Explosive Bonding of Refractory Metal Liners 

by William S. de Rosset 

ARL-TR-3267 August 2004 

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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5069 

ARL-TR-3267 August 2004 

Explosive Bonding of Refractory Metal Liners 

William S. de Rosset 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited.
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Explosive Bonding of Refractory Metal Liners 

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14. ABSTRACT 

TPL, Inc. has successfully bonded a pure tantalum liner to the inside of an M242 Bushmaster barrel using a low-detonationvelocity explosive. This report examines the governing equations of the explosive bonding process as they apply to this 

particular situation. The relevant properties of other higher strength tantalum alloys are examined to see if they are suitable for 

explosive bonding, with the expectation that they would be better able to resist the wear forces at the rifled bore surface. For all 

candidate materials, attention is paid to the values of critical impact pressure, the critical flow transition velocity, the critical 

angle for jet formation, and maximum flyer plate velocity. Example plots are provided to indicate the bounds of explosive 

welding parameters that will result in a good bond. 

15. SUBJECT TERMS

explosive bonding, gun tube liners, refractory metals, wear and erosion, Bushmaster 

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William S. de Rosset 

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iii

Contents 

List of Figures v 

List of Tables v 

Acknowledgments vii

1. Introduction 1

2. Background 2

3. Governing Equations 5

4. Application of Governing Equations 8

5. Discussion 12

6. Summary 14

7. References 15

Distribution List 17 
iv

INTENTIONALLY LEFT BLANK. 
v

List of Figures 

Figure 1. Donor tube wall thickness as a function of the donor tube outer radius for a fixed 

final liner thickness....................................................................................................................3 

Figure 2. Standoff normalized to donor tube wall thickness as a function of donor tube outer 

radius..........................................................................................................................................4 

Figure 3. Strain imparted to cylinder as a function of donor tube outer radius. .............................5 

Figure 4. Geometry of explosive bonding setup.............................................................................6 

Figure 5. Relation of pressure P in MPa vs. α in degrees for Vc = 5 km/s. ..................................10 

Figure 6. Bounding plots for explosive bonding of tantalum and two alloys...............................11 

Figure 7. Bounding plots for niobium. .........................................................................................12 

Figure 8. Relation between α (in degrees) and standoff for a specific case. ................................14 

List of Tables 

Table 1. Tantalum alloy material properties...................................................................................9 

Table 2. Tantalum material properties............................................................................................9 

Table 3. Properties of niobium......................................................................................................12 
vi

INTENTIONALLY LEFT BLANK.
vii

Acknowledgments 

The author is indebted to Brian Scott for providing background information on explosive 

bonding. He also recognizes the help of Steven Segletes for advice in writing the report. 

Dattatraya P. Dandekar was the source of the equation-of-state data. Discussions with Jonathan 

Montgomery and Bob Lowey (TPL, Inc.) were helpful in writing the background section of the 

report. Finally, the author is indebted to Larry Burton for his critical review of the report. 
viii

INTENTIONALLY LEFT BLANK. 
1

1. Introduction 

Gun barrel wear and erosion has been a major determinant in the useful life of most Army guns. 

It is a problem that has been addressed with propellant additives, barrel coatings, and reduced 

flame-temperature propellants. The problem has become more of an issue with the push to use 

higher-performance, higher flame-temperature propellants. Thus, the need to reduce barrel wear 

and erosion is established on prolonging the life of current gun barrels as well as providing the 

opportunity to introduce new propellants into future gun systems. 

As part of a Small Business Innovative Research (SBIR) Phase 2 program, TPL, Inc. has 

demonstrated its ability to line the inside of both a rifled and smooth-bore (honed out) M242 

Bushmaster 25-mm gun barrel with pure tantalum (Lowey, 2002) using an explosive bonding 

process. Initial firing tests at the U.S. Army Aberdeen Test Center showed that the tantalumlined barrels have a remarkable resistance to wear and the explosive bonding process produced 

an extremely strong bond between the tantalum and gun steel. Most of the work was conducted 

with a smooth-bore gun, and the question of wear on a rifled surface was still an issue. 

This successful effort has prompted continuance of the work through a Manufacturing 

Technology (Mantech) program. The goal of the program is to reduce wear and erosion of the 

M242 25-mm Bushmaster gun tube. One of the tasks of this program is to examine the choice of 

liner materials to see if another candidate material is more suitable. It may be that pure tantalum 

is too soft to withstand the forces exerted on the lands and grooves of rifled guns. Tantalum is 

also considered an expensive material, and since cost avoidance is one of the principal tenets of 

the Mantech program, high material cost is an issue. 

One criterion for choice of a liner material is its cladability. This report investigates the material 

properties that make materials amenable to being explosively bonded to gun steel. In the next 

section, the work that TPL did to bond the tantalum liner to the M242 will be reviewed. 

Particular attention will be paid to the characteristics of the explosive and the geometry of the 

tantalum cylinder used in the TPL work. The governing equations used in explosive bonding are 

presented in section 3. These equations indicate what material parameters are important for the 

process to be successful. (Note that other important characteristics of the liner, such as hardness, 

resistance to chemical attack, and machinability, are not addressed in this particular task.) 

Section 4 takes the values of those material parameters for tantalum and several of its alloys to 

calculate the collision angle and collision velocity that give a good explosive bond. Results are 

also presented for niobium. The final section discusses the suitability of these metals and the 

implications for the choice of explosive. 
2

2. Background 

There is a certain amount of trial and error in establishing the operating parameters used in 

explosive bonding. This is evident in the number of different explosive formulation variations 

used by TPL in its work with the M242 Bushmaster gun barrel (Lowey, 2002). The final report 

for the Phase 2 effort omitted several important details; therefore, some suppositions about this 

work will be made for the remainder of this report. For instance, the actual formulation used to 

clad the three M242s was not explicitly specified in the final report; however, it can be inferred 

from the report that the explosive had a detonation velocity between 1.7 and 2.2 km/s. 

The characteristic velocity, known as the Gurney velocity, 2E, can be estimated from the 

following: 

2E D/2.97, = (1) 

where D is the detonation velocity (Cooper, 1996). For this specific case, 2E is calculated to 

be 0.74 km/s, using the upper limit of D (2.2 km/s). Values of the Gurney velocity for standard 

military explosives generally fall between 2 and 3 km/s (Zukas and Walters, 1998). 

There were many steps needed to process the M242 gun tube. The parts dealing primarily with 

the explosive bonding process itself were filling a tantalum donor tube with explosive, inserting 

the donor tube into the gun tube, centering the donor tube so that it was concentric with the gun 

tube, evacuating the gun tube, and detonating the explosive. The gun tube had been bored out to 

an inner diameter of 1.064 in (27.03 mm) to accommodate the liner thickness. (The diameter 

reported in Lowey [2002] was given as 1.0547 in. This is a typographical error [Lowey, 

2004b].) The original dimensions of the tantalum donor tube were 0.75 in (19.05 mm) for the 

diameter and 0.065 in (1.651 mm) for the wall thickness. Given the density of the explosive as 

0.66 g/cm3

 (Lowey, 2004a) and the density of tantalum as 16.65 g/cm3, the charge-to-mass ratio 

(C/M) can be calculated as 0.0856. Using the Gurney equation for the metal velocity V of the 

expanding cylindrical wall, we get the following: 

 V = 2E (M/C + 1⁄2) –1/2 = 0.212 km/s. (2) 

The tantalum donor tube used in the explosive bonding to the M242 gun tube underwent a large 

amount of plastic strain. The radial component of strain ε on the outer surface of the cylinder 

can be found using the values of the following initial and final cylinder outer diameters: 

 ε = ln (final cylinder diameter/initial cylinder diameter) 

 = ln (1.064/0.75) = 35%. (3) 

There is a certain amount of plastic strain associated with the explosive bond itself. 

Consequently, an important material characteristic for explosive bonding is material ductility. 

However, in this particular instance, the need for material ductility is increased due to the fact 
3

that the tantalum donor tube has to expand and stay together within the gun tube. TPL made an 

attempt to use tantalum-10% tungsten (Ta-10W) as the liner material (Lowey, 2002). No 

successful bonds were ever achieved. One possible cause cited for this failure was that the 

Ta-10W might have had too many interstitial impurities. Also, the starting material may have 

been too strain-hardened. Mulligan et al. (2002) point out that “... commercially pure electron 

beam melted tantalum has an elongation of ~30 to 40% and a yield strength of ~5 ksi at 1000 °C, 

while Ta-10W has an elongation of ~25% (within limits of explosive bonding)...” If the same 

initial donor tube dimensions were used for Ta-10W as were used for the pure tantalum, the 

allowable elongation limit may have been exceeded. 

The need to have liner ductility in excess of 30% elongation may be reduced if the initial donor 

tube diameter is increased. (The tantalum tubes used by TPL, Inc. were purchased as off-theshelf items and therefore came in a standard size.) However, there is a limit to the diameter size 

of the donor tubes. This is due to the standoff (initial distance between the outer donor tube wall 

and the inner gun wall) needed in the explosive bonding process. A rough “rule of thumb” is 

that the standoff should be between 1/2 and 1× the flyer plate thickness (Wylie et al., 1970). In 

any event, the cylinder wall thickness can be calculated as a function of the outer radius of the 

cylinder, assuming that the M242 is honed to the same dimensions (1.064-in inner diameter) and 

that the same final liner thickness (0.044 in) is achieved. This relation is shown in figure 1. 

Figure 1. Donor tube wall thickness as a function of the donor tube outer radius for a fixed final liner 

thickness.

Donor Tube Outer Radius, in

0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52

0.045

0.050

0.055

0.060

0.065

0.070

0.075
4

As the donor tube outer radius changes, the standoff (distance from the outer diameter of the 

donor tube to the inner diameter of the gun tube) normalized to the donor tube wall thickness 

changes. This is shown in figure 2. Finally, the amount of strain imparted to the donor tube can 

be calculated as a function of the donor tube outer radius. This is shown in figure 3. 

Figure 2. Standoff normalized to donor tube wall thickness as a function of donor tube outer radius. 

These figures indicate that there is a range of possible initial conditions. The exact choice of 

these parameters will depend upon many other factors, including type of explosive used, 

availability of liner material with specified dimensions, and allowable elongation of the liner 

material. Similar plots can be made for other gun systems or for different choices of final liner 

thickness or initial gun tube diameter. The main point of these three figures is that if a 

normalized standoff less than 2 can be used, a lower elongation requirement can be met. For 

instance, a normalized standoff of 1.5 will result in a final elongation of less than 20%. 

Donor Tube Outer Radius, in

0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52

0.5

1.0

1.5

2.0

2.5

3.0
5

Figure 3. Strain imparted to cylinder as a function of donor tube outer radius. 

3. Governing Equations 

Explosion bonding has been used commercially for over 40 years to weld dissimilar metals that 

are otherwise difficult to join. The technology is relatively mature, and the governing equations 

have been documented in many publications. Carpenter and Wittman (1975) provide an 

excellent review of the technology, and most of what is presented in this section is taken from 

their work. (See this reference for a more thorough discussion of the equations.) In particular, 

they present four boundary conditions necessary to provide optimum explosion bonding 

characteristics. These are the critical angles for jet formation, the critical impact pressure, the 

critical flow transition velocity, and a maximum impact velocity. 

Figure 4 briefly describes these governing equations and their rationale and shows the geometry 

of the explosive bonding setup. A constant standoff geometry is used for bonding the metal liner 

to the gun tube wall. (We distinguish between the initial liner configuration, called the donor 

tube, and the gun barrel.) In this figure, V is the flyer plate velocity, D is the velocity of 

detonation of the explosive, Vc is the collision point velocity, and α is the angle between the 

donor tube and the gun barrel at the collision point. 

Donor Tube Outer Radius, in

0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52

0

10

20

30

40

50
6

Figure 4. Geometry of explosive bonding setup. 

In general, 

 Vc = D, (4) 

and 

 V = 2D sinα/2. (5) 

For small values of α, 

 V = D sinα. (6) 

The first consideration is the minimum impact pressure needed to make the explosive bonding 

process work. Carpenter and Wittman (1975) provide an empirically-successful relation between 

the minimum donor tube impact velocity Vmin and the ultimate tensile strength σts as follows: 

 Vmin = (σts / ρ)

1/2, (7) 

where ρ is the donor tube density. It is presumed that the ultimate tensile strength is that strength 

measured at room temperature. However, it is expected that the donor tube will be heated during 

plastic deformation, lowering its strength. Consequently, the Vmin calculated may overestimate 

the actual value of Vmin. Note also that these same authors acknowledge that it would be better 

to use the Hugoniot elastic limit (HEL) to calculate Vmin (in another formula). However, the 

value of HEL for many alloys is not always available. Consequently, for sake of comparison 

among the alloys examined in this report, the ultimate tensile strength will be used in the 

calculations. 

The second consideration is the existence of a specific collision velocity below, where 

researchers have found the bond line to be flat, and above, where they found it to be wavy. A 

wavy bond line is indicative of a good bond, implying that there is a lower limit to the collision 

velocity for a good bond. This transition velocity will be designated as VT. Cowan et al. (1971) 

relate VT to the density of the donor tube, ρ to the density of the gun barrel ρb, and HF and HB to 

Barrel Wall 

V 

α

Barrel Center Line 

Explosive 

 Donor Tube 

 D 

 Vc

 Standoff 
7

the diamond pyramid hardness of the donor tube and gun barrel, respectively, given a consistent 

set of units, in the following way: 

 VT = FB b 2R (H + H )/(ρ + ρ ) . Τ (8) 

RT is an empirically determined parameter that, for a wide range of metals, averages to 10.6 (no 

units). This is the value that will be used for calculations in this report. 

Wittman (1973) derived a formula for the maximum donor tube velocity that would not result in 

melt-induced defects destroying the bond strength. This maximum velocity, Vmax, can be 

calculated from the following equation: 

 Vmax = 

1/2 1/4

MP B B

1/4

c

(T C ) (KCC ) 

N V (ρh) . (9) 

The material characteristics associated with the flyer plate are as follows: 

• TMP, the melting point in °C; 

• CB, the bulk sound speed; 

• K, the thermal conductivity; 

• C, the specific heat; 

• h, the flyer plate thickness; and 

• ρ, the flyer plate density. 

N is a constant that is not explicitly provided in the Carpenter and Wittman reference (1975). 

However, it can be derived from the table of material properties provided in this reference. First, 

calculate the value of Vmin using the values of ρ and σts with equation 7. Next, determine NVmax

from the other parameters provided in Carpenter and Wittman (1975) and equation 9. The value 

of N can then be determined from the ratio of Vmax to Vmin provided in this reference. For the 12 

metals listed, the average value of N is 0.11, with a mean deviation of 0.009. N will be taken as 

0.11 (using cgs units) for calculations in this report. 

There is experimental evidence that a jet is formed at the intersection of colliding surfaces during 

the explosive bonding process (Bergmann et al., 1966). It is generally accepted that this jet rids 

the colliding surfaces of any oxides and promotes a metallurgical bond. However, not all 

collisions result in a jet. Walsh et al. (1953) first proposed the concept of a critical collision 

angle for jet formation. This is the minimum angle at a specified collision velocity that is 

required for jet formation. Cowan et al. (1971) extended this work to asymmetric collisions. 

They give the angle α in terms of the shock parameters and Vc: 

 tan α = Up(Vc

2

 – Us

2

)

1/2 /(Vc

2

 – UpUs). (10) 
8

At the critical collision angle, the partial derivative of the pressure with respect to α is zero (fixed 

Vc) (Walsh et al., 1953). The pressure P is related to the shock velocity Us and the particle 

velocity Up through the following usual equation: 

 P = ρ UsUp. (11) 

The empirically determined relation between Us and Up is also required to determine the critical 

angle. The relation between the shock velocity and Vc is given by the following: 

 Us = Vc sin β, (12) 

where β is the angle between the shock front and the material flow vector into the collision point 

viewed from a frame of reference that is stationary with respect to the collision point. Rather 

than calculate α explicitly in terms of P and take the partial derivative, it was easier to fix Vc and 

vary β. This generated values of Us, Up, P, and α. A plot of P vs. α showed a distinct maximum, 

and the critical angle for the given value of Vc was obtained. This was done for enough values 

of Vc to generate the required information. 

4. Application of Governing Equations 

Some cautions must be stated before applying the governing equations. First, they are to be 

applied with the understanding that the equations provide guidelines only. The actual parameters 

used to obtain the best possible bond will still be determined through a trial and error 

experimental process. Second, in applying these equations, it is important that a consistent set of 

units be used. In many instances, material property data are gathered from different sources that 

use different units. Some care must be exercised in converting all the data so that the units are 

consistent. Note that in equation 9, the value of N was determined using centimeter-gramseconds °C as the set of units. Finally, it may not be possible to obtain the exact material 

properties for all alloys. In these cases, best estimates will be made. 

While the use of pure tantalum resulted in a successful cladding of a liner to the M242 

Bushmaster barrel, it may be that a higher-strength alloy is needed in a rifled bore configuration. 

Such alloys as tantalum-3% tungsten (Ta-3W) and Ta-10W are likely candidates. The densities 

of these two alloys can be found from a rule of mixtures, where the density of tantalum is taken 

to be 16.65 g/cm3

 and the density of tungsten is taken to be 19.3 g/cm3. The ultimate tensile 

strength of tantalum varies as a function of temperature. A value of 250 MPa = 36 ksi is used for 

the room temperature value of σts (American Society for Metals, 1979). The values of σts for 

Ta-3W and Ta-10W are 60 ksi and 120 ksi, respectively (Aimone, 2004). The calculated values 

of Vmin are given in table 1. 
9

Table 1. Tantalum alloy material properties. 

Material Density 

(kg/m3) 

Ultimate Tensile 

Strength, 

(MPa) 

Vmin 

(km/s) 

VT 

(km/s) 

Tantalum 16.65 × 103 250 0.123 2.05 

Ta-3W 16.73 × 103 414 0.157 2.10 

Ta-10W 16.92 × 103 828 0.221 2.15 

The transition velocity VT for these materials can be found from equation 8. The Vickers 

hardness ranges for tantalum and Ta-3W are 90–100 and 110–130 (Aimone, 2004). An estimate 

of the hardness range for Ta-10W is 140–160 Vickers. Note that the hardness of the tantalum 

liner (after explosively bonding) was measured by Pepi et al. (2003) to be 140 Vickers. It is 

likely that the explosive bonding process increased the hardness of the liner above the original 

hardness. The gun steel hardness reported in Pepi et al. (2003) was 400 Vickers. For purposes 

here, the lower end of the hardness ranges of tantalum and its alloys before explosive bonding 

occurs will be used; the value of 400 Vickers will be used for the steel. The calculated values for 

VT are also shown in table 1. 

It is expected that the critical angle for jet formation and Vmax will depend on the bulk properties 

of the material so that a calculation for tantalum will provide close approximations of these 

values for the Ta-3W and Ta-10W alloys (Furnish et al., 1995 ). The values of the bulk 

properties of tantalum used to calculate Vmax are shown in table 2. The relation between the 

shock velocity Us and the particle velocity Up (Marsh, 1995) is given by the following: 

 Us = 3.43 (km/s) + 1.19 Up. (13) 

In this equation, Us and Up are in kilometers per second. 

Table 2. Tantalum material properties. 

Property Value Reference 

Bulk sound speed 3.43 km/s (Marsh, 1980) 

Density 16.65 × 103

 kg/m3 (American Society for Metals, 1979) 

Melting point 3269° K (American Society for Metals, 1979) 

Thermal conductivity 54.4 w/m K (American Society for Metals, 1979) 

Specific heat 139.1 J/kg K (American Society for Metals, 1979) 

A flyer plate thickness of 0.15 cm (0.059 in) was selected. The table 2 values of input 

parameters were converted to the cgs system, and equation 9 was used to find Vmax in terms of 

Vc. 

 Vmax = 0.923x1010/Vc, (14) 

where Vmax and Vc are now in centimeters per second. We then have the following condition on 

α at V=Vmax: 

α = 2sin-1(Vmax/2Vc) = 2sin-1(.923/2Vc

2

), (15) 
10

with Vmax and Vc in kilometers per second. 

The calculation for the critical angle for jet formation is as follows. First, fix a value of Vc. 

Then, 

 Us = Vc sinβ. (16) 

From the relation between Us and Up, 

 Up = (Vc sinβ – 3.43)/1.19. (17) 

Also, 

 P = ρ (Vc sinβ)(Vc sinβ – 3.43)/1.19. (18) 

Then, from equation 10, 

 tan α = ((sinβ – 3.43/Vc)/1.19)(1 – sin2

β)

1/2/(1 – sinβ(sinβ – 3.43/Vc)/1.19). (19) 

By varying β, values of P and α can be generated. A plot of P vs. α for the case of Vc = 5 is 

shown in figure 5. 

Figure 5. Relation of pressure P in MPa vs. α in degrees for Vc = 5 km/s. 

Oblique Shock Pressure, MPa

0 20 40 60 80 100 120

0

1

2

3

4

5

6
11

It is clear from this figure that the maximum value of α is ~5.4°. Thus, the critical angle for 

Vc = 5 km/s is 5.4°. The relation between Vc and α can be generated with this approach. 

The end result of all these calculations is a plot similar to that shown in Carpenter and Wittman 

(1975), shown in figure 6. For each metal, there is a central area bounded by four lines that 

indicate appropriate ranges of parameters. Bounded from below are the plots of Vmin for each of 

the metals. On the left, the boundary is VT. The values for each metal are so close together that 

VT is represented by a single thick vertical line. On the right, the area is bounded by the 

condition for the critical angle for collision. At the top, the area is bounded by Vmax. 

Figure 6. Bounding plots for explosive bonding of tantalum and two alloys. 

A similar plot can be made for niobium (annealed). Table 3 lists the properties that were used 

for the calculations. All values were obtained from the Metals Handbook (American Society for 

Metals, 1979) except for the bulk sound speed, obtained from Marsh (1980). In addition, the 

relation 

 Us = 4.46 (km/s) + 1.20Up (20) 

and a value of 0.15 cm for the flyer plate thickness were used to generate the plots in figure 7. 

Considering the fact that the material properties for niobium are not too different from those of 

tantalum and its alloys, it is not surprising that the bounding plots in figure 7 appear similar to 

those in figure 6.

Collision Velocity, Vc, km/s

0 2 4 6 8 10

lh d

0

2

4

6

8

10

12

14

16

Vmin, Ta

Vmin, Ta-3W

Vmin, Ta-10W

Transition Velocity

Critical Collision Angle

Vmax
12

Table 3. Properties of niobium. 

Property Value 

Tensile strength 275 MPa 

Density 8.57 g/cm3

Hardness 80 Vickers 

Melting point 2468 °C 

Bulk sound speed 4.46 km/s 

Specific heat (at 20° C) 270 J/kg K 

Thermal conductivity (at 0° C) 52.3 w/m K 

Figure 7. Bounding plots for niobium. 

5. Discussion 

The governing equations presented in section 3 have been developed as a result of many years of 

experience in explosive welding. While they are based on a physical understanding of the 

explosive bonding process, reliance is also placed on fixing certain parameters obtained from 

averages of a large number of tests. For this reason, the governing equations should be taken as 

guidelines to establish the approximate operating parameters for a specific case. Note also that 

the equations were based primarily on experience gained with cladding flat pats on a flat 

Vc, Collision Velocity, km/s

0 2 4 6 8 10 12

lh d

0

2

4

6

8

10

12

14

16

Vmin

Transition Velocity

Vmax

Critical Angle
13

substrate. In the case of explosively bonding a liner to the inside of a gun tube, the geometry is 

different. The large amount of hoop strain that might occur in bonding liners could affect 

material properties to the extent that the equations are no longer good approximations. This is 

especially true if the material properties are highly strain and/or strain rate sensitive. 

In any event, the governing equations help to assess the cladability of a material. Perhaps the 

most important material property is the ultimate tensile strength. As seen in figure 6, as the 

ultimate tensile strength of the various tantalum alloys increases, the Vc-α operating area 

decreases. This is because the lower limit (Vmin) is raised, but the upper limit, being based on 

bulk properties such as density and sound speed, stays about the same. Consequently, the choice 

of high explosive is more restrictive as small alloy additions increase a material’s strength. Note 

that if annealing can lower the tensile strength of the Ta-10W, its cladability would improve 

(Montgomery, 2004). 

The choice of explosive will have a great deal to do with the cladability of a material. The 

explosive used by TPL had an upper limit on the detonation velocity D of 2.2 km/s. Since 

D = Vc, TPL may have been operating at the far left portion of the bounded area for tantalum and 

the two alloys. VT for Ta-10W was calculated to be 2.15 km/s, providing another possibility as 

to why efforts to form a good bond were not successful with this material. For V = 0.212 km/s 

and D = 2.2 km/s, α = 5.5°. This value appears to lie close to the Vmin line shown in figure 6 and 

may provide another reason why the use of this particular explosive was not successful in 

bonding the Ta-10W. However, the explosive should work for the Ta-3W. 

The value of α can be varied by changing V where D is fixed (equations 5 or 6). This can be 

done by changing the charge-to-mass ratio (see equation 2). The possible range of α can be 

calculated with the following assumptions. First, we expect that the liner will be fully packed 

with explosive since allowing a hollow portion down the axis of the explosive may result in a 

dimension less than the failure diameter. Next, consider standoffs between 0.01 and 0.25 in. 

This will allow the mass of both the metal liner and explosive to vary. Finally, we use the 

dimensions previously discussed (1.064-in inner diameter of the gun tube and a final liner 

thickness of 0.044 in). 

The relation between α and standoff is shown in figure 8. The larger standoffs reduce the 

amount of explosive and increase the thickness of the metal liner. Thus, the value of V will 

decrease for larger standoffs, resulting in a decrease in α. Referring to figure 6, it can be seen 

that the values of α in the range of 4–8° at Vc = 2.2 km/s are acceptable and may even allow 

explosive bonding of the higher-strength alloys for the higher values of α (shorter standoff). 

A final consideration in choice of explosives is failure diameter. For all explosives, there is a 

minimum dimension needed to sustain a detonation without confinement. In general, explosives 

with low detonation velocities such as ammonium nitrate have large failure diameters. For the 

current application, this minimum dimension must be less than 25 mm, the bore diameter of the 

M242 gun tube. This condition limits the available choices of explosives for bonding the liner to 

the gun tube. 
14

Figure 8. Relation between α (in degrees) and standoff for a specific case. 

6. Summary 

A pure tantalum liner has been successfully bonded to the inside of an M242 Bushmaster 

medium-caliber cannon in previous work performed by TPL, Inc. under a Phase 2 SBIR. In 

expectation that the tantalum will be too soft to resist wear forces at the lands and grooves in the 

gun barrel, other alloys were examined for suitability for cladding. Semiempirical equations 

governing explosive bonding were applied to two tantalum alloys and niobium. The equations 

indicated that for the particular explosive used by TPL, a shorter standoff would facilitate the 

bonding of higher-strength alloys by increasing the collision angle α and reducing the amount of 

strain in the liner produced by the explosive bonding process. 

Standoff, in

0.00 0.05 0.10 0.15 0.20 0.25 0.30

3

4

5

6

7

8

9
15

7. References 

Aimone, Paul. H. C. Starck Co. Private communication, March 2004. 

American Society for Metals. Metals Handbook, 9th Edition, Volume 2—Properties and 

Selection: Nonferous Alloys and Pure Metals; Metals Park, OH, 1979. 

Bergmann, O. R.; Cowan, G. R.; Holtzman, A. H. Experimental Evidence of Jet Formation 

During Explosion Cladding. Transactions of the Metallurgical Society of AIME 1966, 236, 

646. 

Carpenter, S. H.; Wittman, R. H. Explosion Welding. Ann. Rev. Mat. Sci. 1975, 5. 

Cooper, P. W. Basics of Explosive Engineering; VCH: New York, 1996. 

Cowan, G. R., Bergman, O. R.; Holtzman, A. H. Mechanism of Bond Zone Wave Formation in 

Explosion-Clad Metals. Met. Trans. 1971, 2. 

Furnish, M. D.; Lassila, D. H.; Chhabildas, L. C.; Steinberg, D. J. Dynamic Material Properties 

of Refractory Metals: Tantalum and Tantalum/Tungsten Alloys, in Shock Compression of 

Matter—1995; Schmidt, S. C., Tao, W. C., Eds.; AIP Press: Woodbury, NY, 1995. 

Lowey, R. F. Gun Tube Liner Erosion and Wear Protection; TPL-FR-ER31; under contract 

DAAD19-99-C-0002, TPL, Inc.: Albuquerque, NM, 28 May 2002. 

Lowey, R. F. TPL, Inc., Albuquerque, NM. Private communication, 2004a. 

Lowey, R. F. TPL, Inc., Albuquerque, NM. Private communication, 2004b. 

Marsh, S. P., Ed. LASL Shock Hugoniot Data; University of California Press: Berkley, CA, 

1980. 

Montgomery, J. U.S. Army Research Laboratory, Aberdeen Proving Ground, MD. Private 

communication, April 2004. 

Mulligan, C.; Audino, M.; Cote, P.; Kendall, G.; Rickard, C.; Smith, S.; Todaro, M. 

Characterization of Explosively Bonded and Fired Tantalum Liners Applied to 25-mm Gun 

Tubes; ARCCB-TR-02016; Benet Laboratories: Watervliet, NY, November 2002. 

Pepi, M.; Snoha, D. J.; Montgomery, J. S.; de Rosset, W. S. Examination of Intermetallic 

Phases and Residual Stresses Resulting from Explosive Bonding of Refractory Metal Gun 

Tube Liners; ARL-MR-550; U.S. Army Research Laboratory: Aberdeen Proving Ground, 

MD, February 2003. 
16

Walsh, J. M.; Schreffler, R. G.; Willig, F. J. Limiting Conditions for Jet Formation in High 

Velocity Collisions. Journal of Applied Physics 1953, 24 (3). 

Wittman, R. H. Proceedings of the Second International Symposium Use Explosive Energy Mfg. 

Metallic Materials, Marianske-Lazne, Czechoslovakia, 1973. 

Wylie, H. K.; Williams, P. E. G.; Crossland, B. An Experimental Investigation of Explosive 

Welding Parameters. Proceedings of the First International Symposium, Use of Explosive 

Energy in Manufacturing Metallic Materials of New Properties and Possibilities of 

Application Thereof in Chemical Industry, Marianske-Lazne, Czechoslovakia, 1970. 

Zukas, J. A.; Walters, W. P. Explosive Effects and Applications; Springer-Verlag: New York, 

NY, 1998. 
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 1 NORTHRUP GRUMMAN CORP 

 ELECTRONIC SENSORS 

 & SYSTEMS DIV 

 E SCHOCH MS V 16 

 1745A W NURSERY RD 

 LINTHICUM MD 21090 

 1 GDLS DIVISION 

 D BARTLE 

 PO BOX 1901 

 WARREN MI 48090 

 2 GDLS 

 D REES 

 M PASIK 

 PO BOX 2074 

 WARREN MI 48090-2074 

 1 GDLS 

 MUSKEGON OPER 

 M SOIMAR 

 76 GETTY ST 

 MUSKEGON MI 49442 

 1 GENERAL DYNAMICS 

 AMPHIBIOUS SYS 

 SURVIVABILITY LEAD 

 G WALKER 

 991 ANNAPOLIS WAY 

 WOODBRIDGE VA 22191 

 6 INST FOR ADVANCED 

 TECH 

 H FAIR 

 I MCNAB 

 P SULLIVAN 

 S BLESS 

 W REINECKE 

 C PERSAD 

 3925 W BRAKER LN STE 400 

 AUSTIN TX 78759-5316 

 1 ARROW TECH ASSOC 

 1233 SHELBURNE RD STE D8 

 SOUTH BURLINGTON VT 

 05403-7700 

 1 R EICHELBERGER 

 CONSULTANT 

 409 W CATHERINE ST 

 BEL AIR MD 21014-3613 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

27

 1 SAIC 

 G CHRYSSOMALLIS 

 8500 NORMANDALE LAKE BLVD 

 SUITE 1610 

 BLOOMINGTON MN 55437-3828 

 1 UCLA MANE DEPT ENGR IV 

 H T HAHN 

 LOS ANGELES CA 90024-1597 

 2 UNIV OF DAYTON 

 RESEARCH INST 

 R Y KIM 

 A K ROY 

 300 COLLEGE PARK AVE 

 DAYTON OH 45469-0168 

 1 UMASS LOWELL 

 PLASTICS DEPT 

 N SCHOTT 

 1 UNIVERSITY AVE 

 LOWELL MA 01854 

 1 IIT RESEARCH CTR 

 D ROSE 

 201 MILL ST 

 ROME NY 13440-6916 

 1 GA TECH RESEARCH INST 

 GA INST OF TCHNLGY 

 P FRIEDERICH 

 ATLANTA GA 30392 

 1 MICHIGAN ST UNIV 

 MSM DEPT 

 R AVERILL 

 3515 EB 

 EAST LANSING MI 48824-1226 

 1 UNIV OF WYOMING 

 D ADAMS 

 PO BOX 3295 

 LARAMIE WY 82071 

 1 PENN STATE UNIV 

 R S ENGEL 

 245 HAMMOND BLDG 

 UNIVERSITY PARK PA 16801 

 2 PENN STATE UNIV 

 R MCNITT 

 C BAKIS 

 212 EARTH ENGR 

 SCIENCES BLDG 

 UNIVERSITY PARK PA 16802 

 1 PURDUE UNIV 

 SCHOOL OF AERO & ASTRO 

 C T SUN 

 W LAFAYETTE IN 47907-1282 

 1 STANFORD UNIV 

 DEPT OF AERONAUTICS 

 & AEROBALLISTICS 

 S TSAI 

 DURANT BLDG 

 STANFORD CA 94305 

 1 UNIV OF MAINE 

 ADV STR & COMP LAB 

 R LOPEZ ANIDO 

 5793 AEWC BLDG 

 ORONO ME 04469-5793 

 1 JOHNS HOPKINS UNIV 

 APPLIED PHYSICS LAB 

 P WIENHOLD 

 11100 JOHNS HOPKINS RD 

 LAUREL MD 20723-6099 

 1 UNIV OF DAYTON 

 J M WHITNEY 

 COLLEGE PARK AVE 

 DAYTON OH 45469-0240 

 1 NORTH CAROLINA ST UNIV 

 CIVIL ENGINEERING DEPT 

 W RASDORF 

 PO BOX 7908 

 RALEIGH NC 27696-7908 

 5 UNIV OF DELAWARE 

 CTR FOR COMPOSITE MTRLS 

 J GILLESPIE 

 M SANTARE 

 S YARLAGADDA 

 S ADVANI 

 D HEIDER 

 201 SPENCER LAB 

 NEWARK DE 19716 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

28

 1 DEPT OF MTRLS 

 SCIENCE & ENGRG 

 UNIV OF ILLINOIS 

 AT URBANA CHAMPAIGN 

 J ECONOMY 

 1304 WEST GREEN ST 115B 

 URBANA IL 61801 

 1 UNIV OF MARYLAND 

 DEPT OF AEROSPACE ENGRG 

 A J VIZZINI 

 COLLEGE PARK MD 20742 

 1 DREXEL UNIV 

 A S D WANG 

 3141 CHESTNUT ST 

 PHILADELPHIA PA 19104 

 3 UNIV OF TEXAS AT AUSTIN 

 CTR FOR ELECTROMECHANICS 

 J PRICE 

 A WALLS 

 J KITZMILLER 

 10100 BURNET RD 

 AUSTIN TX 78758-4497 

 3 VA POLYTECHNICAL 

 INST & STATE UNIV 

 DEPT OF ESM 

 M W HYER 

 K REIFSNIDER 

 R JONES 

 BLACKSBURG VA 24061-0219 

 1 SOUTHWEST RESEARCH INST 

 ENGR & MATL SCIENCES DIV 

 J RIEGEL 

 6220 CULEBRA RD 

 PO DRAWER 28510 

 SAN ANTONIO TX 78228-0510 

 1 BATELLE NATICK OPERS 

 B HALPIN 

 313 SPEEN ST 

 NATICK MA 01760 

 3 DIRECTOR 

 US ARMY RESEARCH LAB 

 AMSRD ARL WM MB 

 A FRYDMAN 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

ABERDEEN PROVING GROUND

 1 US ARMY ATC 

 CSTE DTC AT AC I 

 W C FRAZER 

 400 COLLERAN RD 

 APG MD 21005-5059 

 91 DIR USARL 

 AMSRD ARL CI 

 AMSRD ARL O AP EG 

 M ADAMSON 

 AMSRD ARL SL BA 

 AMSRD ARL SL BB 

 D BELY 

 AMSRD ARL WM 

 J SMITH 

 H WALLACE 

 AMSRD ARL WM B 

 A HORST 

 T KOGLER 

 AMSRD ARL WM BA 

 D LYON 

 AMSRD ARL WM BC 

 J NEWILL 

 P PLOSTINS 

 A ZIELINSKI 

 AMSRD ARL WM BD 

 P CONROY 

 B FORCH 

 M LEADORE 

 C LEVERITT 

 R LIEB 

 R PESCE RODRIGUEZ 

 B RICE 

 AMSRD ARL WM BF 

 S WILKERSON 

 AMSRD ARL WM M 

 B FINK 

 J MCCAULEY 

 AMSRD ARL WM MA 

 L GHIORSE 

 S MCKNIGHT 

 E WETZEL 

 AMSRD ARL WM MB 

 J BENDER 

 T BOGETTI 

 L BURTON 

 R CARTER 

 K CHO 

 W DE ROSSET 

 G DEWING 

 R DOWDING 

 W DRYSDALE 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

29

 R EMERSON 

 D HENRY 

 D HOPKINS 

 R KASTE 

 L KECSKES 

 M MINNICINO 

 B POWERS 

 D SNOHA 

 J SOUTH 

 M STAKER 

 J SWAB 

 J TZENG 

 AMSRD ARL WM MC 

 J BEATTY 

 R BOSSOLI 

 E CHIN 

 S CORNELISON 

 D GRANVILLE 

 B HART 

 J LASALVIA 

 J MONTGOMERY 

 F PIERCE 

 E RIGAS 

 W SPURGEON 

 AMSRD ARL WM MD 

 B CHEESEMAN 

 P DEHMER 

 R DOOLEY 

 G GAZONAS 

 S GHIORSE 

 C HOPPEL 

 M KLUSEWITZ 

 W ROY 

 J SANDS 

 D SPAGNUOLO 

 S WALSH 

 S WOLF 

 AMSRD ARL WM RP 

 J BORNSTEIN 

 C SHOEMAKER 

 AMSRD ARL WM T 

 B BURNS 

 AMSRD ARL WM TA 

 W BRUCHEY 

 M BURKINS 

 W GILLICH 

 B GOOCH 

 T HAVEL 

 E HORWATH 

 M NORMANDIA 

 J RUNYEON 

 M ZOLTOSKI 

 AMSRD ARL WM TB 

 P BAKER 

 AMSRD ARL WM TC 

 R COATES 

 AMSRD ARL WM TD 

 D DANDEKAR 

 T HADUCH 

 T MOYNIHAN 

 M RAFTENBERG 

 S SCHOENFELD 

 T WEERASOORIYA 

 AMSRD ARL WM TE 

 A NIILER 

 J POWELL 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

30

 1 LTD 

 R MARTIN 

 MERL 

 TAMWORTH RD 

 HERTFORD SG13 7DG 

 UK 

 1 SMC SCOTLAND 

 P W LAY 

 DERA ROSYTH 

 ROSYTH ROYAL DOCKYARD 

 DUNFERMLINE FIFE KY 11 2XR 

 UK 

 1 CIVIL AVIATION 

 ADMINSTRATION 

 T GOTTESMAN 

 PO BOX 8 

 BEN GURION INTRNL AIRPORT 

 LOD 70150 

 ISRAEL 

 1 AEROSPATIALE 

 S ANDRE 

 A BTE CC RTE MD132 

 316 ROUTE DE BAYONNE 

 TOULOUSE 31060 

 FRANCE 

 1 DRA FORT HALSTEAD 

 P N JONES 

 SEVEN OAKS KENT TN 147BP 

 UK 

 1 SWISS FEDERAL ARMAMENTS 

 WKS 

 W LANZ 

 ALLMENDSTRASSE 86 

 3602 THUN 

 SWITZERLAND 

 1 DYNAMEC RESEARCH LAB 

 AKE PERSSON 

 BOX 201 

 SE 151 23 SODERTALJE 

 SWEDEN 

 1 ISRAEL INST OF TECHLGY 

 S BODNER 

 FACULTY OF MECHANICAL 

 ENGR 

 HAIFA 3200 

 ISRAEL 

 1 DSTO 

 WEAPONS SYSTEMS DIVISION 

 N BURMAN RLLWS 

 SALISBURY 

 SOUTH AUSTRALIA 5108 

 AUSTRALIA 

 1 DEF RES ESTABLISHMENT 

 VALCARTIER 

 A DUPUIS 

 2459 BLVD PIE XI NORTH 

 VALCARTIER QUEBEC 

 CANADA 

 PO BOX 8800 COURCELETTE 

 GOA IRO QUEBEC 

 CANADA 

 1 ECOLE POLYTECH 

 J MANSON 

 DMX LTC 

 CH 1015 LAUSANNE 

 SWITZERLAND 

 1 TNO DEFENSE RESEARCH 

 R IJSSELSTEIN 

 ACCOUNT DIRECTOR 

 R&D ARMEE 

 PO BOX 6006 

 2600 JA DELFT 

 THE NETHERLANDS 

 2 FOA NATL DEFENSE RESEARCH 

 ESTAB 

 DIR DEPT OF WEAPONS & 

 PROTECTION 

 B JANZON 

 R HOLMLIN 

 S 172 90 STOCKHOLM 

 SWEDEN
NO. OF 

COPIES ORGANIZATION 

31

 2 DEFENSE TECH & PROC 

 AGENCY GROUND 

 I CREWTHER 

 GENERAL HERZOG HAUS 

 3602 THUN 

 SWITZERLAND 

 1 MINISTRY OF DEFENCE 

 RAFAEL 

 ARMAMENT DEVELOPMENT 

 AUTH 

 M MAYSELESS 

 PO BOX 2250 

 HAIFA 31021 

 ISRAEL 

 1 TNO DEFENSE RESEARCH 

 I H PASMAN 

 POSTBUS 6006 

 2600 JA DELFT 

 THE NETHERLANDS 

 1 B HIRSCH 

 TACHKEMONY ST 6 

 NETAMUA 42611 

 ISRAEL 

 1 DEUTSCHE AEROSPACE AG 

 DYNAMICS SYSTEMS 

 M HELD 

 PO BOX 1340 

 D 86523 SCHROBENHAUSEN 

 GERMANY 
NO. OF 

COPIES ORGANIZATION 

32

ABERDEEN PROVING GROUND

 15 DIR USARL 

 AMSRD ARL WM TC 

 L MAGNESS 

 AMSRD ARL WM TB 

 J WATSON 

 AMSRD ARL WM TD 

 S SEGLETES 

 AMSRD ARL WM MB 

 W DE ROSSET (10 CPS) 

 AMSRD ARL WM MC 

 V CHAMPAGNE 

 AMSRD ARL WM MD 

 B SCOTT 
33

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