Stress relaxation in titanium

Stress relaxation in titanium

Scripta ~'4ETALLURG]CA Vol. 8, pp. 739-742, 1974 P r i n t e d in the U n i t e d States STRESS RELAXATION F. V. Ellis Department Press, Pergam...

172KB Sizes 1 Downloads 65 Views

Scripta ~'4ETALLURG]CA

Vol. 8, pp. 739-742, 1974 P r i n t e d in the U n i t e d States

STRESS

RELAXATION

F. V. Ellis

Department

Press,

Pergamon

Inc.

IN T I T A N I U M

and C h e - Y u

Li

of M a t e r i a l s Science and E n g i n e e r i n g Cornell University Ithaca, New York 14850

(Received M a r c h

22,

1974)

Introduction Stress

relaxation

i n v e s t i g a t o r s I-3 the

theories

of d i s l o c a t i o n

recently

also

equation

of state 4.

a limited some

concept

to o b t a i n

time

dynamics.

data

stress

The p u r p o s e

relaxation

equation

relaxation

data

Discussion to show

by several

report

on

are used

of p l a s t i c

on t i t a n i u m

will

that

based

experiments

the c o n c e p t

of the p r e s e n t

and

reported

are d i s c u s s e d

relaxation

to support

data.

of state

have been

investigations

Stress

experimental

time.

stress

of p l a s t i c

the p r e v i o u s

on t i t a n i u m

of these

The e x i s t i n g

relaxation

longer

experiments

The results

cover

only

is to p r e s e n t

be made

using

the c o n c l u s i o n s

the

made by

i n v e s t i g a t o r s 2-3 may be questioned.

Experiments Room

temperature

stress

relaxation

experiments

are p e r f o r m e d

in the p r e s e n t

work.

The principle, p r o c e d u r e , and e q u i p m e n t of the e x p e r i m e n t have been 4 d e s c r i b e d p r e v i o u s l y . C o m m e r c i a l p u r i t y t i t a n i u m of a p p r o x i m a t e l y 99.7%

purity

is used.

annealed

two inches at 0.02 stress

Titanium

in v a c u u m

and a grain

in/min,

rods

for an hour

stress

stress given

load-time

particular single level

stress

specimen after

another

data

shown

strain

rate

4.

from each

strain

The

and

length

of

specimen

is p r e - s t r a i n e d

level

to each

strain)

prior

relaxation

a stress

run.

relaxation

shown each

Data

run.

Data

from runs

curves

stress 5-6

of p l a s t i c

hardness

739

from a

from one

(or p l a s t i c

are o b t a i n e d

equation

strain)

from

of state 4

log s t r e s s - l o g

should b e l o n g

to log

the a p p r o a c h the data

1-4 are o b t a i n e d

to a h i g h e r

to the c o n c e p t

These

1 using

represents

from runs

constant

run are c o n v e r t e d

in Fig.

curve

the s p e c i m e n

1 represent

relationships.

stress

figure

relaxation

According

in Fig.

and D i s c u s s i o n

rate plots

In this

by r e l o a d i n g

specimen.

curves

50~.

diameter

has a gage

run.

- log p l a s t i c in r e f e r e n c e

to 0.125"

specimen

(or p l a s t i c

Results The

swaged

The

size of a p p r o x i m a t e l y

to a d e s i r e d

relaxation

are arc cast, at 500°C.

plastic

to a p a r a m e t e r

family

740

STRESS R E L A X A T I O N

IN T I T A N I U M

Vol.

8, No.

of curves w i t h the a r b i t r a r y p a r a m e t e r b e i n g the h a r d n e s s p a r a m e t e r if a p l a s t i c e q u a t i o n of state exists.

A simple way to test the one p a r a m e t e r

family of curves is the p o s s i b i l i t y that these curves can be t r a n s l a t e d along a s t r a i g h t line to o v e r l a p each other.

It is seen from Fig.

these curves are n e a r l y a set of p a r a l l e l s t r a i g h t lines. s t r a i g h t lines can be t r a n s l a t e d p a r a l l e l to the log stress axis.

1 that

A set of p a r a l l e l

to o v e r l a p each o t h e r along a path w h i c h is The curves in Fig.

1 do show h o w e v e r slight

c u r v a t u r e w h i c h is w i t h i n the a c c u r a c y of the experiment.

U n f o r t u n a t e l y the

c u r v a t u r e of these curves does not show s u f f i c i e n t c h a r a c t e r i s t i c s the d e t e r m i n a t i o n of a unique t r a n s l a t i o n path.

The

to allow

d e t e r m i n a t i o n of a

u n i q u e t r a n s l a t i o n p a t h has b e e n p o s s i b l e for c o n s t a n t h a r d n e s s

log stress -

log p l a s t i c strain rate curves of a v a r i e t y of m a t e r i a l s as r e p o r t e d in r e f e r e n c e 4. homologous

In the same r e f e r e n c e it is d i s c u s s e d that in general at low

temperatures

the c o n s t a n t h a r d n e s s

log stress - log p l a s t i c strain

rate curves w i l l show a c u r v a t u r e c o n c a r v i n g u p w a r d and c o n c a r v i n g d o w n w a r d at high h o m o l o g o u s

temperatures.

The i n t e r m e d i a t e h o m o l o g o u s t e m p e r a t u r e s

range c o r r e s p o n d to the t r a n s i t i o n r e g i o n w h e r e the curves will show less characteristics. mediate homologous

It is p o s s i b l e that r o o m t e m p e r a t u r e t e m p e r a t u r e range for titanium.

t h e r e f o r e to d e t e r m i n e

falls in the inter-

It will be d i f f i c u l t

the t r a n s l a t i o n path.

S a r g e n t and C o n r a d 2 has used the slope of load vs log time plot to d e t e r m i n e the a c t i v a t i o n v o l u m e for p l a s t i c covers a p e r i o d of five minutes.

flow.

Their r e l a x a t i o n time

In their data range the load - log time

plot shows a s t r a i g h t line correlation.

The typical results of the p r e s e n t

w o r k in a p l o t of load vs log time are shown in Fig.

2.

It is seen that the

p r e s e n t data show a c o n t i n u o u s l y c h a n g i n g slope at longer r e l a x a t i o n times. The values of the a c t i v a t i o n volume o b t a i n e d by these i n v e s t i g a t i o r s may t h e r e f o r e be questioned. 3 R o d r i g u e z et al. p r o p o s e d several a r g u m e n t s in an a t t e m p t to use stress r e l a x a t i o n data to r a t i o n a l i z e m e c h a n i s m s

for p l a s t i c flow in titanium.

Some of their a r g u m e n t s d e p e n d on the fact that long time limit of load vs log time p l o t a p p r o a c h e s

a s t r a i g h t line.

line limit is shown by the p r e s e n t data

No e v i d e n c e of long time s t r a i g h t

(Fig. 2) w h i c h ~overs a r e l a x a t i o n

time one d e c a d e longer than that involved in the e x p e r i m e n t s of R o d r i g u e z et al.

The p r e s e n t w o r k u l t i l i z e s a d i g i t a l data a c q u i s i t i o n s y s t e m and good

t e m p e r a t u r e control of the entire t e s t i n g s y s t e m 4. Fig.

2 is w i t h i n e x p e r i m e n t a l

The c u r v a t u r e shown in

limit.

R o d r i g u e z et al. 3 p r e s e n t some other a r g u m e n t s relying on the experidP m e n t a l o b s e r v a t i o n that log ~-~ vs P plots give a s t r a i g h t line c o r r e l a t i o n dP w h e r e P is load and t is time. Since ~-~ is p r o p o r t i o n a l plastic strain rate 4, in Fig.

3 the log plastic

typical data of the p r e s e n t work.

strain rate is p l o t t e d vs stress b a s e d on S t r a i g h t line c o r r e l a t i o n is not observed.

The present results suggest that u n c e r t a i n i t y exists in the e x p e r i m e n t a l e v i d e n c e on t i t a n i u m used by these authors. In summary the p r e s e n t w o r k shows that the c o n s t a n t h a r d n e s s

log stress-

7

Vol.

8, No.

7

STRESS

RELAXATION

log plastic strain rate relationships

IN T I T A N I U M

741

for titanium obtained from room tem-

perature stress relaxation experiments exhibit behavior not inconsistent with the requirements of plastic equation of state.

The longer time stress

relaxation data suggest that some of the results reported in the literature based on shorter time data may required further examination. [email protected] This work is supported by the National Science Foundation through the Materials Science Center at Cornell University.

The authors wish to

acknowledge B. Addis for specimen preparation. References i.

C.C.

2.

G. Sargent and H. Conrad,

Law and D. N. Beshers,

Scripts Met. 6, 635

3.

P. Rodriguez, P. Dasgupta, S. L. Mannan, Samuel, Scripta Met. [, 671 (1973).

4.

E . W . Hart, Che-Yu Li, H. Yamada, and G. L. Wire, "Phenomenological Theory: A Guide to Constitutive Relations and Fundamental Deformation Properties" to be published in "Constitutive Equations in Plasticity" edited by A. Argon (MIT Press. planned for 1974).

Scripta Met. ~, 43

5.0

I

I

S. S. Vagardi,

I

I

.,.../"

4.9

,/

/

S" /

s •

(1972).

(1969).

~

and K. G.

I

4

..

3

.

6

,.

n

B, o°

o~

,/ /

4.8



n-

I-

/"

(..9 0 _1

s 5

/

°~."

/

S ~° "

o

4.7

46

-8

I

I

I

I

I

-7

-6

-5

-4

-5

LOG

STRAIN

RATE

SEC- I )

Fig. 1 LOglo(Stress) vs lOglO(strain rate) data for titanium at room temperature and several strain levels.

742

STRESS

RELAXATION

20C

IN T I T A N I U M

I

I

Vol.

I

~5c

8, No.

I

S

_J

S


rF £3 < o

50 c D

aG c ao o

o

o~O 0

I i

0

LOG

Fig. Typical

L

1

5

4

2

load r e l a x a t i o n

for t i t a n i u m

vs l O g l 0 ( t i m e )

I I

T

-5-

.."

" -6-

.

.."

•°• ••

.Z"

j,, •

•°

3

4

,.

/ s.~*"

.-"

I

6



""

/

o•• . , f •

2

,:"

/

/

uJ

I

5

..:

o u] - 4 o9

data

at r o o m t e m p e r a t u r e .

-3

Z

I 2 TIME (SEC)

""''

...

" ""



~"



°. ••••

-7-

0 _1 - B 4 0

I 50

I 60

I

STRESS

Fig. LOgl0(strain

rate)

room temperature

7O

I 80

for t i t a n i u m

at

(PSI)

3

vs s t r e s s d a t a

and s e v e r a l

plastic

strain

levels.

90

7