Brisance is the destructive fragmentation effect of a charge on its immediate vicinity. When an explosive detonates, tremendous pressure is released practically instantaneously in a shock wave which exists only a fraction of a second at any given place. The subsequent expansion of gases performs work but the sudden pressure thus created will shatter rather than displace any object in its path. The ability of an explosive to demolish (fragment, shatter) a solid object (such as steel, concrete, stone) when fired in direct contact with it or in its vicinity is called brisance (from the French "briser" = to break or shatter). From a military viewpoint brisance is of practical importance because it determines the effectiveness of an explosive in fragmenting shells, bomb casings, grenades, mines, etc and in imparting high velocities to the resulting fragments. As the shattering effect is dependent upon the suddenness with which the gaseous products of an expl are liberated, the velocity of detonation is at least a major factor in determining.brisance. It has been found that there is a general linear relationship between velocity of detonation and brisance, and if the velocity is known it is possible to calculate the brisance or vice versa (as will be shown below under Brisance-Detonation Velocity Relationship)Brisance may also be calculated from the formula of Kast (see below) or determined experimentally by one of the test methods. Since brisance is approx proportional to detonation velocity, “force” and density of loading, Kast proposed to determine it by the following equation:

B = F * d * D

Where В is brisance value (BrisanZwert in Ger), d is density of charge, D detonation velocity in m/sec and F "specific energy or force", also called “specific pressure”. The Germans call it "spezifische Kraft oder Energie". The force is expressed in kg/cm and is equal to p0 * v0 * T/273 where p0 is atmospheric pressure expressed as 1.033kg/cm2, v0 volume of gases developed on explosion in cc per g of explosive, reduced to 0C and 760mm Hg pressure and T is the max absolute temperature of explosion. On substituting for F, in the above expression, the following equation is obtained:

В = P0 * v0 * T/273 * d * D

In the above equation T is equal to t+273 or to Qe/C + 273 where Qe is the heat of explosion in cal/g and C is the mean specific heat of the products of expln in cal/g. As an example, for blasting gelatin (NG 92 & NC 8%), Stettbacher gives: p0 = 1. 033, v0 = 711.4cc per g, T = 4410°C, d 1.60 and D = 7500 m/sec. This gives:

B= 1.033*711.4* (4410/273) * 1.6 * 7500 = 151.2E+6

Kast's values for many explosives can be found in references. However, practical tests do not confirm the idea that В is proportional to the square of the deton velocity but that simple proportionality (as in the formula of Kast) agrees better with the facts. Friederich introduced the term "specific brisance" and proposed to calculate it from the formula (D2max*A)/100 kg/cm2, where Dmax is detonation velocity and A specific gravity in g/cc. The following table compares "specific brisance" with Kast's brisance values:

It should be noted that brisance is a very complicated phenomenon and that none of the existing methods of calculation, such as by Kast's formula (see above), Herlin's formula, Bichel's formula, Friederich's formula, etc or of experimental determinations gives exact interpretation of B. The matter of detg it is complicated by the fact that the В of a cartridge of explosive is different in different directions: if a cylindrical cartridge is detonated from one end, the action in the direction in which detonation proceeds is considerably greater than that in the opposite direction. According to Cook the term brisance was used to describe the property now attributed to detonation pressure. This property may in many cases be calculated from fundamental physical laws. For a condensed explosive the detonation pressure p2 may be approx calcd from the equation:

p2 = 0.00987*p*(D^2)/4

Where p, is the original density and D the detonation velocity in m/sec. A more accurate equation is also given by Cook. Lothrop & Handrick discussing the relationship between performance and constitution of pure organic compounds included curves showing the relationship between power & brisance and oxygen balance of many organic explosives. Price, in discussing the dependence of damage effects upon detonation parameters of organic high explosives, substituted the term detanation pressure for brisance and detonation energy for power. She also stated that from data obtained at NOL, it has been possible to show that fragment velocity, shaped charge penetration, airblast, and underwater effects are related to the explosive properties of detonation pressure and detonation energy.

Brisance-Detonation Velocity Relationship has long been recognized that brisance is related to detonation velocity and efforts have been made to determine and express relationship beween these two characteristics of an explosive. According to Rinkenbach, there was developed at Picatini Arsenal the following approx empirical relationship between brisance(B) in grams of sand crushed by 0.4g sample when detonated in a 200-g bomb, and detonation ve-locity (D) in m/sec; logB= 3.451og(D/2450). A similar equation was later reported in a manual compiled at Aberdeen PG. From sand test values (B) detd at PicArsn for ca 20 explosions (using 0.4g samples in both 200g and 1700g bombs) and from data available in the literature for their deton velocities (D) at approx their max densities, Rinkenbach obtained a nearly linear relationship on plotting В vs D. This permitted the following equations to be derived:

D = 63.99B + 4234 m/sec (for 200-g bomb)

D = 76.76B + 3965 m/sec (for 1700-g bomb)

By means of these equations the detonation velocity of an explosive can be calculated with a mean accuracy of ca 45 m/sec. Note: The above equations are not identical because the values for В obtained in the 1700-g bomb were somewhat lower than those obtained for the same expls in the 200-g bomb; but the relative orders of the expls with respect to В were the same in both bombs. The difference between the В values for each explosive in the two bombs is attributed to the different thicknesses of the layers of sand between the cap (contg the chge) and the walls of the two bombs. Table below gives a comparison between D calcd by Rinkenbach and D obtained by averaging the various values in the literature.

To calculate brisance of unknown compounds as discussed in this topic one can simply use above equations provided by Rinkenbach:

B = (D – 4234) / 63.99 (200g bomb)

B = (D – 3965) / 76.76 (1700g bomb)

Using calculated VOD, for example in out test case we get (8899-3965)/76.76 = 64g of crushed sand, experimental value for RDX at density slightly lower then TMD is 59g of crushed sand. As seen in this example, equations above can provide quite accurate prediction of brisance.

Power of Explosives. In its normally used context, power of an explosive is a misnomer. It is generally accepted that power of an explosive is a measure of its strength, its blasting action or available energy, and not necessarily a measure of its rate of energy delivery, which is indeed the true definition of power. Further confusion arises because another frequently used explosives term, called brisance, is sometimes erroneously equated with power. Brisance is a measure of the ability of an explosive to shatter material in its immediate vicinity. The fundamental property of an explosive that determines brisance is its detonation pressure. The power of an explosive (we bow to accepted usage and will keep referring to power rather than the correct terms such as strength or blasting ability), on the other hand, is a measure of the ability of an explosive to do work such as blasting down rock or propelling a chunk of metal. The fundamental explosive property that determines its power (or better, available work) is its heat of detonation, Q, or the related quantity, njTj, where nj is the number of moles of gas under steady (Chapman-Jouguet) detonation conditions and T; is the detonation temperature. As will be shown below, a more exact dependence is that power is proportional to Q-q (rather than just Q), but q, the residual heat of the detonation products, is usually quite small compared to Q. According to Andreev & Belyaev, taking to account that exposion process is substantialy adiabatic, the energy available to do external work (we continue to miscall it power) is:

Where P - pressure, V - volurne, T - ternperature, Cv - specific heat of the detonation products, and the subscripts, i & f refer to initial and final states respectively. The initial state is usually taken to be that achieved in a constant volume explosion, the final state is the state of product expansion, after which no more useful work is available. Final temperature of gasses is not easy to predict, so to make equation more suitable for actuale use it’s more effective to use ratio of pressures instead of temperatures, so taking to account equation of state for ideal gas we can derive equation above to the following form:

Where K is adiabatic index (Cp/Cv), witch in common explosion conditions is aproximately 1.28 for diatomic gasses and 1.17 for triatomic ones. Since gasses will expand until they equalize their pressure with surrounding ambience Pi is simply atmospheric pressure ~1 bar or precisely 101325 Pa. Pf – is initial pressure of expanding gasses, it can be derivated from calculated exposion temperature (watch my posts about calculation of VOD by Keshwarz method above) and by taking to account the fact that at initial moment all explosion produced gasses occupy space witch was occupied by initial solid exposive, so initial gas volume is Vi = m/r0, where m – mass of explosive, r0 – loading density. Since equation of state will include ammount of gasses produced by explosion (Ng, moles of gas per mole of explosive), we should use volume of 1 mole of explosive from witch this ammount of gasses is produced, so Vi = Mw/r0, where Mw is molecular mass of explosive. Substitution of this values into equation of state for ideal gas (written for Ng moles of gas produced by explosion) gives us following equations:

Here Pi – initial gas pressure (Pa), Pf – ambient pressure (101325 Pa), R – universal gas constant (8.31), Ng – moles of explosion gasser per mole of explosive, Ti = Te = temperature of exposion (K), Mw – molecular mass of explosive in (kg/mole), r0 – density of explosive (kg/m3), k – average adiabatic index of gaseous explosion products, Qe – heat of explosion (MJ/kg), A – efferctive work of explosion (MJ/kg), Ne – explosion work efficency coefficent. Using equations above, with explosive density (calculated as shown in previous posts), number of explosion gasses per mole of explosive (derivated from explosion reaction equation), explosion temperature (also computed with calculation of VOD by Keshwarz method described in previous posts), we can now simply calculate effective work of explosion for our model explosive, only additional parameter witch we need to calculate is K – average adiobatic exponent. Let’s look on our model explosion equation again:

C3N6H6O6 = 3H2O + 3CO + 3N2

As we see 1 molecule of explosive produces 9 moles of gaseous products, from witch 6 moles are diatomic gases, and 3 moles are triatomic ones. Since K is simple average and for diatomic gasess for common explosion conditions k = 1.28 and k = 1.17 for triatomic ones we calculate average K:

K = (6/9)*1.28 + (3/9)*1.17 = 1.243

For example let’s calculate effective explosion work for out model explosive from previous posts.For our model explosive we calculated following parameters: T=3731K; r0 = 1.81 g/cm3 = 1810 kg/m3; Ng = 9; Mw = 222.11 g/mole = 0.2221 kg/mole; Pf = 101325 Pa ; Qe = 5.668 MJ/kg (more accurately calculated using computed heat of formation for our model exlosive and experimental ones for explosion gasses); R = 8.31 ; K = 1.243, we get:

Values taken from literature are 86.6% and 4.710 MJ/kg respectively, so computed results are in nice agreement. For example, below are corresponding values for some commonly used exposives, against their heats of explosion and corresponding ratios vs TNT and results of Trauzl lead block expansion tests:

Now when we know exposive power we can compare it against corresponting value for some known explosive with known power test value (for example lead block expansion - Trauzl test) and finaly derivate aproximate test value of explosive power test for our model explosive. There are many explosive blasting power tests mentioned in literature, three of this methods are in common use: 1) Ballistic Mortar; 2) Trauzl block expansion; 3) Underwater explosions; and 4) one method - cylinder expansion - that is now used at Lawrence Iivermore Laboratories.

Trauzl Leod Black Test or Lead Black Expansion Test (Cavite au bloc de Trauzl or Epreuve au bloc de plomb de Trauzl, in Fr) (Trauzlsche Probe or Bleiblockausbachung Methode, in Ger) (Prueba Trauzl or Prueba del bloque de plomo, in Span ) (Metodo del Trauzl or Metodo del blocco di piombo, in Ital). This test measures the "comparstive disruptive power''of an explosive through enlargement of a cavity in a cylindrical lead block under carefully standardized conditions. Standart conditions for conducting this test were defined by a Comm. of the Fifth International Congress of Applied Chemistty. Although one of the oldest tests known for determinating power, it is still widely used today but more common in Europe than in the USA Scheme of apparatus is shown below:

Procedure. A sample of the test explosive (approximately 10 g) is detonated in a cavity or borehole, 25 mm in diameter and 125 mm deep, in a standart lead block 200 mm in diameter and 200 mm in height. The borehole is made centrally in the upper face of each block, previously cast in a mold from desilvered lead of the best quality. An electric blasting cap is placed centrally in the charge. After the charge and detonator are placed in the borehole, 40 cm3 of Ottawa sand are added and tamped lightly. An additional 10 cm3 of sand are added and tamped more thoroughly. The volume of the hole made due to the press exerted by the exploding charge is then detd; and the distension(expansion) is calculated by subtracting from this value, the volume of the borehole before the charge is detonated. Three such tests are made and the results averaged. Expansions for equivalent weights of explosives are calculated, and the test value is expressed in % of the expansion of an equivalent weight of TNT. The Trauzl test in France is somewhat different in procedure although dimensions of the lead block are the same. Initiating efficiency strength of primary explosives can be approximately determinated by firing a small charge (such as 1.0 g) in the cavity of a small lead block, such as 100 mm in height and 100 mm in diam. For testing detonators in such block, a hole is bored in the block of the exact diam of the detonator and of such a depth that the top of the detonator is flush with the top of the block.

As clearly seen from test description above trauzl test results are clearly product of explosive blasting power, determined by effective work of exposion. To derivate trauzl test results for our model explosive we must compare effective work of explosion of our explosive against effective work of explosion for some other known explosive with measured Trauzl test. To do so we must enstablish effective work of explosion equavalency and after that use a graph of Trauzl value vs weight of charge for this known explosive to determine value of Trauzl expansion for our model explosive. A suitable explosive for comparsion is Ammonite №6, proposed by Andreev & Belyaev due to almost complete independence of explosion energy from density. Andreev & Belyaev in their book on explosive theory provide the following graph:

Let’s estimate Trauzl Block test value for our modell explosive, to do so the only thing we need is value of effective work of explosion, witch we calculated in section earlier, for our model explosive (RDX) we calculated Ae = 4.868 MJ/kg ; using data from Ae table in corresponding section we find Ae for ammonite №6 Ae = 1030 ccal/kg = 4.312 MJ/kg. After subdivision of corresponding values we can calculate our explosive/ammonite6 eq. ratio and calculate corresponding Trauzl test estimate value for our explosive:

Ae/Ae(ammonite) = 4.868 / 4.312 = 1.128; Eq.w.(ammonite6) = 10*1.128 = 11.28g

Using graph above we get Trauzl test value for our explosive, aproximately 480 cm3, experimental value for RDX is 495 cm3, so method is usefull and can provide results with good align with experiment.