Instrumented Indentation of M855 Cartridge, Core, and 

Jacket Materials 

by Mark R. VanLandingham, Thomas F. Juliano, and Matthew J. Hagon 

ARL-TR-3570 August 2005 

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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5069 

ARL-TR-3570 August 2005 

Instrumented Indentation of M855 Cartridge, Core, and 

Jacket Materials 

Mark R. VanLandingham, Thomas F. Juliano, and Matthew J. Hagon 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited. 
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Instrumented Indentation of M855 Cartridge, Core, and Jacket Materials 

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Mark R. VanLandingham, Thomas F. Juliano, and Matthew J. Hagon 

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13. SUPPLEMENTARY NOTES 

14. ABSTRACT 

Instrumented indentation was used to estimate the mechanical properties of as-processed materials used in 5.56-mm M855 

projectiles. Three indentation tip geometries were used: a Berkovich tip, a 1-μm-radius conical tip with a 90o cone angle, and a 

25-μm-radius conical tip also with a 90o cone angle. Because the Berkovich tip geometry is close to that of an ideal pyramid, 

the resulting measurements of elastic modulus and hardness for homogeneous, isotropic materials exhibited the least amount of 

scatter compared to the other two tips. For nonisotropic materials, however, the measurements of elastic modulus and hardness 

using the Berkovich and 1-μm-radius conical tip exhibited large amounts of scatter. These two probes were found to test similar 

volumes of material that were on the order of the size scale of the material heterogeneities. Thus, the results were a function of 

the local microstructure rather than being representative of the bulk material. The 25-μm-radius tip was found to provide results 

for the nonisotropic materials that had small amounts of scatter and that were similar to bulk measurements, indicating that the 

volume of material being probed was sufficiently large to average out local microstructural effects. Initial efforts were made to 

provide full stress-strain data from indentation measurements of the brass cartridge case. 

15. SUBJECT TERMS

instrumented nano-indentation, small caliber ammunition, green core materials, brass, copper, nylon, tungsten, tin 

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Mark R. VanLandingham 

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iii

Contents 

List of Figures iv

List of Tables v

1. Introduction 1

2. Experimental 3

2.1 Sample Preparation..........................................................................................................3 

2.2 Indentation Testing..........................................................................................................3 

3. Results 7

3.1 Projectile Cores Testing ..................................................................................................7

3.2 Cartridge Testing...........................................................................................................11 

3.3 Jacket Testing................................................................................................................13 

4. Summary 15

5. References 16

Distribution List 17 
iv

List of Figures 

Figure 1. Schematic illustration of an instrumented indentation system (a) and corresponding 

dynamic model (b). ....................................................................................................................2 

Figure 2. Core (a) and cartridge (b) sample orientation..................................................................4 

Figure 3. Contact area, A, as a function of contact depth, hc, for the three tip geometries.............5 

Figure 4. Elastic modulus, E, as a function of displacement, h, for fused silica and each of 

the three tip geometries..............................................................................................................5 

Figure 5. Hardness, H, as a function of displacement, h, for fused silica and each of the three 

tip geometries.............................................................................................................................6 

Figure 6. Typical loading history for an indentation test (a) and illustration of an indentation 

array pattern (b)..........................................................................................................................6 

Figure 7. A 25-μm conical array in Pb-Sb (a) and 1-μm conical array in brass (b). ......................7 

Figure 8. Elastic modulus, E, as a function of displacement, h, for Pb-Sb samples averaged 

over all orientations for each of the three tip geometries. All error bars signify one 

standard deviation. .....................................................................................................................8 

Figure 9. Elastic modulus, E, as a function of displacement, h, for tungsten-tin samples 

averaged over all orientations for each of the three tip geometries. ..........................................8 

Figure 10. Elastic modulus, E, (a) and standard deviation of E (b) as a function of 

displacement, h, for tungsten-nylon samples. Values are based on averages taken over all 

orientations for each of the three tip geometries. For clarity in (a), only positive error 

bars are shown for the Berkovich tip data, and no error bars are shown for the 1-μm 

conical tip data; both positive and negative error bars are shown for the 25-μm conical 

tip. ..............................................................................................................................................9 

Figure 11. Elastic modulus, E, as a function of displacement, h, for Pb-Sb tested in three 

different sample orientations using the 1-μm conical tip. .......................................................11 

Figure 12. Hardness gradient in a unfired cartridge cases measured using indentation with a 

Berkovich tip and a 25-μm conical tip (a), and measured using a Vickers hardness tip and 

a 2.5-kg load (b). In (a), values averaged over 2.5-mm incremental distances are also 

shown, and in (b), maximum and minimum values are plotted; in both cases, the lines 

connecting the data points are meant only to emphasize overall trends. Location was 

measured from the closed end of the case. ..............................................................................12 

Figure 13. Examples of stress-strain data for a brass cartridge cases estimated from 

indentation with a 25-μm conical tip. Values in legend indicate location along the length 

of the cartridge case as measured from the closed end of the case..........................................14 

Figure 14. Elastic modulus, E, as a function of displacement, h, for the copper jacket for the 

Berkovich tip and the 25-μm conical tip averaged over all locations. ....................................14 
v

List of Tables 

Table 1. Summary of elastic modulus, E, as measured using indentation with three different 

tip shapes along with values determined from compression and ultrasound testing. ..............10 
vi

INTENTIONALLY LEFT BLANK.
1

1. Introduction 

System-level numerical models are being developed to provide a scientific framework for 

design, optimization, and evaluation of current and future small arms systems. These models 

require input regarding material properties, preferably determined experimentally from the asprocessed materials. For 5.56-mm M855 projectiles, thin-walled copper and brass are used for 

the bullet jacket and cartridge case, respectively, the latter of which is processed with a hardness 

gradient. The predominant bullet core material is a lead-antimony (Pb-Sb) alloy at roughly a 

5:95 weight ratio of Pb to Sb. Due to environmental mandates, alternative material systems are 

currently being sought to either replace the Pb-Sb core or to produce a new projectile design. 

Examples of core replacement alternatives are a tungsten particulate-filled nylon and a tungstentin metal blend. Measuring mechanical performance of M855 projectile components, however, 

is difficult using traditional mechanical test methods due to the small dimensions involved. To 

address this challenge, instrumented indentation techniques can be used. 

Instrumented indentation, sometimes referred to as “nano-indentation,” is a technique used for 

measuring mechanical properties, specifically elastic modulus, E, and hardness, H, over 

micrometer-sized regions of a sample (1). A general schematic of an instrumented indentation 

system based on a NanoIndenter XP (MTS Systems Corp.) is shown in figure 1a (2). For this 

system, force (P) is controlled electromagnetically – an electrical current is passed through a coil 

that resides within a round magnet, such that the current passing through the coil is directly 

proportional to P. Displacement (h) is measured relative to the load frame using a 3-plate 

capacitive element. The outer plates are fixed to the load frame and the middle plate is attached 

to the indenter shaft or load train, such that the difference in voltage between the middle plate 

and the two outer plates is proportional to h. 

Force-displacement (P-h) curves produced by instrumented indentation systems are generally 

analyzed according to the work of Doerner and Nix (3) and Oliver and Pharr (2). Their analyses 

were in turn based upon relationships developed by Sneddon (4) for the penetration of a flat 

elastic half space by different probes with particular axisymmetric shapes (e.g., a flat-ended 

cylindrical punch, a paraboloid of revolution, and a cone). These elasticity-based analyses are 

normally applied to the unloading data of an indentation measurement, assuming the unloading 

behavior of the material is characterized by elastic recovery only. The resulting values of E and 

H are single values for the maximum applied depth. To obtain E and H as a continuous function 

of depth, dynamic indentation methods have been developed (2) in which a small harmonic load 

is superposed over the quasi-static load history. This technique allows for a continuous 

measurement of the contact stiffness, S = dP/dh, during the entire indentation process using a 

dynamic model of the system similar to that shown in figure 1b. In this figure, Kf and Ks are the 
2

 (a) (b) 

Figure 1. Schematic illustration of an instrumented indentation system (a) and corresponding dynamic model 

(b). 

stiffness of the load frame and column support springs, respectively, D is the system-damping 

coefficient, and m is the system mass. For magnitudes of the force and displacement oscillations, 

Pos and h(ω) where ω is the oscillation frequency, S, can be found from the following equation: 

{ } ( ) 2 2

2

2 1 1 1

( )

S K K m D

h

P

f s

os ω ω

ω = + + − + − − −  (1)

Using this method, P, h, and S are measured continuously during the test, and the reduced 

modulus, Er, can be calculated as a function of h using 

2 π

S A Er = . (2) 

The contact area, A, is a function of the contact depth, hc, as defined by the tip geometry, which 

must be calibrated prior to testing. The following relation is used to determine hc (and hence A) 

continuously during the indentation test, where ε is a geometric factor usually taken to be ~0.75: 

S

P hc h ε = − . (3) 

Finally, the sample elastic modulus, E, is determined from the calculation of Er assuming 

knowledge of the Poisson’s ratio for the sample, ν, and the Young’s modulus and Poisson’s 

ratio, Ei and νi, of the indentation tip material (usually diamond): 

( ) ( )

i

i

Er E E

2 2 1 1 ν 1−ν

+ − = . (4)

Additionally, the hardness, H = P/A, can be determined as a function of h. 

m

Kf

Ks D

S

m

Kf

Ks D

S
3

In this report, initial efforts to evaluate current and alternative materials for M855 projectiles 

using instrumented indentation are described. Sample preparation and testing are detailed in the 

following section, followed be presentation and discussion of results, which includes 

comparisons to bulk values where possible. 

2. Experimental 

2.1 Sample Preparation 

The general sample preparation procedure was as follows: 

• As-received bullets were placed into a cup mold using plastic clips to hold them in place, 

• A two-part epoxy was mixed and poured into the molds and allowed to cure at room 

temperature for at least four hours prior to removal of the samples from the molds, 

• A 120-grit abrasive pad was used to expose the interior of the bullet, which generally 

required 15-20 min of grinding on a polishing wheel using water and hand pressure, 

• Wet sanding continued using 240-, 320-, 400-, and finally 600-grit abrasives; visual 

inspection with a light microscope was used between sanding and subsequent polishing 

steps to ensure that scratches from the previous steps had been removed, and 

• Al2O3 or diamond suspensions were then used to progressively polish the surfaces using 

12-, 9-, 5-, 3-, and 1-μm particle sizes. 

The bullets were positioned in such a way as to allow for testing at various orientations of the 

core material, as shown in the figure 2a. These positions were chosen so that testing could be 

conducted on vertically, horizontally, and obliquely oriented core surfaces in order to gain more 

insight into the degree of anisotropy of the materials One sample disk was made for each of the 

following core materials: Pb-Sb, tungsten-tin, and tungsten-nylon. In addition to the bullet 

cores, indentation testing was also conducted on brass cartridge cases. The as-received 

cartridges were sectioned longitudinally with a diamond saw to expose a clean surface for 

testing. The mounting procedure was identical to the bullet core procedure except that only a 

horizontal orientation was used. The horizontal orientation was chosen so that material property 

gradients along the length of the cartridge could be investigated. The final sample configuration 

can be seen in figure 2b. 

2.2 Indentation Testing 

The indentation system used in this study was a NanoIndenter XP (MTS Systems Corp.). Tests 

were performed using three separate tip geometries: a Berkovich tip (a 3-sided, triangular-based 

pyramid), a 1-μm-radius conical tip with a 90o cone angle, and a 25-μm-radius conical tip also 
4

 (a) (b) 

 (a) (b) 

Figure 2. Core (a) and cartridge (b) sample orientation. 

with a 90o cone angle. Prior to performing tests on the bullet samples, tip area functions were 

determined from indentation of fused silica using equations 2 and 3, where reduced modulus is 

known (Er = 69.5 GPa), and S, P, and h are measured such that contact area, A, can be 

determined as a function of contact depth, hc. Curve fits were then used to provide the 

indentation software a means to calculate A as a function of depth for the bullet samples. This 

data and the associated curve fits are shown in figure 3. For the 25-μm-radius conical tip, the 

rounded portion of the tip extends many microns from the tip apex, and thus all indentation 

performed with this tip can be approximated using spherical contact mechanics. Additional 

analysis of this tip has shown that it is not a perfect sphere of radius 25 μm, but rather is slightly 

more blunt initially with a radius of about 40 μm which then decreases with distance from the 

apex, approaching 25 μm at contact depths of 600 nm or so. This deviation from ideal geometry, 

however, should not affect the results significantly. 

Modulus and hardness data for fused silica are shown in figures 4 and 5, respectively, for each of 

the three tips using the respective calibrated area functions. A value of E = 74 GPa is 

consistently produced for all three tips, except perhaps at small depths where deviations result 

from measurement uncertainties and artifacts from the curve fits to the area functions, which 

tend to fit best at larger depths and less so at smaller depths. Hardness values are more sensitive 

to the tip shape due to the relative amounts of elastic and plastic deformation that the different tip 

geometries impose as a function of depth. For example, while the Berkovich tip and 1-μm 

conical tip create constant hardness conditions for h > 400 nm, the 25-μm conical tip does not 

create a full plasticity condition at the largest depths obtained. 

In figure 6a, the typical loading history used in this testing is shown. For all indentation tests on 

the samples, the following test sequence was used regardless of tip shape: 

• The instrument first approaches and senses the surface. 

• After the surface of the material is found, the force is increased using a constant ratio of 

loading rate to load of 0.05 s-1 until a displacement of 2000 nm has been reached. 
5

Figure 3. Contact area, A, as a function of contact depth, hc, for 

the three tip geometries. 

Figure 4. Elastic modulus, E, as a function of displacement, h, for 

fused silica and each of the three tip geometries. 

• The load is then held for 10–30 seconds prior to unloading. 

• A constant unloading rate is then used to reduce the applied load to 10% of the maximum 

load, at which point the force is then held constant. This second holding segment is used to 

correct for the system thermal drift, which will correct for thermal expansion or contraction 

of the test sample and/or indenter apparatus during the course of testing. 

A single series of tests on a given material included 16 or 25 indents equally spaced in a either a 

4 × 4 or 5 × 5 square array pattern with a distance of 40 μm between the centers of adjacent 

indentations. An array of indents is illustrated in figure 6b, where the arrows represent the order 

in which the tests are performed. Using the optical microscope integrated into the indentation 

0

10

20

30

40

50

60

70

80

90

0 400 800 1200 1600

Contact depth (nm)

Area (μm2

)

25um conical tip data

25um conical tip fit

1um conical tip data

1um conical tip fit

Berkovich tip data

Berkovich tip fit

0

20

40

60

80

100

0 500 1000 1500 2000

Displacement (nm)

E (GPa)

25 um conical tip

1 um conical tip

Berkovich tip
6

Figure 5. Hardness, H, as a function of displacement, h, for fused 

silica and each of the three tip geometries. 

system, locations for the indentation tests were visually selected. Once the tests have been 

defined, the system automatically moves each of the selected sample positions under the 

indenter, performing the tests one by one at the specified locations. Optical microscopy images 

of actual indentation arrays are shown in figure 7. In figure 7a, a 4 × 4 array made using the 

25-μm conical tip to indent a Pb-Sb core is shown (scale bar is 20 μm in length), and in 

figure 7b, a 4 × 4 array made using the 1-μm conical tip to indent a brass cartridge sample is 

shown (scale bar is 50 μm in length). Poisson’s ratio was taken to be 0.3 for brass and 0.4 for all 

of the core materials. 

 (a) (b) 

Figure 6. Typical loading history for an indentation test (a) and illustration of an indentation array pattern (b). 

0

5

10

15

20

0 500 1000 1500 2000

Displacement (nm)

H (GPa)

25 um conical tip

1 um conical tip

Berkovich tip
7

 (a) (b) 

Figure 7. A 25-μm conical array in Pb-Sb (a) and 1-μm conical array in brass (b). 

3. Results 

3.1 Projectile Cores Testing 

In figures 8–10, elastic modulus, E, is plotted as a function of displacement into the surface, h, 

for three core materials – Pb-Sb, tungsten-tin, and tungsten-nylon – as tested with each of the 

three tip geometries. For h > 500 nm, E is roughly constant with increasing depth for all three 

materials. Average values of E are provided in table 1 along with comparative values for bulk 

sample testing (compression and ultrasound). Ultrasound testing was used successfully only for 

Pb-Sb, as this method is only valid for relatively homogeneous samples. Determining E from 

compression testing of the actual core materials was also of limited success due to problems with 

using strain gages on small cylindrical samples (approximate dimensions of 4.6 mm in both 

length and diameter). Thus, compression modulus values given in table 1 are mainly from 

samples roughly twice the size of the core materials (approximate dimensions of 9.5 mm in both 

length and diameter). 

Values of E for Pb-Sb determined from indentation, compression, and ultrasound testing were all 

approximately 16 GPa, the handbook value for a lightly alloyed Pb material. Further, the values 

for the three indentation tips were similar within the ~10% scatter in the data for h > 1000 nm 

(see figure 8). 

The tungsten-tin material was a metal blend ~60% tin and 40% tungsten by volume, such that no 

alloying was apparent between the two metal constituents. Tin appeared to comprise the 

composite matrix with tungsten dispersed as micron-sized islands. Values of E were only 
8

Figure 8. Elastic modulus, E, as a function of displacement, h, for Pb-Sb samples 

averaged over all orientations for each of the three tip geometries. All 

error bars signify one standard deviation. 

Figure 9. Elastic modulus, E, as a function of displacement, h, for tungsten-tin 

samples averaged over all orientations for each of the three tip 

geometries. 

0

5

10

15

20

25

0 500 1000 1500 2000

Displacement (nm)

E (GPa)

Berkovich Tip

1 um Conical Tip

25 um Conical Tip

0

25

50

75

100

125

150

0 500 1000 1500 2000 2500

Displacement (nm)

E (GPa)

Berkovich

1um Conical

25um Conical
9

 

Figure 10. Elastic modulus, E, (a) and standard deviation of E (b) as a function of 

displacement, h, for tungsten-nylon samples. Values are based on averages taken 

over all orientations for each of the three tip geometries. For clarity in (a), only 

positive error bars are shown for the Berkovich tip data, and no error bars are 

shown for the 1-μm conical tip data; both positive and negative error bars are 

shown for the 25-μm conical tip. 

(a) 

0

10

20

30

40

50

0 500 1000 1500 2000

Displacement (nm)

E (GPa)

Berkovich Tip

1 um Conical Tip

25 um Conical Tip

0

5

10

15

20

25

30

35

40

45

50

0 500 1000 1500 2000 2500

Displacement (nm)

Standard Deviation of E (GPa)

Berkovich tip

1 um conical tip

25 um conical tip

(b) 
10

Table 1. Summary of elastic modulus, E, as measured using indentation with three different tip shapes along 

with values determined from compression and ultrasound testing. 

Indentation E 

(GPa) 

Core Material Berkovich 1-μm cone 25-μm cone Compression E

(GPa) 

Ultrasound E

(GPa) 

Pb-Sb 16.7 ± 2.5 15.2 ± 1.8 17.3 ± 1.5 12.0 ± 2.0 14.0 ± 2.0 

Tungsten-nylon 13.4 ± 7.3 8.2 ± 5.8 6.1 ± 0.5 9.0 ± 2.0 — 

Tungsten-tin 46.8 ± 15.7 48.1 ± 12.1 45.1 ± 11.0 — — 

obtained using indentation and were similar to handbook values for tin (42 GPa). Further, the 

values for the three indentation tips were similar (see figure 9). However, the scatter for all tips 

was larger than for Pb-Sb, even at large depths where the standard deviation as a percentage of E

was between 20% and 35%. Because the sizes of the tungsten islands were generally in the 

range of 10’s to 100’s of microns, data for each of the three tips was sensitive to the local 

microstructure. In fact, the data scatter tended to be skewed to higher E values due to the 

influence of the much stiffer tungsten material (E = 410 GPa). Thus, extracting a representative 

value of E for this material from the indentation measurements may not be possible. 

The tungsten-nylon material was a Nylon 12 polymer filled with micron sized tungsten particles 

with a volume fraction of approximately 50%. Using handbook values for the two materials 

along with micromechanical composite models, E was estimated to be approximately 10 GPa. 

However, the presence of voids had been noted in other studies, and as void content increases, 

the predicted composite modulus decreases substantially. For example, for 3% void volume 

fraction, E is reduced by 7%, and for 10% void volume fraction, E is reduced by 21%. Values of 

E measured for tungsten-nylon from compression testing are in general agreement with the 

micromechanical predictions for a material with 0–10% void-volume fractions. While 

indentation values were similar to those from compression testing, they were a function of the 

indentation tip geometry (see figure 10). For the Berkovich tip, E decreased with h, approaching 

12.5 GPa at h ~ 2000 nm. For the 1-μm conical tip, E = 8.2 GPa for h > 900 nm, and for the 

25-μm conical tip, E = 6.2 GPa for h > 500 nm. In figure 10b, the standard deviations for E are 

shown to be much smaller for the 25-μm conical tip compared to the other two tips. The average 

E values and standard deviations, along with the contact area data in figure 3, indicate that the 

Berkovich tip and the 1-μm conical tip average over similar volumes of material and thus, the 

corresponding data is highly sensitive to local microstructure. While the tungsten particle size 

distribution was quite large, the largest particles were on the order of a few 10’s of microns in 

diameter. Thus, because the 25-μm conical tip probes a much larger volume of material, the data 

appears to be more representative of the bulk material behavior. 
11

Some evidence was found to suggest some slight anisotropy in some of the samples tested with 

indentation. In figure 11, a plot of E as a function of h for Pb-Sb for different sample 

orientations is shown. Similar results were also found using the 25-μm conical tip. However, 

due to the large data scatter, the degree of anisotropy was not clear, and further study of this 

issue is required. 

Figure 11. Elastic modulus, E, as a function of displacement, h, for Pb-Sb tested in three 

different sample orientations using the 1-μm conical tip. 

3.2 Cartridge Testing 

Indentation measurements were made on fired and as-processed (unfired) brass cartridge cases as 

a function of distance along the length of the cartridge using the Berkovich tip and the 25-μm 

conical tip. For both tips, ~200 indentations were made with a spacing of 250 μm along the 

length of the case, and the resulting values of H are plotted in figure 12a. The maximum 

indentation depth for these tests was limited to 500 nm in an attempt to minimize the effects of 

pile-up known to exist in metals that can overestimate hardness measurements. Also shown in 

this figure are values averaged over indentations made within approximately a 2.5 mm length 

along the cartridge case. In figure 12b, a plot of Vickers hardness values measured on a larger 

scale compared to the instrumented indenter is shown, where data is plotted as maximum and 

minimum values at each distance tested. 

For all data, a similar hardness trend was observed. In general, H is larger for the lower half of 

the cartridge case compared to the upper end. Additionally, H appears to increase slightly 

(5–10%) with distance for the first 23.5 mm up the cartridge from the base. This increase is 

followed by a region located between 23.5 and 29 mm from the base where H drops by 25–30%. 

The Vickers and 25-μm tip data indicate a gradual decrease (~15%) in H with distance from 

29 mm up to the open end of the case. The Berkovich tip data indicate a slight increase 

0

5

10

15

20

25

30

0 500 1000 1500 2000 2500

Displacement (nm)

E(GPa)

Vertical

Oblique

Horizontal
12

(b) 

Figure 12. Hardness gradient in a unfired cartridge cases measured using indentation 

with a Berkovich tip and a 25-μm conical tip (a), and measured using a 

Vickers hardness tip and a 2.5-kg load (b). In (a), values averaged over 

2.5-mm incremental distances are also shown, and in (b), maximum and 

minimum values are plotted; in both cases, the lines connecting the data 

points are meant only to emphasize overall trends. Location was measured 

from the closed end of the case. 

0

50

100

150

200

0.0 10.0 20.0 30.0 40.0 50.0

Location on Cartridge Case [mm]

Vickers Hardness

Max Min

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 10 20 30 40 50

Location on Cartridge Case (mm)

Hardness (GPa)

25um conical tip

Berkovich tip

25um conical tip averaged

Berkovich tip averaged

(a) 

(mm)
13

in H over the same region. In fact, the 25-μm conical tip seemed to capture the hardness trend 

better than the Berkovich tip. This result is likely related to the surface roughness, as at 

h = 500 nm, the contact area of the Berkovich tip is over 10 times smaller than that of the 25-μm 

conical tip. Also, H for the 25-μm conical tip was less that that for the Berkovich tip, because 

spherical indenters will not generate full plasticity in the material until the indenter is of a 

sufficient depth, whereas sharp Berkovich indenters generate full plasticity just a few nanometers 

into the surface. However, for all the data, significant amounts of scatter were observed, perhaps 

indicating significant differences in the brass cases. Also, data for the unfired casing relative to 

the fired casings were not significantly different; the decrease in hardness occurred perhaps over 

a slightly larger range. Within scatter, elastic modulus values were constant (E ≈ 100 GPa) along 

the casings, indicating that the material stoichiometry is constant. 

Stress-strain curves were also generated for both a fired and the unfired casing from data taken 

with the 25-μm radius tool. The stress was taken from the CSM current hardness values, and the 

strain was taken as the ratio of the measured displacement into the surface to the contact radius, 

a, where the contact radius is related to the contact area, A, by A = πa

2

. Examples are shown in 

figure 13. The stress-strain data did not seem to show any consistent trend as a function of 

distance along the length of the casing. The material may yield at a higher stress (location where 

the curve starts to significantly bend) where the overall hardness is higher. This hypothesis 

would result in an estimation of the yield stress of ≥1 GPa. However, this value is much higher 

than handbook values for yellow brass, which range from 97 to 427 MPa. Additional efforts are 

needed to reconcile these discrepancies. 

3.3 Jacket Testing 

In figure 14, E is plotted as a function of displacement for the Berkovich tip and the 25-μm 

conical tip indenting on a polished cross-section of a copper bullet jacket. The values for the 

1-μm conical tip (data not shown) were similar to the Berkovich tip. Some slight modulus 

differences were observed as a function of position, but since no significant variations were 

expected, the data was averaged from three separate locations on the jacket, and the error bars in 

figure 14 denote the magnitude of the variations. The values of E for the 25-μm conical tip were 

less than those for the Berkovich and 1-μm conical tips. The origin of these differences are not 

currently known, although it is possible that pile-up of material around the two sharper indenters 

may have occurred, creating a larger contact area and stiffer contact than accounted for in the 

analysis, and thus overestimating E. However, the handbook value for oxygen-free, highconductivity copper is 125 GPa, with which the Berkovich data is in agreement. Thus, further 

study is needed to explore these differences. 
14

Figure 13. Examples of stress-strain data for a brass cartridge cases estimated from 

indentation with a 25-μm conical tip. Values in legend indicate location 

along the length of the cartridge case as measured from the closed end of 

the case.

Figure 14. Elastic modulus, E, as a function of displacement, h, for the copper jacket 

for the Berkovich tip and the 25-μm conical tip averaged over all 

locations. 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.00 0.02 0.04 0.06 0.08 0.10

Strain (h/a)

Stress (GPa)

0.75 mm

20.75 mm

25.0 mm

28.5 mm

44.0 mm

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600 700

Displacement (nm)

E (GPa)

25um conical tip

Berkovich tip
15

4. Summary 

Instrumented indentation was used to estimate mechanical properties of materials used in 

5.56-mm M855 projectiles. Because of the small dimensions of the cores and the small 

thicknesses of the casing and jacket, indentation was able to provide estimates of elastic modulus 

for the component materials in an as-processed condition. Three indentation tip geometries were 

used, including a Berkovich tip, a 1-μm-radius conical tip with a 90o cone angle, and a 25-μmradius conical tip also with a 90o cone angle. The penetration depths used with the 25-μm-radius 

conical tip were such that the contact was within the rounded (approximately spherical) part of 

the tip. This tip was found to provide results for the tungsten particle-filled nylon core material 

that had small amounts of scatter and that were similar to bulk measurements, indicating that the 

volume of material being probed was sufficiently large to average out local microstructural 

effects. Because the Berkovich tip geometry is close to that of an ideal pyramid, the resulting 

measurements of elastic modulus and hardness for homogeneous, isotropic materials exhibited 

the most accurate modulus values with the least amount of scatter compared to the other two tips. 

For nonisotropic materials, however, the measurements of elastic modulus and hardness using 

the Berkovich and 1-μm-radius conical tip exhibited large amounts of scatter. These two probes 

were found to test similar volumes of material that were of the order of the size scale of the 

material heterogeneities. Thus, the results were a function of the local microstructure rather than 

being representative of the bulk material. Initial efforts to extract full stress-strain data from 

indentation measurements using the 25-μm-radius conical tip were not successful in providing a 

reasonable estimation of yield stress. 
16

5. References 

1. VanLandingham, M. R. A Review of Instrumented Indentation. J. Res. Natl. Inst. Stand. 

Technol. 2003, 108 (4), 249–265. 

2. Oliver, W. C.; Pharr, G. M. An Improved Technique for Determining Hardness and Elastic 

Modulus Using Load and Displacement Sensing Indentation Measurements. Journal Mater. 

Res. 1992, 7 (6), 1564–1583. 

3. Doerner, M. F.; Nix, W. D. A Method for Interpreting the Data from Depth-Densing 

Indentation Instruments. J. Mater. Res. 1986, 1 (4), 601–609. 

4. Sneddon, I. N. The Relationship Between Load and Penetration in the Axisymmetric 

Boussinesq Problem for a Punch of Arbitrary Profile. Int. J. Engng. Sci. 1965, 3, 47–57. 
NO. OF 

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