Solutions are presented for two stress distribution problems which result from breaking of the filaments in a composite material composed of high modulus elements embedded in a low modulus matrix. Both problems represent extensions of the two-dimensional filamentary structure stress concentration problem: the first concerns the determination of static stress concentration factors in the unbroken elements of a three-dimensional square or hexagonal array where specified filaments are broken; the second involves the stress concentration factor in the element adjacent to a broken filament in a two-dimensional array where the shear stress in the matrix adjacent to the broken filament is restricted by a limit stress in an ideally plastic sense.
The solution of the two-dimensional, elastic, multiple-filament-failure stress concentration problem led to the treatment of three-dimensional, elastic failure models and a two-dimensional, plastic failure model where an ideally plastic behavior of the matrix material adjacent to a broken filament was assumed. Another plastic behavior is proposed wherein the bond between the broken filament and the adjacent matrix material fails completely after reaching a prescribed stress level. This failure formulation is applied to five- and seven-element-width models as well as to the infinite element case. Both the bond failure and matrix yield models are then extended to the three-dimensional cases with both square and hexagonal element configurations.
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