Transformation potential predictions for the stress-induced austenite

to martensite transformation in steel

A. Creuziger *, T. Foecke

National Institute of Standards and Technology (NIST), 100 Bureau Drive, Gaithersburg, MD 20899, USA

Received 29 May 2009; received in revised form 24 August 2009; accepted 27 August 2009

Available online 28 September 2009

Abstract

The stress-induced transformation behavior of retained austenite is considered in this work. With the development of transformationinduced plasticity (TRIP) steels this deformation mode is of growing importance. Twinned martensite structures were calculated using

the crystallographic theory of martensite. An available work criterion was used to predict the transformation potentials for 16 different

in-plane stress states for sheet sample geometry. By rotating the twinned martensite structures over all crystallographic orientations using

Euler angles, the magnitude of the transformation potential was plotted as an orientation distribution plot for comparison with typical

texture components. From these data, the Brass and Copper orientation components that are typical in retained austenite such as in

TRIP steels were found to have low transformation potential values. Grains aligned with these orientations would require higher stresses

to transform than other orientations, and may therefore never transform. This correlates to experimental observations that heavily

deformed TRIP steel contains residual retained austenite.

Published by Elsevier Ltd. on behalf of Acta Materialia Inc.

Keywords: TRIP steel; Texture; Austenitic steels; Martensitic phase transformation

1. Background

1.1. TRIP steel

Transformation-induced plasticity (TRIP) steels are a

relatively new class of advanced high-strength steels

(AHSS) that show both high strength and high ductility

[1] and are being considered for widespread use in automotive applications to lighten automobile bodies. High

strength and high ductility are typically mutually exclusive,

but are obtained in TRIP steels by stabilization of the austenite phase and strain-induced deformation from the

retained austenite into the martensite phase, as was first

published by [2]. There are two categories of TRIP steels,

TRIP-H and TRIP-L [3], also referred to as TRIP steel

and TRIP-assisted steel, respectively [4]. TRIP-H steels

are almost entirely austenite, due to high volume fractions

(10% mass fraction) of Ni and Cr added for austenite stabilization. These high-alloy steels are fairly expensive due

to the addition of these alloy elements, and have not been

widely used in automotive applications [3]. In comparison,

the TRIP-L steels are initially a mixture of ferrite, bainite

and austenite, with the austenite composing (5–25)% of

the total mass fraction depending on alloying elements

and thermomechanical treatment [5]. For these alloys, the

austenite is stabilized by additions of 2% mass fraction

Mn and 2% mass fraction Al or Si, making these lowalloy steels [6,7]. The lower cost of the TRIP-L steels has

lead to interest in use of these materials in automotive production. However, the lack of knowledge about the forming behavior in multiaxial strain states has limited the

automotive use of these alloys.

This paper focuses on the crystallographic texture of the

austenite phase and its effect on the transformation behavior. Prior investigations into the texture of the austenite

phase [8,9] showed that the initial texture exhibits Brass

1359-6454/$36.00 Published by Elsevier Ltd. on behalf of Acta Materialia Inc.

doi:10.1016/j.actamat.2009.08.059

* Corresponding author. Tel.: +1 301 975 6015.

E-mail addresses: adam.creuziger@nist.gov (A. Creuziger), tim.foecke@

nist.gov (T. Foecke).

www.elsevier.com/locate/actamat

Available online at www.sciencedirect.com

Acta Materialia 58 (2010) 85–91
or Copper orientations, typical for rolled face-centered

cubic (FCC) materials. Materials with FCC structure also

tend to recrystallize in cube orientation [10, page 221;11].

However, there has been little data on how favorable any

of these orientations are to transformation.

Stress-induced martensite can transform into two possible structures: a single variant of martensite or twinned

martensite. Transformation into a single variant of martensite is rare, due to the specific requirements on the lattice

parameters needed for transformation [12]. However,

twinned martensite has been observed in both TRIP-H

steels [13] and TRIP-L steels [14].

There have been a few attempts at predicting the dependence of the orientation on transformation. Van Rompaey

et al. [15] used the single-variant assumption, finite element

analysis (FEA) and analytic solutions to calculate the

mechanical driving force energy under multiaxial loading

conditions, suggesting the use of a twinned martensite technique to advance their analysis. Zhang et al. [16] also

assumed a single-variant transformation, and for uniaxial

compression loading predicts that cube orientations will

transform first. More detailed transformation analysis,

including the difference between Kurdjumov–Sachs (K-S)

and Nishiyama–Wasserman (N-W) was performed in

Ref. [9], but the stress state was not taken into account.

In this work, twinned martensite structures are used, in

conjunction with calculation of a transformation potential,

defined below, which includes the stress required for transformation. Sixteen different in-plane stress states are applied

to the twinned martensite structures. The twinned martensite

structures are rotated over all of orientation space to represent possible grain orientations. This technique allows simultaneous investigation of the stress state and orientation

dependence on the austenite to twinned martensite transformation and will provide a more complete view of what orientations and stress states are favorable for transformation.

1.2. Crystallographic theory of martensite

To calculate the twinned martensite structure, the crystallographic theory of martensite (CTM) was used. The full

details of this method are described in Refs. [12,17,18]. The

terms a0 and c0 are defined to be the body-centered tetragonal (BCT) unit cell dimensions, and a0 is defined as the

FCC unit cell length. For this analysis, the FCC lattice is

assumed to be in the m3m space group and is taken to be

the reference lattice. Using these definitions, for the FCC

to BCT transformation, three stretch tensors or martensite

variants are possible:

U1 1⁄4

c 0 0

0 a 0

0 0 a

2

6

4

3

7

5; U2 1⁄4

a 0 0

0 c 0

0 0 a

2

6

4

3

7

5;

U3 1⁄4

a 0 0

0 a 0

0 0 c

2

6

4

3

7

5; a 1⁄4 2a0

ffiffiffi

2

p a0

; c 1⁄4 c0

a0

ð1Þ

To calculate twinning, two variants labeled UðiÞ and UðjÞ

are used as well as a rotation R of the martensite variant

ðjÞ in the following compatibility equation:

RUðjÞ  UðiÞ 1⁄4 a  ^n ð2Þ

where a is the shearing vector of the twin and ^n is the mirror plane normal between variants. The Bain transformation is assumed in the current analysis; the additional

details of K-S or N-W transformations are not included

in the twinning calculation. These transformations could

be included, but most texture data is described in 5increments, which makes the N-W and K-S transformations difficult to distinguish from the Bain transformation [19].

After the twinning equation is calculated, an additional

compatibility equation between the twinned martensite and

the austenite is required. The terms UðiÞ

; UðjÞ; R terms are

the same as used in Eq. (2), with the additional terms for

the rotation of the twinned structure Rfor compatibility

with the austenite I and the variant volume ratio k describing the relative proportion of the two martensite variants in

the twinned structure. The compatibility equation for an

austenite-twinned martensite interface is:

R kRUðjÞ þ ð1  kÞUðiÞ    I 1⁄4 b  m^ ð3Þ

The austenite to twinned martensite interface can thus be

described as two vectors, containing the plane normal to

the interface m^ and the shearing direction and magnitude

b for the twinned structure. For the FCC m3m point group

and the BCT 23 point group in Hermann–Mauguin notation, there are 24 possible interfaces. A program developed

by T.W. Shield was used for these calculations [20].

1.3. Available work criterion

In order to predict which of the twinned martensite

structures are likely to form, an available work criterion

is applied:

W ðkÞ 1⁄4 bðkÞ

i rijm^ ðkÞ

j ð4Þ

where b and m are the interface vectors for the 24 possible ^

interfaces ðkÞ and r is the stress state. The scalar W represents the value of a transformation potential and is derived

from the Schmid law for plasticity and is similar to the critical resolved shear stress [21]. For a given stress state, the

maximum value of W ðkÞ for all k is denoted as We . The interface associated with the maximum value We , defined as ~k, is

the interface that is most likely to form. This criterion has

been used previously to predict the specific twinned martensite structure that forms in both uniaxial tension and

around a notch in shape-memory alloys with good agreement [21–23]. To avoid confusion when discussing the magnitudes of the maximum transformation potential We , We

will be referred to as the transformation potential for the

rest of this paper.

For the current application, instead of predicting which

interface will form, determining which orientations will

86 A. Creuziger, T. Foecke / Acta Materialia 58 (2010) 85–91
transform first is of interest. Using a 3-1-3 Euler (Bunge)

rotation matrix [24, eqn.2.50], where /1; U; and /2 are

the rotation angles from the sample to crystallographic reference frames about the z; x0 and z00 axes, respectively, it is

possible to rotate the interfaces over all possible crystallographic orientations:

Q 1⁄4

cosð/1Þcosð/2Þ  sinð/2ÞcosðUÞsinð/1Þ cosð/2Þsinð/1Þ þ sinð/2ÞcosðUÞcosð/1Þ sinð/2ÞsinðUÞ

cosð/1Þsinð/2Þ  cosð/2ÞcosðUÞsinð/1Þ sinð/1Þsinð/2Þ þ cosð/2ÞcosðUÞcosð/1Þ cosð/2ÞsinðUÞ

sinðUÞsinð/1Þ sinðUÞcosð/1Þ cosðUÞ

2

6

4

3

7

5 ð5Þ

Applying this to the available-work criterion gives:

W ðkÞ

ð/1; U; /2Þ 1⁄4 Qnið/1; U; /2Þb

ðkÞ

i rnmQmjð/1; U; /2Þm^ ðkÞj

ð6Þ

The magnitude of the transformation potential

W ð/1; U; /2Þ can now be presented in an orientation distribution plot. Considering the whole ð/1; U; /2Þ orientation

space, the larger values for W ð/1; U; /2Þ are the orientations where transformation is likely to occur.

2. Transformation predictions

No data is currently available in the literature for the

lattice parameters for martensite in TRIP steels. Using data

for conventional steels from [25], the following lattice

parameters were calculated based upon 0.1% mass fraction

carbon:

a0 1⁄4 0:35594nm a0 1⁄4 0:28657nm c0 1⁄4 0:28786nm

ð7Þ

These values are similar to the lattice parameters used in

[16]. The calculated variant volume ratio ðkÞ for these values is 0.41, which compares well to the value of 0.35 in [16]

measured from the ratio of variant width in the twinned

structure.

Sixteen different macroscopic stress states will be investigated, listed in Table 1 and illustrated in Fig. 1. The

abscissa is set parallel to the rolling direction (RD) and

the ordinate parallel to the transverse direction (TD). Each

stress state is described by the RD or TD axis that it is

nearest to, and the type of forming operation that creates

this stress state. To compare the transformation potentials,

the different stress states have been normalized using the

equation:

re 1⁄4 1

ffiffiffi

2

p ðr11  r22Þ

2 þ ðr22  r33Þ2 þ ðr33  r11Þ2 h

þ6ðs2

12 þ s223 þ s231Þ

1

2 ð8Þ

such that the effective stress ðreÞ is equal to 1 and assuming

material isotropy. The resulting stress tensors are shown in

Table 1.

For the cubic–orthorhombic symmetry expected for the

austenite phase in sheet steels, only the orientations within

the 0 6 /1 6 90; 0 6 U 6 90 and 0 6 /2 6 90 subset

of orientation space need to be calculated. A script written

in PERL performed these calculations in 5 increments

throughout this subset. Fig. 2 shows orientation distribution (OD) plots of the maximum transformation potential

We on /2 1⁄4 45 sections, which contains the orientations of

interest for FCC materials.

The values of the maximum transformation potential We

calculated in Eq. (6) have also been tabulated in Table 2 for

Brass, Copper and Cube orientations. Brass orientations

occur in three places in the 0 6 /1 6 90; 0 6 U 6

90 and 0 6 /2 6 90 subspace: ð/1; U; /2Þ : ð55; 90;

45Þ;ð35; 45; 0Þ and ð35; 45; 90Þ that will be referred

to as Brass1

, Brass2, and Brass3, respectively. Copper orientations occur at two places in ð/1; U; /2Þ : ð90; 35;

45Þ and ð39; 66; 27Þ which will be referred to as Copper1 and Copper2

. Data from each of these orientations

is included in Table 2. Cube orientations were measured

at three locations of ð/1; U; /2Þ: ð0; 0; 0Þ; ð90; 0;

0Þ and ð45; 0; 45Þ, but were found to be identical, so

Table 2 only lists the data from ð/1; U; /2Þ1⁄4 ð0; 0; 0Þ.

The maximum and minimum values of We for the Euler

angles investigated are listed in Table 3, as well as the

orientations.

As a sensitivity analysis, different values of the austenite

and martensite unit cells were calculated, corresponding to

0.01% and 0.25% mass fraction C. The magnitude of the

Table 1

Tensor descriptions of the 16 different stress states investigated. Key to

notation: Uniaxial tension along RD (RD-T), plane strain along the RD

axis (RD-PS), balanced biaxial tension (BB), plane strain along the TD

axis (TD-PS), uniaxial tension along the TD axis (TD-T), deep drawing

along the TD axis (TD-DD), pure shear with the TD axis positive (TD-S),

extrusion along the RD axis (RD-EX) compression along the RD axis

(RD-C). Shrinking along the RD axis (RD-SH), balanced biaxial

compression (BB-C), shrinking along the TD axis, compression along

the TD axis (TD-C), extrusion along the TD axis (TD-EX), pure shear

with the RD axis positive (RD-S), deep drawing along the RD axis (RDDD).

RD-T RD-PS BB TD-PS

100

000

000

2

4

3

5

2ffiffi

3

p 0 0

0 1ffiffi

3

p 0

000

2

6

4

3

7

5

100

010

000

2

4

3

5

1ffiffi

3

p 0 0

0 2ffiffi

3

p 0

000

2

6

4

3

7

5

TD-T TD-DD TD-S RD-EX

000

010

000

2

4

3

5

 1ffiffi

7

p 0 0

0 2ffiffi

7

p 0

0 00

2

6

4

3

7

5

 1ffiffi

3

p 0 0

0 1ffiffi

3

p 0

0 00

2

6

4

3

7

5

 2ffiffi

7

p 0 0

0 1ffiffi

7

p 0

0 00

2

6

4

3

7

5

RD-C RD-SH BB-C TD-SH

100

0 00

0 00

2

4

3

5

 2ffiffi

3

p 0 0

0  1ffiffi

3

p 0

000

2

6

4

3

7

5

10 0

0 1 0

000

2

4

3

5

 1ffiffi

3

p 0 0

0  2ffiffi

3

p 0

000

2

6

4

3

7

5

TD-C TD-EX RD-S RD-DD

00 0

0 1 0

00 0

2

4

3

5

1ffiffi

7

p 0 0

0  2ffiffi

7

p 0

00 0

2

6

4

3

7

5

1ffiffi

3

p 0 0

0  1ffiffi

3

p 0

00 0

2

6

4

3

7

5

2ffiffi

7

p 0 0

0  1ffiffi

7

p 0

00 0

2

6

4

3

7

5

A. Creuziger, T. Foecke / Acta Materialia 58 (2010) 85–91 87
transformation potential changed slightly, but no significant changes in the orientation distribution plot shape were

found. The calculations shown are for the m3m point

group. Additional calculations for the m3m space group,

which allows improper rotations (det = 1) and increases

the number of possible interfaces from 24 to 48 were also

performed, but the transformation potential values were

found to be identical to the m3m point group.

3. Discussion

The data in Tables 2, 3 and Fig. 2 show the significant

effects of both stress state and orientation on the transformation potential, and therefore on the ability for austenite

to transform into martensite. For TRIP steels, the Brass

and Copper orientations are the most common orientations with which grains are found to be aligned [8,9]. For

all stress states investigated, the values of the transformation potential for grains aligned with Copper and Brass orientations are lower than cube orientations. Transformation

potentials for Copper orientations are generally lower than

Brass. This means that, for austenite grains aligned in the

cube direction, the shear caused by twinned martensite is

closely aligned with the shear direction and plane caused

by the different loading conditions. As the values of the

transformation potential give a ratio of the stress states

required for transformation, this result implies that the

grain orientations that are most common are also more difficult to transform for the investigated stress states.

Comparing the RD-T and TD-T /2 1⁄4 45 sections, mirror symmetry along /1 1⁄4 45 can be seen which occurs due

Fig. 2. /2 1⁄4 45 orientation distribution sections of transformation potential W

f shown for the 16 stress states described in Table 1 and Fig. 1. Cube

orientation in this section is marked with an “O” at ð45; 0; 45Þ, Copper orientation is marked with a “C” at ð90; 35; 45Þ and Brass orientation is

marked with a “B” at ð55; 90; 45Þ.

Fig. 1. Stress tensors investigated plotted in the RD–TD plane. Key to

notation is described in Table 1.

88 A. Creuziger, T. Foecke / Acta Materialia 58 (2010) 85–91
to symmetry of the Bunge Euler angles. Symmetry is

observed in all RD-X and TD-X loading conditions, where

X is a type of loading (T, C, PS, etc.). The orientations for

the maximum and minimum transformation potential in

Table 3 show this symmetry. Cube, and any other orientations along the /1 1⁄4 45; /2 1⁄4 45 line, will be the same for

both RD-X and TD-X loading conditions. The transformation potentials for the Brass or Copper orientations will

not be symmetric between RD-X and TD-X because the

Brass and Copper orientations do not fall along the

/1 1⁄4 45; /2 1⁄4 45 line.

The 90 90  90orientation space explored here is

valid for cubic crystal symmetry and orthotropic sample

symmetry expected in sheet metals, and contains expected

redundancy of the Copper, Brass and Cube orientations

within this space. There is some variation between the

transformation potential value We for the Copper components, this but may be due to the slight misorientation

between the true orientation and measured orientation.

Brass orientations have the same value regardless of where

they are measured, indicating this is not a computational

artifact.

For further discussion, the stress states are separated

into four domains: domain 1 containing the stress states

in the positive–positive quadrant from RD-T to TD-T;

domain 2 the negative–positive quadrant with stress states

TD-DD, TD-S and RD-EX; domain 3 considering the negative–negative quadrant from RD-C to TD-C; and finally

domain 4 with TD-EX, RD-S and RD-DD.

3.1. Domain 1

For the RD-T stress state, the locations of the lowest

transformation potential are close to the Copper orientations. As shown in Table 2, the Brass orientation has

approximately twice the value of the Copper orientation.

Also, the Cube texture potential value is three times the

Copper orientation value. Thus, for tension along the rolling direction and a stress level that will transform austenite

oriented with the Cube orientation ðr 1⁄4 rT Þ, grains aligned

with the Copper orientation would require a stress level of

3rT to transform, and grains aligned with the Brass orientation would require 1:5rT .

Similar behavior is seen in the TD-T stress state. The OD

plots are mirror images due to the symmetry in Bunge notation. In this stress state the Copper and Brass orientations

exhibit transformation potentials that are much lower than

Table 2

Transformation potential We values for Brass, Copper and Cube orientations.

Domain Orientation: Cube Brass1 Brass2 Brass3 Copper1 Copper2

ð/1; U;/2Þ: (0,0,0) (55,90,45) (35,45,0) (35,45,90) (90, 35,45) (39,66,27)*

ðhklÞhuvwi ð001Þh100i ð110Þh112i ð011Þh211i ð101Þh121i ð112Þh111i ð121Þh111i

1 RD-T 0.1325 0.0887 0.0887 0.0887 0.0398 0.0405

RD-PS 0.1467 0.1198 0.1198 0.1198 0.0834 0.0854

BB 0.1215 0.1188 0.1188 0.1188 0.1046 0.1079

TD-PS 0.1467 0.0909 0.0909 0.0909 0.0978 0.1014

TD-T 0.1325 0.0398 0.0398 0.0398 0.0648 0.0678

2 TD-DD 0.1278 0.0513 0.0513 0.0513 0.0535 0.0548

TD-S 0.1187 0.0554 0.0554 0.0554 0.0442 0.0452

RD-EX 0.1054 0.0575 0.0575 0.0575 0.0334 0.0339

3 RD-C 0.0731 0.0562 0.0562 0.0562 0.0133 0.0142

RD-SH 0.0908 0.0419 0.0419 0.0419 0.0233 0.0246

BB-C 0.0841 0.0164 0.0164 0.0164 0.0403 0.0413

TD-SH 0.0908 0.0163 0.0163 0.0163 0.0639 0.0648

TD-C 0.0731 0.0133 0.0133 0.0133 0.0704 0.0719

4 TD-EX 0.1054 0.0386 0.0386 0.0386 0.0678 0.0687

RD-S 0.1187 0.0512 0.0512 0.0512 0.0630 0.0635

RD-DD 0.1278 0.0620 0.0620 0.0620 0.0558 0.0560

* Measured at: (40,65,25).

Table 3

Orientations of the maximum and minimum transformation potential We

for each stress state.

Domain Stress state Maximum Minimum

Orientation Value Orientation Value

1 RD-T (5,35,85) 0.1331 (45,55,15) 0.0397

RD-PS (10,20,80) 0.1536 (0,70,45) 0.0516

BB (20,20,10) 0.1330 (70,55,45) 0.0617

TD-PS (80,20,10) 0.1536 (90,70,45) 0.0516

TD-T (85,35,5) 0.1331 (45,55,75) 0.0397

2 TD-DD (85,20,0) 0.1323 (0,15,45) 0.0270

TD-S (90,20,5) 0.1254 (90,20,45) 0.0236

RD-EX (90,20,5) 0.1140 (50,45,0) 0.0211

3 RD-C (25,60,80) 0.0847 (45,55,15) 0.0131

RD-SH (60,5,50) 0.0975 (20,90,45) 0.0043

BB-C (15,5,20) 0.0844 (30,55,45) 0.0086

TD-SH (30,5,40) 0.0975 (20,45,0) 0.0043

TD-C (65,60,10) 0.0847 (45,55,75) 0.0131

4 TD-EX (0,20,85) 0.1140 (40,45,0) 0.0211

RD-S (0,20,5) 0.1254 (0,20,45) 0.0236

RD-DD (5,20,0) 0.1323 (90,15,45) 0.0270

A. Creuziger, T. Foecke / Acta Materialia 58 (2010) 85–91 89
the Cube orientation, and are comparable to the values of the

Copper orientation in the RD-T stress state. In this case the

minimum in the TD-T stress state is near the transformation

potential values of the Brass orientation, which has a lower

transformation potential than Copper. While the RD-T

stress state had a relatively high value for the transformation

potential in the Brass orientation, neither the transformation

potentials for Brass nor Copper orientations are high in the

TD-T stress state. Transformation in the Brass orientations

would require larger stresses in the TD-T stress state than in

the RD-T stress state, but lower stresses in the Copper orientation than the RD-T stress state.

The general orientation behavior in the RD-PS and TDPS stress states are quite similar to the RD-T and TD-T

stress states, respectively. The transformation potential

has a larger magnitude overall, and the locations of the

minima have been shifted and stretched along the /1 axis.

In the Copper orientations the transformation potential

values in RD-PS are double the transformation potential

values in the RD-T stress state. In the TD-PS stress state

the Brass orientation is nearly doubled compared to TDT stress state. The plane-strain tests have the highest maximum transformation potential value for any of the stress

states investigated, as seen in Table 3, with the value for

cube orientation (shown in Table 2) very close to this maximum value (shown in Table 3).

The transformation potential in the BB stress state is

quite different from either the RD-T and TD-T. The minimum potential occurs along a strip near U 1⁄4 55, which is

referred to as the c-fiber with the {1 1 1} plane parallel to

the sample normal direction. For the RD-T, TD-T and

BB stress states, the maximum transformation potentials

are nearly identical, but the value for Cube orientation in

this stress state is less than those in the RD-T and TD-T

stress states. The values are similar to the Cube orientation

because the Brass and Copper orientations do not lie on

the c-fiber. The value for transformation potential in the

Brass orientation is less than that seen in the RD-PS case,

but the value for Copper orientation is higher than any

other stress state investigated.

For all stress states investigated, the cube orientation has

the highest transformation potential in either PS stress state.

Similarly, the highest overall transformation potential for

the Brass orientation occurs in the RD-PS case, and for

grains aligned with the Copper orientation the highest transformation potential value overall is in the BB stress state. In

domain 1, the lowest value for the Cube orientation occurs in

the BB stress state; for Brass, the TD-T stress state; and for

Copper the RD-T stress state. The transformation potential

for the Copper orientations are higher than Brass only for

the TD-PS and TD-T stress states.

3.2. Domain 2

All of the stress states discussed thus far have been in the

positive–positive quadrant of stress space, where most

forming operations typically occur. Domain 2 contains

deep drawing (TD-DD), pure shear (TD-S) and extrusion

(RD-EX) stress states, which also can be encountered in

production. For each of these stress states the transformation potential for each component has similar values and

shape. The shape is similar to the TD-T stress state with

some stretching along the U axis. The Cube orientation

value is twice as large as that of the Brass or Copper orientations. As the stress state changes from TD-DD to TD-S

to RD-EX the value of the transformation potential for

Cube and Copper orientations decreases while the transformation potential for Brass orientation increases slightly.

3.3. Domain 3

Domain 3, which deals with the negative–negative quadrant, is quite different than the preceding domains. Following the stress-space arc in domains 1 and 2 from RD-T to

RD-EX there is a clear progression in the trends of the

transformation potential. This changes in the RD-C case,

which does not continue the shape of RD-EX, but rather

resets to be similar to the RD-T stress state. There is a correlation between the orientation distribution shape between

the domain 1 and domain 3 stress states. The values for the

transformation potential are much lower in this domain

than others, but are generally still positive, indicating

transformation will occur in compression.

Much like domain 1, the RD-C and TD-C stress states

have the same values for the Cube orientation. For RD-C

stress state the Brass orientation is of a similar magnitude

to the Cube orientation, and the Copper orientation is much

lower. For TD-C stress state the behavior is reversed, the

Copper orientation is of similar magnitude to the Cube orientation and the Brass orientation is much lower, as seen in

their tensile counterparts. For these two stress states the minimum value is still positive, indicating that transformation is

possible for any orientation at high enough stress.

This is not the case for the RD-SH, BB-C and TD-SH

stress states, where there are some orientations where the

transformation potential for that orientation is a negative

value. That implies that in these orientations transformation will never occur, regardless of the applied stress. For

the BB-C stress state the transformation potential for Brass

orientations is approximately one-sixth of the Cube values

and for Copper orientations a third of the cube values. The

BB-C stress state also has the lowest maximum and minimum values of any of the investigated stress states. The

RD-SH and TD-SH stress states have the same values

for the cube orientation, but the Brass and Copper orientations are quite different. In the RD-SH stress state, the

transformation potential for Copper orientations are half

that of Brass, in the TD-SH the Brass orientation is a quarter of the Copper orientation value.

3.4. Domain 4

The transformation potentials for stress states TD-EX,

RD-S and RD-DD in domain 4 are similar to the stress states

90 A. Creuziger, T. Foecke / Acta Materialia 58 (2010) 85–91
in domain 2. The transformation potential values for maximum, minimum and Cube orientations in deep drawing

(DD), pure shear (S) and extrusion (EX) stress states are

the same for either RD or TD values. In contrast to domain

2, the Copper orientations are much higher in this domain

while the Brass orientations vary more significantly.

3.5. Summary

For an as-received TRIP steel, typically hot-rolled, the

austenite texture will be primarily composed of Brass- or

Copper-oriented grains. From the data in Table 2 and

Fig. 2, it is clear that these orientations correspond to

low values of the transformation potential. Cube orientations, the recrystallization texture, have the high values of

transformation potential for all stress states investigated.

From a processing point of view this implies that the Brass

and Copper orientations may not be favorable, because the

applied stress state may never reach the levels required to

transform the austenite in these regions. This may explain

the retained austenite observed in the microstructure of

several experimental studies [15,26]. There is a line of mirror symmetry between RD-X and TD-X stress states, but

this does not imply that the values of the transformation

potential will be the same for the same crystallographic orientations. The mirror symmetry is observed in the overall

maximum, overall minimum and Cube orientation values,

but not the Brass or Copper orientations.

There is clear asymmetry in the transformation potential

between the tensile and compressive stress states, implying

that the hardening behavior will not be completely isotropic. The additional effects of microstructural stresses are

not included in this analysis, but assuming they are known,

could be easily added to the stress states presented. Only

the stress state and lattice parameters have been included

in this model, so the results of this analysis should be valid

for any stress-induced austenite to twinned martensite

transformation. One use of this analysis may be optimization of the texture components for transformation by either

distributing the textures so that the transformation occurs

evenly for a given stress state, ensuring all of the austenite

will be transformed by the end of a forming process, or

delaying the start of transformation until a specified stress

value has been reached.

4. Conclusion

The effects of orientation and stress state on the austenite to martensite phase transformation in TRIP steels were

investigated in this work. Twinned martensite structures

were calculated using the CTM. An available-work criterion was used to predict the transformation potentials for

16 different stress states. By rotating the twinned martensite

structures over all crystallographic orientations using Euler

angles, the magnitude of the transformation potential was

plotted as an orientation distribution plot. From these

data, the Brass and Copper orientation components that

are typical in as-processed TRIP steels were found to correspond to low values of the transformation potential.

Grains aligned with these orientations would require higher

stresses to transform than other orientations, and may

therefore never transform.

Acknowledgments

The authors thank T.W. Shield for use of his CTM-0.0.1

program; Steve Banovic, Thomas Gna ̈upel-Herold, Mark

Iadicola and Mark Stoudt at the Center for Metal Forming

at NIST for advice and assistance; and the Research Associate Program at the National Academies for supporting

this work.

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