On the behavior of stress waves in composite materials—I. A universal set of boundary conditions

In recent years experiments on uniaxially reinforced composites have revealed anomalous behavior in the stress-wave propagation characteristics of these materials. Whenever the exposed ends of both composite constituents were subjected to moderate pressures of a few kilobars the number of stable propagating waves generated within the composite exceeded by one the number of waves calculated through conventional composite models. This effect greatly increased the wave dispersion and rise-time in the experimentally observed stress wave. The key to the origin of this phenomenon is quite elementary. The composite debonds internally. When the bond between the reinforcing and matrix fails, the composite attains an additional degree of freedom which results in an additional stable propagating wave. Since conventional composite models do not allow for this debonding, they cannot account for the resulting wave. However, as was shown in an earlier paper, direct application of the theory of elasticity to this problem results in wave velocities and mode shapes for all of the waves. The solution to the total problem, including the determination of the various wave amplitudes, was previously hampered by an insufficient set of boundary conditions. The usual procedure was to impose continuity of stress and displacement at the boundary between the composite and the adjoining homogeneous material where the volumetric averages of stress and displacement were used for the composite. While these conditions are necessary and sufficient for the bonded composite problem, they are insufficient for the debonded composite problem. The additional degree of freedom in the debonded problem makes the use of an additional boundary condition necessary. This additional boundary condition is the subject of this paper. Ppoвeдeны в пocлeдныч гoдAч экcпepнмeнты oднoocнo ycилeнныч мAтepиAлoв нoкAзывA.ют нeнopмAльнoe пoвeдeннe в чApAктepнcтикAч pAcпpeдeлeння вoлн нAпpяжeння для этнч мAтepнAлoв. КoгдA бы oткpытыe кoнцы oбoич кoмпoнeнтoв cлoиcтич мAтepиAлoв ни были пoдвeoжeны yмepeннoмy дAвлeнию нecкoлькo килoбApoв, чиcлo cтAнциoнApньич pAcпpocтpAпяющичcя вoлн, oбpAзoвAнныч внyтpи cлoиcтoгo мAтepиAлA, пpeвыщAлo нA oдин чнcлo вoлн, нoдcчитAнныч нA ocнoвe oбыкнoвeнныч мoдeлeй cлoиcтыч мAтepиAлoв. Этoт эффeкт знAчитeльнo yвeличAл pAcceяниe вoлн и нApAcтAниe вo вpeмeни в нoлyчeннoй экcнepимeнтAльнo вoлиe нAнpяжeния. Ключ к пpoиcчoждeнию этoгo нeoбыкнoвeннoгo явлeния coвceм элeмeнтApный. жлoиcтый мAтepи