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Characterization and control of the fiber-matrix interface in ceramic ...

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APPENDIX B.<br />

DETAILS OF' THE FIBER-SHEATH ANALYSIS<br />

In <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> tensile method for <strong>the</strong> determ<strong>in</strong>ation <strong>of</strong><br />

<strong>in</strong>terFacia1 stresses, it was assumed that <strong>the</strong> radial contraction <strong>and</strong> <strong>the</strong><br />

forces associated wFth this phenomenon could be ignored. References 89<br />

<strong>and</strong> 92 give detailed ma<strong>the</strong>matical analyses <strong>of</strong> <strong>the</strong> forces act<strong>in</strong>g at <strong>the</strong><br />

<strong><strong>in</strong>terface</strong> <strong>of</strong> a <strong>fiber</strong> conta<strong>in</strong>ed <strong>in</strong> a <strong>matrix</strong>.<br />

The concepts are drawn from<br />

a s<strong>in</strong>gle <strong>fiber</strong> hav<strong>in</strong>g no neighbors; thus, forces exerted by <strong>the</strong> close<br />

proximity <strong>of</strong> ano<strong>the</strong>r <strong>fiber</strong> are not considered.<br />

For a <strong>fiber</strong> embedded <strong>in</strong> a <strong>matrix</strong> <strong>in</strong> which <strong>the</strong> system is subjected to<br />

an external load, <strong>the</strong> forces <strong>in</strong> <strong>the</strong> <strong>matrix</strong> are given by <strong>the</strong> expressions<br />

<strong>and</strong><br />

199

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