INTERNAL FRICTION IN MANGANESE-COPPER AND MANGANESE-COPPER-ALUMINIUM ALLOYS

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INTERNAL FRICTION IN MANGANESE-COPPER AND MANGANESE-COPPER-ALUMINIUM ALLOYS

T. Kê, L. Wang, H. Yi

To cite this version:

T. Kê, L. Wang, H. Yi. INTERNAL FRICTION IN MANGANESE-COPPER AND MANGANESE- COPPER-ALUMINIUM ALLOYS. Journal de Physique Colloques, 1987, 48 (C8), pp.C8-559-C8-565.

�10.1051/jphyscol:1987888�. �jpa-00227192�

J O U R N A L D E P H Y S I Q U E

C o l l o q u e C8, s u p p l 6 m e n t a u n012, Tome 48; d h c e m b r e 1 9 8 7

INTERNAL FRICTION IN MANGANESE-COPPER AND MANGANESE-COPPER-ALUMINIUM ALLOYS

A

T.S. K E , L.T. W A N G and H.C. YI

Institute of Solid State Physics, Academia Sinica, Hefei, China

A b s t r a c t : I n t e r n a l f r i c t i o n and e l a s t i c modulus of Mn-Cu a l l o y s containing 60 and 70 w t % Mn and of Mn-Cu-A1 a l l o y s c o n t a i n i n g about 40 w t % Cu, 1.92-3.59 w t % A 1 were measured with a c o u s t i c frequency i n t h e temperature range of -150 t o 150'C. The m a r t e n s i t i c transformation peak and t h e twin boundary r e l a x a t i o n peak which d i d n o t appear before ageing were observed above room temperature a f t e r a d e f i n i t e ageing time i n t h e temperature range under t h e s p i n o d a l curve within the m i s c i b i l i t y gap. It is shown t h a t t h e transformation peak proper i s o r i g i n a t e d from t h e s t r e s s - i n d u c e d movement of t h e i n t e r f a c e boundaries between t h e parent phase and t h e transformation product, and t h e i n t e r n a l f r i c t i o n background a t the low-temperature s i d e of t h e transformation peak which e x h i b i t s a very s t r o n g amplitude e f f e c t and shows a s t r o n g non-linear behaviour, is o r i g i n a t e d from the h y s t e r e t i c movement of t h e martensite-martensite i n t e r f a c e s .

It has a l s o been found t h a t t h e a d d i t i o n of aluminium enhances t h e s t r e n g t h but reduces t h e i n t e r n a l f r i c t i o n of t h e specimen. A choice of s u i t a b l e ageing time and temperature can give an optimum compromise of high s t r e n g t h and high i n t e r n a l f r i c t i o n .

I. I n t r o d u c t i o n

Previous experiments on t h e i n t e r n a l f r i c t i o n of Mn-Cu a l l o y s were mainly done f o r high Mn contents [I]. Two i n t e r n a l f r i c t i o n peaks were observed : a r e l a x a t i o n peak a t lower temperature and a transformation peak a t higher temperature. I n p r a c t i c e , t h e use of Mn-Cu a l l o y s a s high-damping m a t e r i a l s r e q u i r e s t h a t t h e Mn content should not be too high and i s u s u a l l y about 60 w t

%.

The c a s e o f c a s t Mn-Cu a l l o y s has been s t u d i e d i n our l a b o r a t o r y by Wen e t a l . [ 2 ] . The purpose of t h e p r e s e n t r e s e a r c h is t o study t h e damping mechanism of Mn-Cu and Mn-Cu-A1 a l l o y s of lower manganese content s u b j e c t e d t o d i f f e r e n t ageing treatments. Conditions f o r o b t a i n i n g high damping and high s t r e n g t h around room temperature a r e explored. I n t e r n a l f r i c t i o n and e l a s t i c modulus were measured with a c o u s t i c frequencies s o t h a t t h e system i s b a s i c a l l y i n an a d i a b a t i c s t a t e and the amount of transformation product remains constant during measurements.

11. P r e p a r a t i o n o f Specimens

I n g o t s o f t h e a l l o y s were supplied by Shanghai J i a o t o n g University. Sheet specimens of 80 x 4 x 2 mm were prepared by h o t r o l l i n g and spark c u t t i n g and were homogenized by annealing a t 850'C f o r 100 h and then water quenched. The compositions of t h e specimens a r e shown i n Table 1.

Table 1. Composition of t h e a l l o y specimens

Specimen No Mn Cu A 1 Others

Composition ( w t

J )

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987888

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111. Experiments w i t h Mn-Cu Alloys

1. Measurements of i n t e r n a l f r i c t i o n and e l a s t i c modulus

Acoustic measurements i n f l e x u r e v i b r a t i o n were taken with a frequency of about 340 Hz i n t h e temperature range of from -150 t o +150°C. The s t r a i n amplitude i s from 1 x t o 1 x

.

For t h e specimens i n homogenized condition, no transformation peak was observed i n t h e temperature range where t h e measurements were taken and t h e v a r i a t i o n of e l a s t i c modulus with temperature i s normal.

However, a s w i l l be reported i n SIV of t h i s paper, an ageing i n t h e temperature range under t h e spinodal curve w i t h i n t h e m i s c i b i l i t y gap w i l l s h i f t t h e phase transformation temperature M s t o higher temperatures. For specimen S1 (Mn 60/Cu 4 0 ) . 450'C i s i n t h e middle of t h i s temperature range. Therefore ageing a t 450'C i s s e l e c t e d f o r the following experiments. After S1 was aged a t 450'C f o r 30 min, an i n t e r n a l f r i c t i o n peak appeared around -18'C and an abnormal drop of t h e e l a s t i c modulus curve appeared around -10°C a s shown i n Fig. 1. ( a ) and (b) f o r the s t r a i n amplitude ranging from 1.4 t o 14 x 10-5. This i n t e r n a l f r i c t i o n peak i s e v i d e n t l y t h e m a r t e n s i t i c transformation peak. When amplitude e f f e c t is small, we may c o n s i d e r t h e temperature a t which t h e e l a s t i c modulus becomes minimum as t h e transformation temperature M s . Experiments showed t h a t t h e i n t e r n a l f r i c t i o n peak does n o t change with t h e frequency o f v i b r a t i o n and t h e r a t e of change of temperature of measurements, s o t h a t i t i s a s t a b l e peak. No amplitude e f f e c t was observed when t h e s t r a i n amplitude i s s m a l l e r than 1 x For l a r g e r amplitudes, t h e i n t e r n a l f r i c t i o n i n t h e temperature range TGds (-10'C) i n c r e a s e s approximately l i n e a r l y with t h e s t r a i n amplitude and can be expressed a s 8-'(T)=bQ-l -A, where A, i s t h e s t r a i n amplitude. The amplitude dependent c o e f f i c i e n t bQ-1 i n c r e a s e s with a decrease of temperature and approaches a s a t u r a t i o n v a l u e a t -100°C as shown i n Fig. 2 ( a ) . This s a t u r a t i o n temperature c o i n c i d e s with t h e temperature a t which t h e transformation peak drops t o i t s background value, i . e . when t h e transformation has been completed. Consequently, we conclude t h a t t h e amplitude e f f e c t begins with t h e appearance o f m a r t e n s i t e ( f c t phase) and reaches a maximum value when t h e parent phase ( f c c phase) has been transformed completely t o martensite. A s such, t h e amplitude e f f e c t e v i d e n t l y o r i g i n a t e s from a process t a k i n g p l a c e between t h e m a r t e n s i t e p l a t e s .

A s i s shown i n Fig. 1 ( b ) . t h e e l a s t i c modulus i n t h e temperature range T a s a l s o decreases approximately l i n e a r l y with t h e s t r a i n amplitude and can be expressed a s E(T) = b ,.A,. The amplitude dependent c o e f f i c e n t b, i n c r e a s e s with a decrease of temperature and approaches a s a t u r a t i o n v a l u e a t -100'C [Fig. 2 ( b ) ] . which i s s i m i l a r t o t h a t f o r b p - I .

I n o r d e r t o confirm t h e r e s u l t s shown i n Fig. 2 ( a ) and ( b ) , s i m i l a r a c o u s t i c measurements were taken with S1 (Mn 60/Cu 40) aged a t 430'C f o r 45 min.

The transformation p o i n t s h i f t s now t o M s = 25°C and t h e transformation peak appears a t Tp = -6'C. The b Q - i and b, curves behave s i m i l a r l y t o those shown i n Fig. 2 ( a ) and ( b ) , only t h e s a t u r a t i o n temperature i s somewhat higher but i s s t i l l c o i n c i d e n t with t h e temperature a t which t h e transformation peak drops t o i t s background value. This s t r e n g t h e n s t h e b e l i e f t h a t t h e amplitude e f f e c t of t h e i n t e r n a l f r i c t i o n and e l a s t i c modulus i s c l o s e l y connected with t h e product of m a r t e n s i t i c transformation.

When specimen S1 was aged a t 430'C f o r 1 h. M s s h i f t s t o 59°C [Fig.

3

( b ) ] and t h e transformation peak appears around 34'C [Fig.

3

( a ) ] . I n a d d i t i o n t o t h e transformation peak a new i n t e r n a l f r i c t i o n peak appears a t a lower temperature -16'C. Evidently t h e new peak is t h e r e l a x a t i o n peak a s s o c i a t e d with t h e twin boundaries e x i s t i n g i n t h e transformation product ( m a r t e n s i t e ) . The optimum temperature T,, f o r t h e r e l a x a t i o n peak i s seen t o be -16'C. t h i s i s the peak temperature corresponding t o a frequency of 340 Hz used f o r i n t e r n a l f r i c t i o n measurements.

It can be seen from Fig. 3 ( a ) and ( b ) t h a t i r r e s p e c t i v e of t h e appearance of t h e r e l a x a t i o n peak P

,

^{which i s} u s u a l l y amplitude independent, t h e amplitude dependent behavior of t h e transformation peak P and t h e corresponding e l a s t i c modulus curve i s s i m i l a r t o those shown i n Fig. 1 ( a , b ) .

S i m i l a r experiments have a l s o been done f o r specimen So (Mn 7O/Cu 30). The M s and TP, a f t e r t h e specimen was aged a t 450'C f o r v a r i o u s t i m e s a r e r e s p e c t i v e l y - 1 0 8 ' ~ . -1204C(P2) f o r 15 min ageing, -12'C. -20eC(P2) f o r 30 min ageing, and 59'C, - 1 6 ' c ( ~ 34'C(P2) f o r 45 min ageing. The amplitude dependent behavior of P2 and t h e corresponding e l a s t i c modulus curve is s i m i l a r t o t h e c a s e of S1 (Mn 60/Cu 40) specimen.

Fig. 1 F i g . 2

Fig. 1. V a r i a t i o n of i n t e r n a l f r i c t i o n ( a ) and e l a s t i c modulus ( b ) with temperature of S1 (Mn 60/Cu 40) aged a t 4 5 0 " ~ f o r 30 min and t h e amplitude e f f e c t . Curves 1-6 correspond t o s t r a i n amplitude 14, 8.4, 5.6, 4.2, 2.8, and 1.4 x 10-5.

Frequency = 340 Hz measurements taken i n ascending temperatures stepwise ( T = 0 ) . F i g . 2. V a r i a t i o n of t h e amplitude dependent c o e f f i c i e n t bq-1 f o r i n t e r n a l f r i c t i o n ( a ) and b, f o r e l a s t i c modulus ( b ) with temperature. The arrows i n t h e f i g u r e s i n d i c a t e t h e temperature a t which t h e i n t e n s i t y of amplitude e f f e c t reaches i t s s a t u r a t i o n value.

2. Non-linear d i s t o r t i o n of t h e resonance curve i n f l e x u r e v i b r a t i o n Simultaneously with t h e occurrence of amplitude dependent e f f e c t i n i n t e r n a l f r i c t i o n and e l a s t i c modulus, t h e frequency response curve ( t h e resonance curve) i n f l e x u r e v i b r a t i o n e x h i b i t s an unsymmetrical d i s t o r t i o n a s shown i n Fig. 4. For S1 (Mn 60/Cu 40) aged a t 450'C f o r 30 min. M s = -10'C. the unsymmetrical d i s t o r t i o n o f t h e resonance curve (with frequency of v i b r a t i o n about I kHz) s t a r t s a t temperatures TGls. The t o p of t h e peak l e a n s toward t h e lower frequency s i d e and t h i s behavior i s enhanced with t h e lowering of the temperature of measurement. The v i b r a t i o n becomes u n s t a b l e a t -50, -70 and -89'C a s shown i n F i e .

-

4.

3.

On t h e mechanism of t h e transformation peak proper and t h e low temperature i n t e r n a l f r i c t i o n background

A glance on t h e i n t e r n a l f r i c t i o n curves shown i n F i a . 1 ( a ) r e v e a l s t h a t

-

^{. .}

t h e transformation peak can be resolved i n t o two components : t h e transformation peak proper and t h e low-temperature background. The l a t t e r e x h i b i t s a s t r o n g amplitude e f f e c t and g i v e s rise t o an apparent s h i f t of t h e top of t h e peak toward lower temperatures with an i n c r e a s e of s t r a i n amplitude. I n t h e e a r l y s t a g e of the m a r t e n s i t i c transformation, t h e amount of t h e i n t e r f a c e between t h e p a r e n t phase P ( f c c ) and t h e m a r t e n s i t e M(fct) i n c r e a s e s when t h e temperature i s lowered, s o t h a t t h e i n t e r n a l f r i c t i o n i n c r e a s e s with a lowering of temperature. However, a s the transformation proceeds f u r t h e r , t h e i n c r e a s e of t h e amount of m a r t e n s i t e and the mutual c o n t a c t between t h e m a r t e n s i t e p l a t e s w i l l reduce t h e amount and the mobility of t h e P-M i n t e r f a c e . Consequently t h e i n t e r n a l f r i c t i o n w i l l decrease

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with a f u r t h e r lowering of temperature, g i v i n g r i s e t o an i n t e r n a l f r i c t i o n peak ( t h e transformation peak). A t t h e same time, t h e mutual c o n t a c t of t h e martensite p l a t e s i n c r e a s e s t h e amount of t h e m a r t e n s i t e - m a r t e n s i t e (M-M) i n t e r f a c e . The h y s t e r e t i c movement of t h e M-M i n t e r f a c e s g i v e s rise t o t h e low temperature i n t e r n a l f r i c t i o n background which i s s t r o n g l y amplitude dependent. The amplitude e f f e c t becomes s t r o n g e r with an i n c r e a s e of t h e q u a n t i t y of M-M i n t e r f a c e s .

The s o f t e n i n g of t h e e l a s t i c modulus and non-linear behavior of resonance curve i n f l e x u r e v i b r a t i o n corresponding t o t h e low temperature i n t e r n a l f r i c t i o n background may be a t t r i b u t e d t o t h e non-linear e l a s t i c s t r a i n caused by t h e s t r e s s - a s s i s t e d h y s t e r e t i c movement.

F i g . 3 Fig. 4

Fig. 3. V a r i a t i o n of i n t e r n a l f r i c t i o n ( a ) and e l a s t i c modulus ( b ) with temperature of S1 (Mn 60/Cu 40) aged a t 450'C f o r 1 h and t h e amplitude e f f e c t . Curves 1-4 correspond t o s t r a i n amplitude 8.4, 5.6, 2.8, and 1.4 x 10-5. Frequency = 340 Hz, T = 0.

Fig. 4. The unsymmetrical d i s t o r t i o n of t h e resonance curve a t various temperatures f o r specimen S1 (Mn 60/Cu 40) aged a t 450'C f o r 30 min. Frequency : 1 kHz. = 14 ^X

I V . Experiments w i t h W-Cu-A1 Alloys

1. V a r i a t i o n o f i n t e r n a l f r i c t i o n and e l a s t i c modulus by ageing a t various temperatures

(1) Ageing a t 4 5 0 ' ~ .

According t o t h e phase-diagram of Mn-Cu a l l o y s shown i n Fig. 5 [3], t h e metastable Y-phase formed by quenching t h e high temperature Y-phase t o room temperature has t h e tendency of transforming t o t h e s t a b l e a + Y a t room temperature, and t h i s process can be sped up by ageing i n t h e temperature range under t h e spinodal curve w i t h i n t h e m i s c i b i l i t y gap. For Mn 7O/Cu 30 a l l o y , B u t l e r e t a l . 141 showed t h a t t h i s temperature range i s around 400-500'C. Vitek e t a l . found t h a t t h e hardness i n c r e a s e s by ageing a t 450°C. The purpose of t h e following r e s e a r c h i s t o study t h e changes i n i n t e r n a l f r i c t i o n and some mechanical p r o p e r t i e s of homogenized low manganese c o n t e n t Mn-Cu-A1 a l l o y s aged a t d i f f e r e n t temperatures f o r v a r i o u s times t o f i n d o u t an optimum compromise of high s t r e n g t h and high i n t e r n a l f r i c t i o n and t o understand t h e micro-mechanism underlying t h e s e changes.

Specimen S2 (Mn 59.35/Cu 38.73/Al 1.92) was aged a t 450°C f o r 0.5, 1, 2 , 4, and 9 h, and water quenched t o room temperature. and t h e i n t e r n a l f r i c t i o n and e l a s t i c modulus were measured with f = I H z , A

,

^{= 5.2 x} with ascending temperatures (T = l0C/min). Two i n t e r n a l f r i c t i o n peaks appear a s shown i n Fig. 6.

The portion of t h e lower temperature peak around 15°C i s independent of the ageing time and i s e v i d e n t l y t h e r e l a x a t i o n peak connected with twin boundaries. The p o s i t i o n of t h e higher temperature peak, t h e transformation peak, s h i f t s t o higher temperature with an i n c r e a s e of ageing time although t h e s h i f t i s not evident when t h e ageing time i s l a r g e r than 4 h . It can be seen from the e l a s t i c modulus curves 1-5 t h a t t h e M s p o i n t ( c h a r a c t e r i z e d by the lowest p o i n t on t h e molulus curve) s h i f t s t o high temperatures with an i n c r e a s e of ageing time. The height of the transformation peak reaches its maximum value f o r an ageing of 1 h but drops r a p i d l y a f t e r an ageing of 4 h.

F i g . 5 F i g . 6

Fig.

5.

Phase diagram of Mn-Cu a l l o y and t h e a s s o c i a t e d m i s c i b i l i t y gapC31.

F i g . 6. I n t e r n a l f r i c t i o n and e l a s t i c modulus of specimen S2 (Mn 59.35/

Cu 38.73/Al 1.92) aged a t 450°C f o r various times. Curves 1-5 correspond t o ageing time o f 0.5, 1, 2 ,

4,

and 9 h. f = 1 kHz, A, = 5.2 x T = leC/min with ascending temperatures.

Experiments with specimen S3 (Mn 58.16/Cu 39.13/Al 2.71) and S4 (Mn 56.161 Cu 40.25/A1 3.59) g i v e s i m i l a r r e s u l t s a s t h e s e of S2. only t h e h i g h t of the corresponding transformation peaks i s much lower than those of S2, i n d i c a t i n g t h a t a higher aluminium content has t h e e f f e c t of reducing t h e i n t e r n a l f r i c t i o n . The r e s u l t s f o r specimen 54 a r e shown i n Fig. 7. Comparing t h e r e s u l t s f o r S2 and S4, i t i s seen t h a t doubling t h e aluminium content reduced t h e h e i g h t of t h e i n t e r n a l f r i c t i o n peak almost t o one h a l f .

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Fig. 7. I n t e r n a l f r i c t i o n and e l a s t i c modulus of specimen S4 (Mn 56.16/

Cu 4 0 . 2 5 / ~ 1 3.59) aged a t 450'C f o r various times. Curves 1-5 correspond t o ageing time of 0.5, 1, 2 , 4, and 9 h. f = 1 kHz, A, =

5.2

^x T = l'C/min with ascending temperatures.

( 2 ) Ageing a t 400" and 500'C.

Ageing experiments a t 400" and 500°C ( r e s p e c t i v e l y a t t h e lower bound and t h e upper bound of t h e m i s c i b i l i t y gap) show a s i m i l a r tendency of t h e change i n i n t e r n a l f r i c t i o n and e l a s t i c modulus. However, t h e r a t e of t h e s h i f t of Ms with ageing time i s q u i t e d i f f e r e n t when aged a t d i f f e r e n t temperatures. And the ageing time a t which t h e transformation peak reaches its maximum value is d i f f e r e n t f o r d i f f e r e n t ageing temperatures. The ageing times required a r e 4. 1 and 0.5 h r e s p e c t i v e l y f o r ageing a t 400". 450' and 500°C.

It can be concluded thus t h a t a s i m i l a r change has taken place i n the specimens aged i n 400"-500°C. This change i s t h e spinodal decompostion, only t h a t t h e r a t e of decomposition is d i f f e r e n t f o r d i f f e r e n t ageing temperatures.

( 3 ) Ageing a t 300" and 60oeC.

The temperatures 300' and 600'C l i e both o u t s i d e t h e m i s c i b i l i t y gap f o r t h e Mn content of specimens S1. S2. S3 and S4. Ageing experiments have been done f o r specimen S4 aged a t 300' and 600'C f o r 0.5 and 2 h. t h e i n t e r n a l f r i c t i o n was found t o be very low and no i n t e r n a l f r i c t i o n peak appears i n the temperature range of -150' t o 150QC. The e l a s t i c modulus curve i s normal and no phase transformation occurs a t a l l . This shows d e f i n i t e l y t h a t t h e phase transformation and t h e high i n t e r n a l f r i c t i o n observed i n ageing experiments f o r 400"-500°C a r e a l l o r i g i n a t e d from spinodal decomposition. -

2. Results bf mechanical t e s t i n

I n Fig. 8 a r e shown t h e Rock:ell hardness ( H R B ) ( a ) , o,,

,

^{( b ) .}

^q

( c ) , and 6 ( d ) f o r specimen S1 (Mn 6O/Cu 4 0 ) , S2 (Mn 59.35/Cu 3 8 . 7 3 / ~ 1 1.92). S3 (Mn 58.16/

CU 39.13/A1 2.71). S4 (Mn 56.16/Cu 4 0 . 2 5 / ~ 1 _~. 3.59) aged a t 450°C f o r d i f f e r e n t times. It can be seen t h a t the H,,

,

ao,, and ab a l l i n c r e a s e with ageing time and t h e r a t e of i n c r e a s e becomes lower a f t e r an ageing f o r 4 h. I t can a l s o be seen t h a t S4, which has t h e l a r g e s t aluminium content, e x h i b i t s a l a r g e r i n c r e a s e i n hardness and s t r e n g t h .

Fig. 8. Variation of % , ( a ) , u o . * ( b ) , u b ( c ) and 6 ( d ) of various specimens aged a t 450'C f o r various times. Curves 1.2.3.4, correspond t o Sl,S2,S3 and S4.

The elongation 6 of t h e specimen drops with an increase of ageing time. The r a t e of drop is a l s o slowed down a f t e r an ageing of 4 h. Furthermore, the presence of aluminium has the e f f e c t of reducing t h e elongation 6 of the specimen.

V. Concluding Remarks

Although the Mn content i n the homogenized specimens used i n the present experiment i s only about 60 w t f , but because of micro-inhomogeneity produced by spinodal decomposition during ageing the localized content of Mn can be much higher than 60 w t %, s o t h a t martensitic transformation f c d c t can take place similar t o t h e case of specimens with high Mn content.

Figs. 6 and 7 show t h a t f o r the specimens aged i n the spinodal curve within the m i s c i b i l i t y gap (see Fig.

5).

the i n t e r n a l f r i c t i o n f i r s t increases and reaches its maximum value f o r a c e r t a i n ageing t i m e and then decreases when aged f o r a longer time. The increase i s due t o the increase of the amount of martensite phase due t o spinodal decompobition. and we believe t h a t the decrease is due t o the occurrence of t h e s t a b l e a-Eln phase. A t higher ageing temperatures, the formation of Mn-rich regions i s f a s t e r s o t h a t the i n t e r n a l f r i c t i o n reaches its maximum value a t a s h o r t e r ageing time. However, the occurrence of or-Mn i s a l s o f a s t e r , so t h a t t h e i n t e r n a l f r i c t i o n starts t o decrease a t a s h o r t e r ageing time. The magnitude of t h e i n t e r n a l f r i c t i o n is thus determined by the competition between t h e amount of the transformation product ( f c t martensite) and the amount of the s t a b l e u-Mn.

The increase of the hardness and strength of the specimen is evidently due t o the l a t t i c e d i s t o r t i o n produced by t h e f c t transformation product and the cause of b r i t t l e n e s s is due t o the occurrence of the or-Mn.

An optimum compromise of high i n t e r n a l f r i c t i o n and high strength can be obtained by ageing the specimens a t 450°C f o r 2-3 h.

References [I] K. Sugimoto, T. Mori, and S. Shiode, Met. Soc. J., 1, 103, (1973)

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[2] Y.T. Wen. C.Y. Xie, and H. Chen. J. de Physique, 46, C10-413. (1985)

.

[3]

J . M . Vitek and H. Warlimont. Met. Sci.. No. 1.7, (1976).

[4] E.P. Butler and P.M. Kelly. Trans. Met. Soc., AIME 242, 2099. (1968)