Stress relaxation and deviation from the mechanical equation of state in cold drawn tungsten wires

Scripta METALLURGICA

Vol. 9, pp. 27-30, 1975 Printed in the United States

Pergamon

STRESS RELAXATION AND DEVIATION FROM THE MECHANICAL OF STATE IN COLD DRAWN TUNGSTEN WIRES

Press,

Inc.

EOUATION

A. T. Nagy Research

Institute

for Technical

Physics

Budapest,

of the Hungarian

Academy

of Sciences,

Hungary

(Received November

i, 1974)

Introduction In the case of elastic between

stresses

relations

for

by Hart

of state

in a way

(2)

deformation

strains.

plastic

discussed mechanical

and

deformation

of the strain rate for a material maintained

constant/.

different

hardness

Plots

states

well from

that the

(l~ . The

in a definite

hardness

against

intercept

relation

such

unique

the problem

of the mechanical existence

flow stress

of flow stress

do not

gives a unique made to find

(1) . Recently

the concept

different

of state means

law

have been

as

, who introduced

somewhat

equation

Hoo~e's

Efforts

was

equation of

is a unique

such a function

state /temperRture

strain rate

referring

and can be transformed

is to

into each

other by a scaling relation. It turned ine

A1 (3)

out that

such an equation

, Nb and Fe (4)

when grain boundary ine materials Similarly

sliding

tested

varied

the so called l0 ~ m /width/. the

of the cells

fibres, The

cases

of polycrystall-

out stress relaxation

wires 0.6 mm in diameter.

flat grains,

I mm. In the fibres

The grain sizes

only in

from about 40 ~m to 180 ~m.

to the above works we carried

/thickness/,

in polycrystall-

/For the latter

does not occur./

in (3-5)

on cold drawn tungsten

dimension

of state does exist

, and in Pb (5) ,

These wires

the dimensions

of which

length of the fibres might

dislocations

are arranged

is O.1 ~ m or less

(6)

into

measurements

consist are

of

about

10ng I ~m

be in the order of cell

walls.

The

.

Experimental Our measurements

were carried

K, A1, and Si. The diameter 40 mm. The stress

specimens

were

of the specimens

strained

reached a previously

out on cold drawn tungsten wires was 0.6 mm,

at a strain

fixed value, 27

the gauge

doped with length was

rate of 2.08-10 -3 sec -I. As the

the crosshead

was

stopped

and the

28

STRESS RELAXATION

decreasing

stress

of this curve

~

IN TUNGSTEN WIRES

was recorded

we calculated

as a function

the apparent

Vol.

of time t.

strain rate

9, No. i

By differentation

~

at several

points

using the relation

Ill, where

E is the combined

machine.

modulus

In our case E had a value

ing machine elastic

elastic

is estimated

mcduli

of wires

of 24000

to be 360 kp/mm, having different

In a given experimental

series

of the small

evaluating

the slope

mining the stress the next

differences

one,

significantly

therefore

and

the

kp/mm 2. The stiffness of measuring

testing

of the testthe

virtual

lengths. of determining

the variation

of strain rates had an error of about 20~ coming

curve.

one of the values

the stress-strain

by the relatively

specimen

by means

in stress

of the stress-time

increases

the

the accuracy

of stress was 0.2 ~p/mm 2. The values because

of

into

However,

consideration if an error

of strain rate, rate

large errors

in deter-

it will decrease

curve will not

in the values

when

be

modified

of single

strain

rates. The subsequent the same

relaxation

calibration

comparable

with the accuracy

ed for 40 minutes,

curves

were measured

of the testing

machine

indicated

an extension

on the same

in order

above.Each

specimen

at

should

be

that they

relaxation

curve was record-

for longer times being meaningless

because

read-off error. Thus we could measure the flow stress as a function rate between the limits of about l0 -4 sec -1 and 6"10 -8 sec -I. In the first in such a way

series

that

force reached a value Because

of measurements

it stopped

of the crosshead

the third run on

the value

stress was

~p/mm 2 at t=0;

of overshot

strain curve was a straight

reached

furthermore

than 0.1% during each relaxation

process.

line,

stress

significant

is about

a constant

was set

when the

overshots

the plastic

160 kp/mm2/

value

From

so that the

deformation

deformation

tensile

occurred.

During the loading period

i.e. the plastic

of strain

testing machine

automatically

of 45 ~p. /The corresponding

of the inertia 167.6

the tensile

the crosshead

of

was

less

the stress

/if any/ must

h~ve been less than 0.09~. Fig.

1. shows

by eq. /1/. hardening

has occurred.

in the second ped

the flow stress plotted

It can be seen This

that

strain hardening

run the crosshead

in the first run,

against

in the course

is stopped

as demonstrated

the strain rate of these

does occur 2./Here

strain

e~en in the case when

at a lower stress

in Fig.

determined

experiments

than it was stop-

the stresses

at t=0 were

161 kp/mm 2 and 157 ~p/mm 2 in the first and second ran, respectively./ The same specimen w h i c h has undergone ation runs /Fig.

1./ was strained

a strain hardening

next further.

tion was about 0.15~ and the flow stress

reached

during the relax-

This time the plastic a value

deforma-

of 192 ~p/mm 2. There-

Vol.

9. No i

STRESS R E L A X A T I O N IN T U N G S T E N W I R E S

29

"|

.! 16S

FIG.

i.

Flow stress in a cold w o r k e d t u n g s t e n w i r e as a function of strain rate during s u c c e s s i v e runs

,[,Wl

'

'

'

'

FIG.

2.

Flow stress versus strain rate. At the second run the crosshead was stopped at a lower stress than at the first.

I

FIG.

3.

Flow stress versus strain rate. / T h e same s p e c i m e n as in Fig. 1./ B e t w e e n runs 7 and 9 the wire had been strained until the stress reached a v a l u e of 192 k p / m m 2 . *.[,~')

30

STRESS RELAXATION

after

IN TUNGSTEN WIRES

the specimen was unloaded

same as during These

loading/,

and then

curves are illustrated

last run from Fig. undergone

to about 3.,

1. The relaxation

a greater plastic

next run /N ° 10/ shows

12} Kp/mm 2

the relaxation

in Fig.

Vol.

where

/the

represents

that strain hardening

strain rate was the

experiments

the dotted

run N ° 9 recorded

deformation

9, No. I

were repeated.

line represents

after the specimen

a softened

state,

while

ti~e had the

ta~es place again during success-

ive runs. Discussion Our measurements does not exist has undergone

for cold drawn tungsten e strain hardening.

lated to the strain greater plastic sense. This A oossible

seem to suggest

since

deformation

in walls

locations. stress

into the walls.

hardening

can generate

/run

3. in a

be

N ° 9/

re-

that a

phenomenologlcal

than in the walls. through

on Figs.

The walls

Plastic

of these

from the mechanical

equation

References J. H. Hollomon,

2

E. W. Hart,

Acta Met. 1 8 599 /1970/

3

E. W. Hart,

H. D. Solomon,

4

H. Yamada,

5

G. L. Wire, H. Yamada,

6

E. S. }~eleran, D. A. Thomas,

Che-Yu-Li,

J. appl. Phys.

1~7 69 /1946/

Acta Met. 2 1 295 /1973/

Acta Met. 2 2 249 /1947/ Che-Yu-Li,

Acta Met. 2 2 505 /1974/

Trans.

a higher in the

stress /Fig.

AIME 233 937 /1965/

observed

3./

which

as wor~-

of state can be re-

of the cold formed material.

C. Zener,

sources

from the cell walls,

softening.

1

of mobile dis-

to a decrease

strain rate. This was probably

the deviation

deformation

through the cell. Therefore

the sample to a higher originating

density

after which they

can act as sources

1. and 2. can be related

Reloading

dislocations

lated to the cell structure

The dislocations

the cells

that for the excitation

density.

new mobile

structure.

leads to a higher macroscopic Thus

runs the wire

state cannot

observations.

than for driving the dislocations

dislocation

state

of state

cells within which the dislocation

of dislocations

It can be assumed

is needed

the strain mobile

surround

of magnitude

in the passage

are incorporated

by Fig.

a softened

to previous

equation

During succ@ssive

this hardened

have a characteristic

that

is lower by some orders consists

produces

mechanical

model

Cold formed materials are arranged

wires.

However,

it was demonstrated

is in flat opposition qualitative

that the