Mostafa Shazly and Vikas Prakash

Case Western Reserve University, Cleveland, Ohio

Bradley A. Lerch

Glenn Research Center, Cleveland, Ohio

High-Strain-Rate Compression Testing of Ice

NASA/TM—2006-213966

January 2006
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Mostafa Shazly and Vikas Prakash

Case Western Reserve University, Cleveland, Ohio

Bradley A. Lerch

Glenn Research Center, Cleveland, Ohio

High-Strain-Rate Compression Testing of Ice

NASA/TM—2006-213966

January 2006

National Aeronautics and

Space Administration

Glenn Research Center
Acknowledgments

The authors would like to acknowledge financial support from NASA Glenn Research Center under

NASA Contract Number NNC05VA03P. The authors would also like to thank E.M. Schulson and

the Ice Research Laboratory at Dartmouth College, Hanover, New Hampshire, for providing

ice samples, microstructural analysis of the ice specimens, and many helpful discussions.

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

This report is a formal draft or working

paper, intended to solicit comments and

ideas from a technical peer group.

Trade names or manufacturers’ names are used in this report for

identification only. This usage does not constitute an official

endorsement, either expressed or implied, by the National

Aeronautics and Space Administration.

This report contains preliminary

findings, subject to revision as

analysis proceeds.

Available electronically at http://gltrs.grc.nasa.gov
NASA/TM—2006-213966 1

High-Strain-Rate Compression Testing of Ice 

Mostafa Shazly and Vikas Prakash 

Department of Mechanical and Aerospace Engineering 

Case Western Reserve University 

Cleveland, Ohio 44106–7222 

Bradley A. Lerch 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Summary 

In the present study a modified split Hopkinson pressure bar (SHPB) was employed to study the 

effect of strain rate on the dynamic material response of ice. Disk-shaped ice specimens with flat, parallel 

end faces were either provided by Dartmouth College (Hanover, NH) or grown at Case Western Reserve 

University (Cleveland, OH). The SHPB was adapted to perform tests at high strain rates in the range 60 to 

1400 s–1 at test temperatures of –10 and –30 °C. Experimental results showed that the strength of ice 

increases with increasing strain rates and this occurs over a change in strain rate of five orders of 

magnitude. Under these strain rate conditions the ice microstructure has a slight influence on the strength, 

but it is much less than the influence it has under quasi-static loading conditions. End constraint and 

frictional effects do not influence the compression tests like they do at slower strain rates, and therefore 

the diameter/thickness ratio of the samples is not as critical. The strength of ice at high strain rates was 

found to increase with decreasing test temperatures. Ice has been identified as a potential source of debris 

to impact the shuttle; data presented in this report can be used to validate and/or develop material models 

for ice impact analyses for shuttle Return to Flight efforts. 

Introduction 

Since the catastrophic breakup of the Space Shuttle Columbia, NASA has been active in classifying 

potentially deleterious debris sources and their destructive capability due to impact. Ice has been 

identified as one of the potential sources of debris. In order to better understand the severity of ice 

impacts on aero frames and structures, and to obtain the high-strain-rate behavior of ice, an experimental 

investigation was undertaken at Case Western Reserve University (CWRU, Cleveland, OH) in close 

collaboration with researchers at the NASA Glenn Research Center (Cleveland, OH). The key question 

under investigation was how the dynamic compressive strength of ice varies with the relevant loading 

rates. Besides providing fundamental information on the dynamic properties of ice, the data from the 

present study can also be used to validate and/or develop new material models for ice impact analyses for 

the Shuttle Return to Flight efforts. 

There is a large amount of work in the literature characterizing the compressive and tensile strength 

(refs. 1 to 6), and the fracture toughness (refs. 5 to 9) of ice either in single-crystal or polycrystalline 

forms. However, most of these studies have focused on the mechanical behavior in the creep and quasistatic deformation regimes. At higher strain rates, relatively few studies exist, and these typically only 

cover the strain rate regime from 10 to 100 s–1 (refs. 10 to 12). However, in events such as ice-structure 

interactions, ice drilling and crushing, and high-speed ice impacts, the strain rates in ice are much higher 

than those considered in the studies thus far. Moreover, results of studies conducted at strain rates of 10 to 

100 s–1 (refs. 10 to 12) show counterintuitive results, at least based on the known strain-rate behavior of 

common structural materials. The studies by Dutta (ref. 10) and Dutta et al. (ref. 12) suggest that the 

strength of ice at high strain rates is lower than that obtained in the quasi-static deformation regime (strain 

rates between 10–2 and 10–3 s–1). The study by Jones (ref. 11), however, does not show the same trend in 
NASA/TM—2006-213966 2

the behavior of ice with increasing strain rates. Although results of these studies (refs. 10 and 12) show 

ice following the behavior known as the “brittle to ductile behavior” at strain rates higher than 10–3 s

–1

(ref. 13), they do not explain the increase in impact forces measured at the higher impact velocities (ref. 

14). Additionally, extrapolations of the quasi-static compressive strength to higher strain rates do not 

provide clear trends as to whether the strength of ice increases, decreases or remains the same as the strain 

rate increases from the quasi-static to the dynamic range. Moreover, the quasi-static results indicated that 

the strengths were highly microstructural dependent, and it was unknown if this trend would continue in 

the high-strain-rate regime. These issues are addressed in the current work. 

The findings are described in this report. The report and raw test sample data files have been placed 

on the Orbiter TPS Impact Testing Data Archive Web site at NASA Johnson Space Center. The link for 

the Web site is http://hitf.jsc.nasa.gov/hitfpub/archive/home.cfm. The data can be found under the “series 

50” option “Characterization of ice used for impact testing.” 

A list of the symbols used in this report has been placed in appendix A to aid the reader. 

Experimental Work 

In an effort to explore the strength of ice at elevated strain rates, an experimental study was 

conducted at CWRU in close collaboration with scientists at NASA Glenn. In this study, the conventional 

split Hopkinson pressure bar (SHPB) was modified to accommodate low-temperature testing of ice at 

elevated strain rates. Disk-shaped ice specimens, with end faces that are flat and parallel, were provided 

by Dartmouth College (Hanover, NH) and/or grown at CWRU. The effects of strain rate, sample size, test 

conditions, and temperature on the strength of ice were investigated. 

Low-Temperature Split Hopkinson Pressure Bar Facility 

A split Hopkinson pressure bar (SHPB) was employed to conduct the high-strain-rate compression 

tests. A schematic of the SHPB facility at CWRU is shown in figure 1. The facility comprises a striker 

bar, an incident bar, and a transmitter bar. All the bars are made from 19.05-mm-diameter high-strength 

7075–T6 aluminum alloy having a nominal yield strength of 500 MPa. Striker bars with lengths of 75 and 

152 mm were used in the present study. The incident and transmitter bars were approximately 1.8 m long. 

The striker bar is accelerated using an air-operated gas gun. A pair of BLH SPB3–18–100–U1 

semiconductor strain gages (Vishay Intertechnology, Inc., Malvern, PA) are strategically attached to the 

incident and transmitter bars and are used in combination with a Wheatstone bridge circuit connected 

with a Tektronix 5A22N differential amplifier (Tektronix, Inc., Beaverton, OR) and a Tektronix TDS 420 

digital oscilloscope to monitor the strain pulses during the test. The impact velocity of the striker bar was 

varied between 2 m/s and 14 m/s so as to obtain strain rates in the range 60 s–1 to 1400 s–1. The theory and 

analysis of SHPB is described in the following section. To better understand the failure process of ice, a 

high-speed camera, Hadland IMACON 200,1

 with a maximum framing rate capability of 200 million 

frames per second was used to image the failure process.

To conduct the low-temperature experiments, a cooling chamber (figs. 1 to 3) was designed and built 

at CWRU. The chamber was built from acrylic plates having a thickness of 31.75 mm to maximize 

insulation efficiency and maintain the subzero temperatures in the chamber. A 3/8-in. standard copper 

tube was shaped in a coil form and immersed in liquid nitrogen in a Dewar (fig. 3). One end of the coil 

was connected to a nitrogen gas or air tank while the other end is shaped into a larger coil to surround the 

SHPB bars and the ice specimen in the cooling chamber. The coil carries the cooled air to the cooling 

chamber and helps to maintain it at the desired subambient temperatures. The temperature inside the 

chamber was monitored by a 0.015-in.-diameter chromel-alumel wire placed in close proximity to the 

specimen. Circulation of the cooled air within the cooling chamber helps to maintain a uniform 

temperature. The test temperatures were –10 and –30 °C. 

 

1

 Hadland Photonics, Ltd. (Tring, UK) was acquired by DRS Technologies, Inc. (Parsippany, NJ) and is now DRS Hadland, Ltd. 
NASA/TM—2006-213966 3
NASA/TM—2006-213966 4

In all experiments, copper pulse shapers were employed to promote attaining dynamic equilibrium 

conditions within the specimen; these dynamic equilibrium conditions are essential to achieve constant 

strain rates during the dynamic deformation process. The thickness of the copper shim that was employed 

was approximately 0.25 mm. The shape of the shim was a square, with lateral dimensions depending on 

the strain rate that was desired. For experiments performed on premachined single-crystal ice specimens, 

the specimen was placed between two aluminum inserts (see fig. 4) of the same material and diameter as 

the bars used in the SHPBs. Inserts were held by a Teflon (DuPont, Wilmington, DE) fixture for ease of 

handling. The procedure for assembly is shown in figure 5. The assembly of the ice disk and the inserts 

was transported from the freezer to the test rig in a cryocontainer. A thin layer of vacuum grease was used 

between the ice specimen and the inserts in order to minimize friction, and hence the end constraint, 

during testing and also to hold the ice sample in place during mounting between the SHPB bars. Stressstrain curves are presented for the tests, where stress and strain are represented as engineering values. 
NASA/TM—2006-213966 5

Theory of SHPB 

The theory behind the SHPB operation relies on the one-dimensional wave analysis (ref. 15). The 

governing equation for wave propagation in a thin long rod is given by the second order partial 

differential equation 

2

2

2

2 1

t

u

x c

u

b ∂

∂ = ∂∂ (1) 

where u is displacement, x is axial position along the sample, t is time, and cb = E ρ is the longitudinal 

wave speed expressed in terms of Youngs modulus E and density ρ of the bar.

The solution of this equation by D’Alembert (ref. 16) is given by 

u( ) x t (x c t) (x c t) = − b + g + b , (2) f

where the functions f and g represent pressure waves traveling to the right and the left, respectively. 

The strain ε and displacement rate u are then simply the derivative of the displacement with respect 

to x and t, respectively; that is, 

= εi + εr ε = f (3) ′+ g′

and 
NASA/TM—2006-213966 6

( ) ( ) u cb = cb − εi + εr  = − f ′+ g′ (4) 

In equations (3) and (4) εi and εr are the incident and reflected strain signals, respectively. 

Figure 6 illustrates the displacements and forces generated on the specimen by the test. In view of 

equation (4), the displacement of the left end of the sample u1 is given by 

u c ( ) t

t

= b ∫ − εi + εr

0

1 d (5) 

The transmitted wave system and the displacement of the right end of the sample u2 are given by 

u (x t) (x c t) = h − b , 2 (6) 

where h is a wave traveling to the right. 

Similarly, the transmitted strain signal εt is given by 

(x c t) t − b ε = h (7) ′

and 

( ) b b cb t u = −c h′ x − c t = − ε (8) 

The displacement u2 is then given by 

∫ = − ε

t

b t u c t

0

2 d (9) 

In view of equations (5) and (9), the average strain in the specimen εs is given by 

( ) t

T

c

T

u u

t

t i r

o

b

o

s d

0

2 1

∫ = − ε + ε − ε − ε = (10) 

where To is the original specimen thickness. 
NASA/TM—2006-213966 7

The forces P1 and P2 on the left and the right faces of the specimen, respectively, are given by 

( ) P1 = AE εi + εr (11a) 

P2 = AEεt (11b) 

where A is the cross-sectional area of the incident and transmitted bars. After a few reverberations, the 

wave propagation effects within the specimen become negligibly small, such that P1 = P2. 

It then follows that εi + εr = εt , so that the strain rate, strain, and stress in the specimen are given by 

( ) r

o

b s T

c

ε t = ε

2  (12) 

( ) ∫ ε = − ε

t

r

o

b s t

T

c

t

0

d 2 (13) 

( ) ( )

o

t

o o

s A

AE t

A

P

A

P

t

ε

σ = = = 1 2 (14) 

where Ao is the original cross-sectional area of the specimen. 

In a typical SHPB experiment, the strain gage stations attached to the incident and transmitted bars 

record the incident signal εi, the reflected signal εr, and transmitted signal εt. An in-house MATLAB 

program (The Mathworks, Inc., Natick, MA) is then used to filter the high-frequency noise and construct 

the stress-strain data from the raw data. The input parameters to the program are elastic properties of the 

incident and transmitted bars (Young’s modulus and density), the dimensions of the specimen (diameter 

and thickness), and the shunt calibration of the strain gage stations. 

Ice Specimen Geometry and Specimen Preparation Procedures 

The ice specimens used in the present study were either single-crystal ice provided by the Ice 

Research Laboratory at Dartmouth College or polycrystalline ice samples grown at CWRU. The samples 

provided by Dartmouth College were machined out of cylinders of ice manufactured by Ice Culture, Inc. 

(Hensall, Ontario, Canada). The nominal diameter of the disk samples was in the range 17.5 to 18.5 mm. 

Although the specimens were not exactly cylindrical, the diameter was calculated based on the specimen 

weight and measured thickness. The specimens had a thickness of 5.0 to 9.0 mm, and the impact faces 

were milled parallel to within 0.076 mm. The samples were shipped from Dartmouth College to CWRU 

in containers packed with dry ice and stored upon arrival in a freezer at –15 °C. 

The ice specimens made at CWRU were grown between two flat aluminum inserts, as shown in 

figure 7. The inserts were spaced at a predetermined distance and then were wrapped with masking tape. 

Next, a small hole was made in the masking tape to act as a water feeder to fill the compartment between 

the two inserts. The hole also acted as a breather to drain overflowed water during freezing. The whole 

assembly was then placed inside a freezer at the desired temperature. The subsequent ice nucleation and 

growth process required approximately 30 min. before the samples were taken out of the freezer for 

testing. De-ionized sodium-free water was used to make the ice samples. Due to the high conductivity of 

the aluminum inserts, ice crystals initiated simultaneously from the faces of the aluminum inserts and 

grew towards the center of the compartment, as illustrated schematically in figure 7. This growth process 

resulted in a clear but noticeable interface in the midplane of the ice specimens; the effect of this interface 

on the dynamic compression strength of ice is expected to be negligible. However, as a result of the 
NASA/TM—2006-213966 8

midplane porosity these samples were very weak in tension. Longer specimens made by following this 

technique split at the midplane during handling, as shown in figure 8. 
NASA/TM—2006-213966 9

Experimental Results 

Microstructure of Ice Specimens 

The microstructure of the ice supplied by Dartmouth College was single crystalline containing a lot of 

subgrain boundaries (ref. 1). Figure 9 shows the birefringent pattern of a typical ice disk providing 

evidence that the disks were essentially single crystalline. No effort was made to orient the ice (i.e., relate 

the crystal structure to the axes of the disk sample). It has been shown (ref. 17) under quasi-static 

compression loading that the orientation of single-crystal ice can affect the strength by as much as a factor 

of 3. The birefringent pattern for each single-crystal ice sample tested in the present study is shown in 

appendix B. 

The ice samples grown at CWRU were multigrained structures as shown in figure 10. Ice crystals 

nucleated on the aluminum inserts creating small equiaxed grains up to a diameter of 1.5 mm. As freezing 

continued, the grains grew from both sides with final freezing occurring at the midpoint. This created a 

zone of small bubbles in the middle, which appeared as a cloudy area. The ice at the ends of the sample 

was clear. The grain size of the growth grains was large, being approximately 3 mm in diameter and 5 

mm in length for the longest grain. Transverse sections (fig. 10(b)) indicated that the large grains had an 

extensive substructure. 
NASA/TM—2006-213966 10

Stress Equilibrium and Nearly Constant Strain Rate Experiments 

Based on the available literature (ref. 18), ice has an average Young’s modulus of 10.0 GPa and an 

approximate density of 1000 kg/m3

. These values give a longitudinal elastic wave speed of 3162 m/sec. 

As pointed out by Davies and Hunter (ref. 19), the stress state equilibrates within the specimen after 

approximately π reverberations of the stress pulse within the specimen, that is 

C

T

t

π

equil = (15) 

where T is the specimen thickness and C is the longitudinal wave speed in ice. 

In view of equation (15), for the experiments conducted in the present study, the 8-, 5-, and the 2.3-

mm-thick ice specimens will require approximately 8, 5, and 2.3 μs, respectively, to reach equilibrium 

conditions. Based on this analysis, the times for the attainment of maximum stress in the ice specimens is 

always greater than those required to reach an equilibrium state of stress within the specimen. This 

condition was facilitated by using copper pulse shapers to shape (increase) the rise time of the incident 

pulse. In the present study, annealed copper shims of various sizes were used as the copper pulse shapers. 

The size of the shim was determined by trial and error depending on the impact velocity and the type of 

ice being tested. In the first trial, a test was run with an arbitrary pulse shaper size. The transmitted signal 

was then used to optimize the pulse shaper by matching the slopes of the incident signals (resulting from 

impacting the incident bar with different pulse shapers placed between the incident and striker bars) with 

the transmitted signal of the first test. 

Figure 11 shows results of pulse shaper size optimization for impact velocities of 2.6 and 5 m/s. In 

figure 11(a), an initial trial on a 3- by 3- by 0.25-mm pulse shaper showed that the slope of the input 

signal is lower than that of the transmitted signal. Incremental increases in the pulse shaper dimensions 

(keeping the same thickness) were performed to increase the longitudinal impedance of the pulse shaper, 

to make it appear stiffer, and also to reduce the magnitude of plastic flow upon impact. Two sets of 

experiments were performed at the larger dimensions to assure such behavior. For the case of the higher 

impact velocity, a thinner pulse shaper of 0.13 mm was the first choice as it is expected to show less 

plastic flow and a steeper input signal should be obtained. This trial was unsuccessful and the previous 

thickness of 0.25 mm was then used but with larger lateral dimensions. Similarly, two trials were 

performed for the same dimensions for verification. It is clearly shown in figure 11 that for a given pulse 

shaper material the required dimensions of the pulse shaper depend on the impact speed. 

Since ice is a brittle material (particularly in these ranges of temperatures and strain rates), the failure 

strains are less than 1 percent. Since the strain rate starts at zero in the beginning of the test and must 

increase during loading, there is little time to establish a constant value of strain rate before the samples 

break. Achieving a degree of constant strain rate loading was maximized through the use of pulse shapers. 

The average strain rate listed in the tables represents an average value taken near the maximum load (i.e., 

at fracture). The strain rate can vary by as much as 200/sec during this time. Nonetheless, given the small 

failure strains in ice, it is the best that could be achieved. Similar difficulties have been observed in other 

brittle materials such as ceramics (refs. 20 and 21) and rocks (ref. 22). 
NASA/TM—2006-213966 11
NASA/TM—2006-213966 12

Experiments Performed at –10 °C 

Single-crystal ice: 6SX series.—The first series of experiments was conducted on single-crystal ice 

specimens (6SX series). Tables I and II summarize the experimental parameters and results for this set of 

experiments, respectively. Strain gage signals, stress and strain-rate versus strain profiles, stress versus 

time diagrams, and the high-speed camera photographs for this series of experiments are provided in 

appendix B. 

TABLE I.—EXPERIMENTAL PARAMETERS FOR 6SX EXPERIMENT SERIESa

Test Specimen Shunt voltage Camera settings 

number 

Diameter, 

mm 

Length, 

mm 

Gage 1, 

mV 

Gage 2, 

mV 

Chamber 

temperature, 

°C Delay, 

μs 

Interframe 

time, 

μs 

Striker bar 

 length, 

mm 

Pulse 

shaper size, 

mm 

6SX–3 18.62 5.49 14.7 64 –11.3 210 5 76.2 10×10×0.25 

6SX–4 18.49 5.36 70 65 –11.0 210 10 152.4 No shaper 

6SX–6 18.42 5.77 29 130 –11.4 --- --- 152.4 10×10×0.25 

6SX–7 18.52 5.26 29 130 –9.3 --- --- 152.4 10×10×0.25 

6SX–8 18.39 5.54 29 130 –12.1 --- --- 152.4 10×10×0.25 

6SX–9 18.37 5.38 70 65 –11.0 210 8 152.4 5×5×0.25 

6SX–

11 18.31 5.46 29 65 –12.0 210 8 152.4 9×9×0.25 

6SX–

12 18.38 5.05 14.5 68 –11.0 --- --- 76.2 10×10×0.25 

a

The excitation voltages for gages 1 and 2 were 15 V for each test. Gages 1 and 2 are the strain gages attached to the incident and 

 transmitted bars of the SHPB apparatus, respectively. 

TABLE II.— EXPERIMENTAL RESULTS FOR 6SX EXPERIMENTS SERIES 

Test 

number 

Striker bar 

velocity, 

m/s 

Average strain 

rate, 

s

–1

Maximum stress, 

MPa 

Strain at maximum 

stress (×10–3) 

Time at maximum 

stress, 

μs 

6SX–3 10.0 882 33.5 8.3 21.7 

6SX–4 2.9 130 20.7 5.0 56.5 

6SX–6 4.8 260 24.8 7.8 39.7 

6SX–7 4.6 460 22.0 5.9 30.0 

6SX–8 4.8 425 26.7 4.04 23.3 

6SX–9 3.8 90 23.4 6.5 84.4 

6SX–11 5.8 611 23.7 6.37 23.4 

6SX–12 14.3 1122 34.7 7.7 15.7 

Figure 12 summarizes the stress-strain behavior of single-crystal ice tested at –10 °C. A striker bar of 

length 150 mm was employed in all experiments except 6SX–8 and 6SX–12, where a striker bar of length 

75 mm was used. By employing proper pulse shaping, a near constant strain rate was achieved in the 

specimens during the dynamic deformation process. For the shorter length striker bar the strain 

accumulated in the ice specimen was less than that obtained with a longer striker bar, and consequently, 

the specimen in experiment 6SX–8 did not yield or fail during the loading pulse, and significant elastic 

recovery is evident in figure 41 in appendix B. High-speed photography was employed in experiments 

6SX–4, 6SX–9, and 6SX–11 to better understand the dynamic deformation and failure processes in ice. 

These studies revealed that the drop in peak stress was associated with the formation of a single dominant 

crack in the ice specimen. The first evidence of cracking was observed in frames 5, 12, and 4, 

respectively, with the loads being close to their peak levels. After attainment of the peak stress a large 

number of axial cracks were observed in the sample. The number of these microcracks was observed to 

increase as the deformation proceeded, eventually leading to complete fragmentation of the specimen. At 
NASA/TM—2006-213966 13

relatively higher impact speeds (e.g., experiment 6SX–3), cracking in the specimen was observed to 

initiate during the rise time of the loading pulse well before the attainment of the peak stress levels. 

Moreover, the peak stress levels attained in these experiments were much higher than those obtained in 

the case of the lower impact velocity experiments, and no evidence of catastrophic load drop was 

observed in the transmitted strain gage signal after the attainment of peak stress levels. The peak stress 

was followed by a relatively large tail, with the post peak stress levels indicating the stress still carried by 

the pulverized and/or fragmented ice after failure. 

CWRU-grown ice: HMD series.—In this series of experiments, the multigrained home grown ice 

samples were evaluated under test conditions similar to those employed during testing of the 6SX series 

of experiments, except that no vacuum grease was used between the specimen faces and bar inserts. In 

the 6SX series, for the highest strain rate experiments the maximum stress (failure stress) was attained 

at a time comparable to the equilibrium time. Therefore, in order to attain higher strain rates with failure 

times greater than the corresponding equilibrium times, thinner specimens than those used in the 6SX 

series of experiments were employed. Three different thicknesses of 5.5, 2.3, and 0.89 mm were tested. 

Table III summarizes the experimental parameters, while table IV summarizes the experimental results 

for this series of experiments. Strain gage signals, stress and strain-rate versus strain profiles, stress 

versus time diagrams, and the high-speed camera photographs for this series of experiments are provided 

in appendix C. 
NASA/TM—2006-213966 14

TABLE III.—EXPERIMENTAL PARAMETERS FOR HMD EXPERIMENT SERIESa,b 

Shunt voltage Camera settings Test 

number 

Specimen

length,c

mm

Gage 1, 

mV 

Gage 2, 

mV 

Chamber 

temperature, 

°C 

Delay, 

μs 

Interframe time, 

μs 

Pulse 

shaper size, 

mm 

HMD003 5.5 69 67 –9.8 --- --- 9×9×0.25 

HMD006 5.5 70 70 –10.0 --- --- No shaper 

HMD008 5.5 –11.0 210 8 No shaper 

HMD016 5.5 –12.2 210 5 5×5×0.25 

HMD010 2.3 –10.2 210 8 No shaper 

HMD011 –11.5 210 8 5×5×0.25 

HMD014 –9.7 --- --- 5×5×0.25 

HMD018 –10.0 210 5 No shaper 

HMD019 –9.0 --- --- 5×5×0.25 

HMD022 0.89 –11.0 --- --- 5×5×0.25 

HMD024 0.89 –10.1 --- --- 5×5×0.25 

HMD027 0.89 –10.1 --- --- 5×5×0.25 a

Excitation voltages for gages 1 and 2 were 15 V for each test. Gages 1 and 2 are the strain gages attached 

 to the incident and transmitted bars of the SHPB apparatus, respectively. 

b

Striker bar length was 152.4 mm for each test. 

c

Specimen diameter was 19 mm for each test. 

TABLE IV.—EXPERIMENTAL RESULTS FOR HMD EXPERIMENT SERIES 

Test 

number 

Striker bar 

velocity, 

m/s 

Average strain 

rate, 

s

–1

Maximum 

stress, 

MPa 

Strain at maximum 

stress (×10–3) 

Time at maximum 

stress, 

μs 

HMD003 6.0 770 22.7 10.9 27.7 

HMD006 2.18 140 9.5 2.5 36.0 

HMD008 2.0 92 11.7 4.1 59.5 

HMD016 4.38 180 17.8 4.2 43.1 

HMD010 2.3 312 14.6 11.1 53 

HMD011 4.5 225 23.0 8.1 44 

HMD014 7.4 740 23.5 6.2 21.6 

HMD018 2.57 408 13.2 8.3 35.0 

HMD019 4.57 397 15.1 6.5 28.7 

HMD022 4.44 672 26.1 30.5 57.8 

HMD024 4.53 740 22.0 16.6 33.0 

HMD027 4.27 550 29.0 29.7 82 

In this series of experiments the onset of cracking is observed to occur close to the peak stress level. 

This behavior is similar to that observed for the case of the 6SX series of experiments at comparable 

impact speeds. Cracking is evident in frame numbers 8, 8, 7, and 6 for experiments HMD016, HMD010, 

HMD011, and HMD018, respectively, while no cracking was observed for experiment HMD008, as 

shown in the high-speed camera photographs in appendix C. For the thinner 2.3-mm specimens, multiple 

cracks were seen to propagate simultaneously. This is in contrast with the single cracks that form in the 

thicker 5.5-mm samples. 

The stress-strain diagrams for the different thickness specimens at multiple strain rates are shown in 

figures 13 to 15. In all cases except for experiments HMD008 and HMD027, the ice specimens were 

observed to fracture; in the case of experiments HMD008 and HMD027, evidence of elastic unloading is 

observed. For comparison the average failure strains for both single and polycrystalline ice under static 

loads was approximately 3±0.5×10–3 (ref. 1). The strain at maximum stress is observed to increase as the 

specimen thickness decreases, as shown in table IV. The average strain at maximum stress for specimens 

with 5.5, 2.3, and 0.89 mm thickness are 5.42±3.73×10–3, 8.04±1.94×10–3, and 25.6±7.8×10–3, 

respectively. It should be pointed out that the magnitude for the strains at failure for the 5.5-mm-thick 

specimens are comparable to those obtained for the single-crystal ice specimens (6SX series) with the 
NASA/TM—2006-213966 15

same specimen thickness. Again, the peak stress decreases as the strain rate decreases. The curves also 

exhibit a long tail after the attainment of maximum stress, which approaches some sizable stress as the 

sample thickness decreases and the strain rate increases, for example, 10 MPa for 0.89 mm thickness and 

740 s–1 (fig. 15). Note that 10 MPa is the approximate compression strength of hard ice observed in quasistatic tests (ref. 1). 
NASA/TM—2006-213966 16

Effect of constrained ends: 14SX series.—Next, a series of experiments was conducted to understand 

the effect of end constraint on the measured dynamic failure strength of ice. In these series of experiments 

single-crystal ice specimens (14SX series) supplied by Ice Research Lab at Dartmouth College were used. 

In order to create relatively strong end constraint conditions, a thin layer of water was sprayed on 

precooled aluminum inserts and the ice sample was set on this layer. The assembly was then kept in the 

freezer for at least 10 min to allow the specimen to freeze to the inserts. These specimens were then tested 

in the SHPB at strain rates similar to those employed in the previous experiments having less end 

constraint. The experimental parameters for this set of tests are summarized in table V, while the 

experimental results are summarized in table VI. Strain gage signals, stress and strain-rate versus strain 

profiles, and stress versus time diagrams for this series of experiments are provided in appendix D. 

TABLE V.—EXPERIMENTAL PARAMETERS FOR 14SX EXPERIMENT SERIES 

WITH CONSTRAINED ENDSa,b,c

Test Specimen 

number Diameter, 

mm 

Length, 

mm 

C-axis orientation 

with respect 

to vertical, 

deg 

Chamber 

temperature, 

°C 

Pulse 

shaper size, 

mm 

14SX–02 17.46 5.66 50 –11.5 5×5×0.25 

14SX–03 17.46 5.74 45 –10.3 5×5×0.25 

14SX–06 17.46 5.74 40 –10.3 5×5×0.25 

14SX–07 19.0d 5.89 47 –10.0 5×5×0.25 

14SX–09 19.0d 5.92 45 –10.5 9×9×0.25 

14SX–18 19.0d 8.69 0 –11.0 5×5×0.25 a

Excitation voltages for gages 1 and 2 were 15 V for each test. Gages 1 and 2 are the strain 

 gages attached to the incident and transmitted bars of the SHPB apparatus, respectively. 

b

Shunt voltages for each test were 67 mV for gage 1 and 68 mV for gage 2. c

Striker bar length was 152.4 mm for each test. 

d

Grown from 17.0 mm. 
NASA/TM—2006-213966 17

TABLE VI.—EXPERIMENTAL RESULTS FOR 14SX EXPERIMENTS SERIES WITH CONSTRAINED ENDS 

Test 

number 

Striker bar 

velocity, 

m/s 

Average strain 

rate, 

s

–1

Maximum 

 stress, 

MPa 

Strain at maximum 

stress (×10–3) 

Time at maximum 

stress, 

μs 

14SX–02 5.3 318 14.7 2.6 24.0 

14SX–03 3.9 200 21.8 8.1 55.8 

14SX–06 3.5 139 17.3 4.8 52.5 

14SX–07 3.3 187 10.8 3.9 36.2 

14SX–09 5.2 278 24.0 4.4 31.2 

14SX–18 3.3 80 19.0 3.9 56.6 

Figure 16 shows the stress-strain diagrams for this series of experiments. The strain at maximum 

stress for the constrained end condition is observed to be somewhat less than that obtained for singlecrystal ice specimens (6SX) tested with the unconstrained end condition (i.e., with vacuum grease 

between the specimen faces and the bars). Moreover, the times at which the maximum stress occurs are 

greater than those observed in the case of the 6SX series. However, the maximum stress is the same in 

both cases. 
NASA/TM—2006-213966 18

Experiments Performed at –30 °C 

Previous studies on ice have shown the failure strength to be temperature dependent (refs. 1 to 9). 

However, at elevated strain rates the strength has been reported to be temperature independent (ref. 12). 

In the present study, experiments were conducted at –30 °C on ice specimens grown at CWRU following 

procedures similar to those described earlier. Specimens with thicknesses of 5.8, 2.3, and 0.89 mm 

were grown and evaluated. The experimental parameters for this set of experiments are summarized in 

table VII, while the experimental results are summarized in table VIII. Strain gage signals, stress and 

strain-rate versus strain profiles, and stress versus time diagrams for this series of experiments are 

provided in appendix E. Figures 17 to 19 show the stress-strain diagrams for this series of experiments 

with specimen thicknesses of 5.8, 2.3, and 0.89 mm, respectively. While all other specimens that were 

evaluated failed during the tests, specimens utilized in Test 1 and Test 16 did not fail as evident by the 

elastic unloading curves (see figs. 98 and 116 in appendix E for strain gage signals in which the reflected 

signals showed positive and negative strain rate profiles). Once again the maximum stress is observed to 

have a positive correlation with strain rate. Also, specimens with 0.89 mm thickness show a distinct post 

failure plateau in the stress versus strain curves and maintain a stress level as high as 20 MPa in the post 

peak-stress strain regime, as shown in figure 19. The average strain at maximum stress for the specimens 

with a 5.8 mm thickness was 6.10±1.67×10–3, for specimens with 2.3 mm thickness 10.33±1.87×10–3, and 

for specimens with 0.89 mm thickness 38.17±9.15×10–3. These strain values are slightly higher when 

compared with the same specimen thickness samples tested at –10 °C, which were 5.42±3.73×10–3 for 

specimens with a 5.5 mm thickness, 8.04±1.94×10–3 for specimens with a 2.3 mm thickness, and 

25.6±7.8×10–3 for specimens with a 0.89 mm thickness. Again the times corresponding to the maximum 

stress are larger than the equilibrium time and comparable to those for the specimens tested at –10 °C. 

The most important observation is that the maximum stresses for samples tested at –30 °C were higher 

than for specimens tested at –10 °C (compare figs. 17 to 19 with 13 to 15). 

TABLE VII.—EXPERIMENTAL PARAMETERS FOR EXPERIMENTS PERFORMED AT –30 °Ca 

Test Excitation voltage Shunt voltage 

number 

Specimen 

length,b

mm 

Gage 1, 

V 

Gage 2, 

V 

Gage 1, 

mV 

Gage 2, 

mV 

Chamber 

temperature, 

°C 

Pulse 

shaper size, 

mm 

1 5.8 15 15 67 68 –30.0 5×5×0.25 

5 15 15 29 29 –28.7 11×11×0.25 

6 7.5 7.5 14.4 36 –33.8 12×12×0.25 

8 –31.8 12×12×0.25 

9 –31.9 13×13×0.25 

10 –30.0 13×13×0.25 

11 2.3 –29.7 11×11×0.25 

12 2.3 –32.9 11×11×0.25 

14 2.3 –31.7 13×13×0.25 

16 0.89 –33.0 11×11×0.25 

17 .89 –33.0 12×12×0.25 

19 .89 –30.0 12×12×0.25 

20 .89 –32.0 12×12×0.25 a

The striker bar length was 152.4 mm for each test. 

b

Specimen diameter was 19 mm for each test. 
NASA/TM—2006-213966 19

TABLE VIII.—EXPERIMENTAL RESULTS FOR EXPERIMENTS PERFORMED AT –30 °C 

Test 

number 

Striker bar 

velocity, 

m/s 

Average strain 

rate, 

s

–1

Maximum 

stress, 

MPa 

Strain at maximum 

stress (×10–3) 

Time at maximum 

stress, 

μs 

 1 4.1 62 23 6.0 83.0 

5 7.0 209 39.35 8.8 45.0 

6 7.0 290 35.4 5.1 24.3 

8 6.8 214 36.8 6.8 39.4 

9 8.9 426 31.7 3.8 22.6 

10 10.0 580 34 6.1 20.3 

11 7.2 323 38.4 11.1 40.1 

12 6.8 250 39.6 8.2 44.4 

14 7.4 502 36 11.7 28.0 

16 7.4 596 44.3 46.5 43.4 

17 9.3 978 54 40.7 49.1 

19 8.7 842 53.7 40.4 61.4 

20 10.0 1441 58.4 25.1 25.4 
NASA/TM—2006-213966 20

Discussions 

The experimental results for maximum (failure) stress as a function of the average strain rate and the 

strain at maximum stress as a function of the specimen thickness are summarized in figures 20 and 21, 

respectively. From figure 20, it is clear that both single-crystal and the CWRU-grown polycrystalline ice 

have a positive strain rate dependency. This behavior is contradictory to other SHPB data (refs. 10 and 
NASA/TM—2006-213966 21

12) that is available in the literature in the strain rate regime of 10 to 100 s–1; however, it correlates well 

with data obtained from lower strain rate testing on servo hydraulic machines at strain rates up to 10 s–1

(ref. 11). This behavior of positive strain rate dependency is similar to other brittle materials such as 

ceramics and rocks. For example, Macor glass ceramic (Corning Incorporated, Corning, NY) showed a 

positive strain rate dependency over a wide range of strain rates from 10–6 to 3000 s–1 (ref. 20), silicon 

carbide showed the positive strain rate dependency at strain rates higher than 250 s–1 (ref. 21), and granite 

showed the same behavior over a strain rate range of 100 to 600 s–1 (ref. 22). Moreover, as seen from 

figure 20, no clear evidence of specimen size effects on the failure strength can be deduced from the 

experimental results, but there is a specimen size effect on the strain at maximum stress as shown in 

figure 21.The peak stress reported in the work by Dutta et al. (ref. 12) was 6.53±1.44 MPa and 6.77±3.23 

MPa at –10 °C under quasi-static and dynamic loading conditions, respectively. These values are two to 

three times less than those obtained in the present study. It must be noted that the specimens used in the 

study by Dutta et al. (ref. 12) had a thickness of 76 mm, which according to Davies and Hunter (ref. 19) 

requires about 75 μs to achieve stress equilibrium. However, the representative strain gage signals 

showed a failure time of approximately 80 μs, which is close to the time required for the specimens to 

reach equilibrium. Unfortunately, representative stress and strain-rate versus strain diagrams were not 

provided in their report, and so a judgment on uniform deformation conditions within the specimens can 

not be made with certainty. It should be noted that the values (6.53 MPa) obtained in their static tests 

agree well with the static strengths determined by Schulson et al. (ref. 1). Surprisingly, strains at peak 

stress under dynamic loading in their work were less than 2×10–3 as indicated in the representative stress 

strain diagrams of the SHPB experiments (though no values were tabulated as for the quasi-static 

experiments). These values, however, follow the trend of the dependency of strain at maximum stress on 

the specimen size in the present study as shown in figure 21. 
NASA/TM—2006-213966 22

The log-log plot in figure 22 gives a more conventional look at the strain rate effects on ice for 

experiments conducted at –10 °C. Included in the plot are the data from this report as well as the quasistatic data from Schulson et al. (ref. 1). The plot shows a clear, positive strain rate dependence over the 

range of strain rates of .01 to 1400 s–1 (over 5 orders of magnitude). There are two lines plotted in this 

figure to represent the relationship. The blue line represents the regression taken on the quasi-static 

data only (ref. 1) and extrapolated (dashed line) to the higher strain rates. This line over-predicts the 

strength at higher strain rates. A better fit is given by the orange solid line, which uses only the 

polycrystalline data over all strain rates (HMD series in present work). The equation is similar to that 

given by Schulson et al. (ref. 1) (blue line) and Jones (ref. 11) (pink line) and has the higher degree of 

correlation (R2

 = 0.737). The line is continuous with no jogs. Jones (ref. 11) had previously reported a 

jogged line as shown by the black line. Thus the strength of ice has a steady increase with increasing 

strain rate, and the relationship given by the orange line is preferred. This is a more satisfying relationship 

based on common sense expectations. This behavior also provides more confidence in extrapolating this 

relationship to still higher strain rates that are more typical of the ice impact events. 

Schulson et al. (ref. 1) has shown a strong relationship of microstructure and strength. In their work 

single crystals were found to be the strongest followed by columnar-grained polycrystals followed by 

columnar grains loaded at an angle to the columns. While the difference in strength is not as large at the 

high strain rates, there is still evidence in stratification as can be observed in figure 20. The single-crystal 

samples are slightly stronger than the polycrystalline samples. A more systematic study is needed to better 

define this effect. 
NASA/TM—2006-213966 23

One important consequence of this testing involves the postfracture behavior of the ice. It can be 

observed in the stress-strain curves that the sample still carries some load even after the sample breaks. 

This load is sizable and in most cases is larger than the quasi-static compression strength. This “tail 

strength” is dependent on sample thickness and strain rate, being higher for thinner samples and larger 

strain rates. This is because the shards of ice do not have the opportunity to fall out of the fixture, and thus 

end up maintaining some load. That is, the sample is no longer a coherent structure, but consists of 

fragmented ice. Similar behavior has been observed both during drop tower tests at NASA Langley 

Research Center and impact tests at NASA Glenn. During these tests the ice projectiles fragment upon 

impacting a load cell, but still impart a load due to the continued momentum of the ice particles. These 

results suggest that during modeling of impact events, more than just the initial impact load is required to 

define a state of damage. In fact, in the ballistic ice model used for RTF, the ice impact is treated first as a 

structure and then as a fluid to account for this continued momentum transfer (Dr. Kelly Carney, 2005, 

NASA Glenn Research Center, Cleveland, OH, personal communication). 

Since the ice samples are thin to ensure stress equilibrium, concerns were raised about end effects 

playing a large role in the specimen stress distribution. End effects would result from high frictional 

effects at the sample ends constraining the radial displacement of the sample during loading. These effects 

should be more severe on a thinner sample than a thicker sample. In fact, this is precisely the reason why 

there are minimum sample thickness/diameter (T/D) ratios given for quasi-static compression testing for 

metals in ASTM Standard E9–89 (ref. 23). Here, the problem is approached for the ice by showing that 

frictional effects at high strain rates are minimal. Also, a finite element analysis was performed to show 

the uniformity of stress distribution within the samples. 
NASA/TM—2006-213966 24

The analysis of uniform uniaxial compression of solid cylinders under frictional forces (ref. 24) in 

figure 23 shows that the radial stress σrr is given by 

⎟

⎠

⎞ ⎜

⎝

⎛

σ = − D

r

T

Df rr

2 1 (16) 

where f is the frictional stress and is assumed to be constant across the cross-sectional area of the 

specimen. 

The radial stress σrr is minimized by decreasing the frictional stresses and/or the specimen 

diameter/thickness ratio D/T. Recent experimental work on ice frictional behavior with different materials 

(refs. 25 and 26) showed that the kinetic coefficient of friction is reduced by a factor of 10 as the sliding 

velocity changes from 10–5 m/s to 0.1 m/s. In the present study, assuming constant volume, the radial 

velocity of the outside radius of the specimen is given by 

( ) ( )

[ ] ( ) 2

3

1 d

d

t

r t

t

r t o

− ε

ε =  (17) 

where ro is the original sample radius, and ε and ε are the instantaneous average strain and strain rate in 

the specimen, respectively. For the case of the experiment conducted at the lowest strain rate 62 s–1 and an 

initial diameter of 19.0 mm, the radial component of the particle velocity at the outside diameter of the 

specimen at the peak stress is approximately 0.6 m/s. This velocity would reduce the kinetic friction 

coefficient for ice from approximately 0.06 (ref. 25) by a factor of 10, thus negating the effects of friction. 

The axial stress distribution for two specimen thicknesses (1 and 5 mm) are shown in figures 24 and 25 

for the cases without and with friction, respectively. The externally applied load is 25 MPa, which is 

magnified by the bar to specimen cross-sectional area ratio to be approximately 31 MPa on the specimen. 

In accordance with equation 16, the radial stress in the specimen increases as the height of the specimen is 

decreased, and decreases as we move away from the center of the specimen to its outer periphery. 

Furthermore, it is noted from figures 24 and 25 that the axial stress distribution is reasonably uniform 

within the thickness of the sample, more so in the case of the thicker sample; the axial stress gradient 

becomes steeper near the edge of the sample where the stress concentration is the highest. These 
NASA/TM—2006-213966 25

distributions of axial and radial stress within the specimen are conducive to the failure of the ice in shear, 

especially in the outer periphery of the specimen where the axial stress concentration is the highest. 

Moreover, these results suggest that the thinner specimens should fail at much lower load levels when 

compared to the thicker specimens employed in the present study. However, the experimental results of 

the present study indicate that the thinner and the thicker specimens fail at nearly similar load levels 

during the dynamic deformation process. This observed behavior can only be explained if the material 

strain-rate strengthening effects in the thin ice specimens dominate the aforementioned geometric 

weakening effects, and this reiterates the fact that the strength of ice is positively rate sensitive over the 

strain rate regime employed in the present experiments. 
NASA/TM—2006-213966 26

As suggested in figure 20, the presence of the end constraint at the specimen-bar interface has a 

negligible effect on the measured dynamic failure strength of ice. This is, however, contradictory to 

observations in quasi-static compression experiments (refs. 1 and 27), where constrained ends were 

understood to affect both the mechanical strength and the failure modes. A possible explanation for this 

behavior could be attributed to the rupture of the interface between the ice disk and the bars (shown 

schematically in fig. 26) in the early stages of loading. However, more work is still needed to explore this 

effect completely. 
NASA/TM—2006-213966 27

Summary of Results 

In the present study a modified split Hopkinson pressure bar apparatus was developed to investigate 

the high-strain-rate behavior of ice. Ice was shown to have a positive strain rate sensitivity in the strain 

rate range of 90 to 1400 s–1. Specimen size, within the range studied, was found to have little or no effect 

on the failure strength. The test temperature was observed to have a strong effect on the failure strength 

with ice behaving stronger as the test temperature was decreased. The effect of specimen end constraint 

on failure strength during high-rate deformation of ice was found to be negligible. Results of previous 

experimental studies to investigate the effects of end constraint at quasi-static loading rates are contrary to 

those obtained at higher loading rates in the current study. Also, the results of the present study are in 

contradiction with previous high-strain-rate investigations, where ice was reported to show a negative 

strain rate sensitivity at strain rates of 10 s–1 and higher. 

References 

1. Schulson, Erland M.; Iliescu, Daniel; and Fortt, Andrew: Characterization of Ice for Return-to-Flight 

of the Space Shuttle. Part 1⎯Hard Ice. NASA CR⎯2005-213643⎯PART1, 2005. 

2. Haynes, F.D.: Effect of Temperature on the Strength of Snow-Ice. CRREL−78−27, 1978. 

3. Currier, J.H.; and Schulson, E.M.: The Tensile-Strength of Ice as a Function of Grain-Size. Acta 

Metall., vol. 30, no. 8, 1982, pp. 1511−1514. 
NASA/TM—2006-213966 28

4. Schulson, E.M.: The Structure and Mechanical Behavior of Ice. JOM, vol. 51, no. 2, 1999, pp. 21−27. 

5. Dempsey, J.P.; et al.: Scale Effects on the In-Situ Tensile Strength and Fracture of Ice. Part I: Large 

Grained Freshwater Ice at Spray Lakes Reservoir, Alberta. Int. J. Fract., vol. 95, nos. 1−4, 1999, 

pp. 325−345. 

6. Dempsey, J.P.; Adamson, R.M.; and Mulmule, S.V.: Scale Effects on the In-Situ Tensile Strength and 

Fracture of Ice. Part II: First-Year Sea Ice at Resolute, NWT. Int. J. Fract., vol. 95, nos. 1−4, 1999, 

pp. 347−366. 

7. Nixon, W.A.; and Schulson, E.M.: A Micromechanical View of the Fracture-Toughness of Ice. J. de 

Physique, vol. 48, (C−1), 1987, pp. 313−319. 

8. Weber, L.J.; and Nixon, W.A.: Fracture Toughness of Freshwater Ice. 1. Experimental Technique and 

Results. Trans. ASME J. Offshore Mechanics Arctic Engineering, vol. 118, no. 2, 1996, pp. 135−140. 

9. Uchida, T.; and Kusumoto, S.: Effects of Test Conditions on Fracture Toughness and Fracture 

Morphology of Polycrystalline Ice. JSME International Journal Series A⎯Solid Mechanics and 

Material Engineering, vol. 42, no. 4, 1999, pp. 601−609. 

10. Dutta, Piyush K.: Compressive Failure of Polycrystalline Ice Under Impact. Proceedings of the Third 

International Offshore and Polar Engineering Conference, 1993, pp. 573−580. 

11. Jones, Stephen J.: High Strain-Rate Compression Tests on Ice. J. Phys. Chem. B, vol. 101, no. 32, 

1997, pp. 6099−6101. 

12. Dutta, Piyush K., et al.: A Fracture Study of Ice Under High Strain Rate Loading. Proceedings of the 

Thirteenth International Offshore and Polar Engineering Conference, 2003, pp. 465−472. 

13. Schulson, E.M.: Brittle Compressive Fracture of Ice. Acta Metall. Mater., vol. 38, no. 10, 1990, pp. 

1963−1976. 

14. St. John, J.W.; and Daley, C.: Shipboard Measurement of Ice Pressures in the Bering, Chukchi, and 

Beaufort Seas. Proceedings of the International Offshore Mechanics and Arctic Engineering 

Symposium, vol. 3, 1984, pp. 260−266. 

15. Graff, Karl F.: Wave Motion in Elastic Solids. Dover Publications, New York, NY, 1991. 

16. Haberman, Richard: Applied Partial Differential Equations: With Fourier Series and Boundary Value 

Problems. Fourth ed., Pearson/Prentice Hall, Upper Saddle River, NJ, 2004. 

17. Carter, Donald: Lois et Mécanismes de l’apparente Fracture Fragile de la Glace de Rivière et du Lac. 

Thèse (de dectorat), Université Laval, 1971. 

18. Petrovic, J.J.: Mechanical Properties of Ice and Snow. J. Mater. Sci., vol. 38, no. 1, 2003. 

19. Davies, E.D.H.; and Hunter, S.C.: The Dynamic Compression Testing of Solids by the Method of the 

Split Hopkinson Pressure Bar. J. Mech. Phys. Solids, vol. 11, no. 3, 1963, pp. 155−179. 

20. Weinong, Chen; and Ravichandran, G.: Dynamic Failure Behavior of Ceramics Under Multiaxial 

Compression. Ph.D. Thesis, California Institute of Technology, 1995. 

21. Sarva, S.; Nemat-Nasser, S.: Dynamic Compressive Strength of Silicon Carbide Under Uniaxial 

Compression. Mater. Sci. Eng. A, vol. 317, nos. 1−2, 2001, pp. 140−144. 

22. Shan, Renliang; Jiang, Yusheng; and Li, Baoqiang: Obtaining Dynamic Complete Stress-Strain 

Curves for Rock Using the Split Hopkinson Pressure Bar Technique. Int. J. Rock. Mech. Min. Sci., 

vol. 37, no. 6, 2000, pp. 983−992. 

23. Standard Test Methods of Compression Testing of Metallic Materials at Room Temperature. ASTM 

Designation E9−89a (Reapproved 2000), American Society for Testing and Materials Annual Book 

of Standards, vol. 03.01, ASTM International, West Conshohocken, PA, 2004, pp. 110−118. 

24. Kuhn, H.A.: Uniaxial Compression Testing. ASM Handbook, vol. 8, ASM, Materials Park, OH, 

2000. 

25. Maeno, N., et al.: Ice-Ice Friction Measurements, and Water Lubrication and Adhesion-Shear 

Mechanisms. Canad. J. Phys., vol. 81, nos. 1−2, 2003, pp. 241−249. 

26. Maeno, Norikazu; and Arakawa, Masahiko: Adhesion Shear Theory of Ice Friction at Low Sliding 

Velocities, Combined With Ice Sintering. J. Appl. Phys., vol. 95, no. 1, 2004, pp. 134−139. 
NASA/TM—2006-213966 29

27. Schulson, E.M.; Iliescu, D.; and Renshaw, C.E.: On the Initiation of Shear Faults During Brittle 

Compressive Failure: A New Mechanism. J. Geoph. Res., vol. 104 (B1), 1999, pp. 695−705. 

28. Hobbs, Peter V.: Ice Physics. Clarendon Press, Oxford, 1974. 

NASA/TM—2006-213966 31

Appendix A 

Symbols 

A cross-sectional area of incident and transmitted bars of SHPB apparatus 

C longitudinal wave speed in ice 

cb longitudinal wave speed in bar 

D specimen diameter 

E Young’s modulus 

f function representing pressure wave traveling to right 

f frictional stress 

g function representing pressure wave traveling to left 

h function representing wave traveling to right 

P force on sample face 

T specimen thickness 

t time 

u displacement 

u displacement rate 

x axial position along sample 

ε strain 

ε strain rate 

ρ specimen density 

σ stress 

Subscripts 

a axial 

b bar 

equil equilibrium 

i incident 

o original 

r reflected 

rr radial 

s average 

t transmitted 

1 left end of sample 

2 right end of sample 

NASA/TM—2006-213966 33

Appendix B 

Experimental Results for 6SX Series 

Results for the single-crystal ice samples tested with a modified split Hopkinson pressure bar 

apparatus at –10 °C are presented here in figures 27 through 51. 
NASA/TM—2006-213966 34
NASA/TM—2006-213966 35
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NASA/TM—2006-213966 48
NASA/TM—2006-213966 49

NASA/TM—2006-213966 51

Appendix C 

Experimental Results for HMD Series 

Results for the multigrained ice samples tested with a modified split Hopkinson pressure bar 

apparatus at –10 °C are presented here in figures 52 through 85. 
NASA/TM—2006-213966 52
NASA/TM—2006-213966 53
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Appendix D 

Experimental Results for 14SX Series 

Results for the multigrained ice samples tested with a modified split Hopkinson pressure bar 

apparatus at –10 °C investigating end constraints are presented here in figures 86 through 97. 
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Appendix E 

Experimental Results for Specimens Tested at –30 °C 

Results for the multigrained ice samples tested with a modified split Hopkinson pressure bar 

apparatus at –30 °C are presented here in figures 98 through 123. 
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WBS–22–376–10–30–04

95

High-Strain-Rate Compression Testing of Ice

Mostafa Shazly, Vikas Prakash, and Bradley A. Lerch

Ice; Compression tests; Strain rate; Microstructure; Space shuttles; Impact damage

Unclassified -Unlimited

Subject Category: 27

Mostafa Shazly and Vikas Prakash, Case Western Reserve University, 10075 East Blvd., Cleveland, Ohio 44106;

and Bradley A. Lerch, NASA Glenn Research Center. Responsible person, Bradley A. Lerch, organization code

RSL, 216–433–5522.

In the present study a modified split Hopkinson pressure bar (SHPB) was employed to study the effect of strain rate

on the dynamic material response of ice. Disk-shaped ice specimens with flat, parallel end faces were either provided

by Dartmouth College (Hanover, NH) or grown at Case Western Reserve University (Cleveland, OH). The SHPB

was adapted to perform tests at high strain rates in the range 60 to 1400 s–1 at test temperatures of –10 and –30 °C.

Experimental results showed that the strength of ice increases with increasing strain rates and this occurs over a

change in strain rate of five orders of magnitude. Under these strain rate conditions the ice microstructure has a slight

influence on the strength, but it is much less than the influence it has under quasi-static loading conditions. End

constraint and frictional effects do not influence the compression tests like they do at slower strain rates, and therefore the diameter/thickness ratio of the samples is not as critical. The strength of ice at high strain rates was found to

increase with decreasing test temperatures. Ice has been identified as a potential source of debris to impact the

shuttle; data presented in this report can be used to validate and/or develop material models for ice impact analyses

for shuttle Return to Flight efforts.