Indentation of Bulk Amorphous Metals to Investigate 

Pop-In Effects 

by Tyler Krus, Thomas Juliano, and Mark VanLandingham 

ARL-CR-574 July 2006 

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Army Research Laboratory 

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ARL-CR-574 July 2006 

Indentation of Bulk Amorphous Metals to Investigate 

Pop-In Effects 

Thomas Juliano and Mark VanLandingham 

Weapons and Materials Research Directorate, ARL 

Tyler Krus 

Science and Engineering Apprenticeship Program (SEAP)

prepared by 

Science and Engineering Apprenticeship Program (SEAP) 

U.S. Army Research Laboratory 

under contract 

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Indentation of Bulk Amorphous Metals to Investigate Pop-In Effects 

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Tyler Krus,* Thomas Juliano, and Mark VanLandingham 

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Science and Engineering Apprenticeship Program (SEAP), Loch Raven High School, Baltimore, MD 21286. 

14. ABSTRACT 

Bulk metallic glasses (BMG) are a fairly new class of materials that exhibit high strength, low density, and corrosive resistance, 

as compared to traditional metals, and are useful for various applications. Spherical depth-sensing indentation of BMG reveals

stepwise displacement jumps in the load-displacement curves, known as “pop-ins.” These pop-ins have been found to be 

correlated with plastic deformation; the initial one being associated with the elastic limit of the material. The initial 

displacement bursts are investigated for varying stoichiometries of Zr and Hf-based BMG. Attention is focused on pressure and 

energy per volume at initial pop-in location as a function of different strain rates, indenter tip radius, and material composition. 

This research may provide further insight and understanding for macroscale behavior of BMG. 

15. SUBJECT TERMS

indentation, bulk amorphous metals, mechanical testing 

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Tyler Krus 

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iii

Contents 

List of Figures iv 

Acknowledgments v 

1. Introduction 1 

2. Experimental Setup 1 

3. Results and Analysis 4 

4. Conclusions 10 

5. References 12 

Distribution List 13 
iv

List of Figures 

Figure 1. Typical indentation loading profile as a function of time. ..............................................3 

Figure 2. Comparison of Zr-based and Hf-based energy per volume (a) and pressure at 

pop-in locations (b) as a function of radii..................................................................................5 

Figure 3. Pressure generated for a 3-μm (upper) and 20-μm (lower) radius sphere as a 

function of displacement into the surface. .................................................................................6 

Figure 4. Pop-ins that occur at peak load........................................................................................7 

Figure 5. Pop-in that occurs during unloading segment. ................................................................8 

Figure 6. Stepwise pattern exhibited in excess of 150 mN for indentation of 3-μm sphere...........9 

Figure 7. SEM micrograph of an indentation made by the 3-μm-radius indenter. Clear 

evidence of shear bands can be seen on the surface of the indented area................................10 
v

Acknowledgments 

The authors are grateful to the Science and Engineering Apprenticeship Program for providing 

funds. Special thanks to Mr. Justin Pritchett for helping to polish the surface of the metallic 

glasses and to Dr. Laszlo Kecskes for assisting with SEM analysis, providing samples, and 

generating useful discussion. 
vi

INTENTIONALLY LEFT BLANK. 
1

1. Introduction 

Amorphous metals, otherwise known as metallic glasses, have been fervently researched since 

their discovery in 1960 (1). These materials are lightweight, exceptionally strong, and 

noncorrosive. In the past 15 years, material scientists have devised new bulk forms and families 

of metallic glasses precipitating new studies (2, 3). Furthermore, reinforcement phases have 

improved ductility, increasing applicability in various products and calling for a better 

understanding of deformation behavior. To characterize mechanical behavior of these materials, 

tensile and compression tests have been performed, coupled with nanoindentation (4). 

Nanoindentation has served as a significant resource in elucidating the deformation 

characteristics of these materials. From indentation curves, the elastic modulus, average contact 

pressure, energy per volume, and other parameters may be ascertained based on calculations 

derived from load-vs.-displacement data (5). With nanoindentation, a variety of stress states can 

be achieved, through use of different indenter tip geometries, that are both hydrostatic and 

deviatoric in nature. Furthermore, only small volumes of material are necessary for 

nanoindentation, which allow for investigating microscale material failure mechanisms and 

finding local variation of properties. 

Recent research using nanoindentation has provided insights on nucleation kinetics and mode of 

plasticity for bulk metallic glasses (BMG) (6, 7). Transmission electron microscopy of the 

indentations ex situ unveiled that recrystallization occurs without heating during quasistatic 

loading conditions. However, the nucleation kinetics’ driving force remains unclear. Further, 

nanoindentation studies have shown that lower loading rates exhibit more serrated flow than 

higher loading rates for sharp indenter geometries (6). It has been shown that slower loading 

rates cause BMG to exhibit individual shear bands, while in higher loading conditions, shear 

bands operate at the same instant creating the appearance of a more uniform deformation 

behavior (6). However, studies thus far have failed to consider the pressure conditions or energy 

per volume at the initial pop-in location signifying the initial point of plastic failure. The focus 

of this study is to use nanoindentation to understand the point of initial plastic deformation when 

strain rates, stoichiometry, and indenter tip radius are varied. It is anticipated that extrapolation 

of loading conditions and energy absorption per volume into the macroscale will guide 

understanding of failure conditions across various applications. 

2. Experimental Setup 

The BMG used in this study were 3-mm-diameter cylindrical ingots mounted in epoxy that had 

compositions of (HfxZr1-x)52.5Ti5Ni14.6Cu17.9Al10, where “x” was either 0 (20), 0.4 (22), or 
2

1.0 (25). Numbers in parenthesis indicate the corresponding sample designation for the different 

compositions. X-ray diffraction indicated that the glasses were amorphous except for small 

crystallization peaks in metallic glasses 20 and 25, or the Zr and Hf rich samples, respectively. 

In order to ensure repeatable indentation results, sample surfaces were polished with diamond 

paste to a mirror finish. Finally, the backside of each sample was ground until the BMG was 

exposed at the surface and this piece was in turn glued to a stiff aluminum puck. This was done 

to eliminate compliance effects from the epoxy mount. 

The indentation experiments were conducted using a Nano Indenter XP (MTS Systems), which 

measures load and displacement continually through the duration of the loading and unloading 

cycle. This machine can apply loads of up to 733 mN and has a total displacement range of 

1.5 mm. Experimental resolution of measurement has been typically found to be around 

10 μN and 0.1 nm for load and displacement, respectively. Before each indentation, the 

thermal/electronic drift rate of the indenter resting on the surface was measured to be below 

0.05 nm/s. To create markedly different stress states underneath the indenter, the three diamond 

tips used for indentation had a spheroconical geometry with a nominal radius of either 3, 20, or 

50 μm. Indentation strain rates (loading rate divided by load) of 0.1, 0.05, and 0.01 1/s were 

used for each indenter geometry. Each BMG was tested with each tip under each loading rate. 

For each condition, the maximum applied load was held for either 0 or 10 s and unloading took 

place over 10 s. Figure 1 illustrates a common profile for applied load with time. After 

indentation, selective BMG indents were examined using a Hitachi S4700 field emission 

scanning electron microscope (SEM). 

For each condition, a 5 × 5 array was indented 1000 nm into the surface to ensure at least one 

pop-in, and a 3 × 3 array at a more shallow depth was used to verify purely elastic behavior prior 

to pop-ins. To determine the location of a displacement burst, at least two elastic curves were 

superimposed on the load-vs.-displacement results providing visible deviations from the curve. 

In cases where the displacement burst was unusual or difficult to detect, the curve was not 

considered in the analysis. If the pop-in event was difficult to detect, the method developed by 

Juliano et al. (8) was used to determine event locations based on the derivative of the load-vs.-

displacement graph. The maximum difference in sequential data points that did not indicate a 

pop-in event was determined by the derivative of the elastic curves’ greatest fluctuation between 

successive data points. In each indeterminable curve, if a difference was greater than the greatest 

of the elastic curves, the displacement location of the initial data point was noted and established 

as the initial point of pop-in behavior. The first instance of this effect in a given curve was the 

only value established as a primary pop-in. 

Energy-per-unit volume and contact pressure were calculated in the following manner. Energy 

was taken as the area underneath the load-displacement curve, as determined by the Testworks 4 

software (MTS Systems). The total elastically deformed volume was defined as the volume of 

the indenter displaced into the original surface. This assumption necessitates that the material is 
3

0

10

20

30

40

50

60

70

80

90

100

110

0 100 200 300 400 500 600 700 800

Load On Sample (mN)

Time On Sample (s)

S

U

M H D E

L

Figure 1. Typical indentation loading profile as a function of time. 

incompressible, which is not the case since Poisson’s ratio for these BMG is ~0.3 and not 0.5. It 

is admitted that this assumption will introduce some error into the measurement methodology; 

however, no better option could be conceived at this time. Volume was computed by integration 

of area coefficients calibrated from fused-silica indentation data, with the point of contact and 

total displacement used as evaluation boundaries. Due to the difficulty of calibrating an accurate 

description of tip geometry at shallow depths (<100 nm), energy per volume could not be 

considered for the 3-μm-radius spherical tip because of the shallow initial pop-in location. 

Contact pressure at the location of the pop-in was taken to be the ratio of the applied load to the 

contact area, as determined by calibration of area coefficients for each indenter.
4

3. Results and Analysis 

From the data collected and shown in figure 2, it is seen that Hf-based BMG generally fail at 

greater pressure and energy per volume than the Zr-based BMG, based on the initial point of 

pop-in. Furthermore, Hf-based BMG is more sensitive to indenter tip radius in regards to both 

pressure and energy per volume at initial failure. 

Larger radius spheres required greater energy per volume, but less pressure to pop-in for similar 

indentation conditions. This could be justified by taking into account the time-dependent nature 

of the material. For smaller radius spheres, pressure is generated much more quickly during the 

initial displacement into the surface. This is illustrated in the experimental data shown in 

figure 3. Because BMG is time dependent (4), the greater pressure required to pop-in is a direct 

result of the material being able to withstand greater pressure for a short amount of time. 

Decreasing indentation strain rate in previous research has shown a tendency toward more 

serrated flow (4). Furthermore, in this work pop-ins could occur during the hold at peak load 

(figure 4) and a few that actually exhibited this effect during unloading (see figure 5). 

To explain energy-per-volume trends, the actual indenter tip geometry must be considered. The 

50-μm nominal radius sphere tip geometry initially has a smaller radius (~20 μm) at depths 

below ~200 nm that grows into a larger radius (~50 μm) while the opposite was true for the 

20-μm tip. This was determined by measuring the tip geometry with atomic-force microscopy as 

well as calibration with fused silica. As a result, there would be less and more actual displaced 

volume for the 50- and 20-μm nominal radius tips, respectively, compared to a perfect sphere. 

This does not affect pressure as significantly because it is evaluated past this point of transition 

in geometry and computed at a single location. Energy per volume, on the other hand, takes into 

account the history of contact area throughout the indentation. 

Even though BMG are known to be loading-rate sensitive, the range of strain rates used in this 

study do not appear to affect either pop-in pressures or energy per volume at the point of pop-in. 

However, load-displacement behavior was markedly different between the three different radius 

indenters. When using the 3-μm-radius sphere at loads above 150 mN, a regular stepwise pattern 

was found in the load-displacement curves (see figure 6). This pattern was more pronounced in 

the slower strain rate loading conditions. This fluctuated between periods of pop-ins and elastic 

behavior at a constant rate. It is possible that this effect was not observed for the 20- and 50-μmradius spheres because depths significant enough to generate similar pressure states were not 

obtained. Under large enough contact pressures (~9.5 GPa), for a spherical geometry, pop-in 

behavior becomes much more predictable and regular than for sub-critical values. 
5

Energy per Volume At Pop-Ins 

0

500

1000

1500

2000

2500

0 10 20 30 40 50 60

Radius of Indetner Tip 

Energy per Volume (J*10^8/m^3)

BMG 20

BMG 22

BMG 25

Pressure At Pop-Ins 

0

2

4

6

8

10

12

0 10 20 30 40 50 60

Radius of Indetner Tip 

Pressure (GPa)

BMG 20

BMG 22

BMG 25

Figure 2. Comparison of Zr-based and Hf-based energy per volume (a) and pressure at 

pop-in locations (b) as a function of radii. 

b)

Radius of Indenter Tip 

a)
6

Pressure under 3um and 20um Spheres

0

1

2

3

4

5

6

7

8

10 20 30 40

Displacement into Surface (nm)

Pressure (GPa)

3um

20um

Figure 3. Pressure generated for a 3-μm (upper) and 20-μm (lower) radius sphere as a function of 

displacement into the surface. 
7

178

180

182

184

186

188

190

192

194

196

198

200

202

204

430 440 450 460 470 480 490 500 510 520

Load On Sample (mN)

Displacement Into Surface (nm)

NLU

Figure 4. Pop-ins that occur at peak load. 
8

0

20

40

60

80

100

120

140

160

180

200

220

0 100 200 300 400 500 600

Load On Sample (mN)

Displacement Into Surface (nm)

S

U

M

L N

Figure 5. Pop-in that occurs during unloading segment. 

Beginning of 

unloading 
9

170

180

190

200

210

220

230

240

250

1500 1600 1700 1800 1900

Load On Sample (mN)

Displacement Into Surface (nm)

LU

Figure 6. Stepwise pattern exhibited in excess of 150 mN for indentation of 3-μm sphere. 
10

After indentation, SEM qualified that shear banding occurred underneath the surface under 

various indent locations, with a 3-μm-radius indenter indent shown in figure 7. Bands could be 

found most noticeably under these conditions, around the perimeter of the indent. Furthermore, 

residual imprints of slower strain rates were often deeper, signifying that more plasticity and a 

greater displacement from pop-ins occurred under slower conditions. 

Figure 7. SEM micrograph of an indentation made by the 3-μm-radius indenter. Clear effects of 

subsurface shear bands can be seen on the surface of the indented area. 

4. Conclusions 

A number of indentation tests were performed under various conditions on BMG samples and 

the following conclusions can be made: (1) Zr-based BMG was found to initially fail at lower 

contact pressures than Hf-based BMG. (2) Indentation strain rate was shown to have little effect 

for rates of 0.01 to 0.1 1/s. (3) Increasing the radius of the indenter tip appears to lower the 

pressure and to increase energy per volume necessary for a pop-in to occur.
11

Further research should be guided into understanding if greater magnitude changes in strain rate 

generate unique points of pop-in in regards to pressure and energy per volume. The time 

dependence of this material is essential for an understanding of it. Research on the effect of 

holding at the peak load, the nature of the stepwise pop-ins above pressures above 9.5 GPa, and 

pop-ins on unloading curves would be beneficial to further understanding of BMG. 
12

5. References 

1. Klement, W.; Willens, R.; Duwez, P. Nature 1960, 187, 869. 

2. Johnson, W. Journal of Mechanics 2002, 54, 40. 

3. Li, J. Treatises in Materials Science 1981, 20, 325. 

4. Schuh, C.; Neih, T. Journal of Materials Research 2003, 19, 1. 

5. Fischer-Cripps, A. Nanoindentation; Springer: New York, 2004. 

6. Schuh, C.; Argon, A.; Nieh, T.; Wadsworth, J. Philosophical Magazine A 2003, 83, 2585. 

7. Jiang, W.; Pinkerton, F.; Atzmon, M. Journal of Applied Physics 2003, 93, 9287. 

8. Juliano, T.; Domnich, V.; Buchheit, T.; Gogotsi, Y. Proceedings of the Materials Research 

Society Symposium, 791, 2004, pp Q7.5.1-Q7.5.11. 
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