Measurements of icing hardness

Cold Regions Science and Technology, 17 ( 1989 ) 89-93 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

89

SHORT C O M M U N I C A T I O N

MEASUREMENTS

OF I C I N G H A R D N E S S

J.A. S c h a e f e r 1, R. Ettema 2 and W . A . Nixon 2 ~Department of Physics and Engineering Sciences, Loras College, Dubuque, IA 52004-0178 (U.S.A.) 2Institute of Hydraulic Research, and Department of Civil and Environmental Engineering, The University of Iowa, Iowa City, IA 52242-1585 (U.S.A.) (Accepted for publication March 17, 1989)

INTRODUCTION Impact with one or another mechanical object is perhaps the most c o m m o n method used to remove spray and atmospheric icings from component elements of diverse hydraulic structures, towers and ship superstructures. In icing literature, one comes across fairly numerous anecdotal accounts of people having to wield such crude "impactors" as hammers, picks, lengths of pipe (or similarly unglamorous cylindrical objects) in order to remove icings. One does not come across much on the design of more sophisticated, and likely more efficient, impactors for deicing. Maybe none are needed. If there is a need for them, their design would require information on typical values of icing strengths, and icing hardness. Hardness is a potentially convenient and useful index for estimating strength. Some values of icing hardness are presented herein. They were obtained by way of laboratory experiments performed using an icing windtunnel and a drop-ball technique for determining hardness. Though the authors did not have appropriate equipment for measuring crushing strength of icing ice, the sensitivities of hardness values to such parameters as icing form and icing temperature, as well as the repeatability of the test results and the ease with which hardness values were obtained, do imply the usefulness o f hardness as a strength index.

SOME THEORY Standard hardness tests employ a hard indenter which is pressed at a known rate into the surface o f

0165-232X/89/$03.50

some test material. The diameter of the indentation enables the material's hardness to be determined in accordance with one of several standard scales (e.g., Brinell, Rockwell R and T. ). A softer material gives a larger indentation for a given load. For a material such as ice, which is subject to creep, the rate of indentation is a factor influencing the size of an indentation. It is possible to circumvent creep concerns by means of comparatively short loading times such as can be obtained by impacting a hard ball against samples at a known velocity. A method for determining ice hardness by the dynamic penetration of a hard ball has been used for measuring the hardness of polycrystalline ice (e.g., Barnes et al., 1971) and for floating sheet ice (Khrapaty and Wessels, 1984; Khrapaty et al., 1986). The latter two references document studies in which hardness was used to determine the compressive and tensile strengths of ice sheets. Theoretical analysis of an indentation produced by a sphere impacting an ice surface produces a relationship between the sphere's mass, m, its velocity at impact, v, sphere radius, R, depth of the indentation line, h, and hardness, H. The resulting expression for hardness in terms of the aforementioned parameters is (e.g., as in Khrapaty et al., 1986):

H=(mvZ)/(gRh

2)

(1)

Herein, the Brinell hardness scale is used, as its units relate directly to pressure; e.g., Brinell 100 corresponds to 1O0 kg mm - 2 pressure. Other scales, such as Rockwell R and T scales, could be used. The ve-

© 1989 Elsevier Science Publishers B.V.

90

SCHAEFER ET AL.

70

I

l

g-,

I

I

Indentotion

'E

60

Cn

50

I //

E

/ iI

v

/

./

40

.ii- .... Ir

W Z O~ .< I

30

d

20

ir

Z m

GLAZE

10 0

--I-- RIME I

0

I

I

I

I

I

,

I

,

,

,

-8

-4

I

,

I

I

I

,

,

-16

-12

i

-20

ICE TEMPERATURE (°C)

Fig. 1. Variation of icing hardness (H) with ice temperature. locity o f a sphere as it first contacts the surface o f an icing can be calculated f r o m its initial potential energy as:

v = ( 2 g y ) '/~-

(2)

in which g is acceleration o f gravity; and y is distance dropped. The depth, h, o f the indentation f o r m e d in the icing can be o b t a i n e d by the use o f simple geometrical analyses and m e a s u r e m e n t o f indentation diameter, c (see insert o f Fig. l ):

h=R-(R2-c2/4)

I/2

(3)

Substitution o f Eqs. 2 and 3 into Eq. 1 yields an expression for H in terms o f the mass and radius o f the d r o p p e d sphere, the height from which it was dropped, and the indentation diameter:

H=(2mgy)/{TtR[R-(R2-c'-/4)°5]

2}

(4)

EXPERIMENTS

Icings were formed on b r o a d a l u m i n u m bars, 5 1 76 m m wide, 600 m m long and 10 m m thick, which were m o u n t e d in an icing windtunnel located in a refrigerated r o o m at the Iowa Institute o f Hydraulic Research. The discharge o f moisture spray was adjusted so as to produce translucent glaze icings and

opaque rime icings at air temperatures ranging from - 3 to - 1 5 ° C . T h e experimental conditions are s u m m a r i z e d in Table 1 which also lists the resulting hardness values. Each icing was f o r m e d by setting the air temperature o f the cold r o o m housing the icing windtunnel a n d precooling the a l u m i n u m bar to that air temTABLE 1 Sum mary of tests Temperature Water/airflow Average ( °C ) rate* (%) hardness H (kg mm -2)

Std Devn of hardness H (kg mm -2)

glaze icings -3 -6 -10 - 12

17.6×10 -3 2.7 2.7 2.7

4.6 12.1 12.1 17.3

0.1 0.4 0.4 0.4

-

14

2.7

19.2

1.2

-

15

2.7

21.9

1.0

2.7X 10 -3 2.9 1.2 0.2 0.2 3.3

25.5 35.4 38.1 40.2 52.5 62.9

0.9 5.1 1.7 1.7 2.0 3.2

rime icings -6 - 10 -12 - 13 - 14 - 15

*Volumetric ratio based on an air flow rate of 4.3 m 3 s-'.

91

ICING HARDNESS

Fig. 2. Glaze icing showing hardness test indentation. perature. Air speed past the a l u m i n u m bar was 12 m s-~ for all the experiments. The size range of moisture droplets sprayed into the windtunnel was 1 0 - 6 0 / l m . Icings were formed to thicknesses of at least 6 ram. Once formed, each icing was placed on a test table and subjected to at least three hardness tests. A hardness test comprised dropping a sphere of diameter 19.10 m m and mass 28.3 gm from heights y = 300 m m onto the level surface of an icing. A few tests were conducted with y = 4 0 0 m m ,

Fig. 3. Rime icing showing hardness test indentation.

but no difference was found in H, compared with values found at y = 300 mm. After impact, the ball was removed from the icing and the diameter of the resulting indentation was measured using an optical magnifier with scale graduated in 0.001 m m increments. Indentation diameters ranged from 4.0_+0.1 m m to 7.5_+0.1 mm.

RESULTS For the range of test conditions covered, it was found that the rime icings were harder than the glaze icings, as evident from the data presented in Fig. 1 and Table 1. In fact, at the same air temperature and same thickness, rime icings were at least twice as hard as glaze icings. Hardness, H, increased almost linearly with decreasing air/ice temperature for the glaze icings. For rime icings, the data indicate a concave upwards trend for H versus air/ice temperature. It is of interest to observe from Table 1 that scatter in H values is small, with standard deviations generally being within 5% of average values (except for one test set in which it was about 15%). Typical test icings are depicted in Figs. 2 and 3. Figure 2 illustrates an indentation of diameter 5.5 m m in a clear, glaze icing formed at - 1 2 ° C ; the resulting value of H was 17.3. By way of comparison, Fig. 3 shows an indentation of diameter 4.2 m m

92

SCHAEFER ET AL.

1000

I

-.~0

Q_

I

I

I

I

°C I

v

I

W n~

[] [] []

b9

O0 W n~ O_

I

[]

[]

100

/ J

J

Z 0

[]

Z i,I CI Z

GLAZE RIME BARNES et el. (1971)

•

10

3.60

=

I

3.65

~

I

3.70

~

I

3.75

~

I

3.80

=

I

3.85

i

I

3.90

i

I

3.95

4.00

10~/ABSOLUTE TEMPERATURE

Fig. 4. Comparison of icing hardness values, treated as indentation pressure, with temperature. in an opaque rime icing formed at - 14°C. The data are replotted in Fig. 4 and compared with data presented by Barnes et al. ( 1971 ). Hardness values of glaze icings are approximately twice those obtained by Barnes et al. for polycrystalline ice undergoing impacts at a rate approaching about 10 4 S - J . Their data were obtained under impact conditions similar to those of the present study; though present impact rates are of the order of 103104 s- ~. The rime icings formed in the present study were approximately three to four times harder than the polycrystalline ice tested by Barnes et al. The trends with temperature are parallel to those obtained by Barnes et al. for hardness of polycrystalline ice.

DISCUSSION For most materials, hardness H can be directly related to the material's yield strength, and simple slip-line analysis ( see for instance Ashby and Jones, 1980) suggests a relationship of the form: H=3a:

(5)

In ice, the situation is a little more complex. Ice 1 h, the common molecular structure of ice at the earth's surface, does not have the five independent slip sys-

tems needed for easy plastic deformation. Thus, in addition to limited plastic flow under a hardness indenter, one would also expect cracking in ice. This situation is further complicated by the high homologous test temperatures considered here (test temperatures, on an absolute scale, are at 94% or higher, of the material's melting temperature), meaning that, if loading rates are low enough, thermal processes will allow for extensive plastic deformation (perhaps, for example, by recrystallization to easy slip configurations) under and around the indenter. Thus, any hardness value obtained will relate to ice strength only at the equivalent rate and temperature. Further, while at low rates the hardness may indeed relate to strength by a factor of 3 as in Eq. 5 above, at higher rates this constant may be different, if indeed such direct correlation occurs. Barnes et al. ( 1971 ) did a series of compression and hardness tests on ice, and suggest that at loading rates from 10 -4 to 10 4 S - i compressive strength and hardness are indeed correlated. Even though cracking was observed during their dynamic tests (loading rate was 104 s -~ ) their data were all describable using an equation of the form: ~=A (sinh a a)" exp ( - Q / R T )

(6)

in which A, a and n are material constants; Q is ac-

ICINGHARDNESS

tivation energy; R is universal gas constant (8.31 J mol-~ K-J ); T is absolute temperature; ~ is strain rate; and a is stress. It is interesting to note from Fig. 4 that the hardness values obtained for both glaze and rime icings are somewhat greater than those Barnes et al. obtained in their dynamic (i.e., dropped ball impact) testing. Almost certainly, this reflects differences in the microstructure of the respective ices. Barnes et al. used polycrystalline ice with a grain diameter size of 1-2 mm, whilst the grain size of rime icing was in the range 0.01-0.1 mm, and glaze about 0.1-1 mm, which would lead one to expect a higher strength and therefore hardness (e.g., Cole, 1987). It seems apparent that hardness testing does give an indication of the compressive strength of ice, though future experiments are needed to demonstrate this more definitively. What is not clear is whether the compressive strength of ice is the relevant strength vis-a-vis mechanical deicing. The strength of the ice-substrate interface is of obvious importance in this regard, and the shear and tensile strengths of ice may also play a role. Yet all of these are difficult to measure experimentally. Hardness testing is relatively simple, and these preliminary experiments show that it is an effective and repeatable method for gauging (rather than directly meas-

93

uring) the compressive strength of icing ice. It may also hold some promise for gauging of shear, tensile and, dare we say, adfreeze-bond strength though obviously much work is required in this regard.

ACKNOWLEDGEMENTS The present study is part of a larger study on icings, which was funded under U.S. National Science Foundation Grant No. CES-8611885.

REFERENCES Ashby, M.F. and Jones, D.R.H., 1980. Engineering Materials: An Introduction to their Properties and Applications. Pergamon, Oxford. Barnes, P., Tabor, D. and Walker, J.C.F., 1971. The friction and creep of polycrystalline ice. Proc. R. Soc. London, Ser. A, 324: 127-155. Cole, D.M., 1987. Strain-rate and grain-size effects in ice. J. Glaciol., 33 ( 115): 274-280. Hobbs, P.V., 1974. Ice Physics. Clarendon, Oxford, 322 p. Khrapaty, N. and Wessels, E., 1984. A new testing technique of ice strength in compression and bending. IAHR Ice Symp., Hamburg, 1: 83-91. Khrapaty, N., Takhteyev, V.A. and Gomolsky, S.G., 1986. Ball penetration into a floating ice plate. IAHR Symp. on Ice, Iowa City, Iowa, 1: 319-327.