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Journal of Composite Materials
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Modified Eigenfunctions for Transversely Isotropic Composites with Applications to Stress Analysis of a Broken Fiber

Yijian Jin

Department of Civil Engineering Mechanics and Metallurgy University of Illinois at Chicago P.O. Box 4348 Chicago, IL 60680

T.C.T. Ting

Department of Civil Engineering Mechanics and Metallurgy University of Illinois at Chicago P.O. Box 4348 Chicago, IL 60680

When a transversely isotropic elastic body that contains a notch or a crack is under an axisymmetric deformation, the eigenfunction solution near the singular point is in the form of a power series {delta}f({psi},{delta}), {delta}+1f 1({psi},{delta}), {delta}+2f2({psi},{delta}) ... in which (,{psi}) is the polar coordinate with origin at the singular point and {delta} is the eigenvalue, or the order of singularity. A difficulty arises when {delta} as well as {delta} + k, where k is a positive integer, are also eigenvalues. In this case the higher order terms of the series solution may not exist. A modified solution is required and is presented here. The modified solution has the new terms {delta}+k(ln) F1({psi},{delta}), {delta}+k +1(ln)F2({psi},{delta}).... As an application, we consider the stresses near a broken fiber in a composite which is under an axisymmetric deformation. The interface between the broken fiber and the matrix also suffers a delamination. This creates stress singularities at several points some of which require the modified eigenfunc tions presented here.

Journal of Composite Materials, Vol. 22, No. 3, 224-244 (1988)
DOI: 10.1177/002199838802200302
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