Distribution of Matrix Cracks in a Uniaxial Ceramic Composite

Authors

  • Chongdu Cho,

    1. Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, Michigan 48109–2125
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    • *

      Member, American Ceramic Society.

  • John W. Holmes,

    1. Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, Michigan 48109–2125
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    • *

      Member, American Ceramic Society.

  • James R. Barber

    1. Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, Michigan 48109–2125
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  • A. G. Evans—contributing editor

Abstract

Conventional shear-lag analyses of matrix cracking and debonding in uniaxial composites loaded in tension predict that the matrix stress varies only very slowly with position except near existing cracks. It therefore follows that the location of subsequent cracks is very sensitive to minor local variations in matrix strength, leading to significant statistical variation in crack spacing. This question is investigated using a discrete random process model of a composite and by direct experimental measurements of crack spacing. In the limit of a completely homogeneous composite, it is shown that the crack spacing distribution tends to an inverse square distribution between the theoretical maximum spacing and half that value. The random process model recovers this behavior in the limit and exhibits an approximately Weibull distribution of crack spacings when the matrix strength has significant variance. The theoretical predictions are compared with experimental results obtained for a unidirectional ceramic-matrix composite (SiC fibers in a calcium aluminosilicate matrix). The experimental results exhibit features similar to those predicted by the model and are compatible with a matrix strength whose standard deviation is of the order of 40% of the mean strength. An important point is that, with this magnitude of strength variation, the material exhibits a significant size effect and it is essential to take this into account in estimating the mean crack spacing from the corresponding mean matrix properties.

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