ULTRASONIC ATTENUATION IN STEELS DURING FATIGUE

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ULTRASONIC ATTENUATION IN STEELS DURING FATIGUE

Pan Zhengliang, Li Guangyi

To cite this version:

Pan Zhengliang, Li Guangyi. ULTRASONIC ATTENUATION IN STEELS DURING FATIGUE.

Journal de Physique Colloques, 1985, 46 (C10), pp.C10-329-C10-332. �10.1051/jphyscol:19851073�.

�jpa-00225458�

JOURNAL DE PHYSIQUE

Colloque C10, supplkment au n012, Tome 46, dkcembre 1985 page C10-329

ULTRASONIC ATTENUATION I N STEELS DURING FATIGUE PAN ZHENGLIANG AND LI GUANGYI

Institute of Metal Research, Academia Sinica, Wenhua Road 2-6, Shenyang, China

Abstract

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The change of ultrasonic attenuation Aa as a function of fatigue cycle number n correlates well with the length of fatigue crack. A depinning model of dislocations with kinks is suggested to interpret the experimental results.

I

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INTRODUCTION

In the Ithaca Conference (1961), Hikata et al. /1/ reported that the ultrasonic wave can "see" the motion of dislocations. Sachs and Green /2/ have also researched the orientation dependence of dislocation damping. Some of the early work in this field was summarized by True11 et al. /3/. In the last ten years increasing attention was paid to the effect of a bias stress on the ultrasonic attenuation in metal single crystals /4-7/. It was seen that /6/ the first motion of dislocation is controlled by the existence of the lattice friction stress (Peierls-Nabarro stress). According to a mechanism of interaction between dislocation and point defects some typical shapes of Aa-a curve have been explained and the connection with the low frequency internal friction spectrum has been established /7/. Otherwise Wang et al. /8/ have found that the interaction between ultrasonic shear wave and moving dislocation can give rise to second and third order harmonic waves.

I1

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EXPERIMENTAL PROCEDURE

The composition of the steels used in the present work is given in Table 1. After heat treatment the start materials were carefully ground to standard compactible

Table 1 Composition (wt.%) of Steels

No Steel C Cr Mn Si Ni P S 0

I1 9%Ni Steel 0.06 0.19 0.20 9.1 <0.006 <0.006 <0.0037 tension test sample agreed with ASTM E399-74 and the grinding tolerance is more than 0.5 mm. The thickness of the sample is 20 mm and the pa allelism and planeness of the two opposite planes are approximately equal to 1x10-

Z .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851073

C10-330 JOURNAL DE PHYSIQUE

The measurements of u l t r a s o n i c a t t e n u a t i o n were c a r r i e d o u t u s i n g t h e p u l s e echo method d e s c r i b e d elsewhere / 9 / . We r e c o r d t h e change o f a t t e n u a t i o n by means o f a

X-Y r e c o r d e r w i t h an accuracy o f 0.003 dB/ps. An X-cut q u a r t z t r a n s d u c e r w i t h fundamental frequency 10 MHz and d i a m e t e r 10 mm was c a r e f u l l y c o u p l e d on one sample p l a n e i n c o n t a c t w i t h t h e c r a c k t i p . On t h e o p p o s i t e p l a n e o f t h e sample t h e c r a c k l e n g t h was measured by means of a microscope. The f r e q u e n c y o f f a t i g u e was 95 and 150 Hz f o r s t e e l I and 11, b u t t h e frequency o f 0.02 Hz was u t i l i z e d t o measure a t t e n u a t i o n as a f u n c t i o n o f l o a d P d u r i n g c y c l e d e f o r m a t i o n . The upper and

l o w e r l i m i t s o f f a t i g u e l o a d were chosen as 12 kN and 4 kN f o r s t e e l I, and 20 kN and 4 kN f o r s t e e l I 1 w i t h an accu acy of 0.1 kN. A f t e r a c e r t a i n number o f f a t i g u e c y c l e s ( 2 x 1 0 ~ f o r s t e e l I and 5x10 f o r s t e e l 11), t h e a-P were measured and t h e

5

l e n g t h o f f a t i g u e c r a c k was observed under average s t a t i c l o a d .

I 1 1

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EXPERIMENTAL RESULTS

The a-P curves f o r d i f f e r e n t c y c l e number n a r e shown i n F i g . 1, i n which t h e c u r v e s d u r i n g l o a d i n g and u n l o a d i n g a r e c o i n c i d e n t w i t h each o t h e r . The change o f

a t t e n u a t i o n Aa d u r i n g a c y c l e f r o m F i g . 1 and t h e c r a c k l e n g t h a as a f u n c t i o n of c y c l e number n i s shown i n F i g . 2. It i s c l e a r t h a t t h e Aa n c u r v e i s i n good c o r r e l a t i o n w i t h t h e a-n curve, and t h e v a r i a t i o n o f Aa i s t r a c e d o u t d u r i n g t h e p e r i o d o f c r a c k n u c l e a t i o n . A s i m i l a r r e s u l t was o b t a i n e d f o r s t e e l 11.

The a-P curves o f s t e e l I , shown i n Fig. 3, i n t h e range o f 0-12 kN have been measured f o r d i f f e r e n t d i s t a n c e d between t h e d i s k o f q u a r t z and t h e t i p o f c r a c k , when t h e f a t i g u e c r a c k had developed t o t h e l e n g t h 14 mm. It i s apparent t h a t t h e

a t t e n u a t i o n decreases i n t h e b e g i n n i n g p e r i o d o f l o a d i n g and t h e n d r a s t i c a l l y i n c r e a s e s d u r i n g l o a d i n g o v e r a c r i t i c a l l o a d PC and s i m i l a r ( b u t l e s s ) v a r i e d d u r i n g t h e subsequent unloading. So a h y s t e r e s i s l o o p c u r v e o f a t t e n u a t i o n i s c r e a t e d i n t h e r e g i o n o f s m a l l e r load. The c r i t i c a l l o a d PC i s a p p r o x i m a t e l y equal t o 2, 4 and 6 kN f o r d=O, 0.8 and 4 mm r e s p e c t i v e l y . The t o t a l change o f

a t t e n u a t i o n decreases w i t h i n c r e a s i n g d i s t a n c e d. The same h y s t e r e s i s l o o p c u r v e s a r e a l s o o b t a i n e d d u r i n g t h e c y c l e d e f o r m a t i o n w i t h s m a l l e r l o a d a m p l i t u d e , such as 0-4 kN.

The s t e e l s I and I 1 a r e r e s p e c t i v e l y h i g h and m i d d l e s t r e n g t h s t e e l . S i m i l a r f e a t u r e s o f a-P c u r v e s f o r b o t h s t e e l s were o b t a i n e d . as i n Fig. 4, ' b u t t h e a t t e n u a t i o n o f s t e e l I 1 v a r i e d more smoothly d u r i n g l o a d i n g o r unloading.

I V

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DISCUSSION

A mechanism of d i s l o c a t i o n breakaway /5/ has been used t o i n t e r p r e t t h e u l t r a s o n i c a t t e n u a t i o n o f d i l u t e A1 a l l o y and p u r e A1 d u r i n g b i a s s t r e s s experiment. R e c e n t l y a model o f g e o m e t r i c k i n k c h a i n /10/ has been c o n s i d e r e d t o c a l c u l a t e t h e

a t t e n u a t i o n as a f u n c t i o n o f b i a s s t r e s s . We suggest a c o m b i n a t i o n o f t h e t w o models, sketched i n Fig. 5. The d e n s i t y o f d i s l o c a t i o n s , and a l s o t h e d e n s i t y o f g e o m e t r i c k i n k s , i s v e r y h i g h i n t e m p e r i n g s t e e l s . The s i d e w i s e m i g r a t i o n o f t h e g e o m e t r i c k i n k s f e a s i b l y t a k e s p l a c e under a s m a l l a p p l i e d b i a s s t r e s s and t h e d i s l o c a t i o n l o o p s between p i n n i n g p o i n t s can be bowed o u t , as i n F i g . 5h, so t h a t t h e l e n g t h o f d i s l o c a t i o n segments v i b r a t i n g under t h e s t r e s s o f t h e u l t r a s o n i c wave i s decreased, i .e. L c ( o ) < LclO). As i s w e l l known / 3 / , t h e u l t r a s o n i c a t t e n u a t i o n due t o d i s l o c a t i o n s i s a AL

.

It i s e x p l a i n e d t h a t t h e a t t e n u a t i o n decreases w i t h i n c r e a s i n g b i a s s t r e s s i n t h e b e g i n n i n g p e r i o d o f l o a d i n g . When t h e a p p l i e d b i a s s t r e s s i s o v e r t h e c r i t i c a l v a l u e , t h e d i s l o c a t i o n may break away f r o m p i n n i n g p o i n t s , t h e n l e n g t h LC c a t a s t r o p h i c a l l y becomes t h e f u l l network l o o p l e n g t h Ln, and t h e a t t e n u a t i o n d r a s t i c a l l y i n c r e a s e s w i t h i n c r e a s i n g b i a s s t r e s s . The o p p o s i t e process w i l l t a k e p l a c e d u r i n g unloading, b u t near t h e c r i t i c a l s t r e s s t h e

d i s l o c a t i o n w i l l n o t a g a i n be pinned, u n t i l d i s l o c a t i o n l o o p s move back near t h e i r e q u i l i b r i u m p o s i t i o n , i.e. t h e l e n g t h o f d i s l o c a t i o n l o o p s i s a p p r o x i m a t e l y equal t o t h e o r i g i n a l l e n g t h L c ( 0 ) . 'Hence t h e change o f a t t e n u a t i o n i s a l s o s m a l l e r d u r i n g u n l o a d i n g and a h y s t e r e s i s l o o p o f a t t e n u a t i o n can be o b t a i n e d i n t h e r e g i o n near t h e c r i t i c a l l o a d d u r i n g c y c l e deformation.

The c r i t i c a l l o a d should correspond t o t h e s t r e s s under which a p a r t o f t h e d i s l o c a t i o n breaks away from t h e p i n n i n g p o i n t s under u l t r a s o n i c stress. As an examination o f t h i s model t h e d i s t r i b u t i o n o f s t r e s s near t h e q u a r t s /11/ was

c a l c u l a t e d acc r d i n g t o f r a c t u r e mechanics. It was found t h a t i n about 5% f q u a r t z area a > 10'' Y , P b e i n g shear modulus, when P=Pc i n Figs. 3 and 4. ''01 u was generaYYy r e f e r r e d as t h e breakaway s t r e s s o f d i s l o c a t i o n s /12/. The 5% area i s l a r g e enough t o i n c r e a s e t h e t o t a l a t t e n u a t i o n . The c r i t i c a l l o a d i n a-P curves i s probably a u s e f u l parameter f o r i n v e s t i g a t i n g t h e behavior o f d i s l o c a t i o n s d u r i n g fatigue.

The e f f e c t o f s t r e s s c o n c e n t r a t i o n around t h e c r a c k t i p on a t t e n u a t i o n c a n b e used t o e x p l a i n t h e r e s u l t of F i g . 2

.

The i n c r e a s e of t h e l e n g t h o f c r a c k d u r i n g f a - t i g u e i s accompanied by t h e e x t e n s i o n o f ' a r e a i n which t h e breakaway s t r e s s o f d i s - l o c a t i o n i s a c h i e v e d , s o t h a t t h e Aa-n c u r v e c a n b e a n a l o g o u s t o t h e a-n c u r v e .

REFERENCES

H i k a t a , A., Chick, B . , Elbaum, C. and T r u e l l , R . , Acta M e t a l l . , =(1962), 423.

S a c h e s , W. and Green J r , R.E., T r a n s . TMS-AINE, %(1968), 2185.

T r u e l l , R . , Elbaum, C. and Chick, B., U l t r a s o n i c Methods i n S o l i d s S t a t e P h y s i c s , Academic P r e s s , New York, ( 1 9 6 9 ) .

V i n c e n t , A. and P e r e z , J . , I L Nuovo Cimento, =(I9761

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1 4 7 . V i n c e n t , A. and P e r e z , J . , P h i l . Mag., %(1979), 277.

D e t e r r e , P h . , Esnouf. C., F a n t o z z i , G . , P e g u i n , P . , P e r e z , J . , R i t c h i e , I . , Vanoni, F. and V i n c e n t , A., A c t a M e t a l l . , 1 ( 1 9 7 9 ) , 1779.

Gremaud, G. and B e n o i t , W . , J . d e P h y s i q u e , c ( 1 9 8 1 ) , C5-163 and ~ 5 - 3 6 9 . Wang

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Y.T., B r i t t o n , W. G.B. and S t e p h e n s , R.W.B., J . d e P h y s i q u e , 42 ( 1 9 8 1 ) , C5-387.

- Pan Z h e n g l i a n g and Su Huihe, A c t a A c u s t i c a ( S i n i c a ) , 5 ( 1 9 7 9 ) , 1 8 8 . B u j a r d , M. and Gremaud, G . , J . d e P h y s i q u e , *(1983), C9-673.

Pan Zliengliang, Wang Shuangguan and L i Guanyi, A c t a P h y s i c a S i n i c a =(1985), 1 3 4 .

H i r t h , J . P . and L o t h e , J . , Theory of D i s l o c a t i o n s , 2nd Ed., John Wilay & Sons, New York, 1982, p.674.

~ i g . I u l t r a s o n i c a t t e n u a t i o n

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a s a f u n c t i o n of l o a d V) d u r i n g a c y c l e deforma-

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number o f f a t i g u e cy-

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d i n g o f F i g . 2

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( 3 0 - 3 3 2 JOURNAL DE PHYSIQUE

0.08 Fig.2 The l e n g t h of f a - t i g u e c r a c k a and t h e change of u l - 0.06 Cn

2

t r a s o n i c a t t e n u a -

\ t i o n Aa a s a f u n c -

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t i o n of c y c l e num-

U b e r f o r s t e e l I 0.04

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u

Q 0.02

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0 2 4 6 8 10

n x ^10-5

F i g . 3 a-p c u r v e s f o r d i f f e r e n t d i s t a n c e d Fig.4 Comparison of a-p c u r v e s between t h e c i r c l e of q u a r t z and t h e between s t e e l I and I1 t i p of c r a c k f o r s t e e l I

up r i g h t f i g u r e i n d i c a t e d t h e s h a p e of sample,

o i n d i c a t e d q u a r t z .

A model of d i s l o c a t i o n b r e a k away

a ) I n i t i a l c o n f i g u r a t i o n b) d i s l o c a t i o n bowing o u t and

s i d e w i s e m i g r a t i o n of g e o m e t r i c k i n k s c ) d i s l o c a t i o n b r e a k away