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Some Bulk Properties of Ice
8er TH1 N2l-t2 ne. 255 c . 2 BI,DG
NATIONAL RESEARCH COUNCIL OF CANADA DIVISION OF BUILDING RESEARCH
SOME BULK PROPERTIES OF ICE by
L. \AT. GOLD
Head, Snow and Ice Section
Division of Building Research, National Research Council
A I ' , i A L Y Z E D
A talk presented to a Serninar on Ice o r g a n i z e d b y the Dunlop Research
C e n t r e , S h e r i d a n P a r k , O n t a r i o , l 7 J a n u a r y 1 9 6 7 T e c h n i c a l P a p e r N o . 2 5 6 of the D i v i s i o n of Building Research OTTAWA Septernber L9 67
SOME BULK PROPERTIES OF ICE by
L . W . G o l d
I
N a t u r a l l y o c c u r r i n g i c e i s a product of the weather. I t is an integral paft of our environrnent, providing us with assets that we would hate to give up, and problerns that we would like to be able t o ignore. S o r n e o f these problefits are becorning increasingly
s i g n i f i c a n t because of the increase in our industrial activity and our desire for rnobility under all conditions. Many of thern involve the t h e r r n a l properties o f ice, and sorne of these properties a r e b r i e f l y
r e v i e w e d in this paper. S o r n e p r o b l e r n s , s u c h a s t h e adhesion of i c e to surfaces and predicting the forces ice can exert against structures, involve the properties of ice that deterrnine how it r e s p o n d s to stress. T h e rnajor part of this paper is devoted to a d i s c u s s i o n of these properties a n d t h e f a c t o r s t h a t i n f l u e n c e t h e r n . THERMAL PROPERTIES
W a t e r begins to freeze when its temperature i s r e d u c e d t o 0 " C . O n f r e e z i n g , a b o u t 7 9 . ' 7 c a l o r i e s o f h e a t a r e r e l e a s e d p e r gram of ice, an arnount that is larger than for rnost solids. In the 4lst edition of the Handbook of Physics and Chernistry, only 7 out of a list of about 100 elernents and inorganic cornpounds have a latent heat of fusion greater than that of water. The latent heat of
sublirnation of ice, 675 cal/g:rn, is also large in cornparison with r n o s t solids.
,
Water has the characteristic of expanding on freezing, a p r o p e r t y s h a r e d b y f e w other substances. T h e density of ice at O o C is about O.9L? gnd"c, w h i l e that of water is about L grn/cc. A s a result, ice floats on top of the water. I f this were not so, it is doubtful that life as we know it could have evolved on this earth. I c e at 0"C has a specific heat of about 0.5 caL/grn "C, again a value that is large for inorganic solids. Its therrnal con-d u c t i v i t y is about 5 x 1O-3 caLl(.t12
" " . " C / c r n l , r n a k i n g it a relatively poor conductor of heat. Ice has a therrnal diffusivity of a b o u t O . 0 l l c t n z / s e c , i n d i c a t i n g that it has a relatively h i g h r e -s i -s t a n c e to the pa-s-sage of a therrnal di-sturbance.
z
-B e c a u s e o f t h e s e p a r t i c u l a r p r o p e r t i e s , i c e h a s a v e r y c o n s i d e r a b l e i n f l u e n c e on our life and surroundings. T h e latent h e a t released during the freezing of water or absorbed during the rnelting and sublirnation of ice has a rnarked rnodifying effect on w e a t h e r . T h e forrnation of an ice cover on the surface of lakes and r i v e r s p r o v i d e s a protecting layer of relatively high therrnal
resistance and thus contributes to the survival of plant and fish life i n the waters below.
DEFORMATION BEHAVIOUR
The ice that we are farniliar with norrnally exists at a t e m p e r a t u r e w i t h i n 4 0 C degrees of that at which it rnelts. T h i s fact has irnplications with respect to its behaviour that rnay not be fully appreciated. If we think in terrns of the absolute ,ternperature
s c a I e , i c e norrnally exists at a ternperature greater than ZZ3"R, that is, within 80 per cent of its rnelting point. If steel were to be at the sarne relative ternperature with respect to its rnelting point, i t w o u l d have a ternperature g r e a t e r than 1100"C, very high indeed. W h e n we talk about the bulk properties o f i c e r t h e r e f o r e , w e are talking about the properties of a rnaterial which, as far as the ice i s concerned, i s i n a high ternperature s t a t e " r t exhibits a response to an applied stress when in its norrnal enwironrnent that is encountered with useful engineering rnaterials only at elevated ternperatures.
Deforrnation behaviour at such ternperatures is very inadequately u n d e r s t o o d at present and is the subject of considerable research. U n d e r t a k i n g a serious progranl to enJ.arge our knowledge on the b u l k p r o p e r t i e s o f ice that control the way it responds to stress, therefore, puts us irnrnediately into one of the rnost active areas of p r e s e n t d a y r e s e a r c h o n r n a t e r i a l s .
REGELATION AND SINTERING
We are all farniliar with rnaking snowballs and the packing of snow on roads into ice due to the action of traffic. Most o f us have experienced the tendency for snow to harden with tirne, p a r t i c u l a r l y a f t e r i t h a s b e e n d i s t u r b e d . T h e s e interesting p r o p e r t i e s o f ice have attracted the attention of scientists for rnany years, and are significant factors in rnany of the problerns that this rnaterial c r e a t e s .
I n 1 8 5 0 , Faraday reported that when two pieces of rnelting ice are brought into contact, they will free ze together. He d e r n o n s t r a t e d ( F a r a d a y , 1 8 5 0 , f 860) that this would occur even in vacuurn or underwater. If continually disturbed, the joint could be
3
-rnade flexible, but if allowed to stand for only a short period, would b e c o r n e r i g i d . T h e s e o b s e r v a t i o n s t r i g g e r e d a s e r i e s o f i n t e r e s t i n g e x p e r i r n e n t s a n d p h i l o s o p h i c a l d i s c u s s i o n s o n t h i s e f f e c t . A r n o n g the e x p e r i r n e n t s was the classical one by Bottornl.y ( I 8 7 Z l in which a loaded wire was rnade to pass through a block of rnelting ice without c a u s i n g the ice to separate.
I t was considered that these observations c o u l d b e e x p l a i n e d b y the pressure rnelting theory put forward by Thornson ( 1 8 5 9 ) . T h o r n s o n showed therrnodlmarnically t h a t i f p r e s s u r e i s a p p l i e d t o i c e , its freezing point is lowered because of the increase i n v o l u r n e t h a t o c c u r s when water is transforrned i n t o i c e " T h e a r n o u n t b y w h i c h t h e f.reezing point is depressed depends on the
p r e s s u r e a c t i n g o n t h e i c e a n d o n t h e w a t e r that results frorn rnelting. I f the pressufes o n t h e ice and water are equal, the depression of the f r e e z i n g p o i n t arnounts to about 0"0075oC per atrnosphere. F o r the w i r e e x p e r i r n e n t it was considr:red that the ice under the wire melted b e c a u s e o f t h e p r e s s u r e . T h e r e s u l t i n g w a t e r p a s s e d a r o u n d t h e w i r e w h e r e it refroze on being relieved of pressure o n the other side.
T h e adhesion of the ice blocks in the experirnents con-d u c t e con-d b y F a r a con-d a y was consicon-derecon-d con-due to pressure rnelting effects a s s o c i a t e d w i t h s u r f a c e f i l r n s " A l t h o u g h this explanation was not c o r n p l e t e l y satisfactory, i t w a s g e n e r a l l y accepted until recent e x p e r i m e n t s d e r n o n s t r a t e d i t s i n a d e q u a c y .
N a k a y a ( 1 9 5 3 ) s h o w e d t h a t w h e n t w o i c e s p h e r e s w e r e brought lightly into contact, they would adhere even at ternperatures
a s l o w as -15"C. T h i s ternperatu.re was too low to explain adhesion b y the pressure rnelting effect. K i n g e r y ( I 9 6 0 ) looked at this
phenornenon frorn the point of view of sintering. His work dernonstrated t h a t w h e n t w o i c e spheres are brought lightly into contact, the bond b e t w e e n thern grows at a rate that depends on the radius of the spheres, the width of the bonded area arid the ternperature. The driving force b e h i n d the forrnation of the bonil was the decrease in free energy b r o u g h t about by a reduction in surface area. F r o r n his observations, he concluded that the principal rnechanisrn responsible for the growth of the bond was diffusion of water rnolecules along the surface of the i c e " H o b b s and Mason (19641 questioned this interpretation, h o w e v e r , a n d o n t h e b a s i s of their results concluded that bond growth was by s u b l i r n a t i o n and subsequent condensation in the area of contact. T h i s q u e s t i o n has not yet been cornpletely resolved.
4
-T e l f o r d and -Turner (1963) repeated the wire cutting e x p e r i m e n t u n d e r c a r e f u l l y c o n t r o l l e d c o n d i t i o n s . T h e y w e r e able t o d e r n o n s t r a t e an anomalous increase in the rate of penetration of the wire for ternperature within I C degree of the rnelting point. T h i s increase could be attributed to the pressure rnelting effect" B a r n e s and Tabor (1956) obtained sirnilar behaviour in rneasure-r n e n t s of the harneasure-rdness of ice. F o r ternperatures l o w e r t h a n the e s t i r n a t e d pressure rnelting point, the rate of penetration of the w i r e and the hardness appeare,l to be controlled by the plastic p r o p e r t i e s o f i c e .
R e g e l a t i o n or pressure rneltingn and sintering of ice a r e p r o c e s s e s t h a t g o o n c o n t i n u a l l y to varying degrees throughout t h e w i n t e r season and are associated with rnany situations with w h i c h we rnust learn to cope" Not only does ice readily bond to i t s e l f by pressure rnelting and sintering, i t c a n b o n d i t s e l f t o c o r n r n o n rnaterials s u c h as concrete, s t e e l a n d asphalt with a
s t r e n g t h of adhesion that exceeds that of the ice itself. T h e adhesion o f ice to itself or to other rnaterials involves surface-free e n e r g i e s and the ability of the water rnolecule to attach itself to or penetrate a s u r f a c e . C o n s i d e r a b l e e f f o r t i s b e i n g directed toward increasing our understanding of the nature of the ice surface and in developing w a y s to reduce the strength of adhesion of ice to other rnaterials. T h e s e latter studies have had only lirnited successe
D E F E C T S I N I C E
W a t e r rnolecules are arranged in puckered layers in the i c e crystal. E a c h oxygen atorn has four nearest neighbou.rs, three o f these neighbours being in the layer and the fourth in the nearest a d j a c e n t layer. T h e s e four oxygen atorns are placed tetrahedrally about the central atorn and joined to it by a hydrogen bond. The oxygen atorns in the layer are arranged in a hexagonal pattern, and this gives to the ice crystal a hexagonal syrnrnetry sirnilar to that of zinc and rnagnesiurn"
It is now a well known fact that real crystalline rnaterials d o n o t have a perfect structure, t h a t i s , o n e i n w h i c h t h e a r r a n g e r n e n t o f the atorns with respect to each other is repeated without variation. D e f e c t s are present in the arrangernent. T h e s e rnay be point defects, s u c h as occur when an atorn or rnolecule is displaced well away frorn i t s n o r r n a l position, l e a v i n g a hole. T h e y rnay be line defects, created, for exarnple, when part of a plane of atorns is rnissing. The internal e d g e of the part of the plane that is present is the line defect, and is u s u a l l y called a dislocation. V o l u r n e defects can occur as well, due, for exarnple, to a change in the repetitive pattern of the atorns or rnolecules.
)
-M u c h of the behaviour of ice of interest to us involves t h e rnovernent of atorns or rnolecules either singly or in groups. This is equivalent to saying that it involves the rnoverrrent of point
o r line defects" T h e rrlovernent of these defects is therrnally
a c t i v a t e d , t h a t i s the rate at which it occurs depends upon the
t e r n p e r a t u r e , a n d t h e d e p e n d e n c e usually has the forrn
A = A o " * p t - S )
w h e r e Q is the activation energy T the absolute ternperature
R is the gas constant equal to 1.99 caI/rnole
F o r s o r n e d e f o r r n a t i o n p r o c e s s e s o c c u r r i n g i n i c e , Q h a s b e e n f o u n d
t o h a v e a value of about 15 k cil per rnole. I f t h e ternperature i s
c h a n g e d f r o r n - 5 t o - 2 5 " C , t h e r e f o r e , t h e r a t e a t w h i c h s u c h a p r o c e s s o c c u r s c h a n g e s b y a f a c t o r o f
A 1
7
o ,
9 . 6
A t n o r m a l ternperatures t h e e l a s t i c and plastic properties o f i c e are
e a s i l y r n e a s u r e d , a n d s o a c h a n g e o f a factor of 10 is particularly
s i g n i f i c a n t . I n the ternperature r a n g e o f 0 to -40"C, therefore, t h e
p r o p e r t i e s o f ice deterrnined by point and line defects, that is, the
s t r u c t u r e s e n s i t i v e p r o p e r t i e s , a r e v e r y n o t i c e a b l y i n f l u e n c e d b y t e r n p e r a t u r e .
I c e changes shape under an applied load both elastically a n d b y t h e rnovernent of irnperfection, p r i r n a r i l y d i s l o c a t i o n s , a l o n g
p r e f e r r e d p l a n e s known as the slip planes. T h e rate at which the
d i s l o c a t i o n s r n o v e along the slip planes, that is, the rate at which
t h e solid changes shape, depends upon the ternperature a n d t h e s h e a r
s t r e s s acting on the dislocation. F o r ice there is only one plane of
e a s y slip, and that is the basal plane, the plane perpendicular t o t h e
axis of hexagonal syrnrnetry" It is rnuch rnore difficult to induce
s l i p o n n o n b a s a l planes, such as the prisrn planes perpendicular t o
t h e b a s a l plane. E x p e r i m e n t a l e v i d e n c e i n d i c a t e s t h a t f o r the basal p l a n e there is no preferred s l i p d i r e c t i o n a n d t h a t t h e s h e a r s t r e s s
r e q u i r e d - t o i n i t i a t e slip on this plane is considerably l e s s than
6
-B e c a u s e ice has only one plane of easy slip, and apparently n o p r e f e r r e d s l i p d i r e c t i o n i n t h a t p l a n e , t h e d e f o r r n a t i o n o f a
s i n g l e c r y s t a l i s o f t e n c o r n p a r e d t o t h e s h e a r i n g o f a d e c k o f c a r d s .
This behaviour has a rnarked influence on how ice responds to an
applied load and as a result there can be a rnarked anisotropy in its
deforrnation. In the following sections consideration is given to the
influence that the stress induced rnotion of irnperfections can have on
t h e elastic and plastic properties o f i c e "
ELASTIC BEHAVIOUR
I f a stress is applied to the ice crystal so that there is n o shear stress acting on the dislocations, t h a t i s , i f t h e s t r e s s i s p e r p e n d i c u l a r o r p a r a l l e l t o t h e b a s a l p l a n e , t h e r e s p o n s e o f t h e i c e i s e s s e n t i a l l y e l a s t i c " I f the irnperfections p r e s e n t i n t h e s t r u c t u r e c a n Inove under the applied stress, the resPonse will deviate frorn a purely elastic behawiour.
E a c h type of irnperfection h a s associated with it a
characteristic tirne that it takes to attain a new equilibriurn position.
lf the stress is applied for a sufficiently long period of tirne, the
irnperfections may be incorporated into the structure at new equilibriurn
positions, and thus the strain associated with their rnotion becornes
i r r e c o v e r a b l e . I f the stress is applied and released in a sufficiently
short tirne, as, for exarnple, during the passage of a sound wave, the
irnperfections have little opportunity to rnove, and the deforrnation is
p r i r n a r i l y e l a s t i c . A s the tirne over which the stress is applied is
increaged, there is greater opportr:nity for irnperfections to rnove
and contribute to the deforrnation. For periods of loading less than
a b o u t l 0 s e c o n d s , d e p e n d i n g u p o n t e r n p e r a t u r e , t h e d e f o r r n a t i o n o f i c e i s alrnost entirely recoverable a n d c a n b e c o n s i d e r e d e l a s t i c . F o r p e r i o d s greater than about 10 seconds, sorne of the deforrnation due t o t h e r n o v e r n e n t o f i r n p e r f e c t i o n s w i l l b e i r r e c o v e r a b l e , t h a t i s , t h e i c e w i l l undergo sorne plastic deforrnation. B e c a u s e o f t h i s b e h a v i o u r , the elastic rnoduli of ice depend uPon the rate at which the stress
changes, and the length of tirne that it is applied. Typical values for
t h e Y o u n g r s m o d u l u s and Poissonts ratio for ice are given in Figure 1.
The Youngts rnodulus for ice stressed at a frequen-c)r g r e a t e r t h a n l O o c y c l l s / s e c i s a b o u t 1 . 4 x 1 0 6 p s i o r 9 . 0 * f O 1 0 d y n e " / " t r r Z . I t increases by about 5 per cent for a ternperature
change f5grn 0 to -40"C. The rigidity rnodulus has a value of about
g . 7 ; 1 0 1 0 a y n e t/
7
-I f a s t r e s s i s a p p l i e d t o a s i n g l e c r y s t a l p a r a l l e l o r p e r p e n d i c u l a r t o t h e b a s a l p l a n e so that there is no shear stress a c t i n g on the slip plane, and rernoved within about 10 secs, there
i s l i t t l e tendency for dislocations to^rnove, and Jo*grs r n o d u l u s
i s a b o u t l . ? x l 0 o p s i , o r 8 . 3 x 1 0 r u d y n e r / . t n a , a s s h o w n i n
F i g u r e l . T h e P o i s s o n t s r a t i o i s a b o u t 0 . 3 5 . l f a s t r e s s i s a p p l i e d t o p o l y c r y s t a l l i n e i c e , and rernoved within about lo secs, reversible
Erovernent of dislocations can now contribute to the strain, and the
Y o u n g t s modulus and Poissonls ratio obtained are very dependent on
t h e temperature" R e p r e s e n t a t i . v e values are given in Figure l.
PLASTIC DEFORMATION
If the load is applied to ice for a sufficiently long period
of tirne, irnperfections will be incorporated into new equilibriurn
p o s i t i o n s and the ice will undergo perlnanent or plastic deforrnation.
Studies of the deforrnation of granular ice in creep, that is, under a
c o n s t a n t cornpressive o r tensile load, show that the creep strain
d e p e n d s on tirne as shown by curve I in Figute Z. This type of creep
curve is typical for rnany granular rnaterials at high ternperature.
W h e n the load is first applied there is a period of decelerating creep
r a t e . T h i s is followed by one during which the creep rate tends to a
c o n s t a n t value and then by one during which it accelerates.
O b s e r v a t i o n s b y G l e n ( 1 9 5 5 ) and Steinernann (L9541have shown that
d u r i n g the per,iod of constant or steady state creep, the dependence
of the minirnurn creep rate on ternperature and stress has the forrn
a = Aexp(-#,"'
w h e r e A , r, Q, and R are constants, T is the ternperature and dthe s t r e s s . T h e v a l u e o b s e r v e d f o r n w a s a b o u t 3 . 0 . T h e r e w a s a t e n d e n c y f o r n t o i n c r e a s e w i t h s t r e s s .
l f the load is applied to granular ice at a constant rate o f strain, a d e p e n d e n c e o f s t r e s s on creep strain is observed as s h o w n b y curve I in Figure 3" With increasing s t r a i n , t h e s t r e s s goes to a rnaxirnurn that occurs for strain equal to about 2 to 3 per
cent. The rna:cirnurn in the load vs strain curve corresponds to the
steady state part of the creep curve shown in Figure 2. The rnaxirnurn v a l u e for the stress, that is, the yield strength, depends on the
8
-T h e deforrnation behaviour of granular ice can also be a p p r o x i r n a t e d using viscoelastic r n o d e l s . J e l l i n e k and Brill (1956) found'that a Maxwell unit in series with a Voigt unit provided a good approxirnation to their observations" The values obtained for the elastic constant and coefficient of viscositv of the Maxwell unit were a b o u t 5 x 1 O l 0 d y n e s / " ^ 2 a n d , 4 * 1 0 1 4 p o i s e s r e s p e c t i v e l y - T h e corresp-onding values for the Voigt unit were aboui 8 x lol0 ay^e r/"tnz a n d 1 0 r r p o i s e s . T h e coefficient of viscosity for the Maxwell unit was gbserved to vary exponentially with temperature with an activation energy of about 16 k cat/rnole.
The foregoing inforrnation on the deforrnation behaviour h a s been for granular ice. I c e forrned on lakes and rivers often has a columnar structure with a bias in crystallographic orientation such t h a t the basal plane of all grains tends to be either parallel to the direction of growth, or perpendicular to it" Studies of the deforrnation behaviour of colufirnar-grain ice with basal planes tending to be
parallel to the direction of growth have demonstrated the rnarked influence that crystallographic orientation can have on this behaviour. These observations have shown that if the load is applied perpendicular t o t h e long direction of the grains, the deforrnation is prirnarily t w o -dirnensional, with rnuch less plastic deforrnation parallel to the long d i r e c t i o n o f the grains than perpendicular t o t h a t d i r e c t i o n . T h i s is t o b e expected because of the preferred d i r e c t i o n o f slip in the ice s i n g l e crystal.
Theoretical considerations show that if a polycrystalline rnaterial is to undergo an arbitrary change in shape, the crystals rnust have at least five independent slip systerns if the change in s h a p e is three-dirnensional, a n d t w o i f i t i s two-dirnensional. I f t h e s e conditions are not satisfied, s t r e s s e s w i l l d e v e l o p at grain boundaries due to the inability of the grains to conforrn to the change i n shape of neighbouring grains" F o r columnar-grained i c e w i t h the b a s a l plane parallel to the long direction of the colurnns, each crystal rnust have at least two independent slip systerns if the ice is to undergo a n a r b i t r a r y c h a n g e in shape due to a stress applied perpendicular t o t h e l o n g direction of the grains" B e c a u s e ice that has never been deforrned before has only one independent slip systern it would be e x p e c t e d that stresses would develop at grain boundaries, a n d t h a t t h e e e s t r e s s e s would induce other rnodes of deforrnation.
T h i s has been observed" I f the surface of an ice specirnen is prevented frorn sublirnating and observed while under load, features a p P e a r as a result of the deforrnation" T h e first features to appear
9
-a r e u s u -a l l y t h e t r -a c e s of slip pl-anes -at the surf-ace. S h o r t l y after t h e appearance of the slip planes, grain boundary rnigration can be s e e n . A f t e r the strain exceeds about 0" I per cent evidence of the f o r r n a t i o n of low angle boundaries appearse These boundaries are f o r r n e d in hexagonal crystals by the coalescence of dislocations into a p l a n e initially p e r p e n d i c u l a r t o the basal plane"
T h e developrnent of a Iow angle boundary indicates that t h e g r a i n is being subjected to a bending rnornent. A s rnore dis -I o c a t i o n s are absorbed into the boundary, the planes on one side of t h e b o u n d a r y are gradually rotated with respect to those on the other, t h e low angle boundary being the plane at which the bending occurs.
A s the deforrnation proceeds, the region in the irnrnediate v i c i n i t y o f the grain boundary is observed to undergo quite severe d i s t o r t i o n . I t would appear that as the grains deforrn, rnost of the change in shape of the grain away frorn the grain boundary is
a c c o r n p l i s h e d b y slip on the basal plane and rotation about low angle botrndaries. The accornrnodation that rnust occur between grains
apPears to take place in the irnrnediate vicinity of the boundary" FIere w e see evidence of slip on nonbasal planes, forrnation of srnall cracks and general fragrnentation.
I f the stress in tension or corrrpression exceeds about 5 k g 1 f crn?, cracks are also observed to forrn in the ice. I n the c o l u r n n a r - g r a i n i c e these cracks are long and narrow, i n v o l v e o n l y o n e or two grains, a n d p r o p a g a t e p a r a l l e l to the long direction of the g r a i n . F o r a colnpressive l o a d , the plane of the crack tends to be p a r a l l e l t o t h e a p p l i e d s t r e s s . O b s e r v a t i o n s b y G o l d ( 1 9 6 6 ) s h o w e d t h a t they tend to propagate parallel or perpendicular t o the basal p l a n e in grains in which they occur. T h i s indicates that they forrn in t h o s e g r a i n s that are so oriented that they cannot readily deforrn u n d e r the applied load. T h e forrnation of a crack in these grains r e d u c e s their resistance to deforrnation and aIlows thern to conforrn r n o r e readily to the irnposed change in shape"
I t would be expected that the formation of these rnodes of deforrnation would influence the deforrnation behaviour of ice. E v i d e n c e of this has been obtained for colurnnar-grained i c e w i t h t h e b a s a l p l a n e s tending to be parallel to the long direction of the g r a i n s . I f t h i s i c e h a s n e v e r b e e n d e f o r r n e d b e f o r e , a d e p e n d e n c e o f c r e e p strain on tirne, as shown by curve II in Figure Z, is obtained for
l 0
-a c o n s t -a n t cornpressive lo-ad -applied perpendicul-ar t o the long
d i r e c t i o n o f the grains" r n i t i a l l y the ice has a relatively h i g h r e s i s t a n c e t o d e f o r r n a t i o n . T h i s r e s i s t a n c e g r a d u a l l y d e c r e a s e s a n d t h e n s u b s e q u e n t l y i n c r e a s e s a s t h e s t e a d y s t a t e c r e e p stage is
a p p r o a c h e d " r f after about 2 per cent deforrnation the ice is
annealed for about 24 lnortr s and then subjected to the sarne load, t h e creep behaviour is sirnilar to that observed for granular ice.
I f the ice is deforrned at a constant rate of strain, a d e p e n d e n c e of stress on strain given by curve II in Figure 3 is
o b s e r v e d . T h e load increases very rapidly to a rnaxirnurn within
t h e first I per cent strain. r t then decreases and, d.epend,ing upon
t h e load, can go through a second rnaxirnurn that occurs for about
t h e sarne range of strain as for granular ice. T h e first rnaxirnurn
o r yield point is associated with the sanre range of strain as the
i n i t i a l accelerating c r e e p rate stage in the creep test.
O b s e r v a t i o n s b y G o l d ( 1 9 6 3 , 1965 | have shown that
t h e first accelerating c r e e p stage in the constant load test is
a s s o c i a t e d with the forrnation of rnodes of deforrnation such as low
a n g l e b o u n d a r i e s , g r a i n boundary rnigration and crack forrnation.
T h e first yield in the constant strain rate test is also observed to
b e associated with crack forrnation, a n d p r e s u n r a b l y o t h e r rnodes of
d e f o r r n a t i o n develop also. T h e s e observations dernonstrate the
r n a r k e d influence that the crystallographic p r o p e r t i e s o f ice have on
i t s deforrnation behaviour.
C r a c k forrnation can have an even rnore extrerne effect. E v e r y time a crack forrns it rnodifies the structure and weakens it.
rnitially crack forrnation is uniforrnly distributed throughout the
s p e c i r n e n " I f the stress is high enough and if the deforrnation proceeds
f o r a sufficiently long period of tirne, the cracks begin to concentrate
along planes of rnaxirnurn shear. At this stage the specirnen begins to
e x h i b i t at its boundaries the features that are norlrrally associated.
w i t h failure in a sirnple compression test. T h i s stage of crack
f o r r n a t i o n is also associated with the final accelerating creep rate s t a g e of the creep curve.
Frorn lneasurernents rnade on the load and strain, it would
b e concluded for tests such as the foregoing that the ice had failed in a p l a s t i c r n a n n e r . B e c a u s e i c e i s t r a n s p a r e n t , h o w e v e r , i t i s p o s s i b l e t o observe that failure is really the culrnination of a process that was
i n i t i a t e d rnuch earlier. I n fact, the apparent increase in plasticity and
f a i l u r e of ice in sorne tests is due to the gradual breakdown of the
z .
3 .
l t -CONCLUSION
T h i s paper has presented inforrnation on the therrnal p r o p e r t i e s o f ice and the way it responds to an applied load.
B e c a u s e of the abundance of ice, the ternperature at which it forms a n d the ways in which it influences our activities, i t is considered t h a t such inforrnation is necessary to provide a sound. foundation for o u r search for solutions to the lnany problerns it creates. o u r k n o w l e d g e of the properties o f ice, however, i s still not adequate t o p r o v i d e the understanding that is necessary, and further studies a r e r e q u i r e d . T h e properties o f ice are so interesting that such studies are bound to provide inforrnation and ideas that have rnuch r n o r e gendral application.
R E F E R E N C E S
1 . B a r n e s , P . a n d T a b o r , D . , 1 9 6 6 , Plastic Flow and pressure M e l t i n g in the Deforrnation of rce r" Nature, ?lo, g7g-ggz. B o t t o r n l e y , J " T . , L 8 7 2 , M e l t i n g a n d R e g e l a t i o n o f I c e . N a t u r e , 5 r 1 8 5 . F a r a d a y , M " , 1 8 6 0 , N o t e o n R e g e l a t i o n , p r o c . R o y a l S o c . L o n d o n , L 0 , 4 4 0 - 4 5 O " 4 " G I e n , J " W . , L955, T h e C r e e p o f p o l y c r y s t a l l i n e I c e , p r o c . R o y a l S o c . , A . , Z Z B , 5 1 9 - 5 3 8 . 5 . G o l d , L . I M . , 1 9 5 8 , S o m e O b s e r v a t i o n s o n t h e D e p e n d e n c e o f S t r a i n o n S t r e s s f o r I c e , C a n . J o u r " p h y s . 3 6 , ( 1 0 ) ,
L 2 6 5 _ t 2 7
5 "
6 . G o l d , L.W. , !963, D e f o r r n a t i o n M e c h a n i s r n s in lce, rtlce and S n o w r r , E d i t e d b y W . D . K i n g e r y , M I T p r e s s , 1 9 6 3 . 7 . G o l d , L . w . , L965, T h e r n i t i a l c r e e p o f c o l u r n n a r - G r a i n e d
I c e , Can. Jour. of Phys. , 43, l4I4-L434.
8 . G o l d , L . \ l / . , 1966, Dependence of Crack Forrnation on
C r y s t a l l o g r a p h i c O r i e n t a t i o n for lce, Can. Jour. phys., 4 4 , 2 7 5 7 _ 2 7 6 4 "
9 . H o b b s , P . V . a n d M a s o n , 8 . J . , 1 9 6 4 , T h e S i n t e r i n g a n d A d h e s i o n o f l c e , P h i l . M a g " , 9 , ( 9 g ) , l g l - 1 9 2 .
t z
-1 0 . J e l l i n e k , H . H . G . a n d B r i l l , R . , L 9 5 6 , V i s c o e l a s t i c p r o p e r t i e s o f l c e , J o u r . A p p . P h y s " , 2 7 , ( 1 0 ) , l l 9 8 - l Z O g .
K i n g e r y , \ M . D " , L960, R e g e l a t i o n , S u r f a c e Diffusion and Ice S i n t e r i n g , J o u r . A p p . P h y s . , 3 1 , ( 5 ) , 8 3 3 , g 3 g .
Nakaya, U. and Matsurnoto, A. , 1953, Evidence of the
E x i s t e n c e of a Liquidlike Filrn on Ice Surfaces, R e s e a r c h P a p e r 4, CoId Regions Research and Engineering
L a b o r a t o r y , U . S . A r m y , H a n o v e r , N . H .
S t e i n e r n a n n , S. , 1954, F l o w and RecrystaLlization o f I c e , I n t . U n i o n Geod" and Geophys. e Int. Assoc. Sci. H y d r o l o g y , P u b " #39, Vot. IV, 449-462.
T e l f o r d , J " W . a n d T u r n e r , J . S " , 1 9 6 3 , T h e M o t i o n o f a W i r e T h r o u g h l c e , P h i l " M a g " , !, SZ7-53L.
T h o r n s o n , J . , 1 8 5 9 , O n R e c e n t T h e o r i e s a n d E x p e r i r n e n t s R e g a r d i n g Ice near its Melting Point, Proc. Royal Soc. L o n d o n , 1 0 , 1 5 2 - 1 6 0 " l l .
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