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The mechanics of transverse cracking in an elastic fibrous composite ply is explored for the case of low crack density. Cracks are assumed to initiate from a nucleus created by localized fiber debonding and matrix cracking. Conditions for onset of unstable cracking from such nuclei are evaluated with regard to interaction of cracks with adjacent plies of different elastic properties. It is found that cracks may propagate in two directions on planes which are parallel to the fiber axis and perpendicular to the midplane of the ply. In general, crack propagation in the direction of the fiber axis controls the strength of thin plies, while cracking in the direction perpendicular to the fiber axis determines the strength of thick plies. The theory relates ply thickness, crack geometry, and ply tough ness to ply strength. It predicts a significant increase in strength with decreasing ply thick ness in constrained thin plies. The strength of thick plies is found to be constant, but it may be reduced by preexisting damage. Strength of plies of intermediate thickness, and of unconstrained thick plies is evaluated as well. Results are illustrated by comparison with experimental data.

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The aim of this paper is to formulate a two-dimensional theory for the propagation of fairly long water waves. The approach differs from the usual in that the theory is set up via two-dimensional postulates. Subsequently, it is shown how a simple three-dimensional approxi­mation enables us to relate the two-dimensional theory to the three-dimensional theory. The resulting equations are used to discuss the unidirectional propagation of waves. lt is shown how the results obtained from the theory proposed here are related to the results of Korteweg & de Vries (1895) and to those of Benjamin, Bona & Mahony (1972).

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