Strength of an Explosively-Formed Bond 

by William S. de Rosset, Daniel J. Snoha, and Michael A. Minnicino 

ARL-TR-3889 September 2006 

Approved for public release; distribution is unlimited. 
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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5069 

ARL-TR-3889 September 2006 

Strength of an Explosively-Formed Bond 

William S. de Rosset, Daniel J. Snoha, and Michael A. Minnicino 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited. 
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4. TITLE AND SUBTITLE 

Strength of an Explosively-Formed Bond 

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6. AUTHOR(S) 

William S. de Rosset, Daniel J. Snoha, and Michael A. Minnicino 

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U.S. Army Research Laboratory 

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13. SUPPLEMENTARY NOTES 

14. ABSTRACT 

A test fixture used to determine the shear strength of an explosively-formed bond between a liner and gun tube is described. 

Tests were carried out in which the liner material yielded before the bond was broken. A finite-element analysis of the 

deformation indicated that the bond shear strength was in excess of 45 ksi. Internal stress measurements made by x-ray 

diffraction indicated the presence of residual hoop and radial stresses produced by the explosive bonding process. The hoop 

stresses at and near the bore were comparable to those achieved with the autofrettage process in a larger gun tube. The residual 

radial stress, along with frictional forces, may account for a large portion of the bond shear strength. 

15. SUBJECT TERMS

gun tube liner, explosive bonding, internal stresses, autofrettage 

16. SECURITY CLASSIFICATION OF: 

19a. NAME OF RESPONSIBLE PERSON

William S. de Rosset 

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iii

Contents 

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction 1

2. Experimental Test Procedure 2

2.1 Sample Preparation..........................................................................................................2 

2.2 Test Fixture Description and Development.....................................................................3 

3. Test Results and Interpretation 6

4. Internal Stresses 8

4.1 Measured Internal Stresses..............................................................................................8 

4.1.1 Experimental Procedure ........................................................................................8 

4.1.2 Results ...................................................................................................................9 

4.2 Bond Strength Contribution From Residual Stresses....................................................11 

5. Summary 13

6. References 14

Appendix. Test Fixture Design 15 

Distribution List 16 
iv

List of Figures 

Figure 1. Labeling scheme for the sections saw cut from the gun tubes. .......................................2 

Figure 2. Liner inside diameter as a function of the distance from the leading end.......................3 

Figure 3. Cross-sectional view of the test fixture showing the placement of the sample to be 

tested. .........................................................................................................................................4 

Figure 4. Test fixture parts and sample C45...................................................................................4 

Figure 5. Load-displacement curves for tests C42 and C43. ..........................................................5 

Figure 6. Axisymmetric finite-element model................................................................................7 

Figure 7. Von Mises stress state at 0.053 in of steel pusher vertical displacement........................7 

Figure 8. Shear stress as a function of position along liner-gun tube interface at 0.053-in 

pusher plug displacement...........................................................................................................8 

Figure 9. Hoop direction residual stress data from explosion bonded Stellite 25-lined 

Bushmaster gun tube specimens A2 (leading end) and A5 (trailing end). ..............................10 

Figure 10. Radial direction residual stress data from explosion bonded Stellite 25-lined 

Bushmaster gun tube specimens A2 (leading end) and A5 (trailing end). ..............................10 

Figure 11. Hoop direction residual stress data from explosion bonded Stellite 25-lined and 

Ta-2.5W-lined Bushmaster gun tubes and swage autofrettaged 120-mm gun tube. ...............12 

Figure A-1. Final test fixture configuration; all dimensions in inches. ........................................15 

List of Tables 

Table 1. Compressive loads at 0.045-in displacement....................................................................6 
v

Acknowledgments 

Special thanks go to Jonathan Montgomery, who helped with sample preparation for the x-ray 

diffraction work, as well as Paul Moy, who conducted the push-out tests. Thanks also go to 

Ryan Emerson, who made many helpful suggestions in the preparation of this report. 
vi

INTENTIONALLY LEFT BLANK. 
1

1. Introduction 

In January 2006, High Energy Metals, Inc. (HEMI) explosively bonded a Stellite 25 liner to a 

portion of a reamed-out M242 Bushmaster gun tube (1). This work followed previously 

successful attempts to explosively bond a refractory metal liner to the same type of gun tube by 

TPL, Inc. (2). Initial examination of the Stellite-lined tube revealed some portions of the linertube interface that did not have the characteristic wave pattern that typifies a strong bond. The 

extent of the nonwavy portion could not be discerned with a small number of microscopic 

examinations. Consequently, the overall quality of the bond was in doubt. 

The need to perform a mechanical test to assess the bond shear strength between the gun tube 

and liner was recognized. A simple push-out test was decided upon as the most direct way to do 

this. In section 2, the sample preparation, fixturing, and the test procedure are presented. 

Section 3 presents the results of the measurements, along with a finite-element analysis that 

helps interpret the results. 

High bond strength between a liner and gun tube is needed to keep the liner in place during 

firing. This is especially true for rifled barrels, where the reaction to the engraving forces tends 

to rotate the liner. In the past, mechanically pinning a refractory metal liner to an M242 gun tube 

was unsuccessful because the pins could not withstand the loads produced during the firing, 

resulting in liner movement (3). However, swaging a steel jacket over a Stellite rod can produce 

an acceptable bond in a 5.56-mm gun tube (4). It is reasonable to assume that there is a 

minimum bond strength required for acceptable performance of a given type of gun tube. While 

the exact figure is not known, the results of the present work indicate that the bond shear strength 

produced by explosive bonding is more than adequate for the M242 gun tube, even if there are 

small portions of the tube not perfectly bonded. 

The internal stress generated as a result of the explosive bonding process may also contribute to 

the bond strength. In section 4, x-ray diffraction measurements of the internal stresses produced 

by explosive bonding will be presented and compared to internal stresses in other gun barrels 

that have either been autofrettaged or have had liners explosively bonded to them. Using a 

simple assumption about frictional forces, the contribution to the bond strength will be estimated 

and compared to those attainable with a shrink-fit process. 

Section 5 contains a summary of the work.
2

2. Experimental Test Procedure 

2.1 Sample Preparation 

Three sections of an M242 barrel (labeled A, B, and C) were explosively clad with Stellite 25 by 

HEMI. The tubes were then sectioned, as shown in figure 1, to provide for various 

measurements (1). The dotted lines in this figure indicate additional cuts made at a later time to 

determine the inside diameter of the liner. Sections B3 and C3 were chosen as representative 

portions of the tubes. These parts were sawed into disc specimens, with one side being ground 

smooth. The final thickness of each disc was 0.25 in. This thickness was chosen so that the 

sample was thin enough to be tested (based on the load limit of the Instron machine) but thick 

enough to provide a representative bond surface area. Each saw cut and grinding operation 

accounted for approximately 0.2 in of material. Fifteen discs from each tube were produced and 

labeled B31–B46 for tube B and C31–C36 for tube C. 

From previous work, it was found that the inside diameter of the liner varies with position along 

the tube axis. This was confirmed for sections B3 and C3. Measurements of the inside diameter 

are shown as a function of the distance from the leading (left) end of each tube in figure 2. 

Tube A

Tube B

Tube C

A1 A2 A3 A4 A5 A6

B1 B2 B3 B4 B5

C1 C2 C3 C4 C5

Figure 1. Labeling scheme for the sections saw cut from the gun tubes.
3

Distance from Leading End, inches

123456789

Liner Inside Diameter, inches

0.93

0.94

0.95

0.96

0.97

0.98

Tube B

Tube C

Figure 2. Liner inside diameter as a function of the distance from the leading end. 

2.2 Test Fixture Description and Development 

A cross-section illustration of the test fixture used for the push-out tests is shown in figure 3. It 

consisted of a pusher plug and a base plate. Samples were placed in the test fixture as shown, 

and an Instron machine was used to determine the load needed to extract the liner. The first 

pusher was made of stainless steel hardened to HRC 45. After one of the tests resulted in 

yielding of the pusher plug, the plug material was changed to Maraging 300 steel hardened to 

HRC 55. The base plate was made from 4340 steel hardened to HRC 31. A picture of the test 

fixture parts and a sample is shown in figure 4. 

The dimensions of the test fixture that were adjusted as the tests progressed are shown as D1 and 

D2 in figure 3. These dimensions will depend on the actual size of the samples being tested. 

Since the inside diameter of the samples to be examined in these tests varied, the smallest liner 

inside diameter dictated the value of D2. In this instance, D2 was selected to be 0.93 in, which 

allowed the pusher to be used with all samples. Sample B31 (liner inner diameter of 0.936 in) 

was not used in this series of tests. 

The value of D1 that was chosen to start the tests was 1.110 in. This value was based on the 

measurements of the liner-gun tube interface made in de Rosset (1). All of the measured gun 

tube inner diameter measurements exceeded 1.110 in for the sections of the barrels being 

examined (B3 and C3). The maximum value of the liner-gun tube interface diameter was 

measured to be 1.150 in. However, there was some uncertainty in this value, as well as the 

minimum value.
4

D1 

D2 

Base Plate

Pusher Plug Gun Tube 

Liner 

Figure 3. Cross-sectional view of the test fixture showing the placement of the sample to be tested. 

Figure 4. Test fixture parts and sample C45. 

The first test was conducted with sample C46. An Instron Model 1127 was used to apply a load 

to the test fixture and sample. The sample was loaded to 50 × 103

 lb at a constant crosshead 

speed. No drop in the load was observed, indicating that the liner had not failed. The sample 

was removed from the Instron, at which time, a small amount of deformation in the liner was 

noticed. The test was continued using another load frame (MTS model 204-81) capable of 
5

applying a 100 × 103-lb load. The load was applied at a constant crosshead speed of 0.05 in/min. 

A load of 91.5 × 103

 lb was achieved before the load began to decrease. The sample and test 

fixture were removed from the machine. However, the sample was stuck in the test fixture and 

had to be forcibly removed. After the parts were separated, it was noted that portions of the liner 

were still attached to the gun barrel. This was the first indication that the bond strength was 

higher than the shear strength of the liner. 

The results of the test with C46 indicated that there might be some contact between the pusher 

plug and the gun barrel. Therefore, a paper shim between the liner and pusher plug was used for 

tests C45 and C44 to ensure a more accurate centering of the sample in the test fixture. Loads 

over 90 × 103 lb were also achieved for these tests. As before, the pusher and liner were stuck 

together as a result of the test. 

The pusher plug outer diameter (D1) was reduced to 1.050 in to ensure that there was no 

interference between the pusher plug and gun tube. Tests with samples C43 and C42 resulted in 

a maximum load of over 60 × 103 lb. The load-displacement plots for these two tests are shown 

in figure 5. 

Displacement, inches

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Load, kip

0

20

40

60

80

C 42

C 43

Figure 5. Load-displacement curves for tests C42 and C43. 
6

The test with sample C41 continued until a load of 70 × 103 lb was achieved. The test was 

halted, and after removing the sample and test fixture from the load frame, it was observed that 

the pusher plug had sheared. A new plug made of Maraging 300 steel (HRC 55) was obtained 

and used to complete the tests. The final design of the test fixture is shown in the appendix. 

Based on the analysis presented in section 3, the following standard test procedure was 

developed. A sample was placed in the test fixture, and a shim was applied to help center the 

pusher plug in the gun tube. The sample and fixture were then placed in the load frame, and the 

opening of the load frame was adjusted manually so that there was a very small gap between the 

platens and the sample/test fixture. The test was conducted in displacement-control mode 

(0.05 in/min) to a maximum displacement of 0.05 in, at which time, the test was concluded and 

the sample/test fixture removed from the test machine. The data from each test, taken at a 

sampling rate of one data point per second, were stored in an Excel* file. 

3. Test Results and Interpretation 

Table 1 shows the compressive loads on the sample at a crosshead displacement of 0.045 in into 

the sample. (Due to variation in the zero setting of the load frame, not all samples actually 

experienced a crosshead displacement of 0.05 in.) The mean values of the loads for tubes B and 

C are 46.4 × 103 lb and 49.8 × 103 lb, respectively. The standard deviations for these values are 

1.7 × 103

 lb and 3.5 × 103 lb for tubes B and C, respectively. 

Table 1. Compressive loads at 0.045-in displacement. 

Sample Load 

(103

 lb) 

Sample Load 

(103 lb) 

B32 49.6 C31 53.7 

B33 44.3 C32 54.6 

B34 46.1 C33 56.9 

B35 49.6 C34 50.9 

B36 46.2 C35 49.4 

B37 44.5 C36 50.6 

B38 47.5 C37 45.6 

B39 47.3 C38 45.2 

B40 44.8 C39 47.8 

B41 45.4 C40 47.8 

B42 44.9 C42 47.0 

B43 48.5 C43 47.9 

B44 46.1 — — 

B45 45.6 — — 

B46 45.7 — — 

 *

Excel is a registered trademark of Microsoft Corporation. 
7

The stress at the interface between the gun tube and liner will vary with the applied load and 

location on the interface. To help interpret the experimental results, a finite-element analysis 

was performed using ABAQUS. The finite-element model is shown in figure 6. The finiteelement analysis utilized 6975 axisymmetric elements and frictionless contact between the steel 

pusher and the Stellite liner. The Stellite liner material is assumed to be elastic-perfectly plastic, 

with a yield of 895 MPa. The liner is assumed to be perfectly bonded to the gun tube, and failure 

of this interface is not allowed in the simulation. The assumption that the interface does not fail 

is consistent with the experimental observations. Prestress of the liner and the gun tube due to 

the bonding process is also neglected. The gun tube nodes along the bottom surface are 

constrained in the vertical direction. The simulated load is applied as a downward displacement 

of the nodes along the top surface of the steel pusher. 

Figure 6. Axisymmetric finite-element model. 

Figure 7 shows the simulated von Mises stress state at a steel pusher displacement of 0.0053 in 

(analysis step time is scaled by 1/10). Observation of figure 7 shows the classic 45° shear band 

indicating ductile yielding of the liner. Figure 7 also shows that the steel pusher confines the 

deformed Stellite liner material at the steel pusher’s smaller diameter interface, leading to a 

stress concentration at this location. This plastic deformation of the liner is clearly the reason for 

the pusher plug becoming stuck in the sample. 

Figure 7. Von Mises stress state at 0.053 in of steel pusher vertical displacement.
8

The shear stress along the length of the liner-gun tube interface is plotted in figure 8. This stress 

is achieved for a displacement of 0.053 in of the pusher plug. The shear stress exceeds 65 ksi 

near the outer edges of the sample. At the center, it is above 45 ksi. This calculation provides 

evidence that the bond shear strength is greater than 45 ksi. 

Distance, in

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Shear Stress, psi

0

20000

40000

60000

80000

Figure 8. Shear stress as a function of position along liner-gun tube interface at 

0.053-in pusher plug displacement. 

However, the actual shear strength of the bond was not determined since the bond did not fail in 

any of the standard tests (table 1). 

The finite-element analysis showed that the liner material yielded at very low displacement of 

the pusher plug (less than 0.002 in). This was also observed during testing. As a result, the tests 

were stopped when the crosshead displacement reading reached 0.050 in. Displacements greater 

than 0.050 in would simply have resulted in the pusher plug being more firmly attached to the 

liner. 

4. Internal Stresses 

4.1 Measured Internal Stresses 

4.1.1 Experimental Procedure 

A Technology for Energy Corp. (TEC) Model 1610 X-Ray Stress Analysis System, employing 

the sin2

ψ stress-measuring technique, was used to measure the residual stress (strain) produced in 
9

the steel gun tube from the explosive bonding process. All residual stress data were collected 

from a 4- or 10-positive ψ angle arrangement and CrKα radiation diffracted from the (211) lattice 

planes of the D6AC steel. (Residual stress measurements were not made on the steel gun tube 

prior to bonding.) The incident x-ray beam was collimated to provide a 2-mm diameter round 

irradiated area on the specimen surface. The x-ray elastic constant for D6AC steel, (1 + υ)/E, 

required to calculate the macroscopic residual stress from the measured strain, was taken from 

published literature. 

A 1/2-in thick disc specimen was sectioned from the leading end (specimen A2) and the trailing 

end (specimen A5) of gun tube A for residual stress analysis (see figure 1). After the specimens 

were saw cut from the gun tube, they were ground flat and parallel and chemically polished on 

one face. A polishing solution of 80% H2O2 (30% strength), 17.5% H2O, and 2.5% HF 

(48% strength) was used to remove 0.010–0.015 in of material from the saw cut and ground 

surface, thereby exposing the explosive bonding induced internal stresses. Hoop and radial 

direction residual stresses were measured on the polished, cross-sectional surface along an inside 

diameter (ID) to outside diameter (OD) traverse in the arbitrarily chosen 0° and counter 

clockwise 90° orientations. The ID measurement location refers to the interface of the Stellite 25 

liner and gun tube steel, and the OD measurement location was approximately 1.5 mm from the 

OD free surface. Measurements were performed at 0.05 in (1.27 mm) intervals from the ID to 

the 0.40-in (10.16-mm) location and then every 0.10 in (2.54 mm) for the remainder of the 

traverse. The precision of measurement for all data was ±2 ksi (±14 MPa). This value 

represented the average of the larger of either the counting statistics error or the probable error 

(goodness of fit of the d-spacing vs. sin2

ψ plots), both of which were generated for each 

measurement from statistical error analysis. 

4.1.2 Results 

The residual stress data in the D6AC steel acquired during this investigation are plotted in 

figures 9 and 10. The hoop direction residual stresses are very similar in magnitude and 

distribution at the 0° and 90° orientations for the leading and trailing end specimens (A2 and A5, 

respectively), with the maximum compressive stresses found at the ID location. This beneficial 

hoop stress becomes less compressive along the ID to OD traverse. At approximately 0.35 in. 

(8.89 mm) into the gun tube wall, the hoop stresses change from compressive to tensile and 

become increasingly tensile through the remaining wall thickness. The maximum tensile hoop 

stress was measured at the OD location. 

The magnitude and distribution of the radial direction residual stresses are similar at the 0° and 

90° specimen orientations but less symmetrical when comparing the leading and trailing ends of 

the gun tubes. Of particular note is that the radial stress changes from tensive to compressive at 

the 0.40-in (10.16-mm) measurement location on the trailing end specimen but not until the 0.60-in 

(15.24-mm) location on the leading end specimen. Additionally, the trailing end specimen radial 
10

-100

-80

-60

-40

-20

0

20

40

60

80

100

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

I.D. to O.D. Traverse, inches

Residual Stress, ksi

-690

-552

-414

-276

-138

0

138

276

414

552

690

0.0 5.0 10.0 15.0 20.0 25.0

I.D. to O.D. Traverse, mm

Residual Stress, MPa

Specimen A2, 0 deg. Orientation

Specimen A2, 90 deg. Orientation

Specimen A5, 0 deg. Orientation

Specimen A5, 90 deg. Orientation

Figure 9. Hoop direction residual stress data from explosion bonded Stellite 

25-lined Bushmaster gun tube specimens A2 (leading end) and A5 

(trailing end). 

-40

-30

-20

-10

0

10

20

30

40

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

I.D. to O.D. Traverse, inches

Residual Stress, ksi

-276

-207

-138

-69

0

69

138

207

276

0.0 5.0 10.0 15.0 20.0 25.0

I.D. to O.D. Traverse, mm

Residual Stress, MPa

Specimen A2, 0 deg. Orientation

Specimen A2, 90 deg. Orientation

Specimen A5, 0 deg. Orientation

Specimen A5, 90 deg. Orientation

Figure 10. Radial direction residual stress data from explosion bonded Stellite 

25-lined Bushmaster gun tube specimens A2 (leading end) and A5 

(trailing end).
11

stress data had a greater negative trend along the traverse, with the average 0° and 90° 

orientation OD residual stress equal to –30 ksi (–207 MPa) vs. –16 ksi (–110 MPa) on the 

leading end specimen. Since there was no accounting for these anomalies with the specimen 

sectioning or chemical polishing procedures, the differences may be attributed to the explosive 

bonding setup or operation. Possible explanations are nonuniformity in the standoff distance 

between the liner and gun tube along the tube axis prior to bonding or asymmetrical explosive 

detonation rates, both of which also could have contributed to the inside diameter variation 

displayed in figure 10. However, inasmuch as the hoop direction residual stress data were in 

agreement at all measurement locations, it is likely that the reason(s) for the inconsistencies in 

the radial stresses cannot be precisely identified. 

Of interest is the similarity in the hoop direction residual stress data for three different gun tubes. 

The data displayed in figure 11 came from measurements on an explosion-bonded Stellite 25-

lined (at HEMI), a Ta-2.5W-lined Bushmaster gun tube (explosion-bonded at TPL, Inc.) (5), and 

a 120-mm extended length gun tube (swage-autofrettaged at Benet Laboratories) (6). The 

compressive stresses observed at the ID on the explosively-clad specimens, independent of the 

liner material and manufacturer, are approximately equivalent. Adjacent to the ID, the HEMI 

and TPL plots deviate somewhat. This result is probably due to one or more of the following: 

(1) different gun tube wall thickness (0.94 in and 1.22 in, respectively), (2) different liner 

thickness (see references 1 and 2), and (3) the manufacturer’s particular explosive bonding 

parameters. As with the swage autofrettage process, the beneficial compressive hoop stresses 

produced from explosion bonding can be expected to increase the elastic strength of the gun tube 

and retard fatigue crack growth at the bore. 

4.2 Bond Strength Contribution From Residual Stresses 

The residual hoop stresses at the liner-gun tube interface are compressive, leading to a gripping 

action by the gun tube on the liner. In addition, an estimate of the bond strength contribution 

from the residual radial stress measurement can be made. First, assume that the explosive bond 

results in a smooth surface everywhere (i.e., no characteristic wavy pattern). Next, assume that 

the residual radial stress at the liner-gun tube interface is 25 ksi. (This was the value at three of 

the four measurement orientations shown in figure 10.) Assuming a coefficient of static friction 

between 0.3 and 1.0, the shear strength contribution due to the combination of radial stress and 

friction will be between 7.5 and 25 ksi. 

It is interesting to compare this range of values with those that might be obtained with shrinkfitting a liner inside a gun tube. The shear strength of the bond will also result from the presence 

of a residual radial stress and friction. This process begins by machining the liner and gun tube 

so that the liner outer diameter is greater than the gun tube inner diameter. The gun tube is 

heated, and, at the same time, the liner is cooled. Thermal expansion and contraction effects then 

make it possible to slip the liner into the gun tube. When the temperature of the gun tube and 
12

-100

-80

-60

-40

-20

0

20

40

60

80

100

0.0 0.4 0.8 1.2 1.6 2.0 2.4

I.D. to O.D. Traverse, inches

Residual Stress, ksi

-690

-552

-414

-276

-138

0

138

276

414

552

690

0.0 10.0 20.0 30.0 40.0 50.0 60.0

I.D. to O.D. Traverse, mm

Residual Stress, MPa

HEMI, Explosive Bonding, 25 mm

TPL, Explosive Bonding, 25 mm

Benet, Swage Autofrettage, 120 mm

Figure 11. Hoop direction residual stress data from explosion bonded Stellite 25-

lined and Ta-2.5W-lined Bushmaster gun tubes and swage 

autofrettaged 120-mm gun tube. 

liner has reached equilibrium, internal stresses will develop that depend on the original amount 

of mismatch between diameters. 

The temperature range over which the materials can be heated and cooled is bounded by 

practical considerations. For instance, the liner can be cooled using liquid nitrogen (–196 °C), 

and the steel can be heated up to about 350 °C to keep it below its first phase transformation 

temperature. Given that the coefficients of thermal expansion for the D6AC steel and Stellite 25 

are 16.1 μm/m/°C and 12.9 μm/m/°C, respectively, a total mismatch of 205 μm can be obtained, 

assuming the initial diameters are 25.4 mm. (The mismatch is equivalent to approximately 8 mil.) 

The entire 205 μm cannot be used for the initial mismatch because some clearance will be needed 

to slide the liner into the gun tube. An optimistic assumption is that only 4 mil on the diameter 

will be needed for clearance. The allowable initial mismatch will then be 4 mil (102 μm). 

Initially, the liner would have an inner diameter of 25.4 mm and an outer diameter of 30.48 mm. 

(A liner thickness of 0.1 in [2.54 mm] was used here.) The outer diameter of the gun tube is 

taken to be 76.2 mm (3.0 in). These dimensions can be used in the standard formula (see, for 

instance [7]) to approximate the internal radial stress, σr, generated in the gun tube as a result of 

the shrink-fit process:
13

σr = – (E δ/b) (b2 – a2

)(c2 – b2)/(2b2(c2 – a2)), (1) 

where E is the modulus of the D6AC steel (210 MPa) and δ is 102 μm. In equation 1, a is the 

inner radius of the liner, b is the outer radius of the liner, and c is the outer radius of the gun tube. 

The resulting internal radial stress is compressive 203 MPa (29 ksi). 

The stress necessary to initiate movement between the barrel and liner can be calculated using 

the same range of values for the coefficient of static friction that was used previously. This gives 

a possible range of 8.7–29 ksi values for the shear strength of the bond as a result of the shrinkfitting process. This range is seen to be comparable to that produced by the residual radial stress 

produced by explosive bonding. 

5. Summary 

A test fixture has been designed to determine the shear strength of an explosively-formed bond 

between an M242 medium-caliber gun tube and a Stellite 25 liner. Over 30 tests on two different 

sections of gun barrel were carried out. In each case, the liner yielded before the bond had the 

opportunity to fail. The shear strength of the bond could not be determined using the established 

test procedure because the bond never failed in these tests. However, a finite-element analysis 

indicated that the bond shear strength was likely to be greater than 45 ksi. Internal stresses were 

measured by x-ray diffraction. The measured stresses were used to estimate the contribution that 

a combination of residual radial stress and friction could make the bond shear strength. The 

range of values determined from this calculation, 7.5–25 ksi, was comparable to the range 

provided by a shrink-fit process. 
14

6. References 

1. de Rosset, W. S. Explosive Bonding of Stellite 25; ARL TR-3816; U.S. Army Research 

Laboratory: Aberdeen Proving Ground, MD, June 2006. 

2. 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. 

3. Bagnall, C.; Dalley, A. M.; Huston, J. F.; Martin, N. R.; McMullen, P. J.; Miller, C. S.; 

Papesch, C. A.; Sinosky, J. T. III; Valencia, J. J.; Guillard, S. Advanced Gun Barrel 

Technology Initiative, Final Report: Modeling, Metallurgy and Firing Test Report for the 

M242 Mo-ODS Partially Lined Barrel; TR no. 98–25; National Center for Excellence in 

Metalworking Technology: Johnstown, PA, 2 July 1998. 

4. Livermore, G.; Sadowski, L. Barrel Weight Reduction; ARAEW-TR-05005; U.S. Army 

Armament Research, Development and Engineering Center: Picatinny, NJ, May 2005. 

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

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

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

MD, February 2003. 

6. Snoha, D. J. Letter report to Benet Laboratories, Watervliet, NY, January 1993. 

7. Timoshenko, S. Strength of Materials, Part II, Advanced Theory and Problems; 14th 

printing; D. Van Nostrand Company: New York, NY, June 1953. 
15

Appendix. Test Fixture Design 

The final design recommended for the push-out tests is shown in figure A-1. Note that the 

dimensions of the pusher plug have to be modified for the particular values of the inner 

diameters for the liner and gun tube. 

4.0

1.050

0.5 0.930

.25

1.150

0.32

1.00 

0.060 

3.02

Figure A-1. Final test fixture configuration; all dimensions in inches.
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