A three-dimensional laminated medium is studied by an approach which replaces the heterogeneous medium by an equivalent homogeneous material. A set of macroscopic elastic constants is developed in terms of the properties of the constituent layers by considering a representative small element of the laminated medium and imposing the condition of continuity of stress and displacement at the layer interfaces. An example boundary value problem is also considered. Based on the solution of the boundary value problem for the homogeneous material, stress and strain fields corresponding to each layer are then calculated. This individual layer solution contains certain dis continuous stresses and strains as does the exact solution for the layered material.

This paper presents a stochastic simulation model for the growth of multiple matrix cracks in composite laminates subjected to both static and fatigue loads. Working within the premise of ply-elasticity, a new concept of effective flaws is introduced which replaces the conventional constant ply strength criterion. Thus, the model consists of an application of fracture mechanics and a rational representation of material flaw distributions. Simulation examples are presented on [0 2 /90 2 ] s and [0 2 /90 3 ] s graphite-epoxy laminates which undergo characteristic transverse cracking under uniaxial tension.

E. Hirsch Armament Development Authority, P. 0. BOX 2250, Haifa (Israel) Verbesserte Fomeln fiir die Geschwindigkeit, Beschleunigung und den Projektionswinkel von explosiv beschleunigten Liners Verbesserte eindimensionale Formeln sowohl fur die Richtung als such fur die GroBe der Geschwindigkeit von explosiv beschleunigten Liners werden entwickelt. Zuerst wird eine analytische Formel fur die Bewegungsrichtung des Liners unter veranderlichen Bedingungen abgeleitet. Diese neue Formel wird verglichen sowohl mit zweidimensionalen Berechnungen als auch mit experimentellen Daten und zwar fur Hohlladungs-und explodierende Zylindergeometrien. Die neue Formel ist genauer als es die klassische stationare Taylor-Winkelfor-me1 fur diese Falle ist. Weiterhin wird fur implosive Geometrien eine neue Formel aufgestellt fir die voll beschleunigte Linergeschwindigkeit. Da die Standard-Gurney-Naherung nicht auf implodierte Geometrien anwendbar ist, wird eine modifizierte Naherung angenommen. Die Ergebnisse stimmen gut mit den Resultaten des zweidimensionalen Rechenprogramms fur einen weiten Sprengstoff-und Geometriebereich uberein. AuRerdem wird gezeigt, daR die Geschwindigkeits-Historie einem Exponentialgesetz folgt, und es wird eine brauchbare Formel fur die charakteristische Metallbeschleunigungszeit entwickelt. Formules amkliorees pour le calcul de la vitesse, de I'acceleration et de I'angle de rekvement des revetements projetCs par explosif On a mis au point des formules monodimensionnelles amkliortes pour calculer la direction et la grandeur du vecteur vitesse de revCtements projetCs plar explosif. En premier lieu on Ctablit une expression analytique qui donne la direction du vecteur vitesse du revktement pour diffkrentes conditions de projection. Cette nouvelle formule est comparte aux rCsultats des calculs bidimensionnels et aux donnCes exptrimentales obtenues avec des charges cremes et des charges cylindriques. La nouvelle formule fournit pour ces cas des rCsultats plus precis que la formule classique de Taylor pour 1'Ctat stationnaire.En outre on indique une nouvelle formule pour les gComCtries implosives qui fournit la vitesse du revCtement a pleine accCltration. L'approximation classique de Gurney ne s'appliquant pas aux gComCtries implosives, on adopte une approximation modifike. Les rksultats concordent bien avec ceux du code de calcul bidimensionnel pour une large gamme d'explosifs et de gtomktries. On montre Cgalement que l'holution temporelle de la vitesse suit une loi exponentielle et on dtveloppe une formule pratique pour calcuculer le temps d'acdlkration caractkristique des m6taux. SummaryImproved one-dimensional formulas for both the direction and magnitude of the velocity of explosively driven liners are developed. First, an analytical formula for the direction of motion of the liner under unsteady conditions is derived. This new formula is compared withboth two-dimensional calculations and experimental data for both shaped-charge and exploding cylinder geometries. The new formula is more accurate than the cla...

Criteria on jet formation and jet cohesiveness are proposed for collapsing solid plates and shells. These criteria are also applicable to impinging fluid sheets from plane or annular nozzles. Under the high impact speeds treated here, the solid plates or shells behave as compressible fluids; for the impinging fluid sheets compressibility effects will also be assumed important. Jetting will occur if either the collision is subsonic or the impinging angle is large enough such that the shock in the flow is not attached at the collision point. Jets formed from subsonic collisions are coherent; those from supersonic collisions are not coherent. The criteria are shown to be in general agreement with available experimental evidence. Further, the proposed criteria are also verified by two-dimensional unsteady finite-difference computer calculations. In addition, these calculations indicate the mechanical reasons for the coherency or noncoherency of the jet under various impact conditions. The practical applications of these criteria include collapsing shaped-charge liners, the explosive welding of plates, and steady impinging fluid sheets from annular nozzles.

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