Cumulative Effect

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Cumulative Effect


the effect of an explosion, intensified in a particular direction. It is produced by an explosive charge that has a recess (charge hollow) that faces the target (for example, a steel armor plate). The charge hollow, which is usually conical, is covered with a metal sheath (facing), whose thickness varies from fractions of a millimeter to 1 mm, depending on the charge diameter.

The mechanism of the shaped-charge effect is as follows. After the explosion of the detonator, which is located on the side opposite the hollow in the charge, a blast wave arises and travels along the axis of the charge. The wave breaks down the conical sheath, beginning at its apex, and imparts a high velocity to the material of the sheath. The pressure of the explosion products, which reaches the order of 1010 newtons per sq m, or 105 kilograms-force per sq cm, considerably exceeds the ultimate strength of the metal. Consequently, the motion of the metal sheath produced by the effect of the explosion products is similar to the flow of a fluid film (it must be emphasized that the flow of the metal is not the result of melting but is caused by the extremely high mechanical stress). The moving metal forms a flow that converges at an angle to the axis of the cone and then becomes a fine stream (of the order of the thickness of the sheath) moving along the axis at a very high velocity (˜ 10 km/sec). The action of this stream is responsible for the penetrating power of a shaped-charge explosion. The high-velocity stream pierces steel armor just as a powerful jet of water penetrates soft clay. The depth of penetration, which is approximately equal to the length of the stream, is proportional to the generating line of the conical sheath. The pressure developed when the stream encounters armor plate is so much greater than the rupture stress of the steel that the strength of the target is not important.

During the collapse of the conical sheath the velocities of various parts of the stream are different, and as a result the stream stretches out in flight. Consequently, a small increase in the separation between the charge and the target increases the depth of penetration because of lengthening of the stream. At great distances between the charge and the target, the stream breaks up and the penetrating effect is diminished. When a shaped charge is used without a metal sheath, the cumulative effect is reduced because a stream of gaseous explosion products, rather than a metal stream, is acting on the target.

The term “cumulation” is sometimes used by specialists in a broader sense to designate phenomena in which the flow of a medium brings about concentration of energy in a small volume but is not necessarily attended by the formation of a stream. Examples of such phenomena are the convergence toward the center or axis of spherical or cylindrical detonation or shock waves and the collapse of an empty cavity in a fluid under the influence of high pressure. The cumulative effect is used in military operations, as well as in scientific research to study the properties of substances under high pressures.


Lavrent’ev, M. A. “Kumuliativnyi zariad i printsip ego raboty.” Uspekhi matematicheskikh nauk, 1957, vol. 12, no. 4.
“Teoreticheskie i eksperimentaPnye issledovaniia iavleniia kumuliatsii.” Mekhanika: Sbornik perevodov i obzorov inostrannoi periodicheskoi literatury, 1953, no. 4 (20).
Zababakhin, E. I. “Iavleniia neogranichennoi kumuliatsii.” In Mekhanika v SSSR za 50 let, vol. 2. Moscow, 1970.


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