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An experimental investigation of strain relaxation in ice
Krausz, A. S.
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S e r
TH1
N21r2
no.
387
c . 2
A N A L \ P Z F D
NATIONAL RESEARCH COUNCIL O F C A h A D A
CONSEIL NATIONAL D E RECHERCHES DU CANADA
BLDG
AN E X P E R I M E N T A L INVESTIGATION O F STRALN RELAXATION
IN ICE
by
A . S . K r a u s z
Reprin!;ed f r o m
,.:.V"*.?,' i..i-. Ti ~ A-- -~---~-.,S C R I P T A METALLURGICA
Val. 2 ,
NO. 1 1 , NOV.
1 9 6 8
p .
6 1 5
P r i c e
10
c e n t s
fR e s e a r c h P a p e r N o .
387
of the
D i v i s i o n of Building R e s e a r c h
OTTAWA
Dec-ember
1 9 6 8
N R C
1 0 5 2 2
E T U D E E X P E R I M E N T A L E D E L ' E L A S T I C I T E L I I F F E R E E D E LA G L A C E
SOMMAIRE
O n a CtudiG,
h
l ' a i d e d l C p r o u v e t t e s d e g l a c e c o l o n n a i r e , l a rCduction
d e l a d g f o r m a t i o n p l a s t i q u e ( C l a s t i c i t C diffCrCe) q u i s e p r o d u i t a p r ' e s
l ' a n n u l a t i o n d e l a f o r c e appliquCe. L e s C p r o u v e t t e s a v a i e n t CtC dCformCes
p a r Clongation
>
une t e m p C r a t u r e d e - 9 " c e n t i g r a d e . E l l e s a n t e u
e n s u i t e a m p l e m e n t l e t e m p s d e r e p r e n d r e l e u r f o r m e .
L e s r k s u l t a t s d e l l e x p C r i e n c e o n t Ctk a n a l y s C s
h
l ' a i d e d ' u n e
Cquation fondCe s u r l a t h C o r i e d e l a v i t e s s e d e m o n t k e d e s d i s l o c a t i o n s .
L e v o l u m e d ' a c t i v a t i o n d h t e r m i n a n t l a v i t e s s e d u phCnomkne Ctait
l e s u i v a n t :
3 3
3 3
0 . 3 5 x 1 0 b
,<
V , < 1 x 1 0 b
o'u b e s t l e v e c t e u r d e B u r g e r s .
L ' a u t e u r e n c o n c l u t q u e l e i
d 6 v i a t i o n s e t l e s montCes p e r p e n d i c u l a i r e s a u p l a n d e g l i s s e m e n t n ' o n t
q u ' u n e f f e t nCgligeable s u r l a dCfc!rmation d e l a g l a c e e t q u e l e
p r o c e s s u s e s t c o m m a n d 6 p a r l e m C c a n i s m e d e P e i e r l s o u p a r l a
montCe d e s c r a n s h o r s d e l e u r p l a n d e g l i s s e m e n t . L 1 a u t e u r a
C g a l e m e n t 6valuC l ' i m p o r t a n c e d e s p h 6 n o m k n e s d ' i n t e r s e c t i o n .
Sc ripta
ME
TALLURGIC
A
Val.
2, pp. 615-620, 1968
Printed in the United States
Pergamon Press, Inc.
A. S. K r a u s z
Snow and Ice Section. DivisiSn of Building R e s e a r c h , National R e s e a r c h Council of Canada
(Received August 30, 1968)
In the l a s t t e n y e a r s experimental techniques have been developed for the d i r e c t o b s e r - vation of the motion of dislocations i n ionic and covalent c r y s t a l s . Using the r e s u l t s obtained i n these experiments a r e c e n t investigat..on cn the rate theory of dirlocazion mobility (1) indi- cated that the usual s t r a i n relaxation* t h e o r i e s w e r e inadequate. A detailed study (2) showed that this i s indeed so, and a new theory was proposed f o r the description of the s';rain r e l a x a - tion i n crystalline m a t e r i a l s .
The validity of the proposed r a t e theory of s t r a i n relaxation h a s to be investigated experimentally. A c u r r e n t t e s t s e r i e s on the plastic p r o p e r t i e s of i c e provided a n opportunity to do this; t i i s paper r e p o r t s the r e s u l t s of the s t r a i n relaxation experiments.
T h e o r y
The analysis of the dislocation mobility e x p e r i m e n t s indicated that the plastic deforma- tion p r o c e s s i n L i F , NaCP, Si, Ge, InSb, GaSb, W , F e
-
3. 2570 Si, Zn, Ni, and Mo i s a s s o - ciated with a l i n e a r l y s t r e s s dependent activation enthalpy and a n a s y m m e t r i c a l e n e r g y b a r r i e r (1). The description of any macroscopic experiment must be i r i a g r e e m e n t with t!ler e s u l t s of dislocation velocity m e a s u r e m e n t s , and t h e r e f o r e , in the analysis of s t r a i n r e l a x - ation, the a s y m m e t r i c a l shape of the e n e r g y b a r r i e r and the linear s t r e s s dependence must be taken into consideration.
It has been shown (2) that the dislocation ve1ocit.y v i n s t r a i n relaxation can be d e s - cribed by the r a t e equation
*
In this paper the t e r m s t r a i n relaxation i s used for the r e v e r s e plastic deformation which o c c u r s a f t e r a specimen i s unlokded.6 16
STRAIN
RELAXATION
IN
ICE
Vol. 2, No. 11
~ ~ (
-
M y ) r ; ~ ~ V b ( ~ i f f-
MY
1
v :: A exp
k T
-
,I exp[
-
f , b k T
1
(1)w h e r e s u b s c r i p t s f and b indicate the a s s o c i a t i o n of the quantity with the f o r w a r d and t h e backward movemept of the a c t i v a t e d complex, V is the activation volume, r o i s the effective
eff
s t r e s s a t the begirning of the s t r a i n r e l a x a t i o n , M i s the r e l a x a t i o n modulus ( 3 ) , y i s the s t r a i n i n relaxation, k i s the Boltzmann constant, and T i s the t e m p e r a t u r e . T h e two p r e - exponential f a c t o r s a r e e x p r e s s e d i n t e r m s of physical quantities and w e r e d e r i v e d ( I ) f r o m the activated c o m p l i x theory (4) without introducing any e x p e r i m e n t a l p a r a m e t e r e .
The e x p r e s s i o n f o r the r a t e of s t r a i n r e l a x a t i o n follows i m m e d i a t e l y f r o m E q . ( l ) when the well-known equation of Orowan (5)
.i
= a b p v i s introduced. Thusvf
(riff
-MY
Vb(riff
-
MY
y = a b p A f exp
k T
-
c r b p A b e x p[ -
, kT1
w h e r e p i s the mobile dislocation density and b i s the B u r g e r s v e c t o r .When long s p e c i m e n s of c o n s i d e r a b l e weight a r e u s e d the constant s t r e s s due to t h i s weight l e a d s to a f a c t o r
i n the f o r w a r d velocity t e r m of Eq. ( 2 ) , and to the f a c t o r
i n the backward velocity t e r m . In t h e s e e x p r e s s i o n s W i s the s p e c i f i c weight and L i s the length of the specimen. T h u s the r a t e equation of s t r a i n r e l a x a t i o n f o r long s p e c i m e n s is
Vol. 2, No. 11
STRAIN RELAXATION IN ICE
6
17
(
E x p e r i m e n t a l P r o c e d u r e
Columnar-grained ice s p e c i m e n s , 50 x 100 x 1000 m m , w e r e p r e p a r e d using the tech- nique a l r e a d y d e s c r i b e d (6). The s p e c i m e n s w e r e cut s o that the iong a x i s of e a c h columnar g r a i n was perpendicular to the 50 x 1000 m m face. The [0001] a x i s was randomly oriented i n the plane approximately p a r a l l e l to this face. Most of the t e s t s w e r e c a r r i e d out a t
-q0c!:.
5'.In a typical e x p e r i m e n t the s p e c i m e n was deformed f i r s t in c r e e p under a s t r e s s of 3. 88 kg/cm2 f o r about 6 h o u r s to a s t r a i n of not m o r e than 1 x At the end of this period the specimen was unloaded and allowed to r e l a x f o r 16 h o u r s . It w a s then reloaded and the c r e e p and relaxation s t a g e s w e r e r e p e a t e d but the s t r a i n relaxation was continued to i t s full extent, i. e . , until the contraction c e a s e d and the s p e c i m e n began to elongate v e r y slow1,y under i t s own weight. In s o m e of these e x p e r i m e n t s only one relaxation t e s t was c a r r i e d out. In these c a s e s the relaxation w a s always continued to i t s full extent.
The length change was m e a s u r e d with t h r e e 7DCDT Sanborn differential t r a n s f o r m e r s and monitored with one d i a l gauge during both c r e e p and relaxation. An effort was made to obtain a s a t i s f a c t o r y l o a d - s p e c i m e n alignment and a c c u r a t e elongation m e a s u r e m e n t s . The e x p e r i m e n t a l a r r a n g e m e n t designed to achieve this i s shown in Fig. 1.
E x p e r i m e n t a l R e s u l t s and Conclusions
A typical example of the s t r a i n relaxation behavior obtained in c o l u m n a r - g r a i n e d i c e i s shown in Fig. 2. The analysis indicated that the \j a: s i n h VT e x p r e s s i o n d e r i v e d f r o m the usually a s s u m e d s y m m e t r i c a l e n e r g y b a r r i e r model cannot be fitted to the e x p e r i m e n t a l r e s u l t ? . The analysis a l s o indicated that the e m p i r i c a l e x p r e s s i o n \ j a ~ " , s o m e t i m e s used to d e s c r i b e the s t r e s s relaxation and constant s t r a i n r a t e observations o v e r a limited r a n g e , cannot fully d e s c r i b e the s t r a i n relaxation of ice.
Eight s p e c i m e n s w e r e t e s t e d i n s t r a i n relaxation; a l l of the e x p e r i m e n t a l observations could be d e s c r i b e d well with Eq.(3). A typical example of the a g r e e m e n t obtained between the m e a s u r e d and calculated s t r a i n relaxation i s shown in Fig. 2. This r e s u l t i s considered a s supporting evidence f o r the proposed r a t e theory of s t r a i n relaxation.
A previous a n a l y s i s (1) of Readey and K*gery1s s t r e s s relaxation experiment in i c e single c r y s t a l s ( 7 ) indicated that Vf may be equal to Vb. The m o r e complete m e a s u r e m e n t s c a r r i e d out in the p r e s e n t investigation provide enough information to lead one to expect that the r a t e - controlling mechanism in i c e i s a s s o c i a t e d with a n a s y m m e t r i c a l e n e r g y b a r r i e r having different activation enthalpies and activation volumes for the f o r w a r d and backward
STRAIN RELAXATION IN
ICE
Vol.
2,
No. 11
S n o w I c e
E x t e n s o m e t e r
IC o l u m n a r G r a i n e d
I c e S p e c i m e n
i
D i f f e r e n t i a l
T r a n s f o r m e r s
WLF l e x i b l e W i r e
G r i p
F l e x i b l e W i r e
W e i g h t
FIG. 1T h e e x t e n s o m e t e r used i n the t e s t s , the method of applying the load, and the method
f o r gripping the s p e c i m e n s
FIG. 2
i
A typical e x p e r i m e n t a l resuli: obtained i n s t r a i n relaxation. T h e points indicate the m e a s u r e d v a l u e s ; the solid line was cal-
culated f r o m Eq. ( 3 )
Analysis of the s t r a i n r e l a x a t i o n e x p e r i m e n t s showed that the activation volume f o r the f o r w a r d movement of the dislocation is
w h e r e b i s the B u r g e r s v e c t o r , In the v e r y low s t r e s s r a n g e the m e a s u r e m e n t s w e r e not a c c u r a t e enough f o r a n exact evaluation of the activation volume Vb. It w a s found that
T h e activation volume v a l u e s i n d i c a t e that the r a t e - c o n t r o l l i n g m e c h a n i s m i n i c e a t - 9 O C
Vol. 2 , No. 11
STRAIN RELAXATION IN ICE
a ) P e i e r l s ' b a r r i e r ,
b) dislocation i n t e r s e c t i o n , o r c ) nonconservative motion bf jogs.
It s e e m s improbable that e i t h e r c r o s s - s l i p o r c l i m b would have a significant effect on t h e p l a s t i c d e f o r m a t i o n of i c e .
It i s concluded that the o b s e r v a t i o n s s t r o n g l y indicate t h a t the s t r a i n r e l a x a t i o n of i c e cai. b e d e s c r i b e d fully with the proposed f o r m of the r a t e theory of s t r a i n relaxation.
Acknowledgments
T h e author w i s h e ~ to e x p r e s s h i s appreciation to L . E . Munro and G. W. Mould f o r -- their contribution to t h e e x p e r i m e n t a l work. Most of the tedious calculations w e r e c a r r i e d ou: by G. W. Mould. He a l s o wiehes-to e x p r e s s h i s gratitude to L. W. Gold f o r the helpful d i s c u s s i o n s . T h i s p a p e r i s a contribution f r o m the Division of Building R e s e a r c h , National R e s e a r c h Council of Canada, and i s published with the a p p r o v a l of the D i r e c t o r of the Division.
R e f e r e n c e s 1. A.S. K r a u s z , Acta Met.
16,
897 (1968).2 . A. S. K r a u s z ( s u b m i t t e d f o r publication).
3. C. Z e n e r , E l a s t i c i t y and Anelasticity of M e t a l s , University of Chicago P r e s s , Chicago (1956).
4. S. G l a s s t o n e , K. J. L a i d l e r and H. E y r i n g , The T h e o r y of Rate P r o c e s s e s , McGraw-Hill, New York (1940).
5. E . Orowan, P r o c . Phys. SOC.
