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