Editing Shaped charge (section)

==Function==
[[File:US Army Military Engineers working with explosive device - Exercise Talisman Sabre 2011.jpg|thumb|right|A {{convert|40|lb|kg|0|abbr=on}} [[Composition B]] 'formed projectile' used by combat engineers. The shaped charge is used to bore a hole for a cratering charge.]]

A typical device consists of a solid cylinder of explosive with a metal-lined [[conical]] hollow in one end and a central [[detonator]], array of detonators, or [[detonation]] wave guide at the other end. Explosive energy is released directly away from ([[normal (geometry)|normal to]]) the surface of an explosive, so shaping the explosive will concentrate the explosive energy in the void. If the hollow is properly shaped, usually conically, the enormous [[pressure]] generated by the detonation of the explosive drives the liner in the hollow cavity inward to collapse upon its central axis. 

The resulting collision forms and projects a high-velocity jet of metal particles forward along the axis. Most of the jet material originates from the innermost part of the liner, a layer of about 10% to 20% of the thickness. The rest of the liner forms a slower-moving slug of material, which, because of its appearance, is sometimes called a "carrot".

Because of the variation along the liner in its collapse velocity, the jet's velocity also varies along its length, decreasing from the front. This variation in jet velocity stretches it and eventually leads to its break-up into particles. Over time, the particles tend to fall out of alignment, which reduces the depth of penetration at long standoffs.

At the apex of the cone, which forms the very front of the jet, the liner does not have time to be fully accelerated before it forms its part of the jet. This results in its small part of jet being projected at a lower velocity than jet formed later behind it. As a result, the initial parts of the jet coalesce to form a pronounced wider tip portion.

Most of the jet travels at [[hypersonic]] speed. The tip moves at 7 to 14&nbsp;km/s, the jet tail at a lower velocity (1 to 3&nbsp;km/s), and the slug at a still lower velocity (less than 1&nbsp;km/s). The exact velocities depend on the charge's configuration and confinement, explosive type, materials used, and the explosive-initiation mode. At typical velocities, the penetration process generates such enormous pressures that it may be considered [[hydrodynamic]]; to a good approximation, the jet and armor may be treated as [[inviscid flow|inviscid]], [[compressible flow|compressible]] fluids (see, for example,<ref>[[Garrett Birkhoff|G. Birkhoff]], D.P. MacDougall, E.M. Pugh, and [[Geoffrey Ingram Taylor|G.I. Taylor]], "[https://doi.org/10.1063/1.1698173]," ''J. Appl. Phys.'', vol. 19, pp. 563–582, 1948.</ref>), with their material strengths ignored.

A recent technique using magnetic diffusion analysis showed that the temperature of the outer 50% by volume of a copper jet tip while in flight was between 1100K and 1200K,<ref>{{cite journal |last1=Uhlig |first1=W. Casey |last2=Hummer |first2=Charles |title=In-flight conductivity and temperature measurements of hypervelocity projectiles |journal=Procedia Engineering |date=2013 |volume=58 |pages=48–57 |doi=10.1016/j.proeng.2013.05.008|doi-access=free}}</ref> much closer to the melting point of copper (1358 K) than previously assumed.<ref>{{cite book|last1=Walters|first1=William|title=Fundamentals of Shaped Charges|date=1998|publisher=CMCPress|location=Baltimore Maryland|isbn=0-471-62172-2|page=192|edition=softcover edition with corrections}}</ref> This temperature is consistent with a hydrodynamic calculation that simulated the entire experiment.<ref>{{cite journal |last1=Sable |first1=P. |title=Characterization In-Flight Temperature of Shaped Charge Penetrators in CTH |journal=Procedia Engineering |date=2017 |volume=204 |pages=375–382 |doi=10.1016/j.proeng.2017.09.782|doi-access=free}}</ref> In comparison, two-color radiometry measurements from the late 1970s indicate lower temperatures for various shaped-charge liner material, cone construction and type of explosive filler.<ref>{{cite journal |last1=Von Holle |first1=W.G. |last2=Trimble |first2=J.J. |title=Temperature Measurement of Copper and Eutectic Metal Shaped Charge Jets |journal=U.S. Army Ballistic Research Laboratory |date=1977 |issue=BRL-R-2004}}</ref> 

A Comp-B loaded shaped charge with a copper liner and pointed cone apex had a jet tip temperature ranging from 668 K to 863 K over a five shot sampling. Octol-loaded charges with a rounded cone apex generally had higher surface temperatures with an average of 810 K, and the temperature of a tin-lead liner with Comp-B fill averaged 842 K. While the tin-lead jet was determined to be liquid, the copper jets are well below the melting point of copper. However, these temperatures are not completely consistent with evidence that soft recovered copper jet particles show signs of melting at the core while the outer portion remains solid and cannot be equated with bulk temperature.<ref>{{cite report |last1=Lassila |first1=D. H. |last2=Nikkel |first2=D. J. Jr. |last3=Kershaw |first3=R. P. |last4=Walters |first4=W. P. |date=1996 |title=Analysis of "Soft" Recovered Shaped Charge Jet Particles |publisher=University of North Texas Libraries, Digital Library, Government Documents Department |id=UCRL-JC-123850 |doi=10.2172/251380 |url=https://digital.library.unt.edu/ark:/67531/metadc665285/}}</ref>

The location of the charge relative to its target is critical for optimum penetration for two reasons. If the charge is detonated too close there is not enough time for the jet to fully develop. But the jet disintegrates and disperses after a relatively short distance, usually well under two meters. At such standoffs, it breaks into particles which tend to tumble and drift off the axis of penetration, so that the successive particles tend to widen rather than deepen the hole. At very long standoffs, velocity is lost to [[air drag]], further degrading penetration.

The key to the effectiveness of the hollow charge is its diameter. As the penetration continues through the target, the width of the hole decreases leading to a characteristic "fist to finger" action, where the size of the eventual "finger" is based on the size of the original "fist". In general, shaped charges can penetrate a steel plate as thick as 150% to 700%<ref>''Jane's Ammunition Handbook 1994'', pp. 140–141, addresses the reported ≈700 mm penetration of the Swedish 106 3A-HEAT-T and Austrian RAT 700 HEAT projectiles for the 106&nbsp;mm M40A1 recoilless rifle.</ref> of their diameter, depending on the charge quality. The figure is for basic steel plate, not for the [[composite armor]], [[reactive armor]], or other types of modern armor.

===Liner===
The most common shape of the liner is [[cone (geometry)|conical]], with an internal apex angle of 40 to 90 degrees. Different apex angles yield different distributions of jet mass and velocity. Small apex angles can result in jet [[wikt:bifurcation|bifurcation]], or even in the failure of the jet to form at all; this is attributed to the collapse velocity being above a certain threshold, normally slightly higher than the liner material's bulk sound speed. Other widely used shapes include hemispheres, tulips, trumpets, [[ellipse]]s, and bi-conics; the various shapes yield jets with different velocity and mass distributions.

Liners have been made from many materials, including various metals<ref>{{cite web|url=https://apps.dtic.mil/dtic/tr/fulltext/u2/a278191.pdf|archive-url=https://web.archive.org/web/20190401204607/https://apps.dtic.mil/dtic/tr/fulltext/u2/a278191.pdf|url-status=live|archive-date=April 1, 2019|title=Shaped Charge Liner Materials: Resources, Processes, Properties, Costs, and Applications, 1991|website=dtic.mil|access-date=31 March 2018}}</ref> and glass. The deepest penetrations are achieved with a dense, [[ductile]] metal, and a very common choice has been [[copper]]. For some modern anti-armor weapons, [[molybdenum]] and pseudo-alloys of [[copper-tungsten|tungsten filler and copper binder]] (9:1, thus density is ≈18&nbsp;Mg/m<sup>3</sup>) have been adopted. Nearly every common metallic element has been tried, including [[aluminum]], [[tungsten]], [[tantalum]], [[depleted uranium]], [[lead]], [[tin]], [[cadmium]], [[cobalt]], [[magnesium]], [[titanium]], [[zinc]], [[zirconium]], [[molybdenum]], [[beryllium]], [[nickel]], [[silver]], and even [[gold]] and [[platinum]].{{Citation needed|reason=Source needed on the use of gold and platinum|date=September 2021}} The selection of the material depends on the target to be penetrated; for example, aluminum has been found advantageous for [[concrete]] targets.<!--List of liner materials supplemented from Kennedy, 1983-->

In early antitank weapons, copper was used as a liner material. Later, in the 1970s, it was found [[tantalum]] is superior to copper, due to its much higher [[density]] and very high ductility at high strain rates. Other high-density metals and alloys tend to have drawbacks in terms of price, toxicity, radioactivity, or lack of ductility.<ref>Alan M. Russell and Kok Loong Lee, ''Structure-Property Relations in Nonferrous Metals'' (Hoboken, New Jersey: John Wiley & Sons, 2005), [https://books.google.com/books?id=fIu58uZTE-gC&pg=PA218 p. 218].</ref>

For the deepest penetrations, pure metals yield the best results, because they display the greatest ductility, which delays the breakup of the jet into particles as it stretches. In charges for [[oil well completion]], however, it is essential that a solid slug or "carrot" not be formed, since it would plug the hole just penetrated and interfere with the influx of oil. In the petroleum industry, therefore, liners are generally fabricated by [[powder metallurgy]], often of [[pseudo-alloy]]s which, if [[sintering|unsintered]], yield jets that are composed mainly of dispersed fine metal particles.

Unsintered [[powder metallurgy#Powder compaction|cold pressed]] liners, however, are not waterproof and tend to be [[brittle]], which makes them easy to damage during handling. [[Bimetal]]lic liners, usually zinc-lined copper, can be used; during jet formation the zinc layer vaporizes and a slug is not formed; the disadvantage is an increased cost and dependency of jet formation on the quality of bonding the two layers. Low-melting-point (below 500&nbsp;°C) [[solder]]- or [[braze]]-like alloys (e.g., Sn<sub>50</sub>Pb<sub>50</sub>, Zn<sub>97.6</sub>Pb<sub>1.6</sub>, or pure metals like lead, zinc, or cadmium) can be used; these melt before reaching the well casing, and the molten metal does not obstruct the hole. Other alloys, binary [[eutectic]]s (e.g. Pb<sub>88.8</sub>Sb<sub>11.1</sub>, Sn<sub>61.9</sub>Pd<sub>38.1</sub><!-- Pb??? -->, or Ag<sub>71.9</sub>Cu<sub>28.1</sub>), form a metal-matrix composite material with ductile matrix with brittle [[dendrite (metal)|dendrites]]; such materials reduce slug formation but are difficult to shape.

A metal-matrix composite with discrete inclusions of low-melting material is another option; the inclusions either melt before the jet reaches the well casing, weakening the material, or serve as crack [[nucleation]] sites, and the slug breaks up on impact. The dispersion of the second phase can be achieved also with castable alloys (e.g., copper) with a low-melting-point metal insoluble in copper, such as bismuth, 1–5% lithium, or up to 50% (usually 15–30%) lead; the size of inclusions can be adjusted by thermal treatment. Non-homogeneous distribution of the inclusions can also be achieved. Other additives can modify the alloy properties; tin (4–8%), nickel (up to 30% and often together with tin), up to 8% aluminium, [[phosphorus]] (forming brittle phosphides) or 1–5% [[silicon]] form brittle inclusions serving as crack initiation sites. Up to 30% zinc can be added to lower the material cost and to form additional brittle phases.<ref>{{cite web|url=http://www.freepatentsonline.com/5098487.html|title=Copper alloys for shaped charge liners - Olin Corporation|work=freepatentsonline.com}}</ref>

Oxide glass liners produce jets of low density, therefore yielding less penetration depth. Double-layer liners, with one layer of a less dense but [[pyrophoric]] metal (e.g. [[aluminum]] or [[magnesium]]), can be used to enhance incendiary effects following the armor-piercing action; [[explosive welding]] can be used for making those, as then the metal-metal interface is homogeneous, does not contain significant amount of [[intermetallic]]s, and does not have adverse effects to the formation of the jet.<ref>"Method of making a bimetallic shaped-charge liner" {{US patent|4807795}}</ref>

The penetration depth is proportional to the maximum length of the jet, which is a product of the jet tip velocity and time to particulation. The jet tip velocity depends on bulk sound velocity in the liner material, the time to particulation is dependent on the ductility of the material. The maximum achievable jet velocity is roughly 2.34 times the sound velocity in the material.<ref>Manfred Held. "[http://www.argospress.com/jbt/Volume4/4-3-1.pdf Liners for shaped charges] {{Webarchive|url=https://web.archive.org/web/20110707161507/http://www.argospress.com/jbt/Volume4/4-3-1.pdf |date=2011-07-07}}", ''Journal of Battlefield Technology'', vol. 4, no. 3, November 2001.</ref> The speed can reach 10&nbsp;km/s, peaking some 40 microseconds after detonation; the cone tip is subjected to acceleration of about 25&nbsp;million g. The jet tail reaches about 2–5&nbsp;km/s. The pressure between the jet tip and the target can reach one terapascal. The immense pressure makes the metal flow like a liquid, though x-ray diffraction has shown the metal stays solid; one of the theories explaining this behavior proposes molten core and solid sheath of the jet. The best materials are [[face-centered cubic]] metals, as they are the most ductile, but even [[graphite]] and zero-ductility [[ceramic]] cones show significant penetration.<ref>{{cite journal |last=Doig |first=Alistair |date=March 1998 |title=Some metallurgical aspects of shaped charge liners |journal=Journal of Battlefield Technology |volume=1 |issue=1 |url=http://knygos.sprogmenys.net/knygos-2/Explosives/Shaped%20Charges,%20Penetrators/Some_metalurgical_aspects_of_shaped_charge_liners.pdf |url-status=dead |archive-url=https://web.archive.org/web/20110724081452/http://knygos.sprogmenys.net/knygos-2/Explosives/Shaped%20Charges,%20Penetrators/Some_metalurgical_aspects_of_shaped_charge_liners.pdf |archive-date=2011-07-24}}</ref>

===Explosive charge===
For optimal penetration, a high explosive with a high detonation velocity and pressure is normally chosen. The most common explosive used in high performance anti-armor warheads is [[HMX]] (octogen), although never in its pure form, as it would be too sensitive. It is normally compounded with a few percent of some type of plastic binder, such as in the polymer-bonded explosive (PBX) LX-14, or with another less-sensitive explosive, such as [[trinitrotoluene|TNT]], with which it forms [[Octol]]. Other common high-performance explosives are [[RDX]]-based compositions, again either as PBXs or mixtures with TNT (to form [[Composition B]] and the [[Cyclotol]]s) or wax (Cyclonites). Some explosives incorporate powdered [[aluminum]] to increase their blast and detonation temperature, but this addition generally results in decreased performance of the shaped charge. There has been research into using the very high-performance but sensitive explosive [[CL-20]] in shaped-charge warheads, but, at present, due to its sensitivity, this has been in the form of the PBX composite LX-19 (CL-20 and Estane binder).

===Other features===
A 'waveshaper' is a body (typically a disc or cylindrical block) of an inert material (typically solid or foamed plastic, but sometimes metal, perhaps hollow) inserted within the explosive for the purpose of changing the path of the detonation wave. The effect is to modify the collapse of the cone and resulting jet formation, with the intent of increasing penetration performance. Waveshapers are often used to save space; a shorter charge with a waveshaper can achieve the same performance as a longer charge without a waveshaper.<!--See U.S. Patent 2,809,585, Oct. 15, 1957-->  Given that the space of possible waveshapes is infinite, machine learning methods have been developed to engineer more optimal waveshapers that can enhance the performance of a shaped charge via computational design.<ref>{{cite journal |author= D.M. Sterbentz, C.F. Jekel, D.A. White, R.N. Rieben and J.L. Belof |date= July 24, 2023 |title= Linear shaped-charge jet optimization using machine learning methods |journal= Journal of Applied Physics |volume= 134 |issue= 4 |pages= 045102|doi= 10.1063/5.0156373 |bibcode= 2023JAP...134d5102S |osti= 1999463 }}</ref>

Another useful design feature is ''sub-calibration'', the use of a liner having a smaller diameter (caliber) than the explosive charge. In an ordinary charge, the explosive near the base of the cone is so thin that it is unable to accelerate the adjacent liner to sufficient velocity to form an effective jet. In a sub-calibrated charge, this part of the device is effectively cut off, resulting in a shorter charge with the same performance.