Transformation - strain relationships in trip steels

Scripta METALLURGICA

Vol. 8, pp. 4 4 5 - 4 5 0 , P r i n t e d in the U n i t e d

1974 States

Pergamon

Press,

Inc.

TRANSFORMATION - STRAIN RELATIONSHIPS IN TRIP STEELS

B L Jones and P N Jones Royal Armament Research and Development Establishment Fort Ha]stead, Sevenoaks, Kent, England

{Received

December

I0,

1973;

Revised March

11,

1974)

Introduction

Enhanced ductility can be obtained in high strength austenitic steels which undergo a deformation - initiated martensite transformation.

Such TRIP (Transformation-lnduced

Plasticity) steels have been studied for several years by Zackay, Parker and co-workers (l, 2 ) During a conventional tensile test, the TRIP effect is manifested as a process similar to LUders

band propagation.

Severe local deformation (necking) produces hardening by transforma-

tion, displacement of the locally - deforming region and propagation of the necking zone along the gauge length of the specimen.

Final necking to fracture should therefore be delayed until

the whole gauge length is transformation-hardened and observed ductilities are consequently much increased.

Clearly the successful design of such steels depends on the transformation characteristics and the relative austenite and martensite yield strengths.

Transformation Sensitivity

G e r b e r i c h e t al related

(3) have suggested t h a t

to s t r a i n

v

where m is a c o n s t a n t Earlier

Angel

(4)

the volume f r a c t i o n

o f m a r t e n s l t e produced is b e s t

by

=

m ~½

(I)

for given test conditions

and E is the c o n v e n t i o n a l

found t h a t u s i n g ] 8 - 8 t y p e s t a i n l e s s

In

f l-f

steel

an e m p i r i c a l

= A In ET + k

best fitted

his data.

martensite,

VT is the maximum p o s s l b l e t o t a l

engineering strain. relationship

(2)

Here f = V /V T where V

is the volume o f a u s t e n i t e amount o f m a r t e n s i t e ,

A and k a r e c o n s t a n t s .

445

transformed to

~T is the t r u e s t r a i n

and

446

TRANSFORMATION-STRAIN

RELATIONSHIPS

IN TRIP STEELS

0 80

//~

Vol.

8, No.

5

o

0"40

"~

o

I

°

XEPERIMENTAL

//f-~.~.~,:. ,-o'

/

DATA ('7)

~OOA.,O.(3) "

~020

-----ANGEL

EQUATION

(4)•

/ i

.

,

0

,

00s

•

o ,0 (NGINEERING

,

0z0

o,s

STRAIN

FIG. 1 Comparison of published experimental data with empirical t r a n s f o r m a t i o n - s t r a i n r e l a t i o n s h i p s The forms o f the V

v. c curves produced by e q u a t i o n s (1) and (2) are shown in Fig.

i t may be seen t h a t ,

selecting

and 2, these r e l a t i o n s h i p s Bhandarkar e t al

the most f a v o u r a b l e v a l u e s f o r the c o n s t a n t s

t h a t the i n i t i a l

martensite transformation.

ranges o f s t r a i n .

stages o f p l a s t i c

In p a r t i c u l a r ,

strain will

equations 1

always produce some

Recent o b s e r v a t i o n s by the a u t h o r s on m a r t e n s i t e t r a n s f o r m a t i o n

produced by compressive s t r a i n the case.

in Equations I

g i v e agreement w i t h the data determined e x p e r i m e n t a l l y by

(7), only over very limited

and 2 both p r e d i c t

1, and

in two TRIP s t e e l s however, have i n d i c a t e d t h a t t h i s

is not

The c o m p o s i t i o n s o f the s t e e l s examined a r e g i v e n in Table 1.

TABLE 1

C

Composition o f TRIP s t e e l samples

Cr

Ni

Mo

Mn

Si

Fe

Steel A

0.30

8.92

8.64

4.12

2.00

2.00

Bal

Steel B

0.29

7.00

8.67

3.00

1.93

1.46

Bal

For both the s t e e l s t e s t e d i t was found necessary t o exceed an i n c u b a t i o n s t r a i n any t r a n s f o r m a t i o n whatsoever t o o k p l a c e . f o l l o w e d a course s i m i l a r

Consequently the s t r a l n - i n d u c e d

t o t h a t shown by curve 3 in Fig.

E° b e f o r e

transformation

1 which can best be d e s c r i b e d by

the r e l a t i o n s h i p

V~ : m (E-Co)½ I t can be seen in F i g .

1 that,

(3)

using the v a l u e s m = 2 and £o = 0 . 0 2 , e q u a t i o n 3 g i v e s

e x c e l l e n t agreement w i t h the e x p e r i m e n t a l data p o i n t s o f Ref. 7. In the p r e s e n t e x p e r i m e n t a l work the two s t e e l s were i n i t i a l l y 1175°C and warm-worked using a 60% r e d u c t i o n a t 425°C ( 5 ) . transformation,

either magnetically or metallographically,

solution Steel

until

treated at ll50°C -

'A' d i d not r e v e a l any it

had r e c e i v e d an i n c u b a t i o n

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5

TRANSFORMATION-STRAIN

strain E° equal to 0.06.

RELATIONSHIPS

IN T R I P

STEELS

447

Steel 'B' was designed, using the principles initially outlined by

Schaeffler (6), to be less stable (or more deformation-sensitive) initial transformation after ~

o

than steel 'A' and showed

= 0.03.

The compressive deformation mode was used since it obviates necking and minimises strain inhomogeneities.

Thus locally-obtained values of the volume per cent transformed, particularly

at low strains, are more representative of the transformation throughout the whole specimen. Strain inhomogeneities, and most certainly local variations in the amount of transformation, will however still occur on account of local compositional variations.

The amount of martensite produced by progressive deformation in eech steel was measured using a Tinsley magnetic gauge.

This is a relatively insensitive device and therefore in the

preliminary tests reported here, metallographic examination was carried out to confirm the general validity of the magnetic measurements and particularly to verify the absence of martensite in samples where the magnetic test detected none.

Absolute values of the volume

percentage of martensite present in samples strained beyond the incubation strain could not be determined with reliability by this simple method and therefore as yet no value of the transformation coefficient m has been determined for these steels.

LUders-type Deformations

The process of necking in which an unstable local deformation zone is produced, will only fail to progress to fracture if the loss in load-bearing properties produced by the reduction in area during necking is compensated by the hardening process resulting from deformation in the neck.

If the hardening process over-compensates,

the deformation will proceed more easily in

material away from the neck and a LUders-type process will follow. If the reduction of the load-bearing cross-section due to the geometrical extension during deformation is assumed uniform within the necking zone, then the unit loss in austenite load-bearing capacity is given by

(Ao) L :

oy. (~--$T ~ )

(4)

where e is the additional elongation caused by unstable plastic deformation in the neck. Equation 4 ignores any effects of austenite work-hardening.

Hardness measurements on TRIP

steels similar to those in question here have indicated that during thermo-mechanical treatment at 450°C reductions greater than about 50% give only minimal final material hardness (5).

increases

in the

Since the materials here have undergone 60% reduction at

425°C it seems justified to consider the austenite yield strength a

to be invariant

for

Y

this analysis.

If, on the other hand, local deformation

in the neck produces some transformation to

martensite, then the unit cross-sectional gain in load-bearing capacity in the neck can be expressed as:

(Ao) G =

( o - Oy). v .

(+-~)

(5)

448

TRANSFORMATION-STRAIN

RELATIONSHIPS

IN TRIP STEELS

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8, No. 5

S u b s t i t u t i n g f o r the proposed equation (3), gives _

(AO)G = (o

oy).m (c

1 GO)½. (e--~-~-)

-

(6)

The r e l a t i v e loss and gain in load-bearing c a p a c i t i e s predicted by equations (4) and (6) are shown in Fig. 2.

I t can be c l e a r l y seen t h a t the c r i t e r i o n ,

which determines whether

necking w i l l

propagate to f a i l u r e or whether a LUders-type process w i l l

sufficiently

to d i s t r i b u t e

the deformation, is the value o f Eo.

strengthen the neck

For a l l o y s o f s i m i l a r m,

i f ~o is high the a u s t e n i t e w i l l be r e l a t i v e i y more s t a b l e and deformation-lnduced rnartensite t r a n s f o r m a t i o n w i l l occur too l a t e to prevent f a i l u r e at neck.

the

4

ZOO GEOMETRICAl. STRENGTH LOSS

/ / ' ~

STRENGTH GAIN DUE TO TRANSFORMATION FOR (o = 0 . 0 4 , 0 0 b AND O.OB E E

O" =1780

150

G

j r / / ~..,..'"~~~~

//~//.,~

N/ram ~

=1200 N/ram ~

m'=I

////

i ,°°

// / / /

SO

/i// i

0

t

o.iio

0-0.5

0 I' I$

O" ;tO

ENGINEERING STRAIN

FIG. 2 Geometrical e f f e c t s and t r a n s f o r m a t i o n hardening during local deformation

I t can be seen from Fig. 2 t h a t ,

i f the a u s t e n l t e and martensite y i e l d strengths and the

t r a n s f o r m a t i o n c o e f f i c i e n t m are known, a l i m i t i n g value of E can be found which w i l l , o some f i n i t e value o f s t r a i n , j u s t s a t i s f y the r e l a t i o n s h i p

(Ao) L =

(Ao G)

at

(7)

S u b s t i t u t i n g f o r equations 4 and 6 gives the q u a d r a t i c r e l a t i o n s h i p E

where c =

(o

2

-mc

22

~

+mc

22

E

o

=

0

- Oy)/O , the r e l a t i v e strength increase.

than the l i m i t i n g value, the roots o f t h i s equation w i l l l i m i t i n g value they w i l l

(8)

I f the incubation s t r a i n G° is less be r e a l .

I f i t is l a r g e r than the

be non-real i . e . the transformation-lnduced strength increase w i l l

never compensate f o r the geometrical losses and necking w i l l

proceed to f a i l u r e .

The

Vol.

8, No.

S

TRANSFORMATION-STRAIN

for a material

limiting value of

RELATIONSHIPS

IN T R I P

STEELS

449

is thus given when the roots of equation 8 are real and

0

equal i.e. when (m2c2) 2

=

4 (m2c 2) E 0

or

Values of a

~o

=

2 2 C --4--m

= 1780 N/mm 2 (ll5 tsi) and o

= 1200 N/mm 2 (78 tsi) have been calculated from T microhardness measurements made on the martensite and austenite phases in Steel 'B' and this gives a value of c 2 of 0o24o

No reliable value of m for this steel could be determined using

the Tinsley gauge but the data of Gerberich et al indicates

425°C, may be expected to result Io2o

on an alloy very similar to steel 'B'

that testing at room temperature of this material, after 60% prior deformation at

(Refo 3, Fig. 6).

in a value for the transformation coefficient m of about

This means that the limiting value of the incubation strain for

steel 'B' should be about 0°08o

Since the observed ~o value of 0.03 is significantly less

than this, tensile deformation of steel 'B' should give a LUders propagation effect and yield a high ductility value°

This simple approach thus accounts f o r the LUders e f f e c t s d e f o r m a t i o n o f TRIP s t e e l s of a realistic

order°

e q u i v a l e n t to ~o

(2, 3) and y i e l d s v a l u e s f o r c r i t i c a l

i n c u b a t i o n s t r a i n which are

I t may be noted t h a t the Gerberich r e l a t i o n

0, can not account f o r LUders e f f e c t s

immediately with strain

f r e q u e n t l y observed d u r i n g t e n s i l e

(Eqo I ) ,

and proceed u n l f o r m l y t h r o u g h o u t the gauge lengtho

t h e r e f o r e always be d e l a y e d u n t i l

which is

since hardening should here commence

the whole gauge l e n g t h has been f u l l y

Necking would

transformed.

Concluding Remarks

For testing at room temperature, equation 3 appears to fit the data of refo 7 rather better than do the previously proposed empirical

relations,

except at very low strains where,

particularly in tensile deformation, strain inhomogeneities can be significant and lead to problems in the magnetic determination of transformed fractions°

The concept of an

incubation strain explains the present observations of no transformation at very low strains in specimens deformed in compression.

Bhandarkar e t al (Eq. I)

(7) have however observed a c l o s e agreement w i t h the Gerberich r e l a t i o n

in specimens t e s t e d a t sub-zero temperatures o f in TRIP s t e e ] samples s u b j e c t e d t o a

warm-working t r e a t m e n t a t t e m p e r a t u r e s a t 200°C and 250°C b e f o r e room temperature t e s t i n g °

450

TRANSFORMATION-STRAIN

RELATIONSHIPS

IN TRIP STEELS

Although t h e r m a l l y , and m e c h a n i c a l l y produced m a r t e n s i t e s d i f f e r likely

t h a t in the f i r s t

Vol.

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in morphology, i t seems

i n s t a n c e , t e s t i n g a t temperatures close to MS would c o n s i d e r a b l y

reduce the i n c u b a t i o n s t r a i n necessary to produce t r a n s f o r m a t i o n in a d d i t i o n to i t s p r e v i o u s l y observed increase in the r a t e o f m a r t e n s i t e p r o d u c t i o n (3)° temperature o f warm-work w i l l

effectlvely

Secondly, l o w e r l n g the

increase the r e s i d u a l s t r a i n

m a t e r i a l and the observed i n c u b a t i o n s t r a i n w i l l

inherent in the

be c o r r e s p o n d i n g l y lowered.

I t may be noted in r e f . 7 t h a t o n l y the samples worked a t 450°C and t e s t e d a t 22°C show a c l e a r LUders e f f e c t

in s t r e s s - s t r a i n

diagrams.

Equation 3, l i k e equation 1, is open to the argument t h a t , f o r s u f f i c l e n t l y strain,

it predicts V

to be g r e a t e r than 1.

Nevertheless i t

is f e l t

high values o f

t h a t the concept o f an

i n c u b a t i o n s t r a i n E is s i g n i f i c a n t since i t is a v a l i d and s e n s i t i v e measurement o f o austenite stability. I t is e a s i e r to measure and more o b v l o u s l y o f d i r e c t physical s i g n i f i c a n c e than the t r a n s f o r m a t i o n c o e f f i c i e n t

m, although the l a t t e r

value as an index o f the r a t e o f m a r t e n s i t e f o r m a t i o n . c o n j u n c t i o n w i t h phase s t a b i l i t y

criteria

parameter is o f

The use o f both parameters, in

determined by c o m p o s i t i o n , should a s s i s t in the

design o f s t r o n g e r and more s e n s i t i v e TRIP s t e e l s . British

Crown Copyright reserved.

Published w i t h the permission o f the C o n t r o l l e r o f Her

Britannic Majesty's Stationery Office. References 1.

V F Zackay, E R Parker, D Fahr and R Busch, Trans ASM, 60, 1967, p.252.

2.

J A H a i l , V F Zackay and E R Paker, Trans ASH, 6_.22, 1969, p.965.

3.

W W Gerberich, G Thomas, E R Paker and V F Zackay, "Proc Second I n t Conf on the Strength o f Metals and A l l o y s " A s i l o m a r , C a l i f , August 1970, p.894.

4.

T Angel, J l S l ,

5.

P N Jones and B L Jones, RARDE unpublished work, 1973.

6.

A S c h a e f f l e r , Metals Progress, 56, 1959, p.680.

7.

D Bhandarker, V F Zackay and E R Parker, Met Trans ~ ,

177, 1954, p.165.

1972, p.2619.

5