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