《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_fibrous monoliths-14

Part A: applied scienc and manufacturing ELSEVIER Composites: Part A 32(2001)173-178 Coefficients of thermal expansion of some laminated ceramic composites G M. Gladysz,. K.K. Chawl PLos Alamos National Laboratory, ESA-WMM MS C930, Los Alamos, NM 87545, US Department of Materials and Mechanical Engineering. University of Alabama at Birmingham, 254 BEC, 1530 3rd Ave South, Birmingham, AL 35294, USA Received 14 October 1998, revised 9 June 2000; accepted 4 August 2000 Abstract The coefficients of thermal expansion(CTE) were determined for several non-fibrous alumina-based laminated ceramic composites. The results were compared with the Cte values predicted by the modified equations of Schapery and Chamis. Both models are identical in the ongitudinal direction and showed differences from experimental CTE of 2.3 and 4. 1% for alumina/barium zirconate(AlO,/BaZrO3)and alumina/tin dioxide(Al,O,/SnO,)composites, respectively. For AL,O,/BazrO3 in the transverse direction, Schapery's model showed a 1.9% difference while Chamis model showed a 7. 5%difference. For the AlO3/SnO in the transverse direction, Schapery's model had an 8.2% difference while Chamis' model showed only a 2.3% difference Results for alumina/calcium titanate(Al,,/CaTiO3)laminates showed larger differences, 27.6% in longitudinal CTE and differences of 9.6 and 19.8% transverse CtE for the Schapery and Chamis models, respectively. These differences were attributed to the formation of cracks that occurred in this composite system during processing because of the large CTE mismatch between Al2O3 and CaTiO3. Results for Al2O/BaZrO3 and Al2O SnO composites showed that for continuous minae both the Schapery and Chamis models were adequate predictors of Cte for the systems. C 2001 Elsevier Science Ltd. All rights reserved Keyword: Laminated ceramic composites 1. Introduction expansion is defined as the ratio of the change in length per unit length per unit change in temperature [17]. The Recently, there has been a growing interest in the proces- new length(L)can be expressed as sing and characterization of tough laminated ceramic and glass-based composites [1-15]. Laminates are attractive L=Lo(1+a△ materials because they are inexpensive to produce an compared with fiber composites, the volume fraction of components can be easily controlled, and they have gener △T=(72-T1) ally superior flexure properties. A major aim of the research where L is the length at T2, Lo the length at T1, and a is the ffort in the area of ceramic matrix composites(CMC)is to coefficient of linear thermal expansion. The coefficient a develop damage tolerant, load-bearing structural compo- varies with temperature and usually an average Cte is nents. However, little, if any, work has been devoted to determined and used over the temperature range of interest e characterization of the coefficients of thermal expansio Several models have been developed for predicting the (CTE)of these materials. An understanding and ability to coefficient of thermal expansion of composite materials predict the CtE in laminates is an important design criterion [18-23]. Vaidya et al. [24] and Bowles and Tompkins for producing dimensionally stable structures, especially if [25] compared the predictions of some of these models they are assemblages of many different types of materials. with experimental data. Vaidya used ceramic fiber/glass The increasing amplitude of vibration of atoms with matrix system with several fiber volume fractions and increasing temperature causes thermal expansion. This showed that expressions for transverse Cte due to Schapery increased amplitude generally causes an increase in the [20] best predicted the results. Bowles and Tompkins [251 average interatomic distance [16], thus increasing the length did a sensitivity analysis as well as a comparison to experi or volume of a sample. The coefficient of linear thermal mental results for unidirectional fiber composites. They concluded that all of the models [ 18-21, 23] predicted simi- 4 Corresponding author. Fax: +1-505-665-5548 lar values for CTE along the fiber length. However, they E-mail address: gladysz @lanl. gov (G.M. Gladysz). were not all in good agreement in the transverse direction 1359-835X/01/S- see front matter 2001 Elsevier Science Ltd. All rights reserved Pl:S1359-835X(00)00144-5

Coefficients of thermal expansion of some laminated ceramic composites G.M. Gladysza,*, K.K. Chawlab a Los Alamos National Laboratory, ESA-WMM, MS C930, Los Alamos, NM 87545, USA b Department of Materials and Mechanical Engineering, University of Alabama at Birmingham, 254 BEC, 1530 3rd Ave. South, Birmingham, AL 35294, USA Received 14 October 1998; revised 9 June 2000; accepted 4 August 2000 Abstract The coefficients of thermal expansion (CTE) were determined for several non-fibrous alumina-based laminated ceramic composites. The results were compared with the CTE values predicted by the modified equations of Schapery and Chamis. Both models are identical in the longitudinal direction and showed differences from experimental CTE of 2.3 and 4.1% for alumina/barium zirconate (Al2O3/BaZrO3) and alumina/tin dioxide (Al2O3/SnO2) composites, respectively. For Al2O3/BaZrO3 in the transverse direction, Schapery’s model showed a 1.9% difference while Chamis’ model showed a 7.5% difference. For the Al2O3/SnO2 in the transverse direction, Schapery’s model had an 8.2% difference while Chamis’ model showed only a 2.3% difference. Results for alumina/calcium titanate (Al2O3/CaTiO3) laminates showed larger differences, 27.6% in longitudinal CTE and differences of 9.6 and 19.8% transverse CTE for the Schapery and Chamis models, respectively. These differences were attributed to the formation of cracks that occurred in this composite system during processing because of the large CTE mismatch between Al2O3 and CaTiO3. Results for Al2O3/BaZrO3 and Al2O3/SnO2 composites showed that for continuous laminae both the Schapery and Chamis models were adequate predictors of CTE for the systems. q 2001 Elsevier Science Ltd. All rights reserved. Keyword: Laminated ceramic composites 1. Introduction Recently, there has been a growing interest in the proces￾sing and characterization of tough laminated ceramic and glass-based composites [1–15]. Laminates are attractive materials because they are inexpensive to produce compared with fiber composites, the volume fraction of components can be easily controlled, and they have gener￾ally superior flexure properties. A major aim of the research effort in the area of ceramic matrix composites (CMC) is to develop damage tolerant, load-bearing structural compo￾nents. However, little, if any, work has been devoted to the characterization of the coefficients of thermal expansion (CTE) of these materials. An understanding and ability to predict the CTE in laminates is an important design criterion for producing dimensionally stable structures, especially if they are assemblages of many different types of materials. The increasing amplitude of vibration of atoms with increasing temperature causes thermal expansion. This increased amplitude generally causes an increase in the average interatomic distance [16], thus increasing the length or volume of a sample. The coefficient of linear thermal expansion is defined as the ratio of the change in length per unit length per unit change in temperature [17]. The new length (L) can be expressed as: L ˆ L0…1 1 aDT† and DT ˆ …T2 2 T1† where L is the length at T2, L0 the length at T1, and a is the coefficient of linear thermal expansion. The coefficient a varies with temperature and usually an average CTE is determined and used over the temperature range of interest. Several models have been developed for predicting the coefficient of thermal expansion of composite materials [18–23]. Vaidya et al. [24] and Bowles and Tompkins [25] compared the predictions of some of these models with experimental data. Vaidya used ceramic fiber/glass matrix system with several fiber volume fractions and showed that expressions for transverse CTE due to Schapery [20] best predicted the results. Bowles and Tompkins [25] did a sensitivity analysis as well as a comparison to experi￾mental results for unidirectional fiber composites. They concluded that all of the models [18–21,23] predicted simi￾lar values for CTE along the fiber length. However, they were not all in good agreement in the transverse direction Composites: Part A 32 (2001) 173–178 1359-835X/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S1359-835X(00)00144-5 www.elsevier.com/locate/compositesa * Corresponding author. Fax: 11-505-665-5548. E-mail address: gladysz@lanl.gov (G.M. Gladysz)

G.M. Gladys=, K.K. Chawla/Composites: Part A 32 (2001)173-178 Table 1 and transverse directions as [201 Hot pressing parameters of the laminates used for CTE measurments Composite Temperature Pressure Time Atmosphere ar=y=a=q,E,V, +a,,v2 EIVi+ E2v2 MPa) a1≡(1+n)a1V1+(1+n)a22-a AlOy/, 1400 D=v,1+ 1v2 due to poisson 's ratio effect. models that took this effect into and a is the CTE, E Youngs modulus, v Poisson's ratio account were much closer to experiment and v is the volume fraction. The subscripts I and 2 indicate ulati and Plummer [22] developed an expression longitudinal Cte for laminated plates and axial CTE the components of the composite(indicated by c), and the subscripts I and t indicate the longitudinal and transverse or laminated cylinders. The expression for laminated directions, respectively plates, most relevant to this paper, was developed for Chamis used a force balance to derive expressions for n different materials and is similar to Schapery's longitudinal and transverse CTE for transversely isotropic expression for longitudinal CTE. However, they did fibers embedded in an isotropic matrix. The expression for not formulate expressions for transverse CTE Chamber longitudinal CTe is identical to that of Schapery. The trans- lins expression for longitudinal CTE is identical to that verse CTE expression, simplified for the isotropic nature of due to Schapery [20] and Chamis [19 but the trans- the second phase, is verse expression contained a packing factor term which is not applicable to this paper at= a2 In this paper, the Cte results for some laminated ceramic +(-5(+2 omposites were obtained experimentally and compared with the values predicted by the models for fiber composites due to Schapery [20] and Chamis[19]. Since the Cte of E12= E1 I +E2/2 laminated, non-fibrous, composites is of concern, one of a is the CTE, E Young s modulus, v Poisson s ratio, andV our aims was to check the validity of applying these models is the volume fraction. The subscripts I and 2 indicate the to laminates. The assumptions of these models were modi- fied to reflect the use of laminae rather than fibers. They are components of the composite and the subscript t indicates the transverse direction as follows:(a)bonding at the interface between adjacent laminae is perfect and mechanical in nature,(b) laminae are continuous and perfectly aligned, and(c) properties of 2. Materials and procedure the constituents do not vary with temperature. In a laminated composite, the Cte (as well as other The starting powders of Al2O3 and SnO2 were obtained physical properties)will be identical in any in-plane direc- from Baikowski and Aldrich, respectively. The Al203 was tion, specifically in the directions indicated by the x and y 99.99 pure with a grain size between 1 and 2 um. The axes in Fig. 1. We define the longitudinal CTE (ad)as the SnO2 was 99. pure with a particle size <44 um. Both coefficient of thermal expansion in the x or y direction and BazrO3 and CaTiO, were purchased from Alpha Aesar and the transverse CTE(a)as the coefficient of thermal expan- had grain sizes between I and 2 um. Both had a purity of sion in the z or thickness direction. as shown in Fig. 1. Note 99+% metals basis that in a unidirectional fiber composite a, a. because of Laminated composites were fabricated by tape ca transverse isotropy. The Schapery equations modified for individual powders followed by hot pressing. Table I laminated composites give the CTe in the longitudinal shows the processing conditions used to fabricate laminated The cte of each material was determined with an Orton 1000D Dilatometer that had temperature range between ambient and 1000C. The cte for each monolithic material except for SnO2, was first determined followed by the Cte omposite. The CTE btained from earlier work[26]. The temperature cycle for each monolithic material and composite in the dilatometer was as follows: (a) I Baikowski International Corporation, Charlotte, NC 2 Aldrich Chemical Company, Inc. Milwaukee, WI Alpha Aesar, Ward Hill, MA Fig. 1 Schematic defining the 3D axes in a laminate composite The Edward Orton Jr. Foundation, Westerville, OH

due to Poisson’s ratio effect. Models that took this effect into account were much closer to experimental values. Gulati and Plummer [22] developed an expression for longitudinal CTE for laminated plates and axial CTE for laminated cylinders. The expression for laminated plates, most relevant to this paper, was developed for n different materials and is similar to Schapery’s expression for longitudinal CTE. However, they did not formulate expressions for transverse CTE. Chamber￾lin’s expression for longitudinal CTE is identical to that due to Schapery [20] and Chamis [19] but the trans￾verse expression contained a packing factor term which is not applicable to this paper. In this paper, the CTE results for some laminated ceramic composites were obtained experimentally and compared with the values predicted by the models for fiber composites due to Schapery [20] and Chamis[19]. Since the CTE of laminated, non-fibrous, composites is of concern, one of our aims was to check the validity of applying these models to laminates. The assumptions of these models were modi- fied to reflect the use of laminae rather than fibers. They are as follows: (a) bonding at the interface between adjacent laminae is perfect and mechanical in nature, (b) laminae are continuous and perfectly aligned, and (c) properties of the constituents do not vary with temperature. In a laminated composite, the CTE (as well as other physical properties) will be identical in any in-plane direc￾tion, specifically in the directions indicated by the x and y axes in Fig. 1. We define the longitudinal CTE (al) as the coefficient of thermal expansion in the x or y direction and the transverse CTE (at) as the coefficient of thermal expan￾sion in the z or thickness direction, as shown in Fig. 1. Note that in a unidirectional fiber composite ay ˆ az because of transverse isotropy. The Schapery equations modified for laminated composites give the CTE in the longitudinal and transverse directions as [20]: ax ˆ ay ˆ al ˆ a1E1V1 1 a2E2V2 E1V1 1 E2V2 az ˆ at ù …1 1 n1†a1V1 1 …1 1 n2†a2V2 2 aln where n ˆ n1V1 1 n2V2 and a is the CTE, E Young’s modulus, n Poisson’s ratio, and V is the volume fraction. The subscripts 1 and 2 indicate the components of the composite (indicated by c), and the subscripts l and t indicate the longitudinal and transverse directions, respectively. Chamis used a force balance to derive expressions for longitudinal and transverse CTE for transversely isotropic fibers embedded in an isotropic matrix. The expression for longitudinal CTE is identical to that of Schapery. The trans￾verse CTE expression, simplified for the isotropic nature of the second phase, is: at ˆ a2  V2 p 1 …1 2  V2 p † 1 1 V2n1E2 E12  a1 where E12 ˆ E1V1 1 E2V2 a is the CTE, E Young’s modulus, n Poisson’s ratio, and V is the volume fraction. The subscripts 1 and 2 indicate the components of the composite and the subscript t indicates the transverse direction. 2. Materials and procedure The starting powders of Al2O3 and SnO2 were obtained from Baikowski 1 and Aldrich, 2 respectively. The Al2O3 was 99.99 % pure with a grain size between 1 and 2 mm. The SnO2 was 99.9% pure with a particle size ,44 mm. Both BaZrO3 and CaTiO3 were purchased from Alpha Aesar 3 and had grain sizes between 1 and 2 mm. Both had a purity of 99 1 % metals basis. Laminated composites were fabricated by tape casting individual powders followed by hot pressing. Table 1 shows the processing conditions used to fabricate laminated composites. The CTE of each material was determined with an Orton4 1000D Dilatometer that had temperature range between ambient and 10008C. The CTE for each monolithic material, except for SnO2, was first determined followed by the CTE for the composite. The CTE of SnO2 was obtained from an earlier work[26]. The temperature cycle for each monolithic material and composite in the dilatometer was as follows: (a) 174 G.M. Gladysz, K.K. Chawla / Composites: Part A 32 (2001) 173–178 Table 1 Hot pressing parameters of the laminates used for CTE measurments Composite Temperature (8C) Pressure (MPa) Time (h) Atmosphere Al2O3/BaZrO3 1475 60 1 Vacuum Al2O3/SnO2 1400 30 0.67 Air Al2O3/CaTiO3 1400 60 1 Vacuum Fig. 1. Schematic defining the 3D axes in a laminate composite. 1 Baikowski International Corporation, Charlotte, NC. 2 Aldrich Chemical Company, Inc. Milwaukee, WI. 3 Alpha Aesar, Ward Hill, MA. 4 The Edward Orton Jr. Foundation, Westerville, OH

G.M. Gladys, K.K. Chala/Composites: Part A 32(2001)173-178 Youngs modulus and Poisson's ratio for the monolithic materials for calcu- Sn( BaZrO3 and CaTiO,. The Cte value of 5.30 X 10 fo lO2 was determined in previous research [26] lating theoretical CTE values same dilatometer as in this study. The average CTE values Component Youngs modulus(GPa) Poisson's ratio for SnO2, Al2O,, BaZrO3 and CaTiO, between 35 and 1000 C are listed in Table 3. No phase transitions occur in these material Bazoo, perature range Sno2[26 3.2. laminates 3.2.1. Efects of residual stresses ambient to 1000°C,(b)1000-150°C,and(c)150-1000°C The residual stresses produced in composite structures The linear range for determining CTE was taken between have their origins in the CTE mismatch of the bonded mate- 150and925C rials. In both fiber and laminate composites, high interfacial The CTe was calculated for each heating segment of the shear stresses can induce delamination; however,high resi- cycle. The sample dimensions were approximatel dual tensile stresses can cause cracking and lower the 25mm×5.5mm×30mm. The raw data were imported strength as shown in Fig. 3. In general, when a CMC is to spreadsheet computer software and the cte was deter- fabricated, bonding between the components takes place mined as the slope of the best-fit line of the percent linear at relatively high temperatures. On cooling, one of the change(PLC)vS temperature curve. The elastic constants components contracts less than the other. For the case of for these materials can be found in Table 2. The volume multiple laminae in a bi-component laminated ceramic fraction data of the composites were obtained from image omposite, on cooling from high temperature the compo- analysis of optical micrographs nent with the smaller Cte will be compression while the component with larger CTE will be in tension To better understand the magnitude of the tensile stress 3. Results and discussion that causes these vertical cracks in CaTiO3 laminae consider the following simple equation for calculating the 31. Monolithic materials thermal str =△aE△T The cte of each monolithic material was determined Percent linear change(PLC) vS temperature for alumina where o is the stress, Aa the difference in Cte of the is shown in Fig. 2. The average CTE for AlO3 is given in bonded materials, E Youngs modulus, and AT is the Table 3. An experimental difference of 7% was obtained temperature change. The change in temperature will be between literature and the measured cte values for taken as 1000C. Substituting 280 GPa and alumina. Curves, similar to Fig. 2, were obtained for 4.31x 10K for E and Aa, respectively, a stress of 1.2 GPa is obtained. Because CaTiO3 has a larger CTE 0.9 than Al2O3, theoretically this magnitude of tensile stress 0.8 will develop in CaTiO3. This stress is large enough to cause cracks in the CaTiO3 laminae during cooling after 3.2.2. Longitudinal CTE The volume fractions of laminates determined by image analysis of optical micrographs are given in Table 4. A graph of the PLC as a function of temperature for an Al2O,/SnO laminated composite in the longitudinal direc- 0.3 I st Heating tion is shown in Fig 4 and is typical of the data obtained fo all samples 0.2 2nd Heating Table 5 compares the experimental CTE in the longitu- 0.1 dinal direction (i.e. in the plane of laminate)and the theo- retical values obtained from Schapery s/Chamis model 0 There is very good agreement between experimental values 02004006008001000 and theoretical predications for AlO /BaZrO3 and AlO3/ SnO2 laminates, difference between the experimental and Temperature, C theoretical is 2.8 and 5.5%, respective goo agreement in AL,O, /BaZrO3 even though it is known that Fig. 2. Percent linear change(PLC)vs temperature for monolithic Al],. an interfacial reaction occurs during hot pressing [27]

ambient to 10008C, (b) 1000–1508C, and (c) 150–10008C. The linear range for determining CTE was taken between 150 and 9258C. The CTE was calculated for each heating segment of the cycle. The sample dimensions were approximately 25 mm × 5.5 mm × 3.0 mm. The raw data were imported to spreadsheet computer software and the CTE was deter￾mined as the slope of the best-fit line of the percent linear change (PLC) vs. temperature curve. The elastic constants for these materials can be found in Table 2. The volume fraction data of the composites were obtained from image analysis of optical micrographs. 3. Results and discussion 3.1. Monolithic materials The CTE of each monolithic material was determined. Percent linear change (PLC) vs. temperature for alumina is shown in Fig. 2. The average CTE for Al2O3 is given in Table 3. An experimental difference of 7% was obtained between literature and the measured CTE values for alumina. Curves, similar to Fig. 2, were obtained for BaZrO3 and CaTiO3. The CTE value of 5.30 × 1026 for SnO2 was determined in previous research [26] using the same dilatometer as in this study. The average CTE values for SnO2, Al2O3, BaZrO3 and CaTiO3 between 35 and 1000 8C are listed in Table 3. No phase transitions occur in these materials in the temperature range used for this study. 3.2. Laminates 3.2.1. Effects of residual stresses The residual stresses produced in composite structures have their origins in the CTE mismatch of the bonded mate￾rials. In both fiber and laminate composites, high interfacial shear stresses can induce delamination; however, high resi￾dual tensile stresses can cause cracking and lower the strength as shown in Fig. 3. In general, when a CMC is fabricated, bonding between the components takes place at relatively high temperatures. On cooling, one of the components contracts less than the other. For the case of multiple laminae in a bi-component laminated ceramic composite, on cooling from high temperature the compo￾nent with the smaller CTE will be compression while the component with larger CTE will be in tension. To better understand the magnitude of the tensile stress that causes these vertical cracks in CaTiO3 laminae, consider the following simple equation for calculating the thermal stress: s ˆ DaEDT where s is the stress, Da the difference in CTE of the bonded materials, E Young’s modulus, and DT is the temperature change. The change in temperature will be taken as 10008C. Substituting 280 GPa and 4.31 × 1026 K21 for E and Da, respectively, a stress of 1.2 GPa is obtained. Because CaTiO3 has a larger CTE than Al2O3, theoretically this magnitude of tensile stress will develop in CaTiO3. This stress is large enough to cause cracks in the CaTiO3 laminae during cooling after hot pressing. 3.2.2. Longitudinal CTE The volume fractions of laminates determined by image analysis of optical micrographs are given in Table 4. A graph of the PLC as a function of temperature for an Al2O3/SnO2 laminated composite in the longitudinal direc￾tion is shown in Fig. 4 and is typical of the data obtained for all samples. Table 5 compares the experimental CTE in the longitu￾dinal direction (i.e. in the plane of laminate) and the theo￾retical values obtained from Schapery’s/Chamis’ model. There is very good agreement between experimental values and theoretical predications for Al2O3/BaZrO3 and Al2O3/ SnO2 laminates, difference between the experimental and theoretical is 2.8 and 5.5%, respectively. Note the good agreement in Al2O3/BaZrO3 even though it is known that an interfacial reaction occurs during hot pressing [27]. G.M. Gladysz, K.K. Chawla / Composites: Part A 32 (2001) 173–178 175 Table 2 Young’s modulus and Poisson’s ratio for the monolithic materials for calcu￾lating theoretical CTE values Component Young’s modulus (GPa) Poisson’s ratio Al2O3 380 0.26 BaZrO3 220 0.25 CaTiO3 280 0.25 SnO2 [26] 253 0.293 Fig. 2. Percent linear change (PLC) vs. temperature for monolithic Al2O3

G.M. Gladys=, K.K. Chawla/Composites: Part A 32 (2001)173-178 Table 3 Table 4 Average coefficient of thermal expansion of monolithic materials over the Volume fractions of the laminates used for determining CTE temperature range 35-1000C Laminate type Alumina vol fraction Vol fraction of phase 2 Component a(10-6K-) Sno [26 5.80 develops and if the CTEs of these products are relatively small, they could reduce the Cte of the composite. This is These reaction products were not taken into account in theo- not likely to be very significant however, because the retical calculations of Cte because of their insignificantly volume fraction of this reaction zone is practically negligi small volume fraction in the Al2O /BaZrO3 system. It may ble compared with the volume fractions of the Al203 and be pointed out that there is no interfacial reaction between CaTiO3 in the sample Al2O3 and SnO2 28 The difference between CtE values for the AlO /CaTiO3 laminate was large, see Table 5. The experimental CTE 3.2.3. Transverse CTE Table 4 gives the volume fractions of the composi ence of 27. 7% The CTE of the composite was significantly samples tested for transverse CTE. A representative PLC caused by the presence of the vertical cracks in the shown in Fig. 5 CaTiO3 laminae, see Fig. 3. These cracks developed during The experimental values of CTEs for laminated compo- ites along with the corresponding theoretical values are large CTE mismatch between AL,O, and CaTiO, and are shown in Table 6. Al Bazro, laminate showed a differ- similar to those reported by Cai et al.[29.The cracks in ence of 1.9 and 7.5% according to Schapery and Chamis Fig 3 were caused by thermally generated stresses during respectively. The Al2O3/SnO2 laminates showed a differ ence of8.2 and 2. 3% for the Schapery and Chamis, respec- One of the assumptions of the model is that the laminae tively. The transverse CTE of Al2O3/CaTiO, showed a be continuous. Clearly, in Fig 3 the CaTiO, laminae did not difference of 9.6 and 19.8% for Schapery and Chamis satisfy this requirement. It would appear that the cracks respectively. The transverse CtE was closer to the theore- provided a"cushion,"which allowed for free expansion of tical than the longitudinal CTE for AlO /CaTiO3 laminates gment (materials between two cracks) but did not trans due to the fact that the CatiO, laminae were continuous in late this to an overall change in length in the sample. Thus, the thickness direction. However, there is still a significant the contribution of CaTiO, laminae to the overall Cte was much smaller than its intrinsic value of 13.4x10-6K-I 0.8 Another explanation, perhaps less significant, is the presence of other components besides Al2O3 and CaTiO During the processing of the laminate, a reaction zone Al,O3 Heating 600800 Temperature, C Fig 3 Optical micrograph of a Al2O /CaTiO, laminate. Note the extensive transverse cracks in the CaTiO, caused by the thermal stresses generated Fig. 4. Percent linear change(PLC) in the longitudinal direction vs. during fabrication. perature for a AlyO,SnO laminated

These reaction products were not taken into account in theo￾retical calculations of CTE because of their insignificantly small volume fraction in the Al2O3/BaZrO3 system. It may be pointed out that there is no interfacial reaction between Al2O3 and SnO2 [28]. The difference between CTE values for the Al2O3/CaTiO3 laminate was large, see Table 5. The experimental CTE values, compared with theoretical prediction, gave a differ￾ence of 27.7%. The CTE of the composite was significantly lower than that of either component. This is most likely caused by the presence of the vertical cracks in the CaTiO3 laminae, see Fig. 3. These cracks developed during processing due to the large thermal stresses caused by the large CTE mismatch between Al2O3 and CaTiO3 and are similar to those reported by Cai et al. [29]. The cracks in Fig. 3 were caused by thermally generated stresses during processing. One of the assumptions of the model is that the laminae be continuous. Clearly, in Fig. 3 the CaTiO3 laminae did not satisfy this requirement. It would appear that the cracks provided a “cushion” which allowed for free expansion of a segment (materials between two cracks) but did not trans￾late this to an overall change in length in the sample. Thus, the contribution of CaTiO3 laminae to the overall CTE was much smaller than its intrinsic value of 13.4 × 1026 K21 . Another explanation, perhaps less significant, is the presence of other components besides Al2O3 and CaTiO3. During the processing of the laminate, a reaction zone develops and if the CTEs of these products are relatively small, they could reduce the CTE of the composite. This is not likely to be very significant however, because the volume fraction of this reaction zone is practically negligi￾ble compared with the volume fractions of the Al2O3 and CaTiO3 in the sample. 3.2.3. Transverse CTE Table 4 gives the volume fractions of the composite samples tested for transverse CTE. A representative PLC vs. temperature graph of an Al2O3/BaZrO3 laminate is shown in Fig. 5. The experimental values of CTEs for laminated compo￾sites along with the corresponding theoretical values are shown in Table 6. Al2O3/BaZrO3 laminate showed a differ￾ence of 1.9 and 7.5% according to Schapery and Chamis, respectively. The Al2O3/SnO2 laminates showed a differ￾ence of 8.2 and 2.3% for the Schapery and Chamis, respec￾tively. The transverse CTE of Al2O3/CaTiO3 showed a difference of 9.6 and 19.8% for Schapery and Chamis, respectively. The transverse CTE was closer to the theore￾tical than the longitudinal CTE for Al2O3/CaTiO3 laminates due to the fact that the CaTiO3 laminae were continuous in the thickness direction. However, there is still a significant 176 G.M. Gladysz, K.K. Chawla / Composites: Part A 32 (2001) 173–178 Table 3 Average coefficient of thermal expansion of monolithic materials over the temperature range 35–10008C Component a (1026 K21 ) Al2O3 9.09 BaZrO3 6.26 CaTiO3 13.4 SnO2 [26] 5.80 Fig. 3. Optical micrograph of a Al2O3/CaTiO3 laminate. Note the extensive transverse cracks in the CaTiO3 caused by the thermal stresses generated during fabrication. Table 4 Volume fractions of the laminates used for determining CTE Laminate type Alumina vol. fraction Vol. fraction of phase 2 Al2O3/SnO2 0.69 0.31 Al2O3/BaZrO3 0.70 0.30 Al2O3/CaTiO3 0.75 0.25 Fig. 4. Percent linear change (PLC) in the longitudinal direction vs. temperature for a Al2O3/SnO2 laminated composite

G.M. Gladys, K.K. Chala/Composites: Part A 32(2001)173-178 Table 5 0.8 Comparison of experimental CTE and the calculated CTE by the models of Schapery and Chamis for laminates in the longitudinal direction 0.7 Laminate Experimental CTE Theoretical CTE Difference 0.6 0.5 AlO3/CaTiO3 7 19 0.4 error in the prediction. This is because the longitudinal CtE is included in the equation for transverse CTE. Another 0.3 reason for the poor agreement is that the modulus of the cracked CaTiO3 would be smaller than that of the unda- maged material, which is used in the equations 2 Heating A schematic of the proposed mechanism explaining the esults is shown in Fig. 6. As the temperature increases from Ti to T2, the CaTiO3 will experience a closure of the cracks 0 This will cause a reduction in the contribution of these laminae to the Cte of the composite in the longitudinal 200 600 8001000 direction. In the transverse direction, the experimental Temperature C value CtE will not be significantly affected because conti nuity between the laminae is maintained in the z-direction 5 Percent linear change(PLC)in the transverse direction vs tempera The Cte in the transverse direction will also show error e for an Al2O,/ BazrO3 laminated composite because of the incorrect longitudinal CTE in the expression T2(T1) 4. Conclusions Good agreement was found between theoretical predic- tions and experimental values as long as the criteria for applying the model were obeyed. Both Al2O /SnO2 and Al,O BaZrO3 laminates showed less than 9% differences between theoretical and experimental values. Al2O /CaTio laminates did not show good agreement, especially in the longitudinal direction. This is because the presence of the Fig. 6. Schematic of the proposed mechanism of thermal expansion of cracks in the CaTiO3 phase contradicts the assumption in AlO,/CaTiO, laminates. During temperature increase, the segments of the model that the laminae be continuous CaTiO, would expand, closing the cracks but not contributing to the overall The models of Schapery and Chamis are both identical in longitudinal increase in the length of the lamina. However. in the transverse direction the presence of cracks will not have a significant effect on the the longitudinal direction. However, in the transverse direc- thermal expansion of CaTiO tion the prediction of Shapery's model was closer to the experimental value for the Aloy/BazrO3 composite while Chamis model better predicts the Cte for Al2O3/ SnO upport from the US Office of Naval Research(N00014- 89-J-1459), Dr S.G. Fishman was the program manager Support was also received from the High Temperature Acknowledgements Materials Lab User Program(DE-ACO5-84OR2 1400), the The authors would like to acknowledge the financi hank Dr F.w. Clinard for many helpful discussions parison of experimental CtE and calculated by the models of Schapery and Chamis model for laminates in the transverse direction Laminate Experimental CTE(10-K-) Schapery's CTE (10-6K-) Difference( %) Chamis'CTE(10-K-) Difference(%) Al O3/CaTiO

error in the prediction. This is because the longitudinal CTE is included in the equation for transverse CTE. Another reason for the poor agreement is that the modulus of the cracked CaTiO3 would be smaller than that of the unda￾maged material, which is used in the equations. A schematic of the proposed mechanism explaining the results is shown in Fig. 6. As the temperature increases from T1 to T2, the CaTiO3 will experience a closure of the cracks. This will cause a reduction in the contribution of these laminae to the CTE of the composite in the longitudinal direction. In the transverse direction, the experimental value CTE will not be significantly affected because conti￾nuity between the laminae is maintained in the z-direction. The CTE in the transverse direction will also show error because of the incorrect longitudinal CTE in the expression for az. 4. Conclusions Good agreement was found between theoretical predic￾tions and experimental values as long as the criteria for applying the model were obeyed. Both Al2O3/SnO2 and Al2O3/BaZrO3 laminates showed less than 9% differences between theoretical and experimental values. Al2O3/CaTiO3 laminates did not show good agreement, especially in the longitudinal direction. This is because the presence of the cracks in the CaTiO3 phase contradicts the assumption in the model that the laminae be continuous. The models of Schapery and Chamis are both identical in the longitudinal direction. However, in the transverse direc￾tion the prediction of Shapery’s model was closer to the experimental value for the Al2O3/BaZrO3 composite while Chamis’ model better predicts the CTE for Al2O3/SnO2. Acknowledgements The authors would like to acknowledge the financial support from the US Office of Naval Research (N00014- 89-J-1459), Dr S.G. Fishman was the program manager. Support was also received from the High Temperature Materials Lab User Program (DE-AC05-84OR21400), the US Department of Energy, and NATO. The authors also thank Dr F.W. Clinard for many helpful discussions. G.M. Gladysz, K.K. Chawla / Composites: Part A 32 (2001) 173–178 177 Table 5 Comparison of experimental CTE and the calculated CTE by the models of Schapery and Chamis for laminates in the longitudinal direction Laminate Experimental CTE (1026 K21 ) Theoretical CTE (1026 K21 ) Difference (%) Al2O3/BaZrO3 8.30 8.53 2.7 Al2O3/SnO2 7.87 8.33 5.5 Al2O3/CaTiO3 7.19 9.94 27.7 Fig. 5. Percent linear change (PLC) in the transverse direction vs. tempera￾ture for an Al2O3/BaZrO3 laminated composite. Table 6 Comparison of experimental CTE and calculated by the models of Schapery and Chamis model for laminates in the transverse direction Laminate Experimental CTE (1026 K21 ) Schapery’s CTE (1026 K21 ) Difference (%) Chamis’ CTE (1026 K21 ) Difference (%) Al2O3/BaZrO3 8.33 8.17 1.9 7.75 7.5 Al2O3/SnO2 7.33 7.98 8.2 7.50 2.3 Al2O3/CaTiO3 9.22 10.20 9.6 11.5 19.8 Fig. 6. Schematic of the proposed mechanism of thermal expansion of Al2O3/CaTiO3 laminates. During temperature increase, the segments of CaTiO3 would expand, closing the cracks but not contributing to the overall longitudinal increase in the length of the lamina. However, in the transverse direction the presence of cracks will not have a significant effect on the thermal expansion of CaTiO3

G.M. Gladys=, K.K. Chawla/Composites: Part A 32 (2001)173-178 References [16 Kirchner HP. The thermal expansion of ceramic crystals. In: Reiss H, editor. Progress in solid state chemistry, New York: Macmillan, 19( [1 Cutler WA, Zok Fw, Lange FF. Delamination resistance of two id ceramic-composite laminates. J Am Ceram Soc [17 Faupel JH, Fisher FE. Engineering design: a synthesis of stress analy 99780(12):3027-9 sis and materials engineering. New York: Wiley, 1981 [2 Shigegaki Y, Brito ME, Hirao K, Toriyama M, Kanzaki S. B-SiAION [18] Bowles DE Finite element composite analysis program(FECAP)for silicon nitride multilayer composites. J Am Cerar a microcomputer. 997,80(10)2624-8 [19 Chamis CC. Simplified micromechanics equations for hygral, thermal 3 Kuo DH, Kriven WM. A strong damage-tolerant oxide lamil and mechanical properties. SAMPE Quart 1984; 15(3): 14 Am Ceram Soc1997;809):2421-4 [20] Schapery RA. Thermal expansion coefficient of composite materials [4]Ohji T, Shigegaki Y, Miyajima T, Kanzaki S. Fracture resistance based on energy principles. J Comp Mater 1968: 2(3):380 ehavior of multilayered silicon carbide. J Am Ceram Soc (21 Rogers KF, Phillips LN, Kingston-Lee DM, Yates B, Overy MJ, 1997804):991-4 Sargent JP, McCalla BA. The thermal expansion of carbon fibre- []Kovar D, Thouless MD, Halloran JW. Crack deflection and propaga- reinforced plastics, part I-the influence of fibre type and orientation. tion in layered silicon nitride/boron nitride ceramics. J Am Ceram Soc Mater Sci 1977: 12: 718. 1997;80(4:1004-12. (22 Gulati ST, Plummer WA. Influence of Poisson's ratio on the compo- [6]Kovar D, Thouless M. Simple method for determining frictional slid- site expansion of laminated plates and cylinders. In: API Conf. Proc. ing resistance and frictional energy dissipation in layered ceramics. J No. 17--Thermal expansion, Lake Ozark, MO, 1973: 196-206 Am Ceram Soc 1997: 80(3): 673-9 [23] Rosen Bw, Hashin Z Effective thermal expansion coefficients and Morgan PED, Marshall DB, Housley RM. High temperature stability of specific heats of composite materials. Int J Engng Sci 1970: 8: 157. onazite-alumina composites Mater Sci Engng 1995: 195(A): 215-22 (24 Vaidya RU, Venkatesh R, Chawla KK. Thermal expansion of a [8 Morgan PED, Marshall DB. Ceramic composites of monazite and PRD-166 fibre-reinforced glass-matrix composite. Composites alumina. J Am Ceram Soc 1995; 78(6): 1553-63 99425(4:308-13 [9 Russo CL, Harmer MP, Chan HM, Miller GA Mechanical properties [25] Bowles DE, Tomkins sS. Prediction of coefficients of thermal expan- f laminated ceramic composites in alumina- and zirconia-based ion for unidirectional composites. J Comp Mater 1988; 23(4):370- systems. Ceram Engng Sci Proc 1993: 14(7-8): 998 88. 10 Phillipps AJ, Clegg WJ, Clyne TW. The failure of layered ceramics in [26] Chawla KK, Cai H, Xu Z, Ferber MK Elastic constants of polycrys- ending and tension. Composites 1994; 25(7): 524-33 talline tin dioxide. Unpublished work. 11] Marshall DB. Design of high toughness laminar zirconia composites [27] Gladysz GM, Schmuicker M, Chawla KK, Schneider H, Joslin DL, Ceram Bull is92;71(6):969-73 Ferber MK. Characterization of the reaction products that develop 12 Clegg WJ. The fabrication and failure of laminar ceramic composites AlO,/ BazrO3 lan Acta Metall Mater 1992: 40(11): 3085-93 3] Marshall DB, Ratto JJ. Enhanced fracture toughness in layered micro- [28] Gladysz GM, Schmucker M, Chawla KK, Schneider opposites of Ce-ZrO2 and Al2O3. J Am Ceram Soc 1991: 74(12): DL, Ferber MK. Preliminary studies in processing and 979-8 ization of AlO /SnO laminated composites 4] Clegg WJ, Candle K, Alford NM. A simple way to make tough 99934:4351-5. eramics Nature 1990: 347(6292): 455-7 ng gL. Constrained densification of alumina 15 Maheshwari A, Chawla KK, Michalske TA Behavior of interfaces in irconia hybrid laminates, 1: experimental observation of processing alumina/glass composites. Mater Sci Engng 1989: 107: 269-76 defects. J Am Ceram Soc 1997: 80(8): 1929-39

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