On the Detachment of the Ends of Microfibers from the Matrix Due to Tension in the Composite

Abstract

The above title describes one of several ways in which a mechan ical failure of a composite has been observed to occur.

A rigid oblong elliptic shape has been chosen for the fiber in two-dimensional treatment. Analytical formulation of the problem leads to a mixed boundary value problem of the mathematical theory of elasticity.

Recent advances in reducing dual series formulations to varia tional minimization procedures (via a Fredholm integral equation of the first kind) make a mathematical analysis feasible. The variational method leads to a transcendental equation whose only real root has been evaluated by the computer for various values of the elastic constants of the matrix.

The results show a substantial destruction of the bond between matrix and fiber due to the size of the detached region which ex tends over practically one-fourth of the microfiber at each end.

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References

H.B. Wilson , Jr. , "Contact Stresses in an Infinite Plate Containing a Smooth Rigid Elliptic Insert," J. Appl. Mech. , Vol. 31 (1964), p. 703.

J.G. Goree , "Approximate Determination of Contact Stresses in an Infinite Plate Containing a Smooth Rigid Elliptic Insert," J. Appl. Mech., Vol. 32 (1965), p. 437.

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B. Noble and M. Hussain , "Angle of Contact for Smooth Elastic Inclusions," 10th Midwestern Conf. on Appl. Mech., (1967), (to be published).