Pergamon Actu melall. mater. Vol. 43, No. 6, 2241-2253, 1995 pp. 0956-7151(94)00429-3 Copyright 0 1995 Elsevier ScienceLtd Printed in Great Britain. All rights reserved 0956-7151195 $9.50 + 0.00 THERMAL RESIDUAL STRESSES IN CERAMIC MATRIX COMPOSITES-I. AXISYMMETRICAL MODEL AND FINITE ELEMENT ANALYSIS J.-L. BOBET and J. LAMONf Laboratoire des Composites Thermostructuraux (UMR 47 CNRS-SEP-UBl), Domaine Universitaire, 3, all&e de La Bo&tie, 33600 Pessac, France zyxwvutsrqponmlkjihgfedcbaZYXW (Received 18 January 1994; in revised form 20 September 1994) Abstract-The residual stresses induced in composites when cooling down from the processing tempera- ture were determined using a cylinder model and using a finite element computer program. Various specimen geometries were examined: microcomposites, unidirectional composites and flat substrates coated with one or two layers. Various combinations were investigated involving MoSi, as an interphase, Sic as a fiber, a matrix, a substrate or an external coating layer and C as a fiber, a substrate, an interphase or an intermediate coating layer. The influence of factors such as interphase thickness and uncertainty in interphase properties (including Young’s modulus and coefficient of thermal expansion) was analyzed. It was shown that trends in distribution of thermal residual stresses (TRS) prevailing in 1D composites can be satisfactorily predicted using the analytical cylinder model. The presence of a MoSi, interphase induces the highest interfacial stresses but it relieves stresses in the matrix. The presence of a C interphase essentially reduces the interfacial stresses. 1. INTRODUCTION Continuous fiber ceramic matrix composites are promising candidates for many applications, particu- larly as structural components since they retain the advantages of ceramics while providing an enhanced degree of damage tolerance. Ceramic matrix com- posites and more particularly those made by Chemi- cal Vapor Infiltration (CVI) of a fiber preform [l] are elaborated at elevated temperatures (of the order of 1OOO’C). Thus upon cooling from the processing temperature, thermal residual stresses (TRS) arise due to thermal expansion mismatch between con- stituents (fiber, interphase and matrix). Then, these TRS are superimposed upon the applied stressfield. TRS are influenced by various parameters including volume fractions and properties of constituents. Esti- mation of TRS is a prerequisite to the development and the safe use of high performance composites. This two-part paper has a dual intent: first, assess methods for the determination of TRS in CMC, and second provide data on the residual stresses in CMC having MoSi, or C interfacial layers. In Part I, residual stresses were calculated for various specimen geometries including microcomposites and unidirec- tional fiber reinforced composites and film-substrate assemblies consisting of one or two coating layers deposited on a flat substrate. The former geometries represent different scales of 2D woven composites. In Part II, TRS were measured on microcomposites tTo whom all correspondence should be addressed. and film-substrate assemblies using X-ray techniques [21. Microcomposites represent an elementary cell of the composite. They consist of a single fiber coated with an interfacial material and then embedded in a SIC matrix. Microcomposite test specimens are currently used for investigation of the mechanical behavior and interfacial failure of CMC processed by CVI [3,4]. Sic/Sic and C/Sic fiber-matrix or sub- strate-film combinations were examined. A compen- sating material of high thermal expansion coefficient (MoSi,) and a compliant one of very low modulus (Pyrocarbon) were selected as interfacial materials. Several analytical models [5-91 have been put for- ward to determine the elastic stressfield in a set of two or more coaxial cylinders subject to thermomechani- cal loading. The one developed by Mikata and Taya [8] has been established for a four cylinder structure including the fiber, the coating layer, the matrix and an infinite radius cylinder made of the actual com- posite. Although it seems physically sound to take into account the interacting effects with actual com- posite, the Mikata and Taya approach presents two major drawbacks: (i) the axial force balance imposed as the boundary condition becomes insensitive to the stresses in the fiber and the matrix, so that the predictions become somewhat inconsistent and (ii) equivalent properties for the homogenized actual composite are obtained by a weighting operation which is not rigorous. An analytical model derived from the Mikata and Taya one was used for computation of residual 2241