Comparative study of ice strength data

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Comparative study of ice strength data

Sinha, N. K.

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N21d National Research Conseil national

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Council Canada de redetches Canada

,.

1 0 4 3

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2

COMPARATIVE STUDY OF ICE STRENGTH DATA

by N. K. Sinha

ANALYZED

Reprinted from

Proceedings, 1AHR International Symposium on Ice, Quebec 1981 Vol.

II

-

p. 581

-

595

P

B I B L I ~ T H $ Q u E

Rech.

_B3;itia.

DBR Paper No. 1043 c : -

Division of Building Research

SOMMAIRE

Une 6 t u d e d e l a s e n s i b i l i t a l a d 6 f o r m a t i o n c a r a c t g r i s a n t l a l i m i t e c o n v e n t i o n n e l l e d e p r o p o r t i o n n a l i t ' e l o r s d ' u n e s s a i d e c o m p r e s s i o n u n i a x i a l e , e f f e c t u 6 s u r d e l a g l a c e p o l y c r i s t a l l i n e , a indiqu-ue l e s r 6 s u l t a t s obtenus p a r d i v e r s c h e r c h e u r s r e f l e t e n t l a r i g i d i t 6 d e s s y s t e m e s

expgrimentaux c o r r e s p o n d a n t s . On d6montre que p l u s l e

s y s t h e est s o u p l e , p l u s l a r e p o n s e e f f e c t i v e du m a t g r i a u e s t s o u p l e . En u t i l i s a n t l a n o t i o n d e module d e r u p t u r e , on dgmontre que d e s r u p t u r e s p a r fendage, d e t y p e f r a g i l e , n ' i n d i q u e n t p a s d e s c o n d i t i o n s d e charge pure g l a s t i q u e , e t que l a t r a n s i t i o n a p p a r e n t e d u c t i l i t g - f r a g i l i t 6 dEpend d e l a

reponse du systeme expgrimental. En grande p a r t i e , l a

d i s p e r s i o n d e s r E s u l t a t s o b t e n u s pour ce m6me t y p e de g l a c e e s t donc a t t r i b u a b l e 3 d e s d i f f g r e n c e s d a n s l a rdponse d e s d i v e r s systemes expgrimentaux.

N. K. Sinha Rcscnrch Officer

E F A R A T I V E STUI)Y 01: ICE STHEhC;TtI DATA

Division of Building Research Canada

Sational Research Council of Canada Ottawa, Ontario, Canada

A review of strain rate sensitivity of uniaxial compressive yield

strength of p01)~cr)stalline ice indicaTes that the results obtained by

different investigators reflect the stiffness of the corresponding test systems. It is shown that the softer the system the softer is the cffcctive response of the material. Using the concept of failure modu- lus, it is shown that brittle-like splitting failures do not indicate pure elastic loading conditions, and that apparent ductile-to-brittle transition depends on the response of the test system. Thus, much of the scatter in available results for the same type of ice is attributable to differences in the response of the different test systems.

Reported values of the strength of ice are rather scattered and often difficult to interpret. Lack of detailed information on the conditions under which the mcasure- ments were made is one of the prime difficulties in interpreting strengGh data. It is the purpose of this paper to present results of tests on one type of ice at one temperature obtained by different investigators using different test systems. The ice chosen for this comparison is one of the most common, columnar-grained S-2 type. It was loaded perpendicular to the columns and tested at -lO°C. This choice was dictated primarily by the number of readily available results from Lava1 University [l-53 and

from the Division of Building Research, National Research Council of Canada [6-91.

Results have also been obtained on the dependence of upper yield stress on truly

constant strain rate [lo] using a closed-loop test system.

Conventional test machines capable of delivering a constant or near-constant actuator or cross-head displacement rate have been used in all tests until very recently. Cylindrical or rectangular specimens were used; and strengths were plotted

as functions of nominal strain rate, t = k/k, where k is the actuator or cross-head

displacement rate and k is the specimen length.

For yield type of failure the upper yjeld stress was observed to depend on

nominal strain rate according to t = P of P, where P and p are constants. It is,

however, preferable to express the above power law in a normalized, dimensionally balanced form by

where il is the unit or reference strain rate, ol is the unit or reference stress, and

M and m are constants.

This form of the relation allows a ready comparison of the rate sensitivity of strength to the dependence of viscous flow rate on stress in pure uniaxial creep usually given, and again presented in a normalized form, as

whcrc A and a are constants. The term "viscous" will be used in this article to

dcscribc thc non-rccovcrable (permanent) part of the total deformation, discussed elsewhcrc in detail [11,12].

I'rohlcms

-

-Creep tcsts are relatively simple and can be performed without much difficulty using a dead load system. The stress level can therefore be maintained reasonably constant so long as the load is kept constant and the specimen is not allowed to deform excessively, say not more than a few per cent. Similar comments cannot be made

ior the so-called constant strain rate tests. It has been clearly demonstrated ( 9 1

that conventional test machines are not capable of maintaining a constant strain rate during a test carried out at a constant cross-head rate. Observations have indicated that a conventional test machine is able to impose the specified nominal deformation rate, kn, on the specimen only when the specimen offers no more increase in resistance

with f~lrther increase in deformation. It has been shown that strain rate at yield is

cquiv;llcnt to nominal strain rate. Similar observations were made by Drouin [I].

This genera1i:ation cannot, however, be applied to brittle-like failures in which the

peak strain rate could be a fraction of i [ 9 ] . The use of i. as an independent

variable can therefore be justified on a limited basis for yield type of failure only. Ihe test condition, however, cannot be construed as constant strain rate.

['he difficulty in maklng a comparative study of Ice strength from constant cross-

head rate tests and constant load creen results becomes evident. The difficulties

have been reco~nized by many investigators, hut the subject and possible consequences

have never been openly discussed in glaciological literature. The main reason for this lies, perhaps, in the observed fact that the stress exponents p (or m) and a

were found hy different observers to be close to each other and equal to about 3.

Consccluently, there never seemed to be any requirement to examine the differences, if

any, in the values of I' (or Mi obtained by different investigators, nor has there been

a comparative study of P (or M ) and A . Strength Results

Fluguruma [ h l examined the uniaxial yield strength of columnar-grained S-2 ice of

average grain diameter of 2 to 5 mm loaded perpendicular to the column axis. Thc work

was carried out ;it the I)HR/NRC laboratory using a low capacity ( 0 . 0 2 MN) Ilounsfield

tc,nsomrtcr. Spccimcns ( 0 . 5 x 2 x 2.5 cm) proved to be rather inadequate [I31 since

tlir nulnhcr of xr;iiiis ;\cross the width was not sufficient. Muguruma discussed his

rrC;~~lt5 in terms of :I powci. law similar to that of equation (1). He obtained a strcss

L'X[IOII~'II~ ot' 3 . 0 in his tests, hut did not give a numerical value for the coefficient. - 7

I

~~~~~~r

X of. bl~~~i~rum;~'s I):ll)cr 161 givcs 2 . 4 MN.m

-

for the mean strength of six slwcis~r~~.; of. ;lvrr:igc gr;iin cli;~nlcter of 4 mm, tcstcd at -lO°C and 6 = 2.1 x lo-' s-l. I:ron~ ttlc rcsl~lts of his cxpcriment, cqii;ition (1) can bc expressed as:

Gold and Krausz [7] investigated the compressive strength of various types of

natural river ice, including 5-2 type at -lO°C at the same DBR/NRC laboratory. They

used ;I l;~rgcr capacity (0.05 MN) Wykeham Farrance, Model 57, soil -testing machine.

-

Their results when converted to the form of equation (1) are given b!

-4.0

Gold and Krausz = 10-7

[

171

1

[ ? '

l i (4) 4

Examination o f the experimental procedures disclosed that Gold and Kraus: used two types o f specimen dimensions 5 x 10 x 25 cm and 4 x 8

*

19 cm. The) mentioned that the smaller specimens had to be used at the higher rates of strain to keep the loads within the capacity of the testing machine, but the rate at which the change was made was not mentioned.

In examining the strain rate sensitivity of plane-strain compressive strcngth o f laboratory-made S - 2 ice of average grain diameter of about 5 mm, Frederking 181 also performed tests at -10°C under uniaxial loading conditions (specimens 5 x 10 x 1 5 cm) at DBR/NRC on a 0.1 MN capacity Instron TTDM-L test system. Conversion u f :~edcrling's results to the form of equation (1) gives

i:

$

[

Fre&;king

1

_{-7 1}

=

3.34

f

= 2.32 x 10

,

"I

)

(5

Dependence of compressive strength of columnar-grained S-2 ice on strain rate at -10°C for a loading condition o f constant rate of cross-head displacement was investi- gated extensively by Sinha [9] at D B R / N R C using the same Instron TTDM-L test machine, specimen geometry, and type of ice as was used by Frederking [8]. The dependence of the upper yield stress on nominal strain rate was

3.03

>

[

"I;;"

]

= 3.37 lo-'

$1

( 6

1

(

Sinh:~ 1 1 0 1 has also performed strength tests on S-2 ice at -lO°C using a 1.0 MN capacity, closed-loop, servo-hydraulic system at EXXON Production Research Laboratory in llouston (specimens 5 x ₁₀ x 25 cm and average grain diameters 4 to 5 mm). For conditions of truly constant strain rate, the dcpcndcnce of the yicld stress on strain rate was given by

2 . 9 0

6

[

;;;;a

J

= 1.81 Y

I;:]

(7)

Several investigations of the strength of polycrystalline ice have been carried out in the ice laboratory at Lava1 University [l-4, 141, and the results compiled by

Michcl [S]. _{These investi~ations were carried out on a Wykeham Farrance Model} T 5 7 B 4 with m;~ximum capacity 0.05 MN [.I], the same make and model as that acquired by DBK/NRC

in 1958 and used by Cold and Krausz [7]. For columnar-grained S-2 ice of average grain diameter of 5 mm at -lO°C, loaded perpendicular to the columns, the dependcncc of uppcr yield stress on nominal strain rate was given by

Relatively large specimens were used at Laval, as shown in Table I. nrouin (11 used cylindrical specimens 5 cm diameter and 10 cm long; Carter and Michel [2] used

cylindrical specimens 5 cm diamctcr and 15 cm long. Ramseier [4] used rectangular

spccimens 5 x 10 x 25 cm, the same size as were most frequently used at DBR/NRC.

'fable : . IJniaxi;il compressive strength of columnar-grained S-2 ice of avcrage

grain size of 4 to 5 mm at -lO°C, loaded perpendicular to the columns

Invcstigator(s) Machine Specimen Stress

Refcrcncc Capacity, Geometry, Coefficient Exponent

MN mm M m

Muguruma [ 6 ] 0.02 5 x 20 x 25 1.52 r 3.00

rectangular

Gold and Krausz (71 0.05 5 0 ~ 1 0 0 x 2 5 0 1 . 0 6 x 1 0 - ~ 4 .OO

and

40 x 80 x 190

rectangular

blichcl [5] 0.05 50 mm diam and 1.35 x lo-6 2.96

(reprcsenting 100 or 150 mm

Lavnl results) long cylindrical

or

50 x 100 x 250

rectangular

I.rcdcrling ( 8 1 0.10 50 x 100 x 250 -1.32 x lo-7 3.34

rectangular

S i I~II:I

I!)

1

0. 1 0 50 x 100 x 250 3.37 lo-7 3.03 rectangular

S i nl~:~ 1 1 0

I

1

.

0 50 x 100 x 250 1.81 x 2.90

(t rill y const:~nt (closcd rectangular

~trz~in rate) loop

system)

- - -

Similarities - - Ihe importance of the coefficient and stress exponent in . - - -- . . - --

ccl~~;~tior~ ( I ) has hecn emphasized. Examination of the experimental results given in

cqu:itions (.>I to (8) inciicate, with the exception of equation (41, which corresponds

to thc rcsults of (;old and Krausz [ 7 ] tnat stress exponents were determined by

diffcrcnt investigators to he close to 3. Thus, all the strength-straln rate curves wrrc foulid to have the snmc shape, as may be seen in Figure 1

T 7 N 6 I E 3 FREDERKING, [8] i z 4 GOLD KRAUSZ. [71 I 5 b‘ 6 MUGURUMA. [61 VI 'A 4 u P: 6 VI u a 3 3 A

-

4 L L 2 0 A ",

-

1 0 t I I

1

10'" LO-) S T R A I N R A T E , i , S-' F i g u r e 1 Dependence o f s t r e n g t h o f c o l u m n a r - g r a i n e d i c e on s t r a i n r a t e a t -lO°C D i f f e r e n c e s - - A l t h o u g h t h e c u r v e s a r e s i m i l a r i n F i g u r e 1 , t h e i r p o s i t i o n s a r c s i g n i f i c a n t l y d i f f e r e n t . The p o s i t i o n o f t h e s t r e n g t h - s t r a i n r a t e c u r v e s i s d e t e r m i n e d hy s i g n i f i c a n t d i f f e r e n c e s i n t h e c o e f f i c i e n t s o f e q u a t i o n s ( 3 ) t o ( 8 ) . T h i s may a l s o h e s e e n i n T n h l e I . I n g e n e r a l , l a r g e r c a p a c i t y and p r o b a b l y s t i f f e r m a c h i n e s t e n d e d t o g i v c :I l o w e r v a l u e f o r t h e c o e f f i c i e n t , and t h i s s h i f t e d t h e c u r v e s t o l o w e r s t r a i n r : l t c s . I Y i g u r e 1 , i n c o n j u n c t i o n w i t h T a b l e I , shows c l e a r l y t h a t a l a r g e c a p a c i t y machine g i v e s a h i g h e r s t r e n g t h a t t h e same n o m i n a l s t r a i n r a t e t h a n d o e s a low c a p : ~ c i t y m a c h i n e , and t h a t a c l o s e d - l o o p s y s t e m w i t h e q u i v a l e n t i n f i n i t e s t i f f n e s s y i e l d s t h e h i g h e s t s t r e n g t h .

Anomaly - - A c c o r d i n g t o t h e e v i d e n c e o f t h e p r e v i o u s s e c t i o n , t e s t m a c h i n e s s i m i l a r i n c a p a c i t y and s t i f f n e s s s h o u l d g i v c s i m i l a r r e s u l t 5 . T h i s i s c v i d c n t i n I'igure 1 i f t h e r e s u l t s o f 1:rcderking [ R ] a r c compared w i t h t h o s e o f S i n h ; ~ [ ! I ] . Both u s e d t h e same 0 . 1 M N c a p a c i t y I n s t r o n TTDM-L m a c h i n e and a l m o s t i d e n t i c a l t e s t i n g c o n d i t i o n s . On t h e o t h c r h a n d , t h e r e s u l t s o f Cold a n d Krausz 171 s h o u l d h e s i m i l a r t o t h o s e r e p o r t e d by M i c h e l [ S ] b e c a u s e t h e same 0 . 0 5 MN c a p a c i t y Wykeham F a r r a n c c Model 5 7 t e s t machine was u s e d ; b u t F i g u r e 1 shows t h a t t h e t v o s e t s o f r e s u l t s d i f f e r s i g n i f i c a n t l y .

586

The c o e f f i c i e n t i n e q u a t i o n ( 4 ) o b t a i n e d by Gold and Krausz [ 7 ] i s s i g n i f i c a n t l y

I

s m a l l e r t h a n t h o s e o b t a i n e d a t L a v a l , whereas t h e c o r r e s p o n d i n g s r r c s s exponent i s s i g n i f i c a n t l y g r e a t e r . Thus t h e r e s u l t s a p p e a r t o be anomalous i n comparison w i t h o t h e r s , and t h e anomaly can be seen i n F i g u r e 1 , a s w e l l , where t h e c u r v e i n t e r c e p t s :111 t h e o t h e r c u r v e s .

Anom;~lor~s c h a r a c t e r i s t i c s i n t h e r e s u l t s o f Gold and Krausz [ 7 ] c o u l d be due t o t h e f a c t t h a t e q u a t i o n ( 4 ) r e f l e c t s t h e a v e r a g e dependence f o r a l l t h e i c c t y p e s t e s t e d r a t h e r t h a n j u s t S - 2 i c e . Use o f specimens w i t h d i f f e r e n t geometry by Gold and Kraus:. may a l s o c o n t r i b u t e t o t h e anomaly. Sinha and F r e d e r k i n g [ I S ] showed t h a t change in gcometry a f f e c t s t h e r e l a t i v e s t i f f n e s s and r a t e o f l o a d i n g o f a system and t h e r e f o r e changes t h e s t r c n y , t h a t t h e same nominal s t r a i n r a t e . Note t h a t t h e c o m h i n a - t i o n o f low c a p a c i t y machine and s m a l l specimen geometry used by Muguruma [ 6 ] gave r e s u l t s comparable t o t h o s e r e p o r t e d by Michel 151. T h i s i n d i c a t e s t h a t i f o n l y t h e r e s u l t s o f 5 - 2 i c e a r c t a k e n from t h e r e p o r t o f Gold and Krarrsz [ 7 ] , and a l l o w a n c e i s madc f o r e f f e c t o f specimen s i z e , b e t t e r agreement would be found w i t h t h e r e s u l t s o f blichel ( e q u a t i o n (8)).

Lreep Rate - - In p r o p o s i n g a v i s c o e l a s t i c model f o r i c e , S i n h a 1111 d e s c r i b e d t h e i r r e v e r s i b l e v i s c o u s s t r a i n r a t e component o f t h e c o n s t a n t s t r e s s c r e e p r a t e a t - 1 0 ° C

a S

I.quation ( 9 ) 1 s s u r p r i s i n g l y c l o s e , both i n numerical v a l u e s f o r t h e c o e f f i c i e n t i111d i n exponent t o e q u a t i o n ( 7 ) f o r s t r e n g t h o b t a i n e d under t r u l y c o n s t a n t s t r a i n r a t e . l l r i s indicates s t r o n g l y , and F i g u r e 1 i l l u s t r a t e s i t g r a p h i c a l l y , t h a t t h e r e s u l t s f o r t h r s t r e s s dcpendcncc o f v i s c o u s flow r a t e o b t a i n e d i n c o n s t a n t s t r e s s c r e e p t e s t s may h r coml>:~r:~hlc w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n s on t h e dependence o f y i e l d s t r e s s on s t r : ~ i n r : ~ t c [ I 0 1 o n l y when t h e imposed s t r a i n r a t e i s t r u l y c o n s t a n t .

I ~ ~ s r ~ f S i c _{- . . -} i c n c e s i n I l e j > o r t ~ d _{. - - - - - - - - - - - -} Ilcsrtl t s _{-- -- -.}

Il:,tion;~l a n a l y s i s o f d a t a from t h e i c e l i t e r a t u r e i s d i f f i c u l t i n almost a l l c : ~ s c s owing t o l a c k o f v i t a l i n f o r m a t i o n h e a r i n g on t h e r e s u l t s . Important d e t a i l s :11'r ctlmslollly o m i t t e d c o n c e r n i n g s t r a i n and d u r a t i o n o f t e s t , i n s p i t e o f t h e f a c t t h a t ( : I ) : i l l t r s t s t a k e some s l ~ c c i f i c t i m e t o complete, and (b) specimens deform d u r i n g t e s t i n g . T h i s informiltion c o u l d he o b t a i n e d w i t h l i t t l e a d d i t i o n a l e f f o r t d u r i n g t h e c x p c r i m c n t s .

S t r c s s and S t r a i n ~t F a i l u r e _{.- . -}

_-

_{.. , .} -

- -

Although i t was i m p o s s i b l e t o o b t a i n i n f o r m a t i o n r h c tinlc ;~.;lwcts o f t h e a v a i l a b l e t e s t r e s u l t s , some s t r a i n measurements were madc

f o r c o ~ n l ~ : ~ r n t ivc s t i ~ d y . Gold and Krausz [7] provided t h r e e s t r e s s - s t r a i n diagrams ( s e e

F i g u r e 6 o f t h e i r p a p e r ) c o r r e s p o n d i n g t o i n = 5 . 5 x 1 ( 1 - ~ . 1 . 7 x and

1 . 7 x 10-' 5 - l f o r S - ? i c e a t - 9 . S ° C . ( I t i s n o t c e r t a i n w h e t h e r a l l t h r e e s p e c i m e n s had t h e same g e o m e t r y . ) The s t r a i n s were m e a s u r e d b e t w e e n t h e t o p and t h e b o t t o m p l a t e n s (given h e r e i n F i g u r e 2 ) .

D r o u i n [ l ] a l s o p r o v i d e d o n e s t r e s s - s t r a i n d i a g r a m ( s e e F i g u r e 4 . 7 5 i n h i s t l ~ c , : i s l f o r c o l u m n a r - g r a i n e d S - 2 i c e l o a d e d n o r m a l t o t h e column a x i s a t -9.4OC and s u b j e c t e d t o a n o m i n a l s t r a i n r a t e o f 6 . 9 x s - l . The u p p e r y i c l d s t r e s s and r h e s t r a i n a t y i e l d were o b t a i n e d from t h i s i l l u s t r a t i o n and w i l l b e u s e d l a t e r . T h i s p a i r o f r e s u l t s i s n o t shown i n F i g u r e ? b e c a u s e o f t h e l a r g e amount o f s t r a i n i n v o l v e d . D r o u i n [ l , 141 showed, a s w e l l , t h e v a r i a t i o n i n s t r a i n r a t e d u r i n g t e s t s . R a m s e i e r [ 4 ] i l l u s t r a t e d t h r e e s t r e s s - s t r a i n d i a g r a m s ( F i g u r e 6 . 1 3 o f h i s t h e s i s ) f o r S - ? i c e a t -lO°C f o r n o m i n a l s t r a i n r a t e s o f 1 . 8 x 6 . 1 x and 6 . 7 l o - ' s S 1 . The r e s u l t s f r o m t h e t h r e e c u r v e s a r e shown i n F i g u r e 2 . S t r : ~ i n s were m e a s u r e d b e t w e e n t h e t o p a n d t h e b o t t o m p l a t e n s , b u t n o i n f o r m a t i o n was g i v e n r e g a r d i n g t h e t i m e a s p e c t s o f t h e t e s t s . l l i c h e l [ 5 ] presented t h r e e s t r e s s - s t r a i n d i a g r a m s ( F i g u r e 9 o f h i s p a p e r ) f o r S - 2 i c e a t -10°C f o r t h e n o m i n a l s t r a i n r a t e s o f 2 . 4 x 2 . 5 x l o - ' a n d 4 . 2 x s - l . The u p p e r y i e l d s t r e s s e s a n d t h e s t r a i n s o b t a i n e d f r o m t h e t h r e e c u r v e s a r e shown i n F i g u r e 2. D e f o r m a t i o n s were mc'asured b u t t h e t i m e a s p e c t s o f t h e t e s t s a r e n o t a v a i l a b l e . 0 I I I I 0 1U 20 30 40 5 0 Y I E L D O R F A I L U R E S T R A I N . c t , IPiglirc ? I)cl)criclcrlcc o f y i e l d o r f a i l u r e s t r a i n on t h e c o r r e s p o n d i n g . ; t r e s s ol)scrvcrl t)y v a r i o u s i n v e s t i g a t o r s f o r c o i u m n a r - g r a i n e d S-2 i r c :it -10°(:

Dcpendcncc of strain on stress at yield obtained earlier by Sinha [9, 101 are also shown in Figure 2. Time aspects of the two sets of results have already been discussed in great detail.

Althou~h the scatter is large, Figure 2 shows that the results obtained at Lava1

llnivcrsity [l, 4 , 51 are consistent. This could be related to the use of the same

tcst system, and the results should therefore be comparable to those of Gold and Krausz 171 who used a similar machine. Figure 2 shows that they are comparable, although thc lattcr seem to have obtained somewhat less strain for the same yield stresses. Gold and Krausz do not show any anomaly here, as was pointed out for

Figure 1 . The investigations of Muguruma [6] and Frederking

[ a ]

could not be used

hccausc strain data are lacking.

Rcs~rlts given in Figure 2 indicate strongly that a larger capacity, stiffer

machine tends to deform thc material less in inducing failure at the same stress level. It seems therefore that the harder the system the less the apparent ductility of the material. The closed-loop system with equivalent infinite stiffness deforms material least.

I'ai lurc Flod~~lus

---

Since deformation of material seems to be controlled by the stiffness of the tcsting system, it was decided to examine the effective stiffness of the material at failure for all the available results. Tnis led to the introduction of a concept of "Failure Flodulus," Ef, defined as the ratio of the upper yield or failure stress and corresponding strain,

I::liltirc modullrs is essentially the secant modulus corresponding to the maximum stress

:~n~l I:ig~~rc J i1lustr:ctes the available experimental results discussed in the previous

section in terms of thc corresponding imposed strain rate. Drouin's measurement, n14.ntioncd heforc but not incorporated in Figure 2, can now be used. Irrespective of

thr tcst system, Figure .? shows that the failure modulus increases with increase in

s t I I T11c vnluc of thc modulus at a given strain rate, however, depends on the

stiffness of thc tcst system. The illustration reaffirms that a stiffer system

i ~lc.rc:~scs thc :q>pnrcnt st i ffncss of the material. As 'Sinha's [lo] results were

ol)t;iinccl for trltly constant strain rate under a closed-loop mode of strain control,

thc cffcctivc stiffness of thc system was very high and the corresponding Ef versus h

curvc m:iy hc considcrcd as the limiting one. In spite of the fact that similar

machines wcrc used in both laboratories, Figure 3 indicates that the total systems at

L.aval University uscd by Drouin [I]. Ramseier 141, and Hichel [S] were all softer than

6

N o SINHA. [lo]

.

CLOSED LOOP TESTS E SINHA. [9]

.

NOMINAL STRAIN RATE

z GOLD & KRAUSZ. [7]

.

FIG. 6

a

.

RAMSEIER. [4]

.

FIG. 6.12

-

" 4 - 0 MICHEL. [5]

.

FIG. 9 m X DROUIN, [l]. FIG. 4.75 3 2 3 0 0 I W (L 3 2 4 Y (L m R w C d 0 / / - / /?-/ 0 / / / /

/./

2 W

-

:--/--o >

-

J--

-

-x-

c

---,--

_{I I} 0 1 0 - ~ S T R A I N RATE.

t

, s-'

Figure 3 Dependence of failure modulus on strain rate

of the total system depends also on the stiffness characteristics of the various components of the loading column, for example, the load cell, platens, etc [IS]. It should again be pointed out that the anomaly in the results o f Gold and Krausz shown

in Figure 1 is not present in Figure 3.

All moduli reported in Figure 3 are considerably lower than the Young's modulus

of ahout 9 . 5 GN.~-' determined earlier [I], 121 for the same type of ice, loading

direction, and temperature. Thus the brittle-like, premature failures occurring at

-4 -1

strain .r:ltcs in the ran!:e of about 10 s may not be considered as purc elastic type

of lo:tdi~lg or as truly "brittle-type" failures. This applies very strongly to the investigations of Cold and Krausz [7], Ramseier [4] and Michel [S].

Premature failures were noted by the author [ 9 ] to occur at a nominal strain rate

01. 3 w s-l or higher for a conventional system. For similarly prepared specimens

tile iluthor [10] found abrupt splitting type of failure at a constant strain rate

o f 5 v ~ ( l - ~ , s - I

.

Thus the occurrence of the so-called brittle-like failures also

O('~~cl~rl~ (111 thC stiffness of the test system for the same end conditions.

Cone 1115 ions

, . . . .

- -

. .

IJni;~si;~l strcngth results obtained by different investigators depend on the

stiff~lcss o f the test systems used. The shape of the strength-strain rate curve docs

!lot seem to he affected by the relative stiffness of the system, but its position on the str:iin ratc :lxis is. The limiting position of this curve is determined by a test

system such as the closed-loop system, with effective infinite stiffness. This limit- ing relation has a one-to-one correspondence with the dependence of non-recoverable viscous flow on stress in uniaxial creep.

Thc ductility of ice depends on the stiffness of the test system. A test system kith infinite stiffness dcforms the material least. The softer the system the softer

is the response of the material.

Failure modulus increases with increase in strain rate for a given system.

It also increases with increasc in stiffness at a given strain rate. All the failure

moduli were found to be considerably less than Young's modulus of ice. Apparently, brittle-like, premature failures do not represent pure elastic loading. The strain rate at which premature failure starts as well as that at which the apparent ductile- brittle transition begins, also depends on the stiffness of the test system. Fremature failurc occurs at a lower strain rate in a stiffer system.

Thc author is indebted to Dr. Y.S. Wang and EXXON Production Research Laboratory, Ilouston, for their cooperation in permitting use of the closed-loop machine. This p;~pcr is ;I contribution from the Division of Building Research, National Research Council of Canada, and is published with the approval of the Director of the Division.

References

[I1 Drouin, !.I., Lcs poussdcs d'origine thermique exercees par les couverts de glace sur les structures hydrauliques. Ph.D. Thesis. Lava1 University, (luebec, C;lnad:r. 1971

.

121 Cnrtcr, D . , and Michel, 6 . . Lois et mecanismes de l'apparcnte rupture fragile de 1:1 glace dc riviEre et de lac. Rapport S-22, Departement de Genie Civil, llrlivcrsitf I.:~vnl. Quebec (Qud) , 1971.

1 :

Fli~.hcl, R., :~ntl I'nmdis, F I . . Analyse statistique du fluage secondaire de la glace

dc riviEre et de lac. Rapport GCS 76-02, Ddpartement de Genie Civil,

Ilrli\~ersi t6 I.:lva I, Quebec (Que) , 1976.

I

I

I

I(:tnlscicr. H.O.

.

Growth and mechanical properties of river and lake ice. Ph.D. Thesiis, Lava1 University, Quebec, Canada, 1976.

15) hlirhcl. R., The strength of polycrystalline ice. Can. J. Civ. Eng., V. 5, No. 3 . 1!)7R, p. 285-300.

101 Mup~ruma, J., Effects of surface conditions on the mechanical properties of ice

crystals. d . Phys., D., Ser. 2, V . 2, 1969, p. 1517-25.

171 (;old, L.W., and Krausz, A.S., Investigation of the mechanical properties of

Frederking. R . , Plane-strain compressive strength of columnar-grained and

granular-snow ice. J. Glaciol..

18

(80). 1977, p. 505-516.

Sinha. N.K., Hate sensitivity of compressive strength of columnar-grained Ice.

Experimental Mechanics,

11

(6). 1981, p. 209-218.

Sinha. N.K.. Constant strain rate and constant stress rate compressive strcn~th

of columnar-grained ice. To be 1>11bl ished.

Sinha. N.K.. Rheolo~y of columnar-grained ice. Experimental Mechanics, ( 1 2 ) .

1978. p. 464-470.

Sinha. N.K., Short-term rheology of po!ycrystalline ice. J. Glaciol.,

2

(85),

1978, p . 457-474.

Gold. L.W.. The failure process in columnar-grained ice. Ph.D. Thesis , McGill University, 1970.

Drouin. M.. Laboratory investigation on ice thermal pressures. Proc. IAHR Ice

Symposium, Leningrad, 26-79 September 1972, p. 72-80.

Sinha. N.K.. and Frederking, R . , Effect of test system stiffness on strcngth of

ice. Proc. 5th International Conference on Port and Ocean Engineering under Arctic Conditions, Trondheim, Norway, 13-17 August 1979, p. 708-717.

Discussion on "Comparative Study o f Ice Strength Data" by N. K. Sinha Discussed by Y. S. Wang

Exxon Production Research Company Houston. TX. U.S.A.

This paper is a continuing contribution by Dr. Sinha in his e f f o r t s t o resolve the apparent discreptlncies in the results of laboratory strength tests o f similar ice by different investigators--a fact that has puzzled ice mechanics researchers. Because the stiffness o f an ice sample varies with both stress and stress r a t e (or strain and strain rate), the strain l ~ i s t o r y o f a sample. tested on a conventional machine, strongly depends upon the stiffness o f the loading system which includes the stiffness of the machine frame, the load cell, the load platens, and the compliant platens i f they are used, etc. Thus, t w o samples tested on t w o machines w i t h different stiffness characteristics may be subjected t o t w o different loading histories under the same nominal loading programs. The strengths obtained are, therefore, also different.

The author compared test results from many investigators and concluded that under the same nominal strain rate, s t i f f e r machines produce higher strengths and less sample deformation. This is because, for s t i f f e r machines, a larger portion of the nominal deformation goes t o the sample as compared w i t h a softer machine. Thus, samples tested with a s t i f f e r machine actually are subjected t o higher strain rates compared t o samples tested w i t h softer machines. Also, from my personal experience from strength tests with a closed-loop mnchine, the sample strain a t which failure occurs decreases with thc increase o f strain rate, which is consistent w i t h what the author has found. '1'11~ t ~ u l l ~ o r also presented an interesting observation that the relationship between stress nrid irrrversible viscous strain r a t e i n creep tests is very close t o the one between f t ~ i l u r c strcss and strain r a t e i n constant strain r a t e tests. I am currently working on

t i onr-dimrnsional stress-strain-strain r a t e relationship t o describe the behavior of sea icc under n _{variety o f loading conditions and this formulation predicts that the stress-}

struin r n t c relationships for the t w o types o f tests are the same. I am very much cricolrrtrgcd by Dr. Sinha's results.

COMPARATIVE STUDY 01 ICE STRENGTH DATA

by N.K. Sinha

DISCUSSION BY:

Franz Ulrich Hausler, Hamburgische Schiffbau-Versuchsanstalt GmbH, W-Germany

It was shown that a high system stiffness of the testing apparatus provides for realistic test results. Since the only closed loop system of all the testing apparatus presented here has by far the highest loading capacity. the conclusion that the good results gained on this system are based mostly upon its closed loop control could be questioned. Nevertheless. the results gained at HSVA with a 100 kN spindle

driven and two 125 kN servohydraulic closed loop test systems during a research program on the multiaxial strength of saline ice lead to the same conclusion.

Unquestionably, the closed loop technique represents today's state of the art. It gives us a good tool to achieve reliable results even with rather small testing machines because it provides for equivalent system stiffnesses which are close to infinite. But as a result of the experience we have gained at HSVA during the last three years, it seems important to note that a true constant strain rate will only be obtained if the whole test system, including the specimen to be tested, is optimally tuned. If not, oscillations or the other extreme, long response times may lead to considerably large differences between desired and measured strain rates, especially at higher strain rates, i.e. at

;

> 1.0 x s-'.

Questions:

1

-

How long was the response time of the closed loop control system in the strain rate controlled mode?

2

-

How large were the deviations of the really measured strain rates from the desired value at the different strain rate levels?

AUTHOR'S REPLY to F.U. ~ i u s l e r :

1

-

The tests were carried below s-I and so no problems with response time arose.

2

-

Within 1%. 3

-

Polished steel.

AUTHOR'S REPLY to Y.S. Wang:

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