Elsevier

Composite Structures

Volume 51, Issue 2, February 2001, Pages 181-190
Composite Structures

Selected issues of mechanics of ceramic matrix composites

https://doi.org/10.1016/S0263-8223(00)00140-9Get rights and content

Abstract

This paper presents four different problems of ceramic matrix composites (CMC) with matrix cracks. They include an evaluation of material constants and the stiffness matrix of a unidirectional lamina with bridging cracks. A nonlinear stress–strain relationship for a lamina subjected to an increasing uniaxial tension is derived accounting for the process of a continuous crack density change. Forced and free vibrations of woven ceramic matrix beams with matrix cracks are also considered by assumption that the dynamic stresses are sufficiently small to neglect their effect on the stiffness. Finally, theoretical foundations of thermography for a woven ceramic matrix beam are discussed and a closed-form solution for the surface temperature presented as a function of the matrix crack spacing and other parameters.

Introduction

Ceramic matrix composites (CMC) are attractive in applications, where high temperature and/or damage tolerance are important. Typical applications include internal chambers and nozzles of jet motors, turbine nozzles, aircraft brakes, etc. [1], [2], [3], [4], [5].

A unique feature of CMC is related to their ability to withstand initial damage without immediate failure. The reasons are a deflection of matrix cracks at the fiber–matrix interfaces and a redistribution of stresses in the area of high stress concentration due to a nonlinear stress–strain behavior. This makes a study of damaged CMC particularly important, the purpose of such research is to predict the properties of a damaged CMC component and to estimate its remaining life. Extensive literature has been published to address these problems and a recent review of the authors [6] contains an outline of the state of art in some of related areas.

The present paper illustrates an approach to the solution of four important problems:

  • Stiffness of a unidirectional lamina with bridging matrix cracks.

  • Nonlinear stress–strain behavior of a unidirectional lamina subject to a monotonically increasing load in the presence of developing matrix cracks.

  • Free and forced small-amplitude vibrations of plain-weave woven CMC beams with pre-existing matrix cracks.

  • Surface temperature of plain-weave woven CMC beams with matrix cracks due to frictional heating during forced vibrations (feasibility of using thermography).

Section snippets

Stiffness of a unidirectional lamina with bridging matrix cracks

The modulus of elasticity of a unidirectional lamina with the fibers oriented in the x-direction in the presence of bridging cracks and subjected to axial stresses can be obtained according to Pryce and Smith [7]. Byrd and Birman [8] modified this modulus for a lamina with matrix cracks that emerged during post-processing cooling and affected residual stresses. The expressions for these moduli can be combined yieldingEx=1+[rEmVm/(2sτEfVf)]cEmVm/(EcVf)−nσfT−1Ec,where the subscripts identify

Conclusions

This paper illustrates four representative problems of mechanics of CMC with matrix cracks. The first problem is related to identifying material constants and the matrix of stiffnesses of a unidirectional lamina with bridging cracks. The assumption that the stiffness in the planes perpendicular to the fibers remains unaffected by the cracks enables us to specify all material constants in both plane stress and three-dimensional formulations. The second solution refers to a nonlinear behavior of

Acknowledgements

This research was supported by the Air Force Office of Scientific Research through the contract F49620-93-C-0063. The program manager is Dr. Brian Sanders.

References (16)

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