposites retained relative higher fracture strength in compariso -curve behavior with the bac monolith and the bgl microcomposites under the equivalent indentation load. The B4C Microstructure monolith, the B4C/BN composites and the ba c Bn nanocomposites all exhibited the rising R-curves behavior. The BaC/BN nanocomposites exhibited the higher rising R-curve behavior than that of the BaC monolith and the B,C/BN microcomposites. The toughness mechanisms of the composites were investi- ated The B4C/BN composites with the h-BN content more than 20 wt %exhibited excellent machinabilit The slowly rising R-curves behavior remarkably improved the machinability of the composites O 2008 Elsevier B.V. All rights reserved. 1. Introduction ability of the B4 c ceramics, the b4 c/ Bn microc B4C/BN nanocomposites were fabricated by h Boron carbide(B4C)ceramics is recognized as one of t In this article, the mechanical property and ma promising structural materials for application in various B4C/BN microcomposites and the b4c/Bn nanocomposites were g fields due to the excellent properties including high mainly investigated. and toughness, high melting points (2450.C) and low density For the machinable composites, the fracture resistance (r (2.52g/cm), extremely high Vickers hardness(30 GPa)and excel- behavior) was very importar lent wear resistance [1-4. However, the machinability of the B4C machinability. Some researchers investigated the R-curves behav- ramics is extremely poor 5.6]. On the other hand, the hexagonal ior of machinable composites, such as AIN/BN [14, Si3 N4/BN [15 BN(h-BN)have low strength and toughness, excellent machinabil- and the ceramics composites, such as Si N4[ 16, 17). Si3N4/TiN [18 ty and thermal shock resistance [7-10 In order to improve the and laminated Sic/BN composites [19, 20). However, it has not machinability of B4C ceramics, the h-BN can be incorporated into been reported about the mechanical property and r-curve behav the B4Cmatrix, and the B4C/BN composites were fabricated, which ior of the machinable B4C/BN ceramics composites. Therefore, in would remarkably improve the machinability of B4 C ceramics. this research, the damage resistance and r-curves behavior of the Recently, machinable nanocomposites with high mechanical B4 C/BN nanocomposites and the B4C/BN microcomposites were property and good machinability have been concerned by many investigated and compared with the B4C monolith. On the other researchers [7-13]. Ihara and Kusunose reported that they have hand, the machinability and mechanical property such as frac fabricated the Si3 N4/BN nanocomposites and Al2O3/BN nanocom- ture strength and fracture toughness were related to the r-curves posites by chemical reaction and hot-pressing process [7,8, 11 behavior of machinable composites The machinable composites included Si3N4/BN [7-9, SiC/BN [10 In this research, the phase composition and microstructure of Al2O3/BN [11, 12, Zro2/BN[13 So in order to improve the machin- the B4C/BN ceramics composites were investigated. The mechan- cal property of the B4C/BN microcomposites and the B4 C/BN nanocomposites were investigated. The damage resistance and r ing author. Tel: +86 29 82667942: fax: +8 curves behavior of the BAC/BN microcomposites and the B.C/ BN E-mail address: jiangtaoxjtuemailxjtueducn (T Jiang nanocomposites were evaluated by using the indentation-strength 000 ter 2008 Elsevier B V. All rights re served
Materials Science and Engineering A 494 (2008) 203–216 Contents lists available at ScienceDirect Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea Mechanical property and R-curve behavior of the B4C/BN ceramics composites Tao Jiang∗, Zhihao Jin, Jianfeng Yang, Guanjun Qiao State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China article info Article history: Received 7 January 2008 Received in revised form 7 April 2008 Accepted 21 April 2008 Keywords: Boron carbide Boron nitride Mechanical property Indentation strength R-curve behavior Microstructure abstract The B4C/BN ceramics composites were fabricated by the hot-pressing process. In this paper, the mechanical property and R-curves behavior of the B4C/BN composites were investigated. The fracture strength and fracture toughness of the B4C/BN microcomposites and the B4C/BN nanocomposites decreased gradually with the increasing content of h-BN. The fracture strength and fracture toughness of the B4C/BN nanocomposites were significantly improved in comparison with the B4C/BN microcomposites. The damage resistance and R-curves behavior of the B4C monolith and the B4C/BN composites were evaluated by the indentation-strength in bending technique (ISB). The fracture strength of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites decreased gradually with the increase of the indentation load. The B4C/BN nanocomposites retained relative higher fracture strength in comparison with the B4C monolith and the B4C/BN microcomposites under the equivalent indentation load. The B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites all exhibited the rising R-curves behavior. The B4C/BN nanocomposites exhibited the higher rising R-curve behavior than that of the B4C monolith and the B4C/BN microcomposites. The toughness mechanisms of the composites were investigated. The B4C/BN composites with the h-BN content more than 20 wt.% exhibited excellent machinability. The slowly rising R-curves behavior remarkably improved the machinability of the composites. © 2008 Elsevier B.V. All rights reserved. 1. Introduction Boron carbide (B4C) ceramics is recognized as one of the most promising structural materials for application in various engineering fields due to the excellent properties including high strength and toughness, high melting points (2450 ◦C) and low density (2.52 g/cm3), extremely high Vickers hardness (>30 GPa) and excellent wear resistance [1–4]. However, the machinability of the B4C ceramics is extremely poor [5,6]. On the other hand, the hexagonal BN (h-BN) have low strength and toughness, excellent machinability and thermal shock resistance [7–10]. In order to improve the machinability of B4C ceramics, the h-BN can be incorporated into the B4C matrix, and the B4C/BN composites were fabricated, which would remarkably improve the machinability of B4C ceramics. Recently, machinable nanocomposites with high mechanical property and good machinability have been concerned by many researchers [7–13]. Niihara and Kusunose reported that they have fabricated the Si3N4/BN nanocomposites and Al2O3/BN nanocomposites by chemical reaction and hot-pressing process [7,8,11]. The machinable composites included Si3N4/BN [7–9], SiC/BN [10], Al2O3/BN [11,12], ZrO2/BN [13]. So in order to improve the machin- ∗ Corresponding author. Tel.: +86 29 82667942; fax: +86 29 82665443. E-mail address: jiangtaoxjtu@mail.xjtu.edu.cn (T. Jiang). ability of the B4C ceramics, the B4C/BN microcomposites and the B4C/BN nanocomposites were fabricated by hot-pressing process. In this article, the mechanical property and machinability of the B4C/BN microcomposites and the B4C/BN nanocomposites were mainly investigated. For the machinable composites, the fracture resistance (R-curve behavior) was very important to investigate the toughness and machinability. Some researchers investigated the R-curves behavior of machinable composites, such as AlN/BN [14], Si3N4/BN [15], and the ceramics composites, such as Si3N4 [16,17], Si3N4/TiN [18] and laminated SiC/BN composites [19,20]. However, it has not been reported about the mechanical property and R-curve behavior of the machinable B4C/BN ceramics composites. Therefore, in this research, the damage resistance and R-curves behavior of the B4C/BN nanocomposites and the B4C/BN microcomposites were investigated, and compared with the B4C monolith. On the other hand, the machinability and mechanical property such as fracture strength and fracture toughness were related to the R-curves behavior of machinable composites. In this research, the phase composition and microstructure of the B4C/BN ceramics composites were investigated. The mechanical property of the B4C/BN microcomposites and the B4C/BN nanocomposites were investigated. The damage resistance and Rcurves behavior of the B4C/BN microcomposites and the B4C/BN nanocomposites were evaluated by using the indentation-strength 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.04.047
in bending technique (ISB), and compared with the B4C mono- of specimens were measured by three-points bending tests with lith. The R-curves behavior of the B4C monolith, the B4C/Bn the span of 16 mm and crosshead speed of 0.5 mm/min(Testing nanocomposites and the bac/BN microcomposites were obtained machine: Instron 1195 ) Five specimens were measured for each from conversion of indentation-strength data The r-curves behav- indentation loads, the average indentation strength were obtained ior of the B4C monolith, the B4C/BN nanocomposites and the from results of five measurements. The fracture surface of test spec B4C/BN microcomposites were mainly investigated. The differences imens was observed by S-2700 SEM. The specimens were indented of the indentation strength and R-curves behavior between the B4c by using the vickers diamond pyramid indenter under the load of monolith and the B4C/BN composites were investigated. The tough- 196 N for 15 s on the polished surface, so the indentation cracks was ning mechanisms of the B4 C monolith and the ba C/BN composites produced. The indentation cracks on the surface of specimens were gere investigated. The machinability of the B4C/BN microcompos- observed by S-2700 SEM. tes and B4C/BN nanocomposites were investigated. The relation Conversion of Vickers isB data o P), to generate the fracture between the R-curves behavior and machinability was investigated. toughness curve, T(c)[T(c)=KR was obtained from the follows [19-22. Conversion was accomplished by using an objective 2. Experimental procedures indentation-strength K-fields analysis Under the action of applied stress oA, the radial cracks size c produced at an indentation load P 2.1. Experimental materials and fabrication process extend according to the equilibrium condition, as shown in Eq (1) For fabrication of the B4C/BN nanocomposites, the chemical K'A(c)=oac/2+xPe-3/2=T(c) eaction and hot-pressing process were adopted. The starting mate- rials were B4C powders with mean particle size of 3.5 um. The where KA(c)was a global applied stress intensity factor correspond H3 BO3 and CO(NH2)2 were used to prepare nanostructure BN pow- ing to an applied stress oA. Tc)was the fracture toughness curve ders. The relative BN contents of the produced B4C/BN composites and cp was the crack shape factor which depended on crack and owders were adjusted to be O wt%, 10 wt%, 20 wt%, 30 wt% and specimen geometry. x was the residual contact coefficient which lO wt.%. The mole ratio of H3 BO3 and CO(NH2)2 was 1: 4. The was often expressed in terms of Youngs modulus E and Vickers then heat treated at 850C for 6h in N2 gas. The produced B4C/BN X=&/E/21, 231 B4C powders, H3 BO3 and CO(NH2 )2 were mixed by mechanically illing with ethanol and agate balls for 24 h, and then dried slowly The dried mixture powders were reacted at 550Cfor 15 h in air and (2 composite powders were mixed with 10 wt. sintering aids of Al2O alcohol an mixture solution was mixed by mechanically milling for 24h and The value of E H can be measured by the knoop indentation then dried slowly. The B C/BN nanocomposites were fabricated by proposed by Marshall et a. [19-21.251. For a given indentat hot-pressing process at 1850oC for 1 hunder the pressure of 30 MPa P, failures occurred at that applied stress oA=Or which satisf in the nz gas. For comparison, the micro-sized B4 C powders and h "tangency condition, as shown in the following equation[19-22] BN powders with mean particles size of 4 um together with 10.% dKa(c) dr(c) sintering aids of Al2 O3 and Y203 powders were used to fabricate the B4C/BN microcomposites by the same hot-pressing process Accordingly, given an appropriate calibration of the coefficients 2.2. Characterization p and x. the families of KA(c) curves can be generated from the oP) data. Then T(c) curve can be determined objectively as the The phase composition of hot-pressed composites was deter- envelopes of tangency points to these families of curves, so the mined by XRD(D/max-2400) The microstructure of the B4C/BN R-curve was produced [19-22]. microcomposites and Bac/Bn nanocomposites were observed by by drilling experiments using wc cermets drills. The specimens mission electron microscopy (TEM). The fracture strength was of 280 rpm. The drilling rates of composites were measured.The of 3 mm x 4 mm 30 mm, the span was 16 mm and crosshead materials removal rates of composites were measured The sur speed was 0.5 mm/min. The fracture toughness was measured by ace roughness of drilled hole was measured by surface roughness single edge notch beam(SENB) with the condition as same as meter fracture strength, the span was 16 mm and crosshead speed was 0.05 mm/min The deepness and width of notch were 1.5mm and 3. Results and discussion 0. 2 mm, respectively. The average fracture strength and fracture ughness values were calculated from the results of five mea- 3.1. The phase composition of the B4C/BN composites surements. The vickers hardness was measured by Hv-5 Vickers hardness meter with the load of 49N and holding time of 15 S Fig. 1 shows the XRD patterns of the B4C monolith, the B4C/BN The damage resistance and r-curves behavior were evaluated by nicrocomposites and the B4 C/BN nanocomposites Fig. 1(a)shows the ISB. The B4C monolith, the B4c/BN microcomposites(20 wt %h- that the diffractive peaks of Ba C phase existed in XRD patterns of BN)and the B4C/BN nanocomposites(20 wt %h-BN)were used in B4C monolith. Fig. 1(b)and(c) shows that the diffractive peaks of the indentation-strength test. The dimensions of test specimens B4C phase and h-bn phase existed in XRD patterns of the B4C/bN were 3 mm x 4mm x mm. The test specimens were indented at microcomposites and B4 C/BN nanocomposites. The highest diffI the center of the polished prospective tensile surface using the Vick- tive peak of the h-bn phase was at 20-26.70, and other smaller rs diamond pyramid indenter under the loads ranging from oN to diffractive peaks also corresponded to the h-BN phase. The sintering 300N(HV-5 and HV-100 Vickers hardness meter) and the holding aids of Al203 and Y2 O3 transformed into the liquid phase Y3AlsO12 time was 15s. After the indentation test, the indentation strength at high temperature during the hot-pressing process
204 T. Jiang et al. / Materials Science and Engineering A 494 (2008) 203–216 in bending technique (ISB), and compared with the B4C monolith. The R-curves behavior of the B4C monolith, the B4C/BN nanocomposites and the B4C/BN microcomposites were obtained from conversion of indentation-strength data. The R-curves behavior of the B4C monolith, the B4C/BN nanocomposites and the B4C/BN microcomposites were mainly investigated. The differences of the indentation strength and R-curves behavior between the B4C monolith and the B4C/BN composites were investigated. The toughening mechanisms of the B4C monolith and the B4C/BN composites were investigated. The machinability of the B4C/BN microcomposites and B4C/BN nanocomposites were investigated. The relation between the R-curves behavior and machinability was investigated. 2. Experimental procedures 2.1. Experimental materials and fabrication process For fabrication of the B4C/BN nanocomposites, the chemical reaction and hot-pressing process were adopted. The starting materials were B4C powders with mean particle size of 3.5 m. The H3BO3 and CO(NH2)2 were used to prepare nanostructure BN powders. The relative BN contents of the produced B4C/BN composites powders were adjusted to be 0 wt.%, 10 wt.%, 20 wt.%, 30 wt.% and 40 wt.%. The mole ratio of H3BO3 and CO(NH2)2 was 1:4. The B4C powders, H3BO3 and CO(NH2)2 were mixed by mechanically milling with ethanol and agate balls for 24 h, and then dried slowly. The dried mixture powders were reacted at 550 ◦C for 15 h in air and then heat treated at 850 ◦C for 6 h in N2 gas. The produced B4C/BN composite powders weremixed with 10 wt.% sintering aids of Al2O3 and Y2O3 powders, together with the alcohol and agate balls, the mixture solution was mixed by mechanically milling for 24 h and then dried slowly. The B4C/BN nanocomposites were fabricated by hot-pressing process at 1850 ◦C for 1 h under the pressure of 30 MPa in the N2 gas. For comparison, the micro-sized B4C powders and hBN powders with mean particles size of 4 m together with 10 wt.% sintering aids of Al2O3 and Y2O3 powders were used to fabricate the B4C/BN microcomposites by the same hot-pressing process. 2.2. Characterization The phase composition of hot-pressed composites was determined by XRD (D/max-2400). The microstructure of the B4C/BN microcomposites and B4C/BN nanocomposites were observed by S-2700 scanning electron microscopy (SEM) and JEM-200CX transmission electron microscopy (TEM). The fracture strength was measured by the three-points bending test with the samples size of 3 mm × 4 mm × 30 mm, the span was 16 mm and crosshead speed was 0.5 mm/min. The fracture toughness was measured by single edge notch beam (SENB) with the condition as same as fracture strength, the span was 16 mm and crosshead speed was 0.05 mm/min. The deepness and width of notch were 1.5 mm and 0.2 mm, respectively. The average fracture strength and fracture toughness values were calculated from the results of five measurements. The Vickers hardness was measured by HV-5 Vickers hardness meter with the load of 49 N and holding time of 15 s. The damage resistance and R-curves behavior were evaluated by the ISB. The B4C monolith, the B4C/BN microcomposites (20 wt.%hBN) and the B4C/BN nanocomposites (20 wt.%h-BN) were used in the indentation-strength test. The dimensions of test specimens were 3 mm × 4 mm × 30 mm. The test specimens were indented at the center of the polished prospective tensile surface using the Vickers diamond pyramid indenter under the loads ranging from 0N to 300 N (HV-5 and HV-100 Vickers hardness meter) and the holding time was 15 s. After the indentation test, the indentation strength of specimens were measured by three-points bending tests with the span of 16 mm and crosshead speed of 0.5 mm/min (Testing machine: Instron 1195). Five specimens were measured for each indentation loads, the average indentation strength were obtained from results of five measurements. The fracture surface of test specimens was observed by S-2700 SEM. The specimens were indented by using the Vickers diamond pyramid indenter under the load of 196 N for 15 s on the polished surface, so the indentation cracks was produced. The indentation cracks on the surface of specimens were observed by S-2700 SEM. Conversion of Vickers ISB data f(P), to generate the fracture toughness curve, T(c) [T(c) = KR] was obtained from the follows [19–22]. Conversion was accomplished by using an objective indentation-strength K-fields analysis. Under the action of applied stress A, the radial cracks size c produced at an indentation load P extend according to the equilibrium condition, as shown in Eq. (1) [19–22]: K A(c) = ϕAc1/2 + Pc−3/2 = T(c) (1) where K A(c) was a global applied stress intensity factor corresponding to an applied stress A, T(c) was the fracture toughness curve, and was the crack shape factor which depended on crack and specimen geometry. was the residual contact coefficient which was often expressed in terms of Young’s modulus E and Vickers hardness H [19–21,23]: = E H 1/2 (2) being a factor of proportionality equaled to 0.016 [19–21,24]. The value of E/H can be measured by the Knoop indentation method proposed by Marshall et al. [19–21,25]. For a given indentation load P, failures occurred at that applied stress A = f which satisfied the “tangency condition”, as shown in the following equation [19–22]: dK A(c) dc = dT(c) dc (3) Accordingly, given an appropriate calibration of the coefficients ϕ and , the families of K A(c) curves can be generated from the f(P) data. Then T(c) curve can be determined objectively as the envelopes of tangency points to these families of curves, so the R-curve was produced [19–22]. The machinability of the B4C/BN composites was measured by drilling experiments using WC cermets drills. The specimens were drilled under the load force of 19.6 N and rotational speed of 280 rpm. The drilling rates of composites were measured. The materials removal rates of composites were measured. The surface roughness of drilled hole was measured by surface roughness meter. 3. Results and discussion 3.1. The phase composition of the B4C/BN composites Fig. 1 shows the XRD patterns of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. Fig. 1(a) shows that the diffractive peaks of B4C phase existed in XRD patterns of B4C monolith. Fig. 1(b) and (c) shows that the diffractive peaks of B4C phase and h-BN phase existed in XRD patterns of the B4C/BN microcomposites and B4C/BN nanocomposites. The highest diffractive peak of the h-BN phase was at 2 = 26.70◦, and other smaller diffractive peaks also corresponded to the h-BN phase. The sintering aids of Al2O3 and Y2O3 transformed into the liquid phase Y3Al5O12 at high temperature during the hot-pressing process.
T Jiang et al/ Materials Science and Engineering A 494 (2008)203- 205 ■-BC 500(a) ▲h-BN = 5 方 2000 (c) trength Fracture Toughness 3 000 -microcomposites -A-microcomposites 0 oL-nanocomposites -v-nanocomposites 12 h-BN content(wt%) Fig 4. The effects of h-BN content on the fracture strength and fracture toughness Fig 1. The XRI sites and the of the bac Bn microcomposites and the bac/Bn nanocomposites. B4C/BN nanocomposites: (a)the B4 C monolith; (b) the B C/BN microcomposites; (c) sized h-BN grains was less than 1 um and the thickness was about The microstructure of the B,/BN composites 100-200nm, while the BaC matrix grains size was considerably refined and the size of B4 C matrix grains was about 1-2 um In Fig 2 shows the SEM micrographs of the B4C/BN microcompos- addition, due to the retarding effects of nano-sized h-BN parti- ites with the h-BN content of 20 wt and 30wt. % The micro-sized cles on the grains growth of B4C matrix and the refined matrix h-BN particles were distributed in the B4C matrix, the length of grains, the BAC/BN nanocomposites showed the finer and more micro-sized h-BN particles was about 2-3 um and the thickness homogenous microstructure, the porosity and flaw size decreased was about 300-500nm. The B4C matrix grains size was about remarkably .3 um The Bac/BN microcomposites exhibited rough microstruc ture 3.3. The mechanical property of the B,c/ BN composites Fig 3 shows the SEM micrographs of the B4C/BN nanocompos ites with the h-BN content of 20 wt% and 30 wt.%. The nano-sized Fig 4 shows the effects of h-BN C( on the fracture strength h-BN grains were homogenously distributed at the B4c matrix of the baC/BN microcomposites and the bac Bn nanocomposites grains boundaries and within the B4 C matrix grains, which formed The fracture strength of the B4C/BN microcomposites and the intergranular and intragranular structure. The length of the nano- B4 C /BN nanocomposites decreased gradually with the increasing Fig. 2. The SEM micrographs of the B4 C/BN microcomposites: (a)20wt% h-BN; (b)30wt% h-BN. Fig 3. The SEM micrographs of the B4 C/BN nanocomposites: (a)20 wt% h-BN; (b)30 wt% h-BN
T. Jiang et al. / Materials Science and Engineering A 494 (2008) 203–216 205 Fig. 1. The XRD patterns of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites: (a) the B4C monolith; (b) the B4C/BN microcomposites; (c) the B4C/BN nanocomposites. 3.2. The microstructure of the B4C/BN composites Fig. 2 shows the SEM micrographs of the B4C/BN microcomposites with the h-BN content of 20 wt.% and 30 wt.%. The micro-sized h-BN particles were distributed in the B4C matrix, the length of micro-sized h-BN particles was about 2–3 m and the thickness was about 300–500 nm. The B4C matrix grains size was about 2–3 m. The B4C/BN microcomposites exhibited rough microstructure. Fig. 3 shows the SEM micrographs of the B4C/BN nanocomposites with the h-BN content of 20 wt.% and 30 wt.%. The nano-sized h-BN grains were homogenously distributed at the B4C matrix grains boundaries and within the B4C matrix grains, which formed intergranular and intragranular structure. The length of the nanoFig. 4. The effects of h-BN content on the fracture strength and fracture toughness of the B4C/BN microcomposites and the B4C/BN nanocomposites. sized h-BN grains was less than 1 m and the thickness was about 100–200 nm, while the B4C matrix grains size was considerably refined and the size of B4C matrix grains was about 1–2 m. In addition, due to the retarding effects of nano-sized h-BN particles on the grains growth of B4C matrix and the refined matrix grains, the B4C/BN nanocomposites showed the finer and more homogenous microstructure, the porosity and flaw size decreased remarkably. 3.3. The mechanical property of the B4C/BN composites Fig. 4 shows the effects of h-BN content on the fracture strength of the B4C/BN microcomposites and the B4C/BN nanocomposites. The fracture strength of the B4C/BN microcomposites and the B4C/BN nanocomposites decreased gradually with the increasing Fig. 2. The SEM micrographs of the B4C/BN microcomposites: (a) 20 wt.% h-BN; (b) 30 wt.% h-BN. Fig. 3. The SEM micrographs of the B4C/BN nanocomposites: (a) 20 wt.% h-BN; (b) 30 wt.% h-BN.
500 tion load, the fracture strength was related to the indentation load, 1-a,=465P6 because that the fracture strength was controlled by external flaws. 2-,=352P13 Fig 5 showed that the intersection points P"were different for the B4C monolith(P=2 N), the B4C/BN microcomposites(P=2N 3,=503P1 and the B4 C/BN nanocomposites (P*=3 N). This result indicated that the b4C/bn nanocomposites have the higher damage resistance than that of the BC monolith and the bac/BN microcompos- c巴 ites under the lower indentation load. As seen in Fig. 5, in the high-indentation-load region, the fracture strength of three mate- rials decreased linearly with the increase of the indentation load. 150 ■ BC monolith The B4C/BN nanocomposites maintained relative higher fracture strength in comparison with the B4C monolith and the B4C/BN microcomposites under the equivalent indentation load. The B4C 3▲ B,C/BN nanocomposites monolith retained higher fracture strength than that of the B4 C/BN microcomposites under the equivalent indentation load. These 1000 results indicated that the b4 C/ Bn nanocomposites have improved damage resistance in comparison with the B4C monolith and the bac/Bn microcomposites. It was suggested that the bc/Bn dentation load for the Ba nanocomposites would have the higher rising R-curve behavior than that of the B4 C monolith and the B4 C/BN microcomposites. R-curves behaviors of three materials were obtained from the indentation-strength data in Fig. 5. Linear regression was used to alculate the fit equation of each line, and the slope of each line content of h-BN. Fig. 4 showed that the fracture strength of the was calculated. The slope of the fit equation of the B4Cmonolith was BaC/BN nanocomposites was significantly improved in compari-.216, the slope of fit equation of the B4 C/BN nanocomposites was on with the B4C/BN microcomposites. The fracture strength of the -0.186 and the slope of fit equation of the B4C/BN microcomposites BAC monolith was 409 MPa. The fracture strength of the B4C/BN was -0.173. As seen in Fig. 5. in the high indentation load region, nanocomposites with the h-BN contents of 10 wt% and 20 wt% the relation of fracture strength of and indentation load P can be vere 424 MPa and 415 MPa, respectively. The fracture strength of expressed as following equations: for the B4c monolith the bacOn micr osites with the h-bn contents of 10wt% and 20 wt. were 360MPa and 327 MPa, respectively. The increase of=465P of fracture strength of the Bac/Bn nanocomposites was chiefly for the B4C/BN nanocomposites flaw size caused by the nano-sized h-BN particles homogenous of dispersions. Fig. 4 shows the effects of h-BN content on the fracture for the B4 C/BN microcomposites toughness of the B4C/BN nanocomposites and the B4C/BN micro- 0=352P-0 73 composites. The fracture toughness of the Bac/ BNmicrocomposites nd the B4C/Bn nanocomposites decreased gradually with the The slopes of fitequations of these three materials were all larger ncreasing content of h-BN. Fig 4 showed that the fracture tough 1/3; this result indicated that these three materials all have ness of the BAC/BN nanocomposites was significantly improve the rising R-curves behavior in comparison with the B4C/BN microcomposites. The fracture Griffith materials. for which the R-curve behavior was flat toughness of the B4C monolith was 5.369 MPam /2. The fracture would follow the power law [19-22] toughness of the b4 C/BN nanoc sites with the h-BN contents araP-k of 10 wt% and 20 wt% were 6.085 MPam1 2 and 5.34 MPam/2 respectively. The fracture toughness of the B4C/BN microcom- with k=1/ 3. The specimens have the rising toughness curves(r- posites with the h-BN contents of 10 wt% and 20wt were curves behavior), the relationship between or and Pwas expressed 4.57MPam'/ and 4.35 m /2, respectively. The increase of the as follows[19-22] fracture toughness of the B, C/BN nanocomposites was because that the nano-sized h-bN particles dispersed main cracks into many ng, which where P<1/3, or was fracture strength, P was indentation load. In this research, according to the results of the fit Eqs. (4-6). the facts that the calculated p values of three materials were all lower 3.4. The indentation strength and the r-curve behavior than 1/3, this result indicated that the B4C monolith, the B4 C/BN nanocomposites and the B4 C/BN microcomposites would have the Fig 5 shows the effects of the indentation load (P)on the frac- rising R-curves behavior If the Vickers cracks geometry was con- ure strength(or)of the B4Cmonolith, the B4C/BN microcomposites sidered to be materials independent, the values =1.24[19,20, 26] (20 wt% h-BN)and the B4C/BN nanocomposites(20 wt% h-BN) x values were calculated as the follows the two logarithmically axis systems. Fig. 5 showed that the intersection points P in the corresponding curves(at P=p") sep- X=s(H arated the plots into two regions for these three materials. In the left region, for specimens with the low indentation load, the frac- S=0.016[ 19, 20, 24]. x for the B4C monolith was 0.0737, X for ure strength was microstructure controlled. The fracture strength the B4C/BN nanocomposites was 0.0823, x for the B4 C/BN micro- retained high values under the low indentation load. On the other composites was 0.0923. The same values of and different values hand, in the right regions, where specimens had higher indenta- of x were used. According to Eq (1). the three families of
206 T. Jiang et al. / Materials Science and Engineering A 494 (2008) 203–216 Fig. 5. The fracture strength plotted against the indentation load for the B4C monolith, the B4C/BN nanocomposites (20 wt.% h-BN) and the B4C/BN microcomposites (20 wt.% h-BN). The curves for the three materials deviated slightly from the slope of −1/3. The indentation loads in the figure were from 0.1 N to 294 N. content of h-BN. Fig. 4 showed that the fracture strength of the B4C/BN nanocomposites was significantly improved in comparison with the B4C/BN microcomposites. The fracture strength of the B4C monolith was 409 MPa. The fracture strength of the B4C/BN nanocomposites with the h-BN contents of 10 wt.% and 20 wt.% were 424 MPa and 415 MPa, respectively. The fracture strength of the B4C/BN microcomposites with the h-BN contents of 10 wt.% and 20 wt.% were 360 MPa and 327 MPa, respectively. The increase of fracture strength of the B4C/BN nanocomposites was chiefly attributed to the refined B4C matrix grains and the reduction of flaw size caused by the nano-sized h-BN particles homogenous dispersions. Fig. 4 shows the effects of h-BN content on the fracture toughness of the B4C/BN nanocomposites and the B4C/BN microcomposites. The fracture toughness of the B4C/BN microcomposites and the B4C/BN nanocomposites decreased gradually with the increasing content of h-BN. Fig. 4 showed that the fracture toughness of the B4C/BN nanocomposites was significantly improved in comparison with the B4C/BN microcomposites. The fracture toughness of the B4C monolith was 5.369 MPa m1/2. The fracture toughness of the B4C/BN nanocomposites with the h-BN contents of 10 wt.% and 20 wt.% were 6.085 MPa m1/2 and 5.34 MPa m1/2, respectively. The fracture toughness of the B4C/BN microcomposites with the h-BN contents of 10 wt.% and 20 wt.% were 4.57 MPa m1/2 and 4.35 MPa m1/2, respectively. The increase of the fracture toughness of the B4C/BN nanocomposites was because that the nano-sized h-BN particles dispersed main cracks into many microcracks and prevented main cracks from extending, which improved fracture toughness. 3.4. The indentation strength and the R-curve behavior Fig. 5 shows the effects of the indentation load (P) on the fracture strength (f) of the B4C monolith, the B4C/BN microcomposites (20 wt.% h-BN) and the B4C/BN nanocomposites (20 wt.% h-BN) in the two logarithmically axis systems. Fig. 5 showed that the intersection points P* in the corresponding curves (at P = P*) separated the plots into two regions for these three materials. In the left region, for specimens with the low indentation load, the fracture strength was microstructure controlled. The fracture strength retained high values under the low indentation load. On the other hand, in the right regions, where specimens had higher indentation load, the fracture strength was related to the indentation load, because that the fracture strength was controlled by external flaws. Fig. 5 showed that the intersection points P* were different for the B4C monolith (P* = 2 N), the B4C/BN microcomposites (P* = 2 N) and the B4C/BN nanocomposites (P* = 3 N). This result indicated that the B4C/BN nanocomposites have the higher damage resistance than that of the B4C monolith and the B4C/BN microcomposites under the lower indentation load. As seen in Fig. 5, in the high-indentation-load region, the fracture strength of three materials decreased linearly with the increase of the indentation load. The B4C/BN nanocomposites maintained relative higher fracture strength in comparison with the B4C monolith and the B4C/BN microcomposites under the equivalent indentation load. The B4C monolith retained higher fracture strength than that of the B4C/BN microcomposites under the equivalent indentation load. These results indicated that the B4C/BN nanocomposites have improved damage resistance in comparison with the B4C monolith and the B4C/BN microcomposites. It was suggested that the B4C/BN nanocomposites would have the higher rising R-curve behavior than that of the B4C monolith and the B4C/BN microcomposites. R-curves behaviors of three materials were obtained from the indentation-strength data in Fig. 5. Linear regression was used to calculate the fit equation of each line, and the slope of each line was calculated. The slope of the fit equation of the B4Cmonolith was −0.216, the slope of fit equation of the B4C/BN nanocomposites was −0.186 and the slope of fit equation of the B4C/BN microcomposites was −0.173. As seen in Fig. 5, in the high indentation load region, the relation of fracture strength f and indentation load P can be expressed as following equations: for the B4C monolith: f = 465P−0.216 (4) for the B4C/BN nanocomposites: f = 503P−0.186 (5) for the B4C/BN microcomposites: f = 352P−0.173 (6) The slopes of fit equations of these threematerials were all larger than −1/3; this result indicated that these three materials all have the rising R-curves behavior. Griffith materials, for which the R-curve behavior was flat, would follow the power law [19–22]: f ∝ P−k (7) with k = 1/3. The specimens have the rising toughness curves (Rcurves behavior), the relationship between f and P was expressed as follows [19–22]: f = ˛P−ˇ (8) where ˇ < 1/3, f was fracture strength, P was indentation load. In this research, according to the results of the fit Eqs. (4–6), the facts that the calculated ˇ values of three materials were all lower than 1/3, this result indicated that the B4C monolith, the B4C/BN nanocomposites and the B4C/BN microcomposites would have the rising R-curves behavior. If the Vickers cracks geometry was considered to be materials independent, the values ϕ = 1.24 [19,20,26], values were calculated as the follows: = E H 1/2 = 0.016 [19,20,24]. for the B4C monolith was 0.0737, for the B4C/BN nanocomposites was 0.0823, for the B4C/BN microcomposites was 0.0923. The same values of ϕ and different values of were used. According to Eq. (1), the three families of K A(c)
BC monolith BC monolith B.C/BN microcomposites 1000 Crack size, c(um) 4时BC/ BN nanocomposite Fig. 7. The fracture toughness curves) behavior of the B4 C monolith, th -29.4N(20wt% h-BN B4C/BN nanocomposites(20 wt% h-BN)and the b4c/Bn microcomposites20wt% h-BN) as the function of crack length obtained from the R-curves of Fig. 6(a-c)to see clearly the differences among the curve behavior of the B4C monolith. Fig. 6(b) shows the families of KA(c) curves and R-curve behavior of the B4C/BN nanocomposites ig. 6(c)shows the families of Ka(c)curves and R-curve behavior of the B4C/BN microcomposites. As seen in Fig. 6(a), the envelope of tangency points formed the rising r-curve behavior, this result indicated that the fracture toughness of the B4 monolith increased gradually with the increase of cracks length. As seen in Fig. 6(b), the envelope of tangency points formed the relative higher rising R- Crack size, cum) curve behavior; this result indicated that the fracture toughness of the bac/Bn nanocomposites increased gradually with the Increase of cracks length. As seen in Fig. 6(c, the envelope of tangency points formed the rising R-curve behavior; this result indicated that the 73--3eN B C/BN microcomposites. fracture toughness of the B4 C/BN microcomposites increased grad 20wt% h-BN) ually with the increase of cracks length. Fig. 6 showed that the B4C monolith, the B4c/ BN nanocomposites and the bac/Bn micro- omposites all exhibited the rising R-curves behavior The B.C/BN nanocomposites exhibited the relative higher R-curve behav ior than that of the B4C monolith and the B4 C/BN microcomposites, the bac monolith and the b4c/Bn microcomposites also exhibited the rising R-curves behavior. Fig. 6 showed that the fracture toughness(R-curves)behav- 642 ior of the B4 C monolith, the B4C/BN nanocomposites and the C/BN microcomposites all increased gradually with the increase of the crack length. For the rising R-curves behavior of these hree materials, when the cracks length increased from 40 um to 1000 um, the fracture toughness of the BC monolith increased Crack size,c(μm) from 3.99 MPam/2 to 6.75 MPa m1/2: the fracture toughness of the B4C/BN nanocomposites increased from 4.11 MPam/2 to Fig. 6. The toughness-curve diagrams for (a)the Bac monolith, (b) the BaC/ BN 7.47MPam'; the fracture toughness of the B4C/BN microcom- owt.% h-B posites increased from 3 22 MPa m/2 to 6. 29MP data from Fig 5. Shaded lines were the Tc)functions, plotted as locus of tangency nanocomposites exhibited the relative higher rising R-curve behav- pints to the K'a(c)curves. The envelope of tangency points formed the R-curves ior than that of the B4 C monolith and the B4 C/BN microcomposites. ehavior. The indentation loads in the figures were shown as the follows: 1-4.9N, ig. 7 shows the fracture resist es(R-curves) of the 2-98N,3-294N,4-49N,5-98N,6-196N,7-294N. B4Cmonolith, the B4C/BN nanocomposites (20 wt% h-BN)and the B4C/BN microcomposites(20 wt. h-BN)as the function of crack curves were constructed from the indentation-strength data in length obtained from the r-curves of Fig 6(a-c) to see clearly the Fig 5, inserting oA=of at each values of indentation load P in Eq. difference among them. Fig. 7 showed that the B4C/Bn nanocom- (1). Furthermore, according to Eq(3), the envelope of tangency posites exhibited the higher rising R-curve behavior than that of the points for three materials were constructed. Fig. 6 shows the fam- B4 monolith and the b4 c/Bn microcomposites. The B4C monolith es of KA(c)curves and the envelopes of tangency points for the and the BaC/BN microcomposites also exhibited the rising R-curves three materials. Fig. 6(a)shows the families of KA(c) curves an behavior
T. Jiang et al. / Materials Science and Engineering A 494 (2008) 203–216 207 Fig. 6. The toughness-curve diagrams for (a) the B4C monolith, (b) the B4C/BN nanocomposites (20 wt.% h-BN) and (c) the B4C/BN microcomposites (20 wt.% hBN). Families of solid curves were plots of K A(c) in Eq.(1) using the fracture strength data from Fig. 5. Shaded lines were the T(c) functions, plotted as locus of tangency points to the K A(c) curves. The envelope of tangency points formed the R-curves behavior. The indentation loads in the figures were shown as the follows: 1–4.9 N, 2–9.8 N, 3–29.4 N, 4–49 N, 5–98 N, 6-196 N, 7–294 N. curves were constructed from the indentation-strength data in Fig. 5, inserting A = f at each values of indentation load P in Eq. (1). Furthermore, according to Eq. (3), the envelope of tangency points for three materials were constructed. Fig. 6 shows the families of K A(c) curves and the envelopes of tangency points for the three materials. Fig. 6(a) shows the families of K A(c) curves and RFig. 7. The fracture toughness curves (R-curves) behavior of the B4C monolith, the B4C/BN nanocomposites (20 wt.% h-BN) and the B4C/BN microcomposites (20 wt.% h-BN) as the function of crack length obtained from the R-curves of Fig. 6(a)–(c) to see clearly the differences among them. curve behavior of the B4C monolith. Fig. 6(b) shows the families of K A(c) curves and R-curve behavior of the B4C/BN nanocomposites. Fig. 6(c) shows the families of K A(c) curves and R-curve behavior of the B4C/BN microcomposites. As seen in Fig. 6(a), the envelope of tangency points formed the rising R-curve behavior, this result indicated that the fracture toughness of the B4C monolith increased gradually with the increase of cracks length. As seen in Fig. 6(b), the envelope of tangency points formed the relative higher rising Rcurve behavior; this result indicated that the fracture toughness of the B4C/BN nanocomposites increased gradually with the increase of cracks length. As seen in Fig. 6(c), the envelope of tangency points formed the rising R-curve behavior; this result indicated that the fracture toughness of the B4C/BN microcomposites increased gradually with the increase of cracks length. Fig. 6 showed that the B4C monolith, the B4C/BN nanocomposites and the B4C/BN microcomposites all exhibited the rising R-curves behavior. The B4C/BN nanocomposites exhibited the relative higher rising R-curve behavior than that of the B4C monolith and the B4C/BN microcomposites, the B4C monolith and the B4C/BN microcomposites also exhibited the rising R-curves behavior. Fig. 6 showed that the fracture toughness (R-curves) behavior of the B4C monolith, the B4C/BN nanocomposites and the B4C/BN microcomposites all increased gradually with the increase of the crack length. For the rising R-curves behavior of these three materials, when the cracks length increased from 40 m to 1000 m, the fracture toughness of the B4C monolith increased from 3.99 MPa m1/2 to 6.75 MPa m1/2; the fracture toughness of the B4C/BN nanocomposites increased from 4.11 MPa m1/2 to 7.47 MPa m1/2; the fracture toughness of the B4C/BN microcomposites increased from 3.22 MPa m1/2 to 6.29 MPa m1/2. The B4C/BN nanocomposites exhibited the relative higher rising R-curve behavior than that of the B4C monolith and the B4C/BN microcomposites. Fig. 7 shows the fracture resistance curves (R-curves) of the B4C monolith, the B4C/BN nanocomposites (20 wt.% h-BN) and the B4C/BN microcomposites (20 wt.% h-BN) as the function of crack length obtained from the R-curves of Fig. 6(a)–(c) to see clearly the difference among them. Fig. 7 showed that the B4C/BN nanocomposites exhibited the higher rising R-curve behavior than that of the B4C monolith and the B4C/BN microcomposites. The B4C monolith and the B4C/BN microcomposites also exhibited the rising R-curves behavior.
208 T Jiang et aL Materials Science and Engineering A 494 (2008)203-216 For the rising R-curve behavior, the critical cracks length(Cm) 10 and the fracture resistance(Kg)of tangency points on the R-curves vere calculated by Eqs. (9)-(13)[22, 27-33. So the relation equa gaff*=7, Ic)ou 269(C)185 tions of the critical cracks length(Cm). the initial indentation crack 3K=25C)3 length(Ci), the fracture strength(o ) the indentation load(P)and the fracture resistance(Ke)were constructed 追g6 KR=k(C严 C/+XPC KR=KI a=“ 一 B,C/BN nanocomposites B C/BN microcomposites dc The critical cracks length(Cm)was calculated by the equation 1000 Crack length C(um 4yP (1-2m)k (14) ze AC(AC=C for the B4C monolith, the B4C/BN nanocomposites(20 wt % h The fracture strength(of )and fracture resistance(KR)were cal- BN) and the B,C/BN microcomposites(20 wt% h-BN)expressed by the power-law lated by the equations: +3「4xP1(2m-1)/ k4/2m+3) (15 and indentation load(p)was calculated by Eq (26). The relation of fracture resistance(Kg)and cracks length(C) was calculated by eq. (2m+3) (1-2m)k (xa1/)/(Bo) 1-3B p-1)/4p k=ga(6y)(1+)4+p ()k2=x(1+Xa 1-2m)/4(aBp)2am+3)/4 412/3+2m In this research, the predicted fracture ance(Kg)curve Inserting Eqs. (17)-(20)into Eq (14), so the critical cracks length (R-curve)was presented as the function of crack size(AC)in the (Cm)was also calculated by the following eq where k and m were the constant [34 The relationship between So the relation of the critical cracks length(Cm)and the inden- the fracture strength of and the indentation load P was expressed tation load(P)was calculated by Eq (21). According to Eqs. (17)and as follows (20), so the relation of the initial indentation cracks length( Ci)and log of=log P the indentation load(P) was calculated by the following equation where the exponent B was defined by the equation P(1+B)/2 The values of B were the slopes of the fit equations present (1+p)/2 Fig. 5. So the values of m were calculated by following equation: X According to equation B The values of k were calculated by Eg (27). So the power-law (23) equation KR-kAC)was calculated by Eq(27).Fig8 shows the so the relation of the fracture strength(o )and critical cracks length lith, the BAC/BN nanocomposites and the BaC/BN microcomposites (Cm)was calculated by the following equation The predicted fracture resistance curve(r-curve) was presented as the function of crack size(AC)in the empirical power-law relation +B/B1B/(1+P Cm-2p/(1+P) KR=kACm Fig 8 showed that the B C monolith exhibited the ris ing R-curve behavior having m=0. 1438, the r-curve equation was shown as follows. The relation of fracture resistance(Kr)and fracture strength(oe) was calculated by Eq (25). The relation of fracture resistance(Kg) KR=17.1(AC)
208 T. Jiang et al. / Materials Science and Engineering A 494 (2008) 203–216 For the rising R-curve behavior, the critical cracks length (Cm) and the fracture resistance (KR) of tangency points on the R-curves were calculated by Eqs. (9)–(13) [22,27–33]. So the relation equations of the critical cracks length (Cm), the initial indentation crack length (CI), the fracture strength (f), the indentation load (P) and the fracture resistance (KR) were constructed: KR = k(C) m (9) KI = ϕfC1/2 + PC−3/2 (10) KR = KI (11) dKR dC = dKI dC (12) df dC = 0 (13) The critical cracks length (Cm) was calculated by the equation: Cm+3/2 m = 4P (1 − 2m)k (14) The fracture strength (f) and fracture resistance (KR) were calculated by the equations: m = 2m + 3 4ϕ 4P 1 − 2m (2m−1)/(2m+3) k4/(2m+3) (15) KR = k 4P (1 − 2m)k 2m/(2m+3) (16) m = 1 − 3ˇ 2(ˇ + 1) (17) k = ϕ˛(ˇ) −ˇ(1 + ˇ) (1+ˇ) (18) = P CI 2/(1+ˇ) (19) Cm = CI 4 1 − 2m 2/(3+2m) (20) Inserting Eqs.(17)–(20)into Eq.(14), so the critical cracks length (Cm) was also calculated by the following equation: Cm = P(1+ˇ) ˛ˇϕ 1/2 (21) So the relation of the critical cracks length (Cm) and the indentation load (P) was calculated by Eq. (21). According to Eqs. (17) and (20), so the relation of the initial indentation cracks length (CI) and the indentation load (P) was calculated by the following equation: Cm = ˛ˇϕ1/2 P(1+ˇ)/2 CI = ˛ˇϕ1/2 ˇ ˇ + 1 (1+ˇ)/2 P(1+ˇ)/2 (22) According to equation: P = ˛ f 1/ˇ (23) so the relation of the fracture strength (f) and critical cracks length (Cm) was calculated by the following equation: f = ˛(1+ˇ)/ˇ ˛ˇϕ ˇ/(1+ˇ) Cm−2ˇ/(1+ˇ) (24) The relation of fracture resistance (KR) and fracture strength (f) was calculated by Eq. (25). The relation of fracture resistance (KR) Fig. 8. The predicted fracture resistance curves (R-curves) as the function of crack size C ( C = C) for the B4C monolith, the B4C/BN nanocomposites (20 wt.% hBN) and the B4C/BN microcomposites (20 wt.% h-BN) expressed by the power-law equation: KR=k(C)m. and indentation load (P) was calculated by Eq. (26). The relation of fracture resistance (KR) and cracks length (C) was calculated by Eq. (27): KR = (˛1/ˇ) 1/4 (ˇϕ) 3/4 ˇ/(1 + ˇ) (f) (3ˇ−1)/4ˇ (25) KR = 1/4(1 + ˇ)(˛ˇϕ) 3/4 ˇ P(1−3ˇ)/4 (26) KR = (1−2m)/4(˛ˇϕ) (2m+3)/4 (1 − 2m)/4 Cm (27) In this research, the predicted fracture resistance (KR) curve (R-curve) was presented as the function of crack size ( C) in the empirical power-law relation: KR = k( C) m (28) where k and m were the constant [34]. The relationship between the fracture strength f and the indentation load P was expressed as follows: log f = log˛ − ˇ log P (29) where the exponent ˇ was defined by the equation: ˇ = 1 − 2m 2m + 3 (30) The values of ˇ were the slopes of the fit equations presented in Fig. 5. So the values of m were calculated by following equation: m = 1 − 3ˇ 2ˇ + 2 (31) The values of k were calculated by Eq. (27). So the power-law equation KR = k( C)m was calculated by Eq. (27). Fig. 8 shows the predicted fracture resistance curves (R-curves) of the B4C monolith, the B4C/BN nanocomposites and the B4C/BN microcomposites. The predicted fracture resistance curve (R-curve) was presented as the function of crack size ( C) in the empirical power-law relation KR = k( C)m. Fig. 8 showed that the B4C monolith exhibited the rising R-curve behavior having m = 0.1438, the R-curve equation was shown as follows: KR = 17.1( C) 0.1438 (32)
T Jiang et al Materials Science and Engineering A 494(2008)203- The B4 C/BN nanocomposites exhibited the rising R or having m=0. 1855, the R-curve equation was shown as follows KR=26.9(△C (33) 27=1017( 3165 The B4C/BN microcomposites exhibited the rising R-curve 3O=1423 behavior having m=0. 2044, the R-curve equation was shown as F 3 KR=255(△C2044 The B4Cmonolith, the BaC/BN nanocomposites and the b4 C/BN microcomposites all exhibited the rising R-curves behavior. The 12E1·Bmom B4C/BN nanocomposites exhibited the higher rising R-curve behav- 2· B, C/BN microcomposites ior than that of the B4C monolith and the B4 C/BN microcomposites. 3 A BC/BN nanocomposites Fig 9 shows the effects of the critical cracks length on the frac- ture strength of the B4 C monolith, the B4C/BN microcomposites nd the Bac/ BN nanocomposites. The fracture strength of the Bac Critical cracks length C(um) monolith, the B4 C/BN microcomposites and the b4C/Bn nanocom so the relation of the fracture strength(on) and the critical cracks length(O) was calculated by the equations For the B4 C monolith For the B4C/BN nanocomposites or=1450(c)-0.34757 (35)ar=1423(C)031673 For the BaC/BN microcomposi The B4C/BN nanocomposites retained the remarkably higher or=1017(c)-029273 fracture strength in comparison with the B4C monolith and (36) the BAC/BN microcomposites under the equivalent critical cracks 1C=24.32( 1C1=8.51(P) EoE 2C=34.96P) 2C=1138(P) 3Cn=2663(P) 3C1=888P) ￥ogoo 1一 一- B monolith 2-.-B, C/BN microcomposites 3-A-B, C/BN nanocomposites 3-A-B C/BN nanocomposites Indentation Load P(N) Indentation Load P(N) Fig. 10. The effects of the indentation load on the critical cracks length and the initial indentation cracks length of the Ba C monolith, the b C/ Bn microcomposites and the B4C/BN nanocomposites (a)The indentation load plotted against the critical cracks length; (b)the indentation load plotted against the initial indent racks length. (a)1 (b) 187()m 2K-31XP) 3K8-1375(7) 3K:=381(P) 1· B C monolith 1一■ B C monolith 2· B C/BN microcomposites 3· B, C/BN nanocomposites 3-4-B, C/BN nanocomposites 200250300350400450500 50100150200250300 Fracture Strength S(MPa) ation Load P(N Fig. 11. The effects of the fracture strength and the indentation load on the fracture resistance(ka)of the B4C monolith, the BaC/Bn microcomposites and the b4C/ BN nanocomposites (a)The fracture resistance plotted against the fracture strength; (b)the fracture resistance plotted against the indentation load
T. Jiang et al. / Materials Science and Engineering A 494 (2008) 203–216 209 The B4C/BN nanocomposites exhibited the rising R-curve behavior having m = 0.1855, the R-curve equation was shown as follows: KR = 26.9( C) 0.1855 (33) The B4C/BN microcomposites exhibited the rising R-curve behavior having m = 0.2044, the R-curve equation was shown as follows: KR = 25.5( C) 0.2044 (34) The B4C monolith, the B4C/BN nanocomposites and the B4C/BN microcomposites all exhibited the rising R-curves behavior. The B4C/BN nanocomposites exhibited the higher rising R-curve behavior than that of the B4C monolith and the B4C/BN microcomposites. Fig. 9 shows the effects of the critical cracks length on the fracture strength of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. The fracture strength of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites decreased linearly with the increase of the critical cracks length in the two logarithmically axis system. According to Eq.(24), so the relation of the fracture strength (f) and the critical cracks length (C) was calculated by the equations. For the B4C monolith: f = 1450(C) −0.34757 (35) For the B4C/BN microcomposites: f = 1017(C) −0.29273 (36) Fig. 9. The effects of the critical cracks length on the fracture strength of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. For the B4C/BN nanocomposites: f = 1423(C) −0.31673 (37) The B4C/BN nanocomposites retained the remarkably higher fracture strength in comparison with the B4C monolith and the B4C/BN microcomposites under the equivalent critical cracks Fig. 10. The effects of the indentation load on the critical cracks length and the initial indentation cracks length of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. (a) The indentation load plotted against the critical cracks length; (b) the indentation load plotted against the initial indentation cracks length. Fig. 11. The effects of the fracture strength and the indentation load on the fracture resistance (KR) of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. (a) The fracture resistance plotted against the fracture strength; (b) the fracture resistance plotted against the indentation load.
10 1 0.8 dentation load dentation load P=294N 0.85 080 B, C/BN microcomposites B C/BN nanocomposites B.C/BN nanocomposites 0.75 3040.5060.7 Crack length(C/CM Fig. 12. The effects of the cracks length (CA/Cm)on the ns of the applied stress(alam)and the fracture resistance(Ka/Km) for the Bac monolith, the Bac/Bn icrocomposites and the BaC/BN nanocomposites (a)The effects of the cracks length(CA/Cm)on the variation of the applied stress(oAJoM (b)the effects of the cracks ngth(CA/Cm)on the variation of the fracture resistance(KA/Km). length. The fracture strength of the B4C monolith was also higher indentation cracks length of the B4C monolith, the B4C/BN micro- than that of the B4 C/BN microcomposites under the equivalent crit- composites and the B4 C/BN nanocomposites increased linearly ical cracks length. with the increase of indentation load in the two logarithmically axis Fig. 10(a)shows the effects of the indentation load on the critical system. According to Eq (22), so the relation of the initial indenta- cracks length of the B4 Monolith, the B, C/BN microcomposites and tions cracks length(C)and the indentation load(P)was calculated the B4C/BN nanocomposites. The critical cracks length of the B4c by the following equations For the B4 C monolith nolith, the B4C/BN microcomposites and the b4 c/ bn nanocom- osites all increased linearly with the increase of th C1=851(P)9 load in the two logarithmically axis system. According to Eq (21). For the B4C/ BN microcomposites so the relation of the critical cracks length(Cm)and the indentation load(P) was calculated by the equations For the B4c monolith C1=1138(P)9 m=24,32(P)0603 For the B4C/BN nanocomposites For the bac/ Bn microcomposites: C1=888(P m=3496(P9 .5865 The initial indentation cracks length of the B4C/BN microcom posites was remarkably higher than that of the B4c monolith and For the B4 C/BN nanocomposites the B4 C/ BN nanocomposites under the equivalent indentation load. Fig. 11(a) shows the effects of the fracture strength on the fracture resistance( KR)of the B4Cmonolith, the B4C/BN microcom- The critical cracks length of the Bac/BN microcomposites was posites and the bac/ BN nanocomposites. The fracture resistance remarkably higher than that of the B4C monolith and the b4 c/bn (KR) of the B4C monolith, the B4 C/BN microcomposites and the Ites under the equivalent indentation load. B4C/BN nanocomposites all increased gradually with the decrease Fig. 10(b) shows the effects of the indentation load on the ini- of the fracture strength in the two logarithmically axis system. tial indentation cracks length of the B4C monolith, the B4 C/Bn According to Eq. (25). so the relation of the fracture resistance(Ke) microcomposites and the B4 C/BN nanocomposites. The initial and the fracture strength(oe) was calculated by the equations For a)5657585960616263 (b)4950515253545.556 100 m=2094 m=2309 2· B C/BN microcomposites ym=245m=266110 1401601802002202402607 Fracture Strength(MPa) Fracture Strength(MPa) ites and the indented composites with th /BN microcomposites and the baC/BN nanocomposites (a The weibull distribution of the fracture strength for the hot-pressed composites (b)The Weibull distribution fracture strength for the indented composites with the indentation load of 49N
210 T. Jiang et al. / Materials Science and Engineering A 494 (2008) 203–216 Fig. 12. The effects of the cracks length (CA/CM) on the variations of the applied stress (A/M) and the fracture resistance (KA/KM) for the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. (a) The effects of the cracks length (CA/CM) on the variation of the applied stress (A/M); (b) the effects of the cracks length (CA/CM) on the variation of the fracture resistance (KA/KM). length. The fracture strength of the B4C monolith was also higher than that of the B4C/BN microcomposites under the equivalent critical cracks length. Fig. 10(a) shows the effects of the indentation load on the critical cracks length of the B4Cmonolith, the B4C/BNmicrocomposites and the B4C/BN nanocomposites. The critical cracks length of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites all increased linearly with the increase of the indentation load in the two logarithmically axis system. According to Eq. (21), so the relation of the critical cracks length (Cm) and the indentation load (P) was calculated by the equations. For the B4C monolith: Cm = 24.32(P) 0.608 (38) For the B4C/BN microcomposites: Cm = 34.96(P) 0.5865 (39) For the B4C/BN nanocomposites: Cm = 26.63(P) 0.593 (40) The critical cracks length of the B4C/BN microcomposites was remarkably higher than that of the B4C monolith and the B4C/BN nanocomposites under the equivalent indentation load. Fig. 10(b) shows the effects of the indentation load on the initial indentation cracks length of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. The initial indentation cracks length of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites increased linearly with the increase of indentation load in the two logarithmically axis system. According to Eq. (22), so the relation of the initial indentations cracks length (CI) and the indentation load (P) was calculated by the following equations. For the B4C monolith: CI = 8.51(P) 0.608 (41) For the B4C/BN microcomposites: CI = 11.38(P) 0.5865 (42) For the B4C/BN nanocomposites: CI = 8.88(P) 0.593 (43) The initial indentation cracks length of the B4C/BN microcomposites was remarkably higher than that of the B4C monolith and the B4C/BN nanocomposites under the equivalent indentation load. Fig. 11(a) shows the effects of the fracture strength on the fracture resistance (KR) of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. The fracture resistance (KR) of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites all increased gradually with the decrease of the fracture strength in the two logarithmically axis system. According to Eq. (25), so the relation of the fracture resistance (KR) and the fracture strength (f) was calculated by the equations. For Fig. 13. The Weibull distributions of the fracture strength of the hot-pressed composites and the indented composites with the indentation load of 49 N for the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. (a) TheWeibull distribution of the fracture strength for the hot-pressed composites. (b) TheWeibull distribution of the fracture strength for the indented composites with the indentation load of 49 N.
the Bac monolith: the increase of the cracks length(CA/CM). Fig. 12(a) showed that KR=46.1(0)-040732 he applied stress(oalom)increased gradually with the increase of (44) the cracks length(CA/GM when the CA/CM=4/(1-2m)1-2/3+2m) For the BaC/BN microcomposites: SO OAlOM=0: when the CA/CM=1. So oAloM=1. Fig 12(b)showed (45) that the fracture resistance(KA/KM)increased with the ind the cracks length(CA/CM). when the CA/CM=[4/(1-2m BAC/BN nanocomposites SO KA/KM=[4/(1-2m)1-2m/(3+2m): when the CA/CM=1, so KA/KM=1. KR=1375(a)05531 The strength variability was investigated by Weibull distribution (46) [35]. The failure probability F was expressed as the equations The B4 Monolith, the B4C/BN microcomposites and the b4 C/BN anocomposites all exhibited the rising R-curves behavior with the F=1-exp-gc decrease of the fracture strength. The fracture resistance( Kg)of resistance(Kg)of the BA monolith was slightly higher than that of Fl-s the failure probability [35] the Bac/ Bn nanocomposites was remarkably higher than that of the B4C monolith and the B4 C/BN microcomposites. The fracture the b4c/BN microcomposites Fig. 11(b)shows the effects of the indentation load on the ac was the fracture strength. So the failure probability Fwas shown fracture resistance(Kg)of the BACmonolith, the B4C/BN microcom- as the equation (28 posites and the B4c/BN nanocomposites. The fracture resistance (KR) of the BAC monolith, the BAC/BN microcomposites and the InInIi-F=mInde-mInoo of the indentation load. The fracture resistance(Kg)of the B4 C/BN where m was Weibull modulus. Fig. 13 shows the Weibull dis- nanocomposites was remarkably higher than that of the Bac tribution of fracture strength of the B4c monolith, the Bc/Bn monolith and the B4 C/BN microcomposites under the equivalent microcomposites and the baC/BN nanocomposites. Fig 13(a)shows indentation load. According to Eq(26), so the relation of the frac- the Weibull distribution of fracture strength of hot-pressed B4C/BN ture resistance(Kg)and the indentation load(P)was calculated by omposites. For the B4C monolith, m=23.09: for the B4C/BN micro- he equations For the B4 C monolith composites, m=20.94; for the B4C/BN nanocomposites, m=20.09 KR=3.71(P083 (47) Fig. 13(b) shows the Weibull distribution of fracture strength of For the B4C/BN microcomposites monolith, m=22. 43: for the B4C/BN microcomposites, m=20. 15 KR=313(P9198 for the BaC/BN nanocomposites, m=26.61. There was no obvious difference in strength distribution for hot-pressed composites and For the B4C/BN nanocomposites indented composites. For the hot-pressed composites, the fracture KR=381(P)91 strength was controlled by the internal microstructure; while for (49) the indented composites, the fracture strength was controlled by The B4Cmonolith, the B4C/BN microcomposites and the B4C/BN external flaws. The B4C monolith, the B4C/BN micro nanocomposites all exhibited the rising R-curves behavior with the BaC/bn nanocomposites exhibited the rising R-curves behav- he increase of the indentation load. The B4C/BN nanocomposites ior; so the rising R-curve behavior reduced the scatter of fracture exhibited the higher rising R-curve behavior than that of the B4c strength monolith and the b4c/BN microcomposites The r-curve behavior was also expressed by the other empirical In the indentation-strength test, during the fracture process, equations [33, 36]. Therefore, the R-curve behavior was calculated before the applied stress( a) did not achieve the maximum applied by the following equation: stress(oM), and the cracks length(Ca)did not achieve the critical cracks length(CM), the variation of the applied stress(oa/om)was calculated by cracks length(CA/CM), the calculated equations 22: OA 1「[4/1-2m)CA/CMm+32-1 where Koo, Ko and a were calculated by the equations 严14/(1-2m-1 50) Kg=0 C1/2+XPC-3/2 According to the equation of the critical crack length( CM)and dKg the initial indentation cracks length(G) dc CM< M the 0SoAloMsl. Before the fracture resistance(Ka) did not achieve the maximum fracture resistance(KM). the relation of the of=aP-p fracture resistance(KA/KM)and the cracks length(CA/ M)was cal- d by the following equation because C/CM≤CACM≤1.so[4(1-2m)]-23+2m)≤CACM≤1.so [4/(1-2m)1-2m/(3+2m)<KA/KM< 1. Fig 12 shows the variations of K,- XP the applied stress(oa/om)and the fracture resistance( KA/km)with
T. Jiang et al. / Materials Science and Engineering A 494 (2008) 203–216 211 the B4C monolith: KR = 46.1(f) −0.40752 (44) For the B4C/BN microcomposites: KR = 187(f) −0.69476 (45) For the B4C/BN nanocomposites: KR = 137.5(f) −0.57531 (46) The B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites all exhibited the rising R-curves behavior with the decrease of the fracture strength. The fracture resistance (KR) of the B4C/BN nanocomposites was remarkably higher than that of the B4C monolith and the B4C/BN microcomposites. The fracture resistance (KR) of the B4C monolith was slightly higher than that of the B4C/BN microcomposites. Fig. 11(b) shows the effects of the indentation load on the fracture resistance (KR) of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. The fracture resistance (KR) of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites all increased gradually with the increase of the indentation load. The fracture resistance (KR) of the B4C/BN nanocomposites was remarkably higher than that of the B4C monolith and the B4C/BN microcomposites under the equivalent indentation load. According to Eq. (26), so the relation of the fracture resistance (KR) and the indentation load (P) was calculated by the equations. For the B4C monolith: KR = 3.71(P) 0.08743 (47) For the B4C/BN microcomposites: KR = 3.13(P) 0.11988 (48) For the B4C/BN nanocomposites: KR = 3.81(P) 0.11 (49) The B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites all exhibited the rising R-curves behavior with the increase of the indentation load. The B4C/BN nanocomposites exhibited the higher rising R-curve behavior than that of the B4C monolith and the B4C/BN microcomposites. In the indentation-strength test, during the fracture process, before the applied stress (A) did not achieve the maximum applied stress (M), and the cracks length (CA) did not achieve the critical cracks length (CM), the variation of the applied stress (A/M) was calculated by cracks length (CA/CM), the calculated equations [22]: A M = 1 (CA/CM) 2 [4/(1 − 2m)](CA/CM) m+3/2 − 1 [4/(1 − 2m)] − 1 (50) According to the equation of the critical crack length (CM) and the initial indentation cracks length (CI): CM = CI 4 1 − 2m 2/(3+2m) because CI/CM ≤ CA/CM ≤ 1, so [4/(1−2m)]−2/(3+2m) ≤ CA/CM ≤ 1, so the 0 ≤ A/M ≤ 1. Before the fracture resistance (KA) did not achieve the maximum fracture resistance (KM), the relation of the fracture resistance (KA/KM) and the cracks length (CA/CM) was calculated by the following equation: KA KM = CA CM m (51) because CI/CM ≤ CA/CM ≤ 1, so [4/(1−2m)]−2/(3+2m) ≤ CA/CM ≤ 1, so [4/(1−2m)]−2m/(3+2m) ≤ KA/KM ≤ 1. Fig. 12 shows the variations of the applied stress (A/M) and the fracture resistance (KA/KM) with the increase of the cracks length (CA/CM). Fig. 12(a) showed that the applied stress (A/M) increased gradually with the increase of the cracks length (CA/CM), when the CA/CM = [4/(1 − 2m)]−2/(3+2m) , so A/M = 0; when the CA/CM = 1, so A/M = 1. Fig. 12(b) showed that the fracture resistance (KA/KM) increased with the increase of the cracks length (CA/CM), when the CA/CM = [4/(1 − 2m)]−2/(3+2m) , so KA/KM = [4/(1 − 2m)]−2m/(3+2m) ; when the CA/CM = 1, so KA/KM = 1. The strength variability was investigated byWeibull distribution [35]. The failure probability F was expressed as the equations: F = 1 − exp − c 0 m (52) where F was the failure probability [35]: F = i − 0.5 n (53) c was the fracture strength. So the failure probability F was shown as the equation [28]: ln ln 1 1 − F = m ln c − m ln 0 (54) where m was Weibull modulus. Fig. 13 shows the Weibull distribution of fracture strength of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites. Fig. 13(a) shows the Weibull distribution of fracture strength of hot-pressed B4C/BN composites. For the B4C monolith, m = 23.09; for the B4C/BN microcomposites, m = 20.94; for the B4C/BN nanocomposites, m = 20.09. Fig. 13(b) shows the Weibull distribution of fracture strength of indented composites with the indentation load of 49 N. For the B4C monolith, m = 22.43; for the B4C/BN microcomposites, m = 20.15; for the B4C/BN nanocomposites, m = 26.61. There was no obvious difference in strength distribution for hot-pressed composites and indented composites. For the hot-pressed composites, the fracture strength was controlled by the internal microstructure; while for the indented composites, the fracture strength was controlled by external flaws. The B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites exhibited the rising R-curves behavior; so the rising R-curve behavior reduced the scatter of fracture strength. The R-curve behavior was also expressed by the other empirical equations [33,36]. Therefore, the R-curve behavior was calculated by the following equation: KR = K∞ − (K∞ − K0) exp − C (55) where K∞, K0 and were calculated by the equations: KR = ϕfC1/2 + PC−3/2 (56) dKR dC = 0 and df dC = 0 f = ˛P−ˇ so K∞ = 4 33/4 (ϕ3) 1/4 (Pf 3) 1/4 (57) and K0 = P C0 3/2 (58)
12 10 For the B4C/BN microcomposites, the equations of R-curve 1-Ka=6.15-2.99exp(-△C246 behavior: 2-K=5.99-3.38eXp(-△C312) △C 3-K=6.83-349exp(-△C261) KR=599-3.38eXp For the B4C/BN nanocomposites, the equations of KR=6.83-3.49eXp (25) Fig 14 showed that the B4C monolith the B4C/BN microcom- B C monolith posites and the b4 C/BN nanocomposites all exhibited the rising R-curves behavior The B4C/BN nanocomposites exhibited the rel- ative higher rising R-curve behavior in comparison with the B4c B,C/BN nanocomposites monolith and the b4C/BN 600 8001000 3.5. The toughening mechanisms Crack length C(um) Fig. 14. The R-curves behavior of the B4C monolith, the B4C/BN microcom- The B4C monolith, the B4C/BN nanocomposites and the b4 C/BN osites and the BaC/BN nanocomposites expressed by the empirical equation: microcomposites exhibited the rising R-curve behavior. These were attributed to the different toughening mechanisms. The bacmono- lith exhibited the rising R-curve behavior. This was explained from microstructure. Fig. 1(a)showed that the weak phase YAG Y3Al5O12)existed in B4C monolith. During the fracture proces Kk=oo, m /2+XPCm-3/=Kx-(kK-Ko)expm*o when the microcracks reached to the weak phase YAG, the micro- cracks would be deflected and diverged along the weak phase, and prevented from further extending, the length of crack path was P was indentation load, or was fracture strength [26, 33]. The elongated and the work of fracture( wOF)increased. On the other cracks length Cm and Co were calculated by Eqs. (59)and (60)[26]: hand, the B4C monolith exhibited the compact and homogene microstructure, which resulted in the increase of crack propaga- (59) tion resistance. So the fracture toughness of B4 increased with the increase of crack length. The B4C/ BN nanocomposites and the Bac/BN microcomposites β P+1)/2 (60) exhibited the rising R-curves behavior: the toughening mecha- nisms were explained from microstructure Fig 15(a)and(b) show: the TEm crographs of the b4c Bn microcomposites and the so the value of a was calculated according to the above equations. B4C/BN nanocomposites. The weak interface between BAC matrix Fig 14 shows the R-curves behavior of the B4C monolith, the B4 C/B grains and h-BN particles, as well as the microcracks within h-BN microcomposites and the BA C/BN nanocomposites expressed by the particles existed in TEM micrographs. The weak interface between exponent equation B4C matrix grains and h-BN particles, and the microcracks within h-BN particles would improve the toughness of composites Dur- KR= Koo-(Koo-Ko)exp ing the fracture process, the microcracks would propagate along the weak interface between BC matrix grains and h-BN particles For the B4 monolith the equations of r-curve behavior: and propagate along the microcracks within h-BN particles. The cleavage behavior of the h-BN particles would disperse main cracks KR=6.15-299c/-4C (61) into many microcracks and prevent microcracks from extending, so the microcracks would be deflected and diverged and the defle (b) BA eak interfac 400nm 250nm Fig. 15. The TEM micrographs of the B4C BN microcomposites and the B4 C/ BN nanocomposites (a)The TEM micrograph of the Ba C/BN microcomposites; (b) the TEM
212 T. Jiang et al. / Materials Science and Engineering A 494 (2008) 203–216 Fig. 14. The R-curves behavior of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites expressed by the empirical equation: KR = K∞ − (K∞ − K0)exp(− C/ ). KR = ϕfCm1/2 + PCm−3/2 = K∞ − (K∞ − K0) exp −Cm − C0 P was indentation load, f was fracture strength [26,33]. The cracks length Cm and C0 were calculated by Eqs. (59) and (60) [26]: Cm = 3P ϕf 1/2 (59) Cm = C0 ˇ + 1 ˇ (ˇ+1)/2 (60) so the value of was calculated according to the above equations. Fig. 14 shows the R-curves behavior of the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites expressed by the exponent equations: KR = K∞ − (K∞ − K0) exp − C For the B4C monolith, the equations of R-curve behavior: KR = 6.15 − 2.99 exp − C 246 (61) For the B4C/BN microcomposites, the equations of R-curve behavior: KR = 5.99 − 3.38 exp − C 312 (62) For the B4C/BN nanocomposites, the equations of R-curve behavior: KR = 6.83 − 3.49 exp − C 261 (63) Fig. 14 showed that the B4C monolith, the B4C/BN microcomposites and the B4C/BN nanocomposites all exhibited the rising R-curves behavior. The B4C/BN nanocomposites exhibited the relative higher rising R-curve behavior in comparison with the B4C monolith and the B4C/BN microcomposites. 3.5. The toughening mechanisms The B4C monolith, the B4C/BN nanocomposites and the B4C/BN microcomposites exhibited the rising R-curve behavior. These were attributed to the different toughening mechanisms. The B4C monolith exhibited the rising R-curve behavior. This was explained from microstructure. Fig. 1(a) showed that the weak phase YAG (Y3Al5O12) existed in B4C monolith. During the fracture process, when the microcracks reached to the weak phase YAG, the microcracks would be deflected and diverged along the weak phase, and prevented from further extending, the length of crack path was elongated and the work of fracture (WOF) increased. On the other hand, the B4C monolith exhibited the compact and homogenous microstructure, which resulted in the increase of crack propagation resistance. So the fracture toughness of B4C monolith increased with the increase of crack length. The B4C/BN nanocomposites and the B4C/BN microcomposites exhibited the rising R-curves behavior; the toughening mechanisms were explained from microstructure. Fig. 15(a) and (b) shows the TEM micrographs of the B4C/BN microcomposites and the B4C/BN nanocomposites. The weak interface between B4C matrix grains and h-BN particles, as well as the microcracks within h-BN particles existed in TEM micrographs. The weak interface between B4C matrix grains and h-BN particles, and the microcracks within h-BN particles would improve the toughness of composites. During the fracture process, the microcracks would propagate along the weak interface between B4C matrix grains and h-BN particles, and propagate along the microcracks within h-BN particles. The cleavage behavior of the h-BN particles would disperse main cracks into many microcracks and prevent microcracks from extending, so the microcracks would be deflected and diverged, and the deflecFig. 15. The TEM micrographs of the B4C/BN microcomposites and the B4C/BN nanocomposites. (a) The TEM micrograph of the B4C/BN microcomposites; (b) the TEM micrograph of the B4C/BN nanocomposites.