CERAMICS INTERNATIONAL ELSEVIER Ceramics International 30(2004)441-446 Effect of geometrical factors on the mechanical properties of Si3N4/bn multilayer ceramics Qingfeng Zan*, Chang-an Wang, Yong Huang, Shike Zhao, Cuiwei Li The State Key Laboratory of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua Univer Beijing 100084, Peoples Republic of China Received 5 December 2002: received in revised form 14 April 2003: accepted 15 May 2003 Abstract The relationships between mechanical properties of Si3 N4/BN multilayer materials and the geometrical factors, number of layers (N) and layer thickness ratio (in), have been studied. At a given number of layers, with the increase of layer thickness ratio, the toughness and bending strength both increase, and when it continues to increase, the two curves both level off. Keeping the layer thickness ratio of about 10 and increasing the number of layers, the bending strength decreases slightly, and a maximum toughnes was obtained at Ns30. Furthermore, a mechanical model was established and used to analyze the above experimental results According to the experimental and calculated results, suitable geometrical parameters were advised in the design of Si3 N4/BN multilayer materials as 2≈l0andN≈30 C 2003 Elsevier Ltd and Techna S.r.L. All rights reserved Keywords: Si3N4/BN; Multilayer; Geometrical factor; Number of layers: Layer thickness ratio 1. Introduction It was proposed that the mechanical properties of Si3N4/BN multilayer ceramics were strongly dependent Since Clegg et al. [1] first fabricated SiC/C multilayer on geometrical factors(such as layer thickness and composites in 1990, multilayer ceramics have received thickness ratio)[6]. Unfortunately, it has not beer much attention because of their improved properties. documented particularly so far, although a lot of litera The improved properties can be achieved by designing ture has been accumulated on Si3 N4/BN multilayer weak interfaces for crack deflection [2-5], controlling ceramics the frontal shape of the transformation zones in ZrO2 In this work, a series of experiments were designed ceramics with barrier layers, and forming residual com- and conducted to investigate the influences of geome pression in surface layers [6-8]. As one of the most trical factors on the mechanical properties of the Si3 N4/ promising systems, Si3 N4/BN multilayer ceramics have BN multilayer ceramics. A mechanical model based on been studied intensively in the past tens of years [2-6], the flexure beam was also established to analyze the their bending strength and work of fracture can reach relationships between theoretical predictions and the 500 MPa and 5000 J/m respectively. In Si3 N4/Bn experimental results multilayer ceramics, there exists a weak interface between Si3 N4 and BN layers, which was formed by the incorporation of weak BN interlayer. The weak inter- 2. Experiment procedure face can deflect the crack propagating perpendicularly to the plane of laminates repeatedly during fracture, The raw powders of Si3 N4(Founder High Tech hus leading to extremely high work of fracture Ceramic Co. China)with 8 wt%Y2O3(99.9%), 2.5 wt%Al,O3(99.9%), and 1.5 wt. Mgo(99.9%)were ball-milled for 24 h in an alcohol medium Then the Corresponding author. Tel:+86-10-6278-5488: fax: +86-10 suny was dried and sieved in a 60-mesh screen. Select- 6277-28 ing PVa as a binder, the mixed powders were ball- milled for 24 h to prepare the slurry, and then the slurry 0272-8842/$30.00C 2003 Elsevier Ltd and Techna S.r.l. All rights reserved doi:10.1016/S0272-8842(03)001299
Effect of geometrical factors on the mechanical properties of Si3N4/BN multilayer ceramics Qingfeng Zan*, Chang-an Wang, Yong Huang, Shike Zhao, Cuiwei Li The State Key Laboratory of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China Received 5 December 2002; received in revised form 14 April 2003; accepted 15 May 2003 Abstract The relationships between mechanical properties of Si3N4/BN multilayer materials and the geometrical factors, number of layers (N) and layer thickness ratio (lh), have been studied. At a given number of layers, with the increase of layer thickness ratio, the toughness and bending strength both increase, and when it continues to increase, the two curves both level off. Keeping the layer thickness ratio of about 10 and increasing the number of layers, the bending strength decreases slightly, and a maximum toughness was obtained at N30. Furthermore, a mechanical model was established and used to analyze the above experimental results. According to the experimental and calculated results, suitable geometrical parameters were advised in the design of Si3N4/BN multilayer materials as lh10 and N30. # 2003 Elsevier Ltd and Techna S.r.l. All rights reserved. Keywords: Si3N4/BN; Multilayer; Geometrical factor; Number of layers; Layer thickness ratio 1. Introduction Since Clegg et al. [1] first fabricated SiC/C multilayer composites in 1990, multilayer ceramics have received much attention because of their improved properties. The improved properties can be achieved by designing weak interfaces for crack deflection [2–5], controlling the frontal shape of the transformation zones in ZrO2 ceramics with barrier layers, and forming residual compression in surface layers [6–8]. As one of the most promising systems, Si3N4/BN multilayer ceramics have been studied intensively in the past tens of years [2–6], their bending strength and work of fracture can reach 500 MPa and 5000 J/m2 respectively. In Si3N4/BN multilayer ceramics, there exists a weak interface between Si3N4 and BN layers, which was formed by the incorporation of weak BN interlayer. The weak interface can deflect the crack propagating perpendicularly to the plane of laminates repeatedly during fracture, thus leading to extremely high work of fracture. It was proposed that the mechanical properties of Si3N4/BN multilayer ceramics were strongly dependent on geometrical factors (such as layer thickness and thickness ratio) [6]. Unfortunately, it has not been documented particularly so far, although a lot of literature has been accumulated on Si3N4/BN multilayer ceramics. In this work, a series of experiments were designed and conducted to investigate the influences of geometrical factors on the mechanical properties of the Si3N4/ BN multilayer ceramics. A mechanical model based on the flexure beam was also established to analyze the relationships between theoretical predictions and the experimental results. 2. Experiment procedure The raw powders of Si3N4 (Founder High Tech. Ceramic Co. China) with 8 wt.% Y2O3 (99.9%), 2.5 wt.% Al2O3 (99.9%), and 1.5 wt.% MgO (99.9%) were ball-milled for 24 h in an alcohol medium. Then the sluny was dried and sieved in a 60-mesh screen. Selecting PVA as a binder, the mixed powders were ballmilled for 24 h to prepare the slurry, and then the slurry 0272-8842/$30.00 # 2003 Elsevier Ltd and Techna S.r.l. All rights reserved. doi:10.1016/S0272-8842(03)00129-9 Ceramics International 30 (2004) 441–446 www.elsevier.com/locate/ceramint * Corresponding author. Tel.: +86-10-6278-5488; fax: +86-10- 6277-2857. E-mail address: zanqf98@mails.tsinghua.edu.cn (Q. Zan)
0. Zan et al. Ceramics International 30(2004)441-446 was cast into tapes on a polyester film and formed green Si,n4 fractures catastrophically. For the Si3N4/BN tapes with different thickness. The obtained tapes were multilayer composite, after the first load drop the load dried in air and punched into a rectangle(32x 38 mm). bearing ability of the testing bar still retains over 50% Then the punched tapes were coated with slurry of bn of the peak load. Until totally fractured, the Si3N4/BN (commercial powder), whose thickness was controlled multilayer composite gives a prolonged deflection y the slurry concentration and the immerging time in besides the elastic deformation. This shows that the slurry. The coated green tapes were dried and multilayer ceramic exhibits a different fracture behavior stacked into the graphite die. After the removal of the from that of the monolithic ceramic. Hence it may be binder, the green body was hot pressed at 1820C for inferred that the mechanical properties of ceramic 5 h in a flow on N2 atmosphere. materials can be substantially improved by a special The sintered specimens were sliced into test bars with structural design similar to that conducted on biom the dimensions of 4x3x36 mm for bending strength terials as already indicated in the literature [2, 5 ind 4x 6x30 mm for fracture toughness and work of Fig. 2 shows the fracture behaviors of the Si3N4/BN fracture. a three-point bending test for bending multilayer ceramics. It can be observed from Fig. 2(a) strength was carried out at room temperature with a that Si3N4 layers are about 80-100 um thick and Bn span of 30 mm and crosshead rate of 0.5 mm/min. The interlayers only 10-20 um thick. The multilayer structure work of fracture was defined and calculated as the area mainly contributes to high toughness of the Si3N4/BN under the load-displacement curve divided by two-fold multilayer composites. The main toughening mechan of the cross-section area of the bend bar, which was ism of the multilayer composites is that the interlayer measured by the single-edge-notch-beam method deflects the crack repeatedly [as shown in Fig. 2(a)], and (SENB)at room temperature with a span of 24 mm and there are other toughening mechanisms in the ceramics, rosshead rate of 0.05 mm/min. Five specimens were such as crack bridging [Fig. 2(b)], friction and sliding tested for each test to get an average value. All the tests [Fig. 2(c)], and matrix- layer pull-out [Fig. 2(d)] and so was performed on a A-2000 Shimadzu universal mate- on. These toughening mechanisms from the interlayers rials testing machine. The loads were applied perpend- are considered to mainly contribute to high fracture he materials was observed by scanning electron micro- posites because a large amount of fracture energy is scope(SEM) of CSM950 absorbed during fracture 3. 2. Efect of thickness ratio(h) 3. Results At a given number of layers, the change of 3. 1. Fracture behavior of the SigN BN multilayer ness ratio between matrix-layers and interlayers tandard specimen, 3 mm thick, will change the absolute thickness of matrix-layers and interlayers respectively Fig. I (L-D curves) shows two typical load-displace- Therefore, thickness ratio (h=h2/hl, where h is the ment curves of Si3 N4/BN multilayer composite and layer thickness, the subscript I and 2 denoted the inter- conventional monolithic Si3 N4, respectively. It can be layer and matrix-layer, respectively)must be a sensitive seen that the Si3N4/BN multilayer composite exhibits a geometrical parameter influencing the mechanical non-brittle failure while the conventional monolithic properties of Si3 N4/BN multilayer ceramics. Fig. 3 hows the curves of the bending strength and work of fracture of the Si3 N,/BN multilayer materials with var- ious ih. With the increasing of the thickness ratio, the work of fracture increases firstly, and then levels off multilayer materials after about h=4-5. The similar curve of bending strength vs. layer thickness ratio is investigated from Fig 3 This can be easily understood from the structure of the Si3 N4/BN multilayer ceramics. With the increase of Zh, the matrix-layers become thicker, and the interlayers become thinner, correspondingly. In the Si3N4/BN multilayer ceramics, bending strength is mainly deter mined by matrix-layers, and work of fracture depends Displacement (um) on the crack deflection by the interlayer. Hence if the ih is Fig. 1. Typical lo cement curves of Si N /BN multilayer very small(about ih=2 in Fig 3), the thick and loose BN naterials and conven monolithic Si3N4 applies a large space and small resistance of transverse
was cast into tapes on a polyester film and formed green tapes with different thickness. The obtained tapes were dried in air and punched into a rectangle (3238 mm). Then the punched tapes were coated with slurry of BN (commercial powder), whose thickness was controlled by the slurry concentration and the immerging time in the slurry. The coated green tapes were dried and stacked into the graphite die. After the removal of the binder, the green body was hot pressed at 1820 C for 1.5 h in a flow on N2 atmosphere. The sintered specimens were sliced into test bars with the dimensions of 4336 mm for bending strength and 4630 mm for fracture toughness and work of fracture. A three-point bending test for bending strength was carried out at room temperature with a span of 30 mm and crosshead rate of 0.5 mm/min. The work of fracture was defined and calculated as the area under the load–displacement curve divided by two-fold of the cross-section area of the bend bar, which was measured by the single-edge-notch-beam method (SENB) at room temperature with a span of 24 mm and crosshead rate of 0.05 mm/min. Five specimens were tested for each test to get an average value. All the tests was performed on a A-2000 Shimadzu universal materials testing machine. The loads were applied perpendicular to the plane of the layers. The microstructure of the materials was observed by scanning electron microscope (SEM) of CSM950. 3. Results 3.1. Fracture behavior of the Si3N4/BN multilayer ceramics Fig. 1 (L–D curves) shows two typical load–displacement curves of Si3N4/BN multilayer composite and conventional monolithic Si3N4, respectively. It can be seen that the Si3N4/BN multilayer composite exhibits a non-brittle failure while the conventional monolithic Si3N4 fractures catastrophically. For the Si3N4/BN multilayer composite, after the first load drop, the load bearing ability of the testing bar still retains over 50% of the peak load. Until totally fractured, the Si3N4/BN multilayer composite gives a prolonged deflection besides the elastic deformation. This shows that the multilayer ceramic exhibits a different fracture behavior from that of the monolithic ceramic. Hence it may be inferred that the mechanical properties of ceramic materials can be substantially improved by a special structural design similar to that conducted on biomaterials as already indicated in the literature [2,5]. Fig. 2 shows the fracture behaviors of the Si3N4/BN multilayer ceramics. It can be observed from Fig. 2(a) that Si3N4 layers are about 80–100 mm thick and BN interlayers only 10–20 mm thick. The multilayer structure mainly contributes to high toughness of the Si3N4/BN multilayer composites. The main toughening mechanism of the multilayer composites is that the interlayer deflects the crack repeatedly [as shown in Fig. 2(a)], and there are other toughening mechanisms in the ceramics, such as crack bridging [Fig. 2(b)], friction and sliding [Fig. 2(c)], and matrix-layer pull-out [Fig. 2(d)] and so on. These toughening mechanisms from the interlayers are considered to mainly contribute to high fracture toughness and work of fracture of the multilayer composites because a large amount of fracture energy is absorbed during fracture. 3.2. Effect of thickness ratio (lh) At a given number of layers, the change of the thickness ratio between matrix-layers and interlayers in a standard specimen, 3 mm thick, will change the absolute thickness of matrix-layers and interlayers respectively. Therefore, thickness ratio (lh=h2/hl, where h is the layer thickness, the subscript 1 and 2 denoted the interlayer and matrix-layer, respectively) must be a sensitive geometrical parameter influencing the mechanical properties of Si3N4/BN multilayer ceramics. Fig. 3 shows the curves of the bending strength and work of fracture of the Si3N4/BN multilayer materials with various lh. With the increasing of the thickness ratio, the work of fracture increases firstly, and then levels off after about lh=4–5. The similar curve of bending strength vs. layer thickness ratio is investigated from Fig. 3. This can be easily understood from the structure of the Si3N4/BN multilayer ceramics. With the increase of lh, the matrix-layers become thicker, and the interlayers become thinner, correspondingly. In the Si3N4/BN multilayer ceramics, bending strength is mainly determined by matrix-layers, and work of fracture depends on the crack deflection by the interlayer. Hence, if the lh is very small (about lh=2 in Fig. 3), the thick and loose BN applies a large space and small resistance of transverse Fig. 1. Typical load–displacement curves of Si3N4/BN multilayer materials and conventional monolithic Si3N4. 442 Q. Zan et al. / Ceramics International 30 (2004) 441–446
0. Zan et al. Ceramics International 30(2004)441-446 180 (d) Fig. 2. SEM photographs of crack propagating paths in Si3N4/BN multilayer ceramics:(a) crack deflection;(b)crack bridging: (c) friction and sliding:(d)matrix-layer pull-out the preparation procedure becomes difficult, would lead to a defect in the interlayer increasing and lowering the strength of the multilayer material; on the other hand the too thin interlayer weakens the abil ity of deflecting crack, when the multilayer material is loaded, crack is difficult to deflect and propagate in the interlayer, in other words, the material is easy to frac ture catastrophically and low work of fracture obtained. these are the reasons that the two curves tend to level off when the layer thickness ratio is large enough Considering both bending strength and work of frac The Layer Thickness Ratio ture, a suitable value of layer thickness ratio is sug- Fig 3. Bending strength and work of fracture with various layer gested as about 10 in the multilayer structure design. thickness ratios(.. bending strength; - work of fracture) 3.3. Efect of layer number (N crack propagation, hence it will lower both the bending ih is too large (i.e. the matrix layer is too thick and e In the case of approximately fixed thickness ratio, for strength and work of fracture On the other hand if the mple about 10 for thickness ratio designed in the interlayer too thin), it is favorable to the strength present work, the effect of matrix-layer thickness on bviously. but, because of the interlayer being too thin, mechanical properties of the laminated Si3 n4/Bn cera-
crack propagation, hence it will lower both the bending strength and work of fracture. On the other hand, if the lh is too large (i.e. the matrix layer is too thick and interlayer too thin), it is favorable to the strength obviously. But, because of the interlayer being too thin, the preparation procedure becomes difficult, which would lead to a defect in the interlayer increasing largely and lowering the strength of the multilayer material; on the other hand the too thin interlayer weakens the ability of deflecting crack, when the multilayer material is loaded, crack is difficult to deflect and propagate in the interlayer, in other words, the material is easy to fracture catastrophically and low work of fracture is obtained. These are the reasons that the two curves tend to level off when the layer thickness ratio is large enough. Considering both bending strength and work of fracture, a suitable value of layer thickness ratio is suggested as about 10 in the multilayer structure design. 3.3. Effect of layer number (N) In the case of approximately fixed thickness ratio, for example, about 10 for thickness ratio designed in the present work, the effect of matrix-layer thickness on mechanical properties of the laminated Si3N4/BN ceraFig. 3. Bending strength and work of fracture with various layer thickness ratios (- - - bending strength; ––– work of fracture). Fig. 2. SEM photographs of crack propagating paths in Si3N4/BN multilayer ceramics: (a) crack deflection; (b) crack bridging; (c) friction and sliding; (d) matrix-layer pull-out. Q. Zan et al. / Ceramics International 30 (2004) 441–446 443
0. Zan et al. Ceramics International 30(2004)441-446 mIcs can be interpreted in terms of the effect of layer number(N)of a specimen with fixed thickness(3 mm). strength decreases with the layer number increasing. But the extent of decrease is very small(no more than 100 MPa), and with the layer number exceeding more than about 30, the curve tends to level off. For work of frac- Fig. 5. The illustration of the flexure test ture of the multilayer materials, a maximum is observed atN≈30 Similar to the analysis of the effect of thickness ratio width and span of the specimen are H, B and 2L in four on mechanical properties, the results above are also point bending, respectively. And some hypotheses are easily understood. Because the thickness of specimen is described as follows: (a) H/L<0. 2;(b) The ratio of fixed, the increase of layer number means the thickne flexibility [w(x)]and the curvature radius [p(x)] is far less decrease of both matrix-layer and interlayer. Obviously, than 1, i.e. w(x)lp(x)<<l;(c)h<<h2 this will reduce the strength of the materials. It is well The number of the matrix-layer (m) is odd, i.e known that work of fracture is determined by both dis- m= 2n-1, then H=mh-hy. Hence, the maximum ten tance and times of crack deflection [3]. With an increase sile stress and the maximum shear stress can be expres of layer number, the thickness of interlayers is deduced, sed a nd the following crack deflection distance is reduced At the same time. the crack deflection times are (mh-h) increased obviously because of the interlayer number is increasing. These two factors influence the work of fracture together, and will lead to an optimal value in various numbers of layers, which was determined to be about 30 in this experiment where M is the bending moment in the segment with the stress of pure bending, 2 is the equivalent bending 4. Analysis and Discussions rigidity, O is the shear stress, and S-max is the maximum equivalent static moment 4.1. Mechanical model of the Si3N4/ BN multilayer materials in bendt H/2 WB1 In order to simplify the calculation process, a for point bending test is used to analyze the stress of the multilayer ceramics, which is illustrated in Fig. 5. The BEc)ydy cimen possessed the following parameters: layer hickness(h1, h2), Youngs modulus(E, e2), and Pois- sons ratio(u1, U2), and the total thickness of a couple of matrix-layer and interlayer h=h1+hz. Total thickness, Sz.max= E(v)ydA EB E2-E1 (m2-1) 4.2. Bending strength analysis In the flexural test with the crosshead speed of 0 mm/min, the specimen will fracture by way of shear lapse or bending lapse due to the maximum shear stress (Tmax)or the m tensile stress(omax), respectively. The latter is more familiar to the Si3 N4/BN multilayer ceramics, when the expression below is satisfied: Fig 4. Bending strength and work of fract
mics can be interpreted in terms of the effect of layer number (N) of a specimen with fixed thickness (3 mm). According to Fig. 4, it is found that the bending strength decreases with the layer number increasing. But the extent of decrease is very small (no more than 100 MPa), and with the layer number exceeding more than about 30, the curve tends to level off. For work of fracture of the multilayer materials, a maximum is observed at N30. Similar to the analysis of the effect of thickness ratio on mechanical properties, the results above are also easily understood. Because the thickness of specimen is fixed, the increase of layer number means the thickness decrease of both matrix-layer and interlayer. Obviously, this will reduce the strength of the materials. It is well known that work of fracture is determined by both distance and times of crack deflection [3]. With an increase of layer number, the thickness of interlayers is deduced, and the following crack deflection distance is reduced. At the same time, the crack deflection times are increased obviously because of the interlayer number is increasing. These two factors influence the work of fracture together, and will lead to an optimal value in various numbers of layers, which was determined to be about 30 in this experiment. 4. Analysis and Discussions 4.1. Mechanical model of the Si3N4/BN multilayer materials in bending In order to simplify the calculation process, a fourpoint bending test is used to analyze the stress of the multilayer ceramics, which is illustrated in Fig. 5. The specimen possessed the following parameters: layer thickness (h1, h2), Young’s modulus (E1, E2), and Poisson’s ratio (1, 2), and the total thickness of a couple of matrix-layer and interlayer h=h1+h2. Total thickness, width and span of the specimen are H, B and 2L in fourpoint bending, respectively. And some hypotheses are described as follows: (a) H/2L40.2; (b) The ratio of flexibility [w(x)] and the curvature radius [(x)] is far less than 1, i.e. w(x)/(x)< <1; (c) h1< <h2. The number of the matrix-layer (m) is odd, i.e. m=2n1, then H=mhh1. Hence, the maximum tensile stress and the maximum shear stress can be expressed as: max ¼ E2M 2S ð Þ mh h1 ð1Þ max ¼ Q BS SZ;max ð2Þ where M is the bending moment in the segment with the stress of pure bending, is the equivalent bending rigidity, Q is the shear stress, and Sz,max is the maximum equivalent static moment: M ¼ ðH=2 H=2 WBy2 dy ð3Þ S ¼ ðH=2 H=2 BE yð Þy2 dy ð4Þ SZ;max ¼ ð A E yð ÞydA ¼ E2B 8 H2 h2 2 E2 E1 8 Bhh1 m2 1 ð5Þ 4.2. Bending strength analysis In the flexural test with the crosshead speed of 0.5 mm/min, the specimen will fracture by way of shear lapse or bending lapse due to the maximum shear stress (max) or the maximum tensile stress (max), respectively. The latter is more familiar to the Si3N4/BN multilayer ceramics, when the expression below is satisfied: max max 5 b i ð6Þ Fig. 4. Bending strength and work of fracture with a various number of layers (- - - bending strength; ––– work of fracture). Fig. 5. The illustration of the flexure test. 444 Q. Zan et al. / Ceramics International 30 (2004) 441–446
0. Zan et al. Ceramics International 30(2004)441-446 where omax is the strength of the matrix- layer, Tmax is the ted into interlayer and propagates along the shear strength of the interlayer interlayer between the fractured matrix -layer and to the eq. (1)and below. Such through-thickness an fracture condition of omax Ob, the expression of the interfacial cracking then takes place alternately bending moment is until the beam is completely broken 2Σb The through-thickness cracks occur in the center Mh= of the beam and the interfacial cracks propagate trically the cer For monolithic sina ceramic 3. It is assumed that the portion of a layer between the through-thickness crack and the tip of an naxBH2b Mo BH2ob 6M interfacial crack (a"debonded ligament")can 6 carry no load and that such ligaments do not interfere with each other Now the decreasing coefficient (x) of the bending 4. The critical strain energy release rate, Tm, of strength is defined by through-thickness crack propagation is mainly determined by the matrix- layer. Because of the presence of weal ng dyer, (1-)m=0+m21 critical strain energy release rate, Tv, can be expressed as T Imh2/h+rh/h according to the (m -ih) mixed rule. In general, p; appears to be depen- dent he balance of opening to shearing where /e is ratio of Youngs modulus (E2/E1), and its modes. This is commonly characterized by the value is larger than 10 in this material O-called phase angle of loading, y, defined as the From the expression [Eq(9). the strength curve with angle having a tangen to the ratio of the various thickness ratio (h) and layer number (N)is shearing intensity fac obtained and illustrated in Figs. 6 and 7. The trends of During delamination bending. the crack he two curves are similar to experimental results( Figs. 3 tip loading is strongly mixed mode and the value and 4) of y is thought to remain approximately constant of40-60° 43. Toughness analysis Considering the hypotheses and using the model According to the propagation conditions of long- above, we can plot the curve of load-displacement in itudinal and interfacial crack, a hypothesis of crack the case of given structural and geometrical factors of propagation process was made as follows [7, 8 the multilayer materials. According to the area of load- displacement curve, the work of fracture can be calcu 1. Displacement loading mode was used. The lated(the details of algorithm and calculation process sequence of events is that a crack propagates about the model were discussed in Ref [9]). The work of instantaneously through the topmost layer (in the fracture of the multilayer material with a different through-thickness direction), and then is deflec- number of layers(N) and thickness ratio of layers(h2/ 50 N, the number of layers Fig. 6. Calculated result about the mechanical properties with various layer thickness ratios(-Ko/oo: -w/Wo
where max is the strength of the matrix-layer, max is the shear strength of the interlayer. For this material, according to the Eq. (1) and the fracture condition of max ¼ b; the expression of the bending moment is: Mb ¼ 2Sb e2H ð7Þ For monolithic Si3N4 ceramic: 0 max ¼ 6M BH2 ¼ b M0 b ¼ BH2b 6 ð8Þ Now the decreasing coefficient () of the bending strength is defined by: ¼ Mb M0 b ¼ 1 1 1 le ð Þ m 1 l2 h þ m mð Þ 2 lh ð Þ m lh 3 ð9Þ where le is ratio of Young’s modulus (leE2/E1), and its value is larger than 10 in this material. From the expression [Eq. (9)], the strength curve with various thickness ratio (lh) and layer number (N) is obtained and illustrated in Figs. 6 and 7. The trends of the two curves are similar to experimental results (Figs. 3 and 4). 4.3. Toughness analysis According to the propagation conditions of longitudinal and interfacial crack, a hypothesis of crack propagation process was made as follows [7,8]: 1. Displacement loading mode was used. The sequence of events is that a crack propagates instantaneously through the topmost layer (in the through-thickness direction), and then is deflected into interlayer and propagates along the interlayer between the fractured matrix-layer and the one below. Such through-thickness and interfacial cracking then takes place alternately until the beam is completely broken. 2. The through-thickness cracks occur in the center of the beam and the interfacial cracks propagate symmetrically from the center. 3. It is assumed that the portion of a layer between the through-thickness crack and the tip of an interfacial crack (a ‘‘debonded ligament’’) can carry no load and that such ligaments do not interfere with each other. 4. The critical strain energy release rate, Gm, of through-thickness crack propagation is mainly determined by the matrix-layer. Because of the presence of weak bonding interlayer, the total critical strain energy release rate, Gv, can be expressed as vmh2/h+ih1/h according to the mixed rule. In general, i appears to be dependent on the balance of opening to shearing modes. This is commonly characterized by the so-called phase angle of loading, , defined as the angle having a tangent equal to the ratio of the shearing to opening stress intensity factors. During delamination under bending, the crack tip loading is strongly mixed mode and the value of is thought to remain approximately constant in the range of 40–60. Considering the hypotheses and using the model above, we can plot the curve of load–displacement in the case of given structural and geometrical factors of the multilayer materials. According to the area of load– displacement curve, the work of fracture can be calculated (the details of algorithm and calculation process about the model were discussed in Ref. [9]). The work of fracture of the multilayer material with a different number of layers (N) and thickness ratio of layers (h2/ Fig. 6. Calculated result about the mechanical properties with various layer thickness ratios (- - - k,=0; —— W=W0). Fig. 7. Calculated results about the mechanical properties with various numbers of layers (- - - k,=0; —— W=W0). Q. Zan et al. / Ceramics International 30 (2004) 441–446 445
0. Zan et al. Ceramics International 30(2004)441-446 h,)are plotted in Figs. 6 and 7, respectively, where w(2)Keeping the layer thickness ratio of about 10 and and Wo are the work of fracture of multilayered Si3N4/ increasing the number of layers, the bending strength BN and monolithic SI3 N4 ceramics respectively decreases slightly, and a maximal toughness was Comparing Figs 6 and 7 to Figs. 3 and 4, the similar obtained at NA30 curve trend was found, but different critical points and ()According to the mechanical model arid experi- absolute value of mechanical properties. That is because mental results, it is suggested that the number of layers of the following two reasons. On the one hand, in the and ratio of layer thickness are 30 and 10 in structural model calculation only the absorbed energy by the crack design. deflection is calculated. However, in fact many other toughening mechanisms in Si3 N4/BN multilayer materi- als were identified, such as bridging, frictional sliding, References whisker toughening, and so on [2, 3, 5]. A mass of energy absorbed during the fracture process by these [I] W.J. Clegg, K. Kendall, NMcN. Alford, T.W. Button, mechanisms. On the other hand. some defects will be J D. Birchall, A simple way to make tough ceramics, Nature unavoidably introduced into the multilayer materials in London)347(1990 fabrication processing; therefore the me 2]H. Liu, S.M. Hsu, Fracture behavior of multilayer silicon nitride/ canicE al boron nitride ceramics, J. Am. Ceram Soc. 79(1996)2452-2457. erties of the multilayer materials are lower than those 3 D. Kovar, M.D. Thouless, J.W. Halloran, Crack deflection and calculated results by the model propagation in layered silicon nitride/boron nitride ceramics According to the above four figures, synthetically Am. Ceran.Soc.81(1998)10041012 considering bending strength and work of fracture 4Y. Huang, H. Guo, Z P. Xie, The fine micro-structure of inter- optimal geometrical factors are selected as ih 10 and face layer for laminated Si]N4 ceramics, J. Mater. Sci. Lett. 17 (1998)569-571 5 C.A. Wang. Y. Huang, Q F Zan, H. Guo, S.Y. Cai, Biomimetic for Si3N4 layer and 10 um for bn layer) for work of ructure design-a possible approach to change the brittleness of fracture reaching optimum and bending strength t. Sci. Eng. C: Biomimetic and Supra- maining relative high level. molecular Systems 11(2000)9-12. 6 S.Y. Cai, PhD Dissertation, Tsinghua University, 1998 [7 C.A. Folsom, F.w. Zok, F.F. Lange, Flexural properties of brit- tle multilayer materials: I, modelling, J. Am. Ceram. Soc. 77 5. Conclusions (1994)689696 [8A.J. Phillipps, W.J. Clegg, T.w. Clyne, Fracture behavior of (1)At a given number of layers, with the increase of ramic laminates in bending--l. modeling of crack propagation, layer thickness ratio in a range, the toughness and Acta Metall. Mater. 41(1993)805-817. 9x.H. Guo, Q.H. Cai, C.A. Wang, Y Huang, A mechanics ana- bending strength both increase, and when it continues lysis of strengthening toughening design of multilayer structure increasing, the two curves both level off. ceramics. Acta Mech. Solid Sina 21(2000)313-324
h1) are plotted in Figs. 6 and 7, respectively, where W and W0 are the work of fracture of multilayered Si3N4/ BN and monolithic S13N4 ceramics respectively. Comparing Figs. 6 and 7 to Figs. 3 and 4, the similar curve trend was found, but different critical points and absolute value of mechanical properties. That is because of the following two reasons. On the one hand, in the model calculation only the absorbed energy by the crack deflection is calculated. However, in fact many other toughening mechanisms in Si3N4/BN multilayer materials were identified, such as bridging, frictional sliding, whisker toughening, and so on [2,3,5]. A mass of energy is absorbed during the fracture process by these mechanisms. On the other hand, some defects will be unavoidably introduced into the multilayer materials in fabrication processing; therefore the mechanical properties of the multilayer materials are lower than those calculated results by the model. According to the above four figures, synthetically considering bending strength and work of fracture, optimal geometrical factors are selected as lh10 and N30 (corresponding to a thickness of about 100 mm for Si3N4 layer and 10 mm for BN layer) for work of fracture reaching optimum and bending strength remaining relative high level. 5. Conclusions (1) At a given number of layers, with the increase of layer thickness ratio in a range, the toughness and bending strength both increase, and when it continues increasing, the two curves both level off. (2) Keeping the layer thickness ratio of about 10 and increasing the number of layers, the bending strength decreases slightly, and a maximal toughness was obtained at N30. (3) According to the mechanical model arid experimental results, it is suggested that the number of layers and ratio of layer thickness are 30 and 10 in structural design. References [1] W.J. Clegg, K. Kendall, N.McN. Alford, T.W. Button, J.D. Birchall, A simple way to make tough ceramics, Nature (London) 347 (1990) 455–457. [2] H. Liu, S.M. Hsu, Fracture behavior of multilayer silicon nitride/ boron nitride ceramics, J. Am. Ceram. Soc. 79 (1996) 2452–2457. [3] D. Kovar, M.D. Thouless, J.W. Halloran, Crack deflection and propagation in layered silicon nitride/boron nitride ceramics, J. Am. Ceram. Soc. 81 (1998) 1004–1012. [4] Y. Huang, H. Guo, Z.P. Xie, The fine micro-structure of interface layer for laminated Si3N4 ceramics, J. Mater. Sci. Lett. 17 (1998) 569–571. [5] C.A. Wang, Y. Huang, Q.F. Zan, H. Guo, S.Y. Cai, Biomimetic structure design—a possible approach to change the brittleness of ceramics in nature, Mat. Sci. Eng. C: Biomimetic and Supramolecular Systems 11 (2000) 9–12. [6] S.Y. Cai, PhD Dissertation, Tsinghua University, 1998. [7] C.A. Folsom, F.W. Zok, F.F. Lange, Flexural properties of brittle multilayer materials: I, modelling, J. Am. Ceram. Soc. 77 (1994) 689–696. [8] A.J. Phillipps, W.J. Clegg, T.W. Clyne, Fracture behavior of ceramic laminates in bending—I. modeling of crack propagation, Acta Metall. Mater. 41 (1993) 805–817. [9] X.H. Guo, Q.H. Cai, C.A. Wang, Y. Huang, A mechanics analysis of strengthening toughening design of multilayer structure ceramics, Acta Mech. Solid Sina 21 (2000) 313–324. 446 Q. Zan et al. / Ceramics International 30 (2004) 441–446
