DAMPING MEASUREMENTS FOR STUDYING THE RELATION BETWEEN TYPE OF DISLOCATIONS INTRODUCED BY PLASTIC DEFORMATION

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DAMPING MEASUREMENTS FOR STUDYING THE RELATION BETWEEN TYPE OF DISLOCATIONS

INTRODUCED BY PLASTIC DEFORMATION

W. Alnaser, M. Zein

To cite this version:

W. Alnaser, M. Zein. DAMPING MEASUREMENTS FOR STUDYING THE RELATION BE-

TWEEN TYPE OF DISLOCATIONS INTRODUCED BY PLASTIC DEFORMATION. Journal de

Physique Colloques, 1987, 48 (C8), pp.C8-83-C8-87. �10.1051/jphyscol:1987808�. �jpa-00227112�

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JOURNAL DE PHYSIQUE

Colloque C 8 , supplkment au n012, Tome 48, dkcembre 1987

DAMPING MEASUREMENTS FOR STUDYING THE RELATION BETWEEN TYPE OF DISLOCATIONS INTRODUCED BY PLASTIC DEFORMATION

W.E. ALNASER and M. ZEIN

P h y s i c s D e p a r t m e n t U n i v e r s i t y of B a h r a i n , C o l l e g e o f A r t s , S c i e n c e and E d u c a t i o n , PO Box 1 0 8 2 , B a h r a i n

ABSTRACT

A qua1 i t a t i v e and q u a n t i f a t i v e i n v e s t i g a t i o n i n r e v e a l i n g t h e t y p e o f d i s l o c a - t i o n s (edge-screw) produced by compressional d e f o r m a t i o n i n pl y c r y s t a l l i n e aluminium i s presented. However, no e l e c t r o n microscope was u t i l iz e d t o r e v e a l such an e f f e c t . The t h e o r y o f Granato and Lucke was t h e master key f o r such a study. The e f f e c t o f small ( (3%) and l a r e d e f o r m a t i o n s (> 10%) on t h e maxima o f t h e d i s l o c a t i o n resonance s t r e n g t h max and i t s frequency fmax

3

a t temperatures 100,200 and 300K i s discussed. The e f f e c t o f t h e t e m p e r a t u r e on t h e d i s l o c a t i o n d e n s i t y , i.e. d e f o r m a t i o n , was s t u d i e d .

INTRODUCTION

I t i s b e l i e v e d t h a t t h e d i s l o c a t i o n resonance s t r e n g t h which occurs a t a f r e q u e n c y fmax i s equal t o /1/

w i t h

fmax = 0.113 C / L ~ B

. . .

⁽²⁾

Where n i s t h e o r i e n t a t i o n f a c t o r c o n s t a n t , G i s t h e shear modulus ( ~ m - ~ ) , b i s t h e b u r g e r s v e c t o r (m), A i s t h e d i s l o c a t i o n d e n s i t y (m?), L i s t h e l o o p l e n g t h o f d i s l o c a t i o n (m), C i s t h e l i n e t e n s i o n (N) and B i s t h e damping f o r c e c o e f f i c i e n t ( ~ s m - * ) .

It was n o t e d by Schmidt e t a1 /2/ t h a t %ax s h i f t s t o a h i g h e r v a l u e w i t h i n c r e a s i n g t e m p e r a t u r e ,T, which i s n o t expected s i n c e i t c o n t a i n s no dependence on B where t h e l a t t e r i s p r o p o r t i o n a l t o T ( B a T) /3/ and /4/. T h i s b e h a v i o u r o f %ax w i t h T was a t t r i b u t e d t o t h e dependence o f A on t h e tem-

p e r a t u r e /2/, i .e. h a x ^aA L~ assuming L i s f i x e d . The a u t h o r s d i d n o t i n v e s t i g a t e t h e e f f e c t of t h e t e m p e r a t u r e on t h e v a l u e o f t h e d i s l o c a t i o n den- s i t y , which i s a p i n t we a r e g o i n g t o i n v e s t i g a t e q u a l i t a t i v e l y .

The screw d i s l o c a t i o n s a r e known t o have a l i n e t e n s i o n many t i m e s h i g h e r t h a n edges i n copper /5/ and /6/. Since l e v e l s o f d e f o r m a t i o n a t room temperature a r e known t o produce d i f f e r e n t t y p e s o f d i s l o c a t i o n s , /8/, e.g. h i g h l e v e l s o f d e f o r m a t i o n i n t r o d u c e edge d i s l o c a t i o n s /9/ and l o w l e v e l s o f d e f o r m a t i o n i n t r o d u c e screw d i s l o c a t i o n s /7/ and /14/, t h e n t h e maximum decrement and f r e - quency a r e e x p e c t e d t o change remarkably as t h e d e f o r m a t i o n i s changed. T h i s

p o i n t i s t h e purpose o f o u r i n v e s t i g a t i o n i n t h e p r e s e n t work.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987808

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C8-84 JOURNAL DE

PHYSIQUE EXPERIMENTAL PROCEDURES

AND

RESULTS

One polycrystalline aluminium specimen of 5

N

purity was used in t h i s study.

This specimen was supplied by Metal Research Ltd. in the form of a cylinder which, a f t e r cutting and lapping, retained a length of lOmn and a diameter of 13mm. I t was deformed by compression in a Monstanto tensometer a t room tem- perature. The ultrasonic attenuation was measured d i r e c t l y a f t e r the defor- mation. The measurement technique was similar t o t h a t described by Zein 1161.

Temperature measurement was achieved by using two platinum sensors placed close t o the specimen and connected t o a Lakeshore d i g i t a l thermometer and control 1 er.

The ultrasonic attenuation f o r each deformation was measured a t temperatures of 121, 200 and 300K in the frequency range between 5 and 70 MHz, as shown i n figures 1 and

2.

DISCUSSION

The r e s u l t s show that the dislocation resonance strength &rnax, and i t s f r e - quency fmax, are affected by the deformation and the temperature T.

In f a c t , increasing the deformation will have three effects:

( 1 ) i t changes the loop length, (2) i t changes the dislocation density, (3) i t changes the type of dislocations existing in the specimen. This l a s t point i s important because the l i n e tension value will change in changing the defor- mation, i.e. from screws t o edge dislocations

/5/ and

161. The temperature variation changes the damping force c o e f f i c i e n t ,

6,

especially f o r T> 50

K

/3/

and 141. Also variation of

T

will r e s u l t in a change of

A

121. This point

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i s important in our study. I t was reported t h a t low levels of deformation a t room temperature introduce screw dislocations,

/7/, /8/

and 1141, and high l e v e l s of deformation a t room temperature introduce edge dislocations

/9/.

Therefore, t h e l i n e tension a t low deformation will be larger than t h a t a t high deformation. I t was found in copper t h a t the r a t i o of

CS/CE

i s almost 10

/5/

and /6/ (CS and

CE

are the 1 ine tensions f o r screw and edge dislocations respectively). I t i s necessary t o calculate the theoretical values of

CS

and

C E

f o r aluminium. Our calculations are based on the following equations /5/

where

b i s the burgers vector,

R

and r are the outer and the inner cut of radii f o r the dislocation s t r e s s f i e l d respectively.

K 1

and

Kg

were found t o be equal t o 3.2777 x 10 and 7.254 x

lo8 Nm-2 respectively. This gives a r a t i o (CS/CE)

of 5.1, which i s a factor of two l e s s than that in copper, which might be a t t r i b u t e d t o the d i f f e r e n t stacking f a u l t energy.

Let us now study the e f f e c t of

CS

and

CE

on the values of 6max and fmax.

Since &max i s proportional t o the inverse of

C

(equation 1 ) .

%ax

i s expected t o be smaller a t low deformations than a t higher ones, which has been observed in our r e s u l t s .

Meanwhile, fmax i s d i r e c t l y proportional t o

C

(equation 2) which leads t o the

conclusion that a t low deformations fmax should be higher than at high defor-

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mations, which does not agree w i t h our r e s u l t s . This disagreement can be explained as f o l l o w s :

A t low deformations, t h e l o o p l e n g t h s are l a r g e r than those a t h i g h deformations, b u t by what order depends on t h e way t h e d i s l o c a t i o n s a r e formed. We m i g h t have h i g h d i s l o c a t i o n d e n s i t y b u t a d i s l o c a t i o n l o o p l e n g t h not much smaller than t h a t a t low deformations. It a l l depends on whether t h e loops a r e tangled w i t h each other o r not. If we assume t h a t we are experiencing a simi 1 a r s i t u a t i o n t o t h a t mentioned above, then a t low deformation (screw d i s l o c a t i o n s

-

l a r g e value o f C) t h e value o f L w i l l oppose t h e e f f e c t o f C and t h e r e f o r e cause a s h i f t o f fmax t o t h e lower side. Meanwhile, a t high deformation (edge d i s l o c a t i o n s

-

small value o f C) t h e d i s l o c a t i o n resonance s t r e n g t h &max i s l i k e l y t o be a f f e c t e d by A more than L~ and obviously by t h e term C ( & m x a 1/C). The c a l c u l a t i o n s of CS/CE from our r e s u l t s a t 121K g i v e t h e value o f 3.2, which i s i n a f a i r agreement w i t h t h e t h e o r e t i c a l c a l c u l a t e d r a t i o . This p o i n t proves t h a t low l e v e l s o f deformation i n t r o d u c e screw d i s l o c a t i o n s . The value o f B i n our c a l c u l a t i o n s was taken t o be equal t o 4 x ~ s m - ~ obtained from Parameswaran e t a1 1121 f o r aluminium having t h e same p u r i t y as our specimen (5N). The previous authors measured B a t d i f - f e r e n t temperatures. The values o f L were taken t o be 5-10

v

m.

Our next s t e p was t o study t h e e f f e c t o f T on both finax and Gmax. fmax was a l r e a d y found t o decrease w i t h i n c r e a s i n g temperature T (since B a T

-

^see

references 131, 141 and 1121) 121 and 1151; t h i s observation i s i n agreement w i t h our r s u l t s .

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However &max contains no dependence on B; t h e r e f o r e t h e change o f m x w i t h T was a t t r i b u t e d t o a change i n A 121; (%ax a A (T)).

Our r e s u l t s show t h a t the v a r i a t i o n w i t h T a t t h e low deformation i s more pro- nounced than a t t h e h i g h deformation. This p o i n t leads us t o conclude t h a t i f t h e d i s l o c a t i o n d e n s i t y i s high, then t h e temperature has l e s s e f f e c t on A, and t h e opposite i s true. A p o i n t which was n o t discussed p r e v i o u s l y 121.

S t e r n and Granato

/ l o /

concluded t h a t t h e l i n e t e n s i o n f o r screw d i s l o c a t i o n s i n copper i s o n l y s l i g h t l y temperature dependent, b u t t h a t f o r edge d i s l o c a - t i o n s i t increases by 30% i n going from 300 t o 4K, a p o i n t which does n o t agree w i t h our r e s u l t s . We cannot c m e n t on t h i s p o i n t unless we know i f , i n aluminium, t h e s i t u a t i o n i s s i m i l a r t o t h a t i n copper; according t o the

knowledge o f t h e authors, t h e r e i s no a v a i l a b l e information.

The discrepancy a t low frequencies, f = 5 MHz, was a l s o observed elsewhere /11/ and was a t t r i b u t e d t o a second d i s l o c a t i o n resonance component.

Inconsistency i n our r e s u l t s can be a t t r i b u t e d t o t h e low value o f the a c t i v a - t i o n energy f o r m i g r a t i o n o f d e f e c t s i n t h i s metal 1131, which causes t h i s metal t o be s e n s i t i v e t o aging a t room temperature and handling. This w i l l r e s u l t i n inaccurate values o f t h e attenuation.

The c o n t r i b u t i o n o f t h e Bordoni r e l a x a t i o n t o t h e graph o f Log6 versus Logf, can be seen i n f i g u r e 2. I n t h i s f i g u r e , t h e curve r e p r e s e n t i n g measurements a t d i f f e r e n t temperatures i s not behaving s y s t e m t i c a l l y as i n f i g u r e 1. It can be seen t h a t the 200K curve l i e s above the 300k curve, u n l i k e f i g u r e 1.

This i s expected since t h e Bordoni peak occurs i n t h i s r e g i o n and may c o n t r i - bute s i g n i f i c a n t l y t o t h e damping f o r the higher deformation 1171.

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JOURNAL DE PHYSIQUE

Fig. 1: Decrement versus frequency f o r aluminium given a deformation o f 2% by compression a t room temperature.

10 -3 t

-

I 1 I 1 1 1 1 1 ' I Î Î Î Î ^{I I}^{1 1 3}

300k--a.

- -

-

f -

⁴^A

_._.-.-.-.-.

-

lo -4

- _-

- -

-

1 1 1 1 1 1 1 1 1 1 I I l l I I I I I

10 6 to' Hz

roe

Fig.2: Decrement versus frequency f o r aluminium g i v e n a deformation o f 32% by compression a t room temperature.

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REFERENCES

/1/ Granato, A. and Lucke, K., J. Appl. Phys. 27 (1956) 583.

/ 2 / Schmidt, H., Lenz, D. and Lucke, K., J o u r n a l de Phys. 42 (1981) C5-351.

/ 3 / B r a i l s f o r d , A.D., Proc. 5 ICIFUAS, v o l 11. (1975) 1.

/ 4 / H i k a t a , A., Johnson, R.A. and Elbaum, C., Phys. Rev. L e t t . 24 (1969) 215.

/ 5 / D e B a t i s t , R. I n t e r n a l F r i c t i o n o f S t r u c t u r a l D e f e c t s i n C r y s t a l l i n e Sol i d s , N o r t h - H o l l and Pub1 i s h i ng Company, Amsterdam. London. (1972).

/ 6 / ^par;, ^V.K. and Guberman, H.D., J. Appl. Phys. 44 (1973) 32-47.

/ 7 / Alnaser, W.E., Thesis, U n i v e r s i t y o f Kent a t Canterbury, (1986).

/ 8 / Ameen, D.L., Thesis, c o r n e l 1 U n i v e r s i t y (1952).

/ 9 / A b d e l g a d i r , M.A., Garcia, J.A. and Lomer, J., P h i l . Mag. A, 53 (1986) 751-764.

/ l o / Stern, R.M. and Granato, A.V., Acta Met. 10 (1962) 358.

/11/ Schmidt, H., Lenz, D., Drescher, E. and Lucke, K., J o u r n a l de Phy., 42 (1981) C5-339.

/12/ Parameswaran, V.R., Urabe, N. and Weertman, T.J. Appl. Phys. 43, (1972) 2982.

/13/ Granato, A., H i k a t a , A. and Lucke, K., Acta Met. 6 (1958) 470-480.

/14/ L o r e t t o , M.H. P r i v a t e Comnunication.

/15/ A l e r s , G.A. and Thompson, D.O., J. Appl. Phys. 32 (1961) 283.

/16/ Zein, M., Journal de Phys. 46 (1985) C10, 297-300.

/17/ Alnaser, W.E. and N i b l e t t , D.H., t o be p u b l i s h e d i n t h i s J o u r n a l ( 1 9 8 7 ) .