Thermodynamic-Mechanical Modeling of Strain-Induced α′-Martensite Formation in Austenitic Cr-Mn-Ni As-Cast Steel

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Thermodynamic-Mechanical Modeling of Strain-Induceda(-Martensite Formation in Austenitic Cr–Mn–Ni As-CastSteel**

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By Alexander Kovalev,* Marco Wendler, Andreas Jahn, Andreas Weiß and Horst Biermann
Due to the excellent combination of strength and ductility

properties, austenitic Cr–Mn–Ni steels are subject of many

recent investigations. Examples are the studies of mechanical

behavior and microstructure evolution during deformation as

well as the characterization of TRIP/TWIP effects and their

relation to thermodynamics.[1–4] The main advantage of these

Cr–Mn–Ni steels is that they have equal properties and

behavior in the wrought and the cast state despite the

enormous difference in the grain size which is about 30 mm in

the wrought state and more than 1000 mm in the cast state.[1,5]

This allows an application directly in the as-cast state without

further processing.

In austenitic Cr–Mn–Ni steels, different stress- and

strain-induced deformation mechanisms and phase transfor-

mations can occur. The stress-induced processes occur during

the elastic deformation, i.e. at stresses below the yield strength

of the austenite. By contrast, the strain-induced processes

occur during the plastic deformation of the austenite, i.e. at

stresses above the yield strength.[6] The type of deformatio-

n-induced process activated depends on the chemical

composition and temperature. Previous studies have indi-

cated the possibility of g!a0, g! e, e!a0, and g! e!a0

martensite formations, twinning, and dislocation glide

mechanisms (regular dislocations, formation of extended

stacking faults by movement of Shockel partial dislocations,

formation of glide bands with high density of stacking faults)

in the austenitic Cr–Mn–Ni steels.[2] A significant increase in

ductility is obtained when martensite and twins are formed

during plastic deformation of metastable austenite. Therefore,

it is necessary to define the temperatures and stress values

where stress- and strain-induced martensite and twins can

form. Understanding transformation- and twinning-induced

[*] A. Kovalev, M. Wendler, Prof. A. Weiß, Prof. H. BiermannInstitute of Iron and Steel Technology, TU BergakademieFreiberg, 09596 Freiberg, GermanyE-mail: [email protected]

Dr. A. JahnVallourec and Mannesmann Deutschland GmbH, 40472Dusseldorf, Germany

[**] The authors would like to thank all of the staff involved in thecollaborative research centre 799, especially Dipl.-Wi.-Ing.Steffen Wolf for the carrying out of the tensile tests, and theGerman Research Foundation (DFG) for financial support ofthese investigations.

ADVANCED ENGINEERING MATERIALS 2013,

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plasticity requires the knowledge of the formed martensite

fractions and twin activity as well as the additional elongation

values imparted by the phase transformation and twinning.

For this purpose, Stress-Temperature-Transformation (STT)

and Deformation-Temperature-Transformation (DTT) dia-

grams are used. STT und DTT diagrams summarize all

knowledge about the deformation-induced structure trans-

formations including martensite formation and twinning, and

illustrate the TRIP and TWIP effects. In the present study, the

STT and DTT diagrams are presented for a new austenitic

Cr–Mn–Ni cast steel, which shows depending on the

temperature both, the TRIP as well as the TWIP effect.

The close relation between STT and DTT diagrams and

thermodynamics was shown in earlier publications.[3,7] Thus,

the course of the triggering stress for the deformation-induced

martensitic transformation correlates with the chemical

driving force available for this transformation. The transfor-

mation of austenite into martensite starts at a critical Gibbs

free energy change, the so-called ‘‘nucleation threshold’’. By

definition, reaching this threshold produces 1% martensite.

The nucleation threshold for the martensitic transformation

depends upon the chemical composition.[8–10]

The thermodynamic stability of the phases and the kinetics

of deformation-induced twinning and martensite formation

are reflected in the STT and DTT diagrams. In this context, the

present work aims at predicting, thermodynamically, the

maximum deformation-induced martensite fraction as a

function of temperature. For simplifying the calculation,

following conditions were set: (i) a quasi-static uniaxial tensile

deformation with a very low strain rate and (ii) the exclusion

of the grain size effect on the thermodynamics. The influence

of the austenitic grain size on the deformation-induced

transformations as well as on the martensite start temperature

MS is discussed in some publications.[11,12] However, the

strong effect can be observed more probable in the range of

very fine grain sizes.[12] In the Cr–Mn–Ni steels, no significant

differences in material properties and behavior were observed

comparing the austenite grain sizes of about 30 mm and more

than 1000 mm in the wrought and the cast state, respectively.[1,5]

1. Theoretical Background

1.1. Thermodynamics of Martensitic Transformation

The thermodynamics of thermal as well as deformation-

induced martensitic transformations is explained schematically

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A. Kovalev et al./Thermodynamic-Mechanical Modeling of Strain-Induced a0-Martensite Formation

Fig. 1. Schematic representation of the mechanical energy contribution to the thermo-dynamic driving force for the martensitic transformation. Fig. 2. Schematic illustration of chemical and total (chemicalþmechanical) driving

forces for the martensitic transformation.

in Figure 1. The change of the Gibbs free energy, DG, for

the g!a transformation is negative at temperatures below

the T0 temperature (where g and a have an identical Gibbs

free energy). The metastable austenite can transform below

T0 into martensite spontaneously when the nucleation

threshold DGK (a critical change in Gibbs free energy) is

reached at temperatures below the MS temperature (marten-

site start temperature) or by mechanical loading at tempera-

tures higher than MS. With the addition of mechanical

energy Wmin (see the energy coordinate system on the right

side of Figure 1), the nucleation threshold for martensite

formation will be achieved above the MS temperature and

the stress- or strain-induced martensite transformation will be

enabled.[11,13] The ‘‘nucleation thresholds’’ can be defined for

martensite fractions other than 1%, for instance 2% and up to

100% martensite (DG2%. . .DG100%), as shown in Figure 1. These

thresholds can be reached thermally, through the cooling. For

example, the energy threshold for the formation of 100%

martensite is equal to the DG value for the g!a transforma-

tion at the MF temperature (martensite finish temperature

for full martensitic transformation). Analogous to DGK, the

thresholds DG2%. . .DG100% can also be reached through a

combination of chemical driving force provided by cooling

and the mechanical energy. The resulting or total driving force

available for the martensitic transformation during deforma-

tion would then be the sum of the chemical driving force and

the mechanical energy:

DGtotal ¼ DGg!a þW (1)

The energy Wgmax denotes the mechanical energy, which

can be supplied by the austenite for the martensitic

transformation during the deformation. Wgmax is proportional

to the tensile strength of austenite. Wfg marks the maximum

mechanical energy, which can be supplied to the steel by

tensile loading up to the yield strength. At the Md temperature

(deformation-induced martensite start temperature), which is

the highest temperature for the deformation-induced mar-

tensite formation, the minimum energy needed to start the

martensite formation Wmin reaches its maximum value that is

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equal to Wgmax at this temperature. At the MSs temperature (the

stress-induced martensite start temperature) the energy Wmin

is equal to Wfg. The strain-induced martensite formation

occurs at temperatures below Md and the stress-induced

martensite formation occurs below the MSs temperature

depending on the level of the mechanical load. For example,

below the MSs temperature, the stress-induced martensite

forms at low stresses followed by the strain-induced

transformation at stresses above the yield strength.

Figure 2 is an alternative representation of Figure 1. The

mechanical energy coordinate is eliminated and instead, the

mechanical energy contribution to the thermodynamic

driving force is taken into account by offsetting the latter

by the values of Wfg and Wg

max as shown in Figure 1. The line

DGg!a is therefore the pure chemical driving force for the

g!a transformation. The distance between DGg!a and the

nucleation threshold DGK defines the minimum mechanical

energy Wmin, which is required for the start of the

deformation-induced martensitic transformation in the tem-

perature range between MS and Md. This condition is

described by the following equation:

DGtotal ¼ DGK ¼ DGg!a þWmin (2)

The Wfg offset line shows the total driving force, i.e. the

sum of the chemical driving force and mechanical energy

(DGg!aþWgf) at the load up to the yield strength. This line

intersects the nucleation threshold DGK at the MSs tempera-

ture. At this temperature, the energy Wmin is equal to the

energy Wfg. The largest possible driving force is represented

by the Wgmax offset line, which is the sum of the chemical

driving force and the maximum mechanical energy Wgmax

provided by the austenite:

DGmaxtotal ¼ DGg!a þWgmax (3)

The intersection of the Wgmax offset line with the nucleation

threshold defines the Md temperature at which the energy

Wmin is equal to the energy Wgmax.

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Fig. 3. Spontaneous (athermal) and deformation-induced martensitic transformation for steels with anincreasing austenite stability from (a) to (d).

Fig. 4. Schematic STT diagram for the deformation-induced martensitic transform-ation.

The schemes in Figure 3 are intended to clarify, thermo-

dynamically, the spontaneous (athermal) and deformatio-

n-induced martensitic transformations in four hypothetical

steels with different austenite stabilities.

Thus, the steel with the lowest austenite stability

(Figure 3a) can become fully martensitic by cooling to the

MF temperature even without deformation. At a higher

austenite stability (Figure 3b), the spontaneous martensitic

transformation does not proceed to completion and mechan-

ical deformation is needed to obtain a fully martensitic

microstructure. At a still higher austenite stability (Figure 3c),

no spontaneous martensitic transformation can take place

and no MS temperature can be defined. Nevertheless, the

deformation-induced martensite formation is still possible,

both stress- and strain-induced. In the most stable steel

(Figure 3d), neither MS nor MSs temperature can be defined.

Only strain-induced martensite formation occurs in this steel,

because the nucleation threshold can be reached only by

plastic deformation.

1.2. Schematic STT and DTT Diagrams

The STT and DTT diagrams will be explained in the

following using the example of an alloy in which dislocations

glide and only one martensitic transformation are the possible

deformation mechanisms.

The schematic STT diagram in Figure 4 shows the

characteristic stresses and phase transformations as functions


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of temperature. The tensile strength RmSteel

and the yield strength sf of the steel, the

tensile strength of the austenite Rmg, and the

triggering stress for the deformation-induced

martensite formation sAg!M are also plotted

in the diagram.

The characteristic temperatures MS, MSs,

and Md are deducible from diagrams of this

type.[14–16] At the Md temperature, the

triggering stress sAg!M reaches the tensile

strength of the austenite Rgm. The tempera-

ture MSs is defined at the intersection of the

triggering stress sAg!a0 and the yield

strength of the austenite sgf. The stress Rg

m

is the tensile strength of austenite in the

absence of a phase transformation. Rmg is the

highest stress which the austenitic phase can

obtain by the shear band deformation

mechanism.[17] The deformation-induced

martensite fraction increases proportional

to the difference between sA and the strength

of austenite. Figure 5 shows schematically the

temperature dependence of strain-induced,

stress-induced and spontaneous martensitic

fraction.

In the temperature range between Md and

MSs, the strain-induced martensite fraction

increases proportional to the difference

between sA and the strength of austenite.

Below the MSs temperature, the stress-induced martensite

fraction increases. At temperatures lower than the MS

temperature, the spontaneous martensite fraction increases

at the expense of the stress- and strain-induced martensite

fractions. Since the additional elongation caused by the TRIP

effect is proportional to the strain-induced martensite fraction,

as will be demonstrated in the DTT diagram, the maximum

uniform elongation takes place at the temperature where the

strain-induced martensite fraction is highest.

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Fig. 5. Spontaneous, strain-induced and stress-induced martensite fractions afterdeformation as functions of the temperature.

Some similarities can be recognized between the thermo-

dynamic diagrams of the type shown in Figure 1 and the STT

diagrams. The energy term Wmin for instance relates to the

triggering stress sAg!M for the deformation-induced mar-

tensite formation. Similarly, the energy term Wgmax, which is

the largest mechanical energy, which can be supplied to the

austenite, is proportional to the tensile strength of austenite

(compare Figure 1 and 4). The yield strength on the other hand

correlates with the energy term Wfg.

The DTT diagram is directly related to the STT diagram, as

a corresponding strain or elongation value exists for each

phase transformation field in the STT diagram. The DTT

diagram, Figure 6, shows the uniform elongation of austenite

Agg caused by the dislocation glide deformation and uniform

elongation of the steel AgSteel. The elongation of austenite Deg

decreases continuously with decreasing temperature. The

uniform elongation of the steel, however, increases in the

temperature range of Md to MSs. It reaches a maximum at

the MSs temperature where the strain-induced martensite

fraction is highest. When the martensite formation takes place

during elastic deformation (below MSs) or spontaneously (below

MS), the elongation of the steel decreases again. The additional

elongation denoted by DeM in Figure 6 is caused by the TRIP

effect and is proportional to the fraction of the strain-

induced martensite. The consequence of the strain-induced

Fig. 6. Schematic DTT diagram for the deformation-induced martensitic transform-ation.


transformations is a temperature anomaly in the elongation of

the steel. This temperature anomaly is typical for steels with

TRIP or TWIP effect, starts at the Md temperature and displays

a maximum at lower temperatures. The temperature anomaly

ends slightly above the MF temperature where the strain-

induced martensite formation no longer arises.

1.3. Calculation of Mechanical Energy

For the calculation of mechanical energy provided by the

austenite for the martensite formation, a relationship must be

sought between the acting stress and the mechanical energy.

There are some publications treating this question.

The critical mechanical energy per unit transforming

volume for initiation of the martensite formation DGcr is

related to the uniaxial stress using the following equation:[18]

DGcr ¼ scrl3 (4)

where scr is the critical stress for start of the transformation

and l3 is the largest eigenvalue of the transformation

deformation tensor.

In another approach proposed by Shin et al.[19], the internal

strain energy uI can be expressed as:

uI ¼ 0:5sIa (5)

where sI and a are the internal stress and the internal strain,

respectively. The authors remarked that it is difficult to

determine the internal strain directly. But an approximate

incremental relationship exists between the internal strain and

elongation.

Already Patel and Cohen[13] examined the relation between

the energy needed for the transformation and the applied

stress. The energy is considered as a sum of two components:

the shear component (t0 g0) including the shear stress and

strain along the habit plane and the component (s0 e0)

including the normal components of the stress and of the

transformation strain. For uniaxial tensile deformation, the

mechanical energy can be expressed as a function of

orientation of habit plane (u – angle between the specimen

axis and the normal to the habit plane) using the value of the

applied or macroscopic stress (s):

U ¼ 0:5sðg0sin2u þ "0ð1þ cos2uÞÞ (6)

The parameters g0 and e0 are characteristics of the

transforming area and have the values of 0.2 and 0.04

respectively, in iron-nickel alloys.[13]

Thus, considering the approaches mentioned above, the

mechanical energy can be inferred from the acting stress

during the tensile deformation. For simplifying the matter, a

linear relationship between the mechanical energy provided

by the austenite for the transformation and the acting stress

can be used:

W ¼ Fs (7)

where F is a factor including the internal or the transformation

strain, the relation between the external and internal or

transformation stress, scaling from the transformation volume



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to energy per mol. In simplified terms, the factor F

considering Equation (6) can be expressed as:

F � a10:5ðg0sin2u þ "0ð1þ cos2uÞÞrm

(8)

where rm is the molar density for the conversion of the energy

per transformation volume into the energy per mol, and a1 is a

material-dependent constant including other influences.

Many terms in Equation (8) cannot be directly determined.

But they can be considered as constant for a given steel.

Therefore the factor F can be resolved using experimental

data and the calculated chemical driving force at the Mdg!a0

temperature, where the following condition is valid:

Wmin¼Wgmax¼FRm

g, and Rmg is known.

1.4. Experimental Procedure

The chemical composition of the investigated Cr–Mn–Ni

as-cast steel is given in Table 1. The steel was melted in an

induction furnace and cast into a sand mould. The tensile test

specimens (DIN50125-B6� 30, round cross-section with

threaded shoulder, 6 mm in diameter with a gauge length

of 30 mm) were machined from the cast ingots. After the final

machining, each sample was heat treated at 10508C for 30 min

under vacuum, followed by gas quenching. As isothermal

conditions or constant temperature of the specimens were

required for the tensile tests, the static tensile tests were

performed at a low strain rate of 4� 10�4 s�1 to avoid the

adiabatic heating of specimens by deformation. The flow

curve analysis was done after conducting tensile tests at

different temperatures in the range of �196 to 3008C.

Moreover, interrupted tensile tests were carried out for the

clear identification of phases and for the investigation of

martensite formation kinetics. The a0-martensite fraction was

determined by measurement of the ferromagnetic fraction

using a magnetic scale. In this method, the force of

the magnetic field induced by ferromagnetic phases in the

material is measured. The force is proportional to the

ferromagnetic volume fraction of the specimen. The ferro-

magnetic fraction of unknown materials can be determined

using a calibrated specimen with a measurement accuracy of

approximately 5%. In our steel, d-ferrite and a0-martensite

are the only possible ferromagnetic phases. To separate the

d-ferrite and martensite fractions, the fraction of d-ferrite in

the specimens was determined before deformation by light

optical microscopy (LOM). A detailed microstructure analysis

by LOM and EBSD of this steel is available in references.[2,20]

Furthermore, in situ SEM analysis using backscattered

electron contrast (EBSD) and electron channelling contrast

imaging during tensile tests can be found in ref.[21]

Table 1. Main Alloying Elements of the Investigated Steel, wt%.

C N Si Cr Mn Ni

0.034 0.033 1.0 15.5 6.1 6.1


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Dilatometric investigations were performed using a BAHR

805A/D quenching and deformation dilatometer with a low

temperature unit. The dilatometry specimens were hollow

cylinders with a length of 10 mm, an outer diameter of 4 mm,

and an inner diameter of 2 mm. Each specimen was heated at

10 K s�1 to 10508C and held for 30 min. The specimens were

subsequently cooled at 10 K s�1 in order to measure the MS

temperature.

For the determination of the driving force and the

nucleation threshold for the g!a0 phase transformation,

the Gibbs energy change DG for this transformation was

calculated as a function of temperature. The calculations were

performed using Fact Sage (Thermfact and GTT Technologies)

with the SGSL database.

2. Results and Discussion

2.1. STT and DTT Diagrams

The deformation-induced processes described by the

tensile strength RmSteel and the yield strength s0.2 of the steel,

the tensile strength of the austenite Rmg, the triggering stresses

sAg!a0 and sA

g! e for deformation-induced a0- and

e-martensite formation, respectively, and the triggering stress

sAg!Tw for twinning are all shown for the studied steel in the

STT diagram of Figure 7 as functions of temperature. The

triggering stresses and the tensile strength of the phases

involved in the deformation-induced processes determine the

stress-temperature fields for the possible deformatio-

n-induced structural changes (martensite formation, twin-

ning, deformation by dislocation glide etc.). The position of

these fields will vary when the chemical composition is

changed. The corresponding DTT diagram indicating the

uniform elongation of the steel AgSteel and the uniform

elongation of austenite Agg is also shown in Figure 7. Here, the

height of a plasticity mechanism field at a given temperature

denotes the amount of the elongation or plasticity caused

by that mechanism. In contrast to STT diagrams, the field

boundaries in DTT diagrams do not indicate the initiation of

deformation-induced processes. It must be noted that all

solid lines in the diagrams of Figure 7 are experimentally

determined from analysis of tensile stress-strain curves.

The dashed lines, on the other hand, are predicted or

approximated.

According to microstructural investigations,[20,21] defor-

mation-induced twinning, g!a0, and g! e martensitic

transformations occur in this steel within the investigated

temperature range. The formation of twins and a0 martensite

can be induced by deformation at temperatures below Td

(deformation-induced twinning start temperature) and Md

temperatures, respectively. The Td temperature is the highest

temperature for deformation-induced twinning. Below the

Tdg!Tw temperature, twinning occurs upon reaching the

triggering stress for twinning sAg!Tw, which is, however, not

verified by experiments yet. This results in a minor increase in

the strength, combined with a significant gain in elongation as

shown in the DTT diagram. The temperature anomaly of

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Fig. 7. STT and DTT diagrams for a austenitic cast steel 16Cr–6Mn–6Ni.

elongation begins at the Tdg!Tw temperature, which is

approximately 2508C. The e-martensite was indexed by EBSD

in the microstructure at the deformation temperatures below

608C.[20] Therefore, the Mdg! e temperature is marked at 608C

in the STT diagram.

The austenite, which is strain hardened by dislocation

glide, formation of shear bands and twinning transforms into

martensite below the MdgþTw!a0 temperature. This is the

highest temperature at which a0-martensite is observed and

lies in the vicinity of 1008C. Additionally, at temperatures

below Mdg!a0, the austenite deformed by dislocation glide

transforms preferentially in glide bands of high stacking fault

density directly into a0-martensite[20,21] upon reaching the

triggering stress sAg!a0. In the temperature range between

approximately 0 and �508C, the triggering stress for

a0-martensite formation is very low, and austenite transforms

directly into martensite almost without twinning or

e-martensite formation. At lower temperatures, the

e-martensite formation and twinning activate before the

a0-martensite formation, and counteract the pronounced

decrease in plasticity initiated below the Mdg!a0 temperature.

For complete characterization of the strain-induced a0

martensite formation, the isolines for the a0-martensite

volume fraction are drawn on the g!a0 martensitic

transformation field of the STT diagram. These isolines

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illustrate the kinetics of a0-martensite forma-

tion depending on temperature and tensile

stress. It has to be noted, that the volume

fraction of a0 martensite is very sensitive on

the chemical composition of the studied steel,

in particular on the C and Ni concentration,

respectively.

In addition, isothermal martensite forma-

tion can be observed in the Cr–Mn–Ni steel.[1]

Hence, the MSi temperature in the STT and

DTT diagrams marks the highest tempera-

ture for the isothermal martensitic transfor-

mation. Therefore, the stress value measured

at the second inflection point in the flow

curves is higher than Rmg and corresponds

to the stress Rmgþa0(isotherm).[3] Therefore,

Rmg was estimated based on the measured

Rmgþ a0(isotherm) values. A revision of the Rg

m

course showed, that its increase at low

temperatures was too high compared with

similar austenitic steels.[14,22] The course of

Rmg was therefore accordingly corrected.

The deformation mechanism map, with

corresponding values of uniform elongation

of steel AgSteel and that of austenite Ag

g, is

illustrated in the DTT diagram. Additionally,

the degree of elongation contributed by

glide Deg, twinning DeTw and strain-induced

martensite transformation Dea0 are shown in

the DTT diagram. At the onset of temperature

anomaly of elongation at 2508C, the twinning

mechanism is responsible for the strong increase of elongation

with decreasing temperature (DeTw). Below approximately

�508C, the strain-induced g!a0 mechanism (Dea0) is

partially replaced by the g! e or twinning mechanism. The

changes of microstructure at low temperatures were

studied only by magnetic measurement during and after

deformation and microscopically after deformation. The exact

mechanism of straining running before the a0-martensite

formation, i.e. the stacking fault formation and/or e-formation

and/or twinning, respectively, was not studied microscopi-

cally. The maximum uniform elongation of about 0.45 is

achieved at 708C. A superposition of three-deformation

mechanisms glide of regular and partial dislocations in

austenite, TWIP, and TRIP effects – takes place at this

temperature and causes the highest uniform elongation. It

has to be mentioned that the borderline between the fields of

TWIP and a0-TRIP was corrected in a short temperature range

below the MdgþTw!a0 temperature, compared with earlier

publications.[22]

2.2. Gibbs Free Energy Change in the g!a Transformation

The DG value was calculated as the difference between the

Gibbs free energy of the a-(BCC)-phase and g-(FCC)-phase,

both of which have the same chemical composition, i.e.

the nominal chemical composition of the steel, because the


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Fig. 9. Calculated and corrected DG curves for the g!a0 transformation.Fig. 8. Driving force and triggering stress for the g!a0 transformation of steels with 6and 9% Ni.

Fig. 10. Volume fraction of a0-martensite, normalized difference between the austenitestrength and the triggering stress sA

g!a0, and elongation gain by the a0-TRIP effect.

martensitic transformations run without diffusion. It should

be noted that the thermodynamic data for many components

are not available for temperatures below RT. The calculations

for lower temperatures are done using the extrapolated

thermodynamic data, and thus the calculated values may be

inaccurate at such temperatures. Therefore, the DG curve has

to be corrected below RT prior to using it for the modeling.

For this correction as well as for the determination of the

nucleation threshold, and of the mechanical energy for

triggering the g!a0 transformation, i.e. the Wmin energy, a

juxtaposition of the calculated driving force and the triggering

stress for the g!a0 transformation in the temperature range

of 60 to 1008C was used (Figure 8) together with the data of a

similar steel containing 9% Ni[22] at 508C. Moreover, the

driving force and the triggering stress can be considered

as practically linear and correlate to each other in this

temperature range.

The factor F (see Equation 7) and the nucleation threshold

DGK were calculated using the following relation:

Wmin¼FsAg!a0 ¼ jDGK�DGg!a j which is valid for both

steels simultaneously. Assuming, that the differences in the

triggering stresses between the two steels are caused by the

differences in the chemical driving forces, and that the nickel

variation does not influence the nucleation threshold, the

variables F and DGK can be resolved using the data of the two

steels together. After the regression analysis the following

values were obtained: F¼ 0.4566 and the nucleation threshold

for the g!a0 transformation DGK¼�2060 J mol�1 at a

temperature of about 608C. The value of the nucleation

threshold distinguishes from the value of �2270 J mol�1 as

reported in our earlier publication.[22] The integration of the

force-displacement curve obtained in the tensile test was

applied in the old method of calculation of mechanical energy.

This is too imprecise due to the amount of the heat energy

dissipated during the deformation, which is difficult to

quantify.

Then, given the correlation between DG and the course of

the mechanical energy for triggering the transformation Wmin,



the DG curve was corrected at the temperatures below 608C,

see Figure 9. In addition, the DG values when just the

extrapolated thermodynamic data are used in the calculations

are shown.

2.3. Strain-Induced a0-Martensite Formation and AdditionalElongation by a0-TRIP

Important information, such as the additional elongation

due to the a0-TRIP effect and the normalized difference

between the strength of austenite and the triggering stress

sAg!a0 can be derived from the STT and DTT diagrams.

These variables are shown in Figure 10 together with the

a0-martensite volume fraction as functions of the temperature.

It can be seen that these three curves correlate. There is a direct

relationship between the strain-induced martensite fraction

and the additional elongation. Moreover, these two variables

are directly related to the course of triggering stress, which

immediately reflects the chemical driving force. This fact

allows an approach to predict the maximum strain-induced


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martensite volume fraction as function of temperature based

on the thermodynamics of austenitic Cr–Mn–Ni steels.

2.4. Calculation of the Strain-Induced a0-Martensite VolumeFraction

For prediction of the strain-induced a0-martensite forma-

tion and its maximum volume fraction, the calculation of the

maximum total driving force is needed. As mentioned above,

the maximum total driving force can be calculated as the sum

of the chemical driving force and the highest mechanical

energy Wgmax, which can be provided by the austenite

(cf. Equation 3). The chemical driving force was calculated

using software for thermodynamic calculations and then it

was corrected using experimental data from tensile tests (see

Figure 9).

The F value of 0.4566 as determined above was used for

the calculation of the energy Wgmax and the maximum total

driving force for the g!a0 transformation, as shown in

Figure 11.

For each total driving force below the nucleation threshold

or for each temperature below Mdg!a0, a corresponding

Fig. 11. Chemical and total driving forces and the nucleation threshold (a) and a zoomedarea of a0-martensite formation with superimposed isolines of the volume fraction ofa0-martensite (b).


experimentally measurable volume fraction of a0-martensite

Va0 exists. Therefore a relationship can be established between

the volume fraction of a0-martensite and the total driving

force. The data analysis showed, that a JMAK-type function

expresses the energetic and temperature dependence of the

volume fraction of strain-induced a0-martensite very pre-

cisely. As a result, the following equation was obtained after

the regression analysis:

Va0 ¼ 1� exp

�9:887�

�ð8:95þ 5:65� 10�3 � TÞ

� ðDGtotal � DGKÞDGK

�5:57! (9)

where the term (DGtotal�DGK)/DGK is the relative total

driving force above the nucleation threshold scaled by the

nucleation threshold. Figure 11b shows the area of the

strain-induced a0-martensite formation with isolines of

a0-martensite volume fraction, i.e. the energy thresholds for

several martensite fractions. It should be noted that this

energy thresholds or the isolines of a0-volume fraction are

obtained to be temperature-dependent for better matching the

experimental data. This possibility has been suggested earlier

in some publications.[9–10,13,23]

3. Conclusions

The microstructure evolution during deformation and the

mechanical behaviour of an austenitic Cr–Mn–Ni as cast steel

were investigated at various temperatures using several

complementary techniques. The deformation-induced twin-

ning and e/a0-martensite formation, i.e. the TWIP and TRIP

effects, occur in the investigated steel depending on the

deformation temperature. For characterisation and illustra-

tion of the TRIP/TWIP effects STT and DTT diagrams were

developed. These diagrams summarise all gained knowledge

regarding the deformation-induced processes and their

impact on the mechanical properties. The nucleation thresh-

old for the g!a0 transformation was determined, and the

calculated chemical driving force was corrected for tempera-

tures below 60 8C using experimental data. Finally, an

equation was proposed to describe the volume fraction of

strain-induced a0-martensite as a function of the total driving

force and the temperature.

Received: November 8, 2012

Final Version: April 8, 2013

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