deformation behaviour of steels having different stacking fault energies - mm694 seminar report...

Deformation Behaviour of Steels Having Different Stacking Fault Energies

MM694: Seminar Report

Submitted in partial fulfilment of the requirements

of the degree of

Master of Technology

by

Karthik V V Subramaniyan Iyer

(Roll No. 123114004)

Supervisor

Prof. Prita Pant

Department of Metallurgical Engineering and Materials Science

INDIAN INSTITUTE OF TECHNOLOGY BOMBAY

(October 2012)

ABSTRACT

There is a ubiquitous need to increase tensile strength while simultaneously reducing yield strength and maintain high ductility for better formability of steels. To address this challenge it is essential to understand the various strengthening & deformation mechanisms at work and the factors that influence them. Stacking fault energy (SFE) is an important parameter that significantly affects the mechanical properties in steels. In the present work a comprehensive review of literature published on the relation between deformation mechanism & stacking fault energy is presented. A general description of stacking fault energy, the various approaches to determine it is also discussed. The influence of alloy chemical composition & temperature on SFE from numerous references is tabulated. It was found that there is consensus in the published literature about influence of SFE on deformation mechanism/ products, however there is a scatter in the value at which these mechanisms start or are active. The results on influence of alloying elements on SFE are also widely scattered and depend on the approached (experimental or theoretical) followed with each approach having its own set of limitations. It is crucial to further develop experimental methods and modelling tools to enhance the knowledge relating to SFE & deformation.

i

CONTENTS

Abstract.......................................................................................................................................i

Contents.....................................................................................................................................ii

List of Figures..........................................................................................................................iii

List of Tables............................................................................................................................iii

Chapter 1 Introduction.............................................................................................................1

1.1 Aim of Study.....................................................................................................................1

Chapter 2 Literature Survey....................................................................................................3

2.1 Stacking Fault Energy (SFE)............................................................................................32.1.1 Effect of Alloying Elements on Stacking Fault Energy 72.1.2 Effect of Temperature on Stacking Fault Energy 8

2.2 Mechanisms of Plastic Deformation in Steels................................................................122.2.1 ε-martensite 122.2.2 α`-martensite 132.2.3 Deformation Twins 13

2.3 Correlation between Deformation Mechanism & Stacking-Fault Energy......................17

References................................................................................................................................22

Acknowledgement...................................................................................................................25

ii

LIST OF FIGURES

Figure 2.1 Schematic representation of slip in a (1 1 1) plane of a fcc crystal.........................5Figure 2.2 Dark-field TEM micrographs of the deformation microstructure of a Fe–22Mn–

0.6C steel at 77 K (ε-martensite platelets) and at room temperature (mechanical twins)........................................................................................................................9

Figure 2.3 Schematic representation of the formation of twinning in FCC.............................15

LIST OF TABLES

Table 2.1 Effect of alloying elements on stacking fault energy...............................................10Table 2.2 Twelve possible twinning systems in FCC materials...............................................15Table 2.3 Stacking fault energy & deformation behaviour.......................................................19

iii

Chapter 1

Introduction

1.1 Aim of Study

Steels as engineering materials are of utmost importance to society because of their wide

range of properties which are used in variety of applications. Theoretically, steels are

interstitial alloys of carbon in iron where carbon is 0.008 to 2% by weight. The need to further

enhance their properties has led to the development of variety of steels spanning various

generations. Each new generation of steels is a result of advancement in understanding the

physical metallurgy leading to a better insight into various parameter property relationships.

There is a ubiquitous need to increase tensile strength while simultaneously reducing yield

strength and maintain high ductility for better formability especially in the automobile sector.

To address this challenge it is essential to understand the various strengthening & deformation

mechanisms at work and the factors that influence them. Stacking fault energy (SFE) is an

important parameter that significantly affects the mechanical properties in steels.

1

The aim of the present work was to carry out a survey of existing literature and understand the

deformation behaviour of steels with different SFE. Steels having BCC structure were not

studied for the reasons discussed as follows.

The stacking sequence in BCC metals is ABABAB. Stacking faults associated with BCC

structure may lead to two A or B layers coming in contact with one another. This leads to very

high theoretical stacking fault energy (~200 mj/m2) and hence stacking faults in BCC

structure have not been observed directly12. Even though the SFE of BCC iron has been

simulated3, to the best of my knowledge no experimental information exists about its SFE &

its effect on deformation.

2

Chapter 2

Literature Survey

2.1 Stacking Fault Energy (SFE)

Stacking faults are extremely significant feature in a crystal structure. They arise because

there is little to choose electrostatically between the stacking sequence of the close packed

planes in the FCC metals ABCABC… and that in the HCP metals ABABAB…. It is possible

that atoms in a part of one of the close-packed layers may fall into the ‘wrong’ position

relative to the atoms of the layers above and below, so that a mistake in the stacking sequence

occurs (e.g.ABCBCABC …). Even though such an arrangement will be more stable; work

needs to be performed to produce it.

The shortest lattice vector in the FCC structure joins a cube corner atom to a neighbouring

face centre atom and defines the observed slip direction; one such slip vector a/2[1 0 1] is

shown as b1 in Figure 2.1a, which is for glide in the (1 1 1) plane. However, an atom which

sits in a B position on top of the A plane would move most easily initially towards a C

3

position and, consequently, to produce a macroscopical slip movement along [1 0 1] the

atoms might be expected to take a zigzag path of the type B→C→B following the vectors b2

=a/6[2 1 1] and b3 =a/6[1 1 2] alternately.

It will be evident, of course, that during the initial part of the slip process when the atoms

change from B positions to C positions, a stacking fault in the (1 1 1) layers is produced and

the stacking sequence changes from ABCABC . . . to ABCACABC . . .. During the second

part of the slip process the correct stacking sequence is restored.

To describe the atoms movement during slip, discussed above, Heidenreich and Shockley

have pointed out that the unit dislocation must dissociate into two half-dislocations, which for

the case of glide in the (1 1 1) plane would be according to the reaction:

Such a dissociation process is algebraically correct as well energetically favourable since it

reduces the energy of the system (the sum of value of the partial dislocations is less the single

dislocation). These half dislocations, or Shockley partial dislocations, repel each other by a

force and separate, as shown in Figure 2.1b. A sheet of stacking faults is then formed in the

slip plane between the partials, and it is the creation of this faulted region, which has a higher

energy than the normal lattice, that prevents the partials from separating too far.14

Both partials are glissile on the (111) plane. If the stacking sequence of the (111) planes

changes from the regular stacking to the ‘faulted’ stacking by removing part of a {111} plane,

i.e., ABCABCABC→ABCACABCA, the fault is called an intrinsic stacking fault. In the case

of an extrinsic stacking fault, an additional part of a (111) plane is inserted in the crystal and

the stacking sequence consequently changes for instance as ABCABCABC→ABCACBCAB,

hence containing an excess plane with C stacking. In some cases it can be more convenient to

think of an extrinsic stacking fault as the overlapping of two intrinsic stacking faults on

successive (111) planes.

4

Figure 2.1 Schematic representation of slip in a (1 1 1) plane of a fcc crystal1

As mentioned earlier there is net repulsion force associated with the formation of the

Shockley partials. With increasing separation r of the partials there is also an increase in

energy ESF of the stacking fault associated with it given by the relation,

where L is the length of the dislocation and γSFE the stacking fault energy (per unit area) & r is

the shift of the dislocation line perpendicular to itself, so that a force opposing the repulsion of

the partials is

The equilibrium separation of the dissociated dislocation is hence controlled by the minimum

of the total stored energy in the stacking fault, corresponding to the force balance at the partial

dislocations:

5

Based on this the separation width d of the stacking fault is given by the relation5

d=G bp

2

4 π γ SFE

where G is the shear modulus and bp the absolute value of the Burger’s vector of the Shockley

partials. From the equation it is apparent that the width d of the stacking fault is essentially

controlled by the stacking fault energy γSFE. d in turn controls the ease of cross slip of screw

dislocations and is thus largely responsible for the prevailing deformation mechanism or

deformation type, i.e. planar glide, wavy glide, deformation twinning, or martensitic

transformation678.

Different methods to determine SFE has been reported in literature. They fall broadly under

two categories: experimental and theoretical calculations. One of the methods based on

observation of extended dislocation nodes is used to measure SFE experimentally from

electron diffraction measurements in transmission electron microscopy910. This method is

direct & considered to be especially accurate for the materials with the low SFE1112. The line

profile analysis of XRD spectrum is another experimental technique which is used indirectly

to determine SFE111314. Neutron diffraction has also been used to determine SFE & as

reported by the authors is better than the earlier mentioned experimental methods 15.

Experimental measurements of the SFE are particularly subtle and are subject to many

sources of bias. They are not widely reported in literature and are often sources of

controversy. For a given steel composition and temperature, the values reported can vary

significantly from one author to another1617.

Most authors have thus chosen an indirect approach trying to correlate calculations of SFE on

a thermodynamic basis with direct observations of deformation mechanisms by TEM. These

6

calculations are based on a relationship that exists between the SFE and the driving force for

ε-martensite formation first established by Hirth18 and popularized by Olson and Cohen19.

The approach considers that an intrinsic SF is in fact equivalent to a platelet of ε-martensite of

a thickness of only two atomic layers creating two new γε

interfaces. It follows that:

SFEintrinsic = 2ρ∆Gγ→ε + 2σγ/ε

Where ρ is the molar surface density along {1 1 1} planes and σγ/ε is the surface energy of the

interface γ/ε. The molar surface density ρ can be calculated using the lattice parameter a and

Avogadro’s constant N as

ρ= 4

√31

a2 N

The estimation of the Gibbs energy ∆Gγ→ε for the bulk γ→ε transformation is critical for

calculation of SFE162021.

An alternate approach for calculating SFE from quantum-mechanical first principles by using

exact muffin-tin orbital method (EMTO) is also reported1722. Also Peierls-Nabarro model

fitted to generalized stacking fault energies is also used to determine SFE23.

In order to optimize the mechanical properties of austenitic steels as desired, γSFE has to be

adjusted to an appropriate value24. The predominant variables; chemical composition &

temperature which affect γSFE are discussed below.

2.1.1 Effect of Alloying Elements on Stacking Fault Energy

The alloying effects on γSFE are quite complicated and sometimes contradict each other from

different experimental measurements. Additionally, as mentioned earlier the experimental γSFE

values are not accurate and are usually associated with large error bars. Based on the existing

databases, several empirical relationships between γSFE and chemical compositions have been

proposed1325. However, the application of these empirical relationships is limited and in

most cases they are unable to reproduce the complex nonlinear dependence of γSFE on the

composition17. Moreover, these empirical relationships hardly address the interactions

7

between the different alloying elements. A review of stacking fault energy maps based on

subregular solution model in high manganese steel is presented here26.Table 2.1 provides the

tabulated data of alloying element effect on SFE at a given temperature for a particular

element from various referenced sources. The approach used to find SFE is also mentioned.

2.1.2 Effect of Temperature on Stacking Fault Energy

For a given steel composition, the SFE increases as a function of the temperature according to

the following relationship272816:

d SFEintrinsic

dT=−8

√31

a2 N∆ Sγ →ε

where a is the lattice parameter, N the Avagadro number & ∆ Sγ → ε the change in entropy

during the γ→ε transformation. This equation comes from the derivative of the equation

presented above for intrinsic SFE. If the temperature is higher than the ε-martensite start

temperature Es, ∆ Sγ → ε is negative. Thus, the SFE increases with temperature above Es.

For a given steel composition, at a temperature that is high compared to Es, the SFE is high,

and the energetic cost of dissociation of perfect dislocation is unfavourable. The only possible

deformation mechanism is dislocation glide. The high temperature and high SFE enable cross-

slip events and activation of multiple slip systems. At lower temperatures, dislocation glide

becomes more and more planar, and below a certain value, large dissociation of dislocations

becomes favourable. This enables the twinning process to occur as a competitive mechanism

to dislocation glide since the energetic cost of twinning becomes sufficiently low. At even

lower temperatures, ε-martensite formation replaces deformation twinning. The transition

between mechanical twinning and ε-martensite formation is sustained by a shift of the

character of the stacking fault (SF) available to serve as a nucleus for these processes

(intrinsic or extrinsic for twin & martensite respectively)1629. Figure 2.2 shows TEM

micrographs of the deformation microstructure of a Fe–22Mn–0.6C steel at two different

8

temperature. It can be seen that at lower temperature (77 K) ε-martensite platelets are visible

whereas at higher temperature (300 K) mechanical twins can been seen.

Figure 2.2 Dark-field TEM micrographs of the deformation microstructure of a Fe–22Mn–0.6C steel at 77 K (ε-martensite platelets) and at room temperature (mechanical twins)16.

9

Table 2.1 Effect of alloying elements on stacking fault energy

ElementTemp.

(K)Base Composition SFE (mJ/m2)

Effect on

SFEMethod Remarks Ref.

Mn

300(69.5-74.5)Fe13.5Cr12Ni(0-5)Mn at% 44.6-32.1 ↑Mn ↓SFE

EMTO ↑Cr ↓SFE 17(65.5-70.5)Fe17.5Cr12Ni(0-5)Mn at% 28.6-17.6 ↑Mn ↓SFE

300Fe20Cr(8-16)Ni(0-8)Mn at% Varied range ↑Mn ↓SFE

EMTO 22Fe20Cr(16-20)Ni(0-8)Mn at% Varied range ↑Mn ↑SFE

Al

300

Fe22Mn0.6C

Fe22Mn0.6C3Al

Fe22Mn0.6C6Al

wt% 21.5

36.5

50.7

↑Al ↑SFE T 30

300

Fe22Mn0.6C

Fe22Mn0.6C3.5Al

Fe22Mn0.6C4.5Al

mass

%

~22.5

~38

~45

↑Al ↑SFE T 31

Si

300

Fe31Mn0.25Si0.77C

Fe31Mn2.03Si0.77C

Fe31Mn5.31Si0.77C

Fe31Mn8.67Si0.77C

at% 17.39

14.69

10.51

6.33

↑Si ↓SFE XRDγSFE (mJ/m2)=17.53-1.30 (Si at

%)11

300

Fe31Mn0.25Si0.77C

Fe31Mn2.03Si0.77C

Fe31Mn5.31Si0.77C

Fe31Mn8.67Si0.77C

at% 17.39

~19

~22.5

~25

↑Si ↑SFE T

Both non-magnetic & magnetic

effect on SFE.

Anomaly in shear modulus due

to antiferromagnetic order.

32

300 Fe22Mn0.6C

Fe22Mn0.6C3Si

Fe22Mn0.6C8Si

mass

%

~22.5

~25.5

~23

↑Si ↑SFE &

then

↑Si ↓SFE

T Inflection point observed at

3.5% Si

31

10

ElementTemp.


Effect on


Cr

300Fe(13-25)Cr14Ni at% ~45-15 ↑Cr ↓SFE

EMTO ↑Ni ↑SFE 17Fe(13-25)Cr16Ni at% ~47-25 ↑Cr ↓SFE

300

Fe22Mn0.6C

Fe22Mn0.6C4Cr

Fe22Mn0.6C6Cr

mass

%

~22.5

~18.5

~17

↑Cr ↓SFE T 31

Ni

300Fe17Cr(8-20)Ni at% ~9-40 ↑Ni ↑SFE

EMTO ↑Cr ↓SFE 17Fe19Cr(8-20)Ni at% ~0-35 ↑Ni ↑SFE

300Fe20Cr(8-16)Ni

Fe20Cr(16-20)Ni

at%~0-27.5

~27.5-25

↑Ni ↑SFE

& then

↑Ni ↓SFE

EMTOInflection point observed at

16% Ni22

Nb

300

(69.5-74.5)Fe13.5Cr12Ni(0-5)Nb at% 44.6-43.2 ↑Nb ↓SFE

EMTO

(↑Nb&↑Cr &↓Fe) ↑SFE

Opposite effect due to

interaction

17(65.5-70.5)Fe17.5Cr12Ni(0-5)Nb

at%28.6-40.6 ↑Nb ↑SFE

300Fe20Cr(<16)Ni(0-3)Nb

Fe20Cr(8-16)Ni(3-8)Nb

at% ↑Nb ↑SFE

↑Nb ↑SFEEMTO 22

Cu 300

Fe22Mn0.6C

Fe22Mn0.6C3.5Cu

Fe22Mn0.6C7.5Cu

mass

%

~22.5

~26

~30

↑Cu ↑SFE T 31

Co 300 Fe20Cr(8-20)Ni(0-8)Co at% Varied range ↑Co ↓SFE EMTO 22

N 300 Fe18Cr10Ni(0-0.3)N

Fe18Cr10Ni(0.3-0.6)N

wt% ~23-24

~24-8

↑N ↑SFE

↑N ↓SFE

T Inflection point observed at 0.3

% Ni

33

11

ElementTemp.


Effect on


Fe18Cr10Ni8Mn(0-0.3)N

Fe18Cr10Ni8Mn(0.3-0.6)N

~27.5-28.5

~28.5-13.5

↑N ↑SFE

↑N ↓SFE

EMTO - Exact Muffin-Tin Orbital Method, T- Thermodynamic Calculations, XRD- X-Ray Diffraction Line Profile Analysis

12

2.2 Mechanisms of Plastic Deformation in Steels

Generally plastic deformation occurs by dislocation glide in steels. However, especially in the

case of metastable austenite, either as retained austenite or fully austenitic structure;

mechanical twinning & various phase transformation can take place sometimes being the

dominant deformation mechanism.

Dislocation glide is the primary mechanism responsible for the change in shape during plastic

deformation of most metals; both twinning and phase transformations can produce additional

obstacles to dislocation glide and thus reduce the free mean path of dislocations. A reduction

in the free mean path of dislocations, in turn, gives rise to higher strain hardening rates. In

TRIP and TWIP steels advantage is taken of this phenomenon where martensitic phase

transformation and twinning, respectively, occurs during the progress of straining. A certain

amount of stress/strain is required to initiate the phase transformation or twinning of crystal

planes6. The products of alternative deformation mechanisms are discussed briefly below.

2.2.1 ε-martensite

During the γ fcc → ε hcpMs phase transformation, the close-packed planes and directions in the two

structures are parallel, i.e., γ{111}||ε{0001} and γ<110>||ε<1120>, and ε-martensite forms a

hexagonal close-packed (hcp) crystal structure. In terms of {111} planes of the cubic crystal

structure, the stacking sequence in the ε -martensite can be expressed as CACA. Therefore,

each single intrinsic stacking fault contains a thin layer of ε -martensite phase. As mentioned

earlier this consideration is used in the SFE calculation approach proposed by Olson and

Cohen19. Single stacking faults can be regarded as ε -martensite nuclei, while the growth of

‘perfect’ ε -martensite occurs by overlapping of the intrinsic stacking faults on every second

{111} plane or extrinsic stacking successive parallel {111} planes16. The distinction between

single stacking faults, bundles of overlapping stacking faults, and faulted or perfect ε -

martensite is therefore not quite unambiguous. Numerous authors have even observed that

both processes could be detected within the same shear bands.34

13

2.2.2 α`-martensite

Through comparison of the close packed planes of the fcc and hcp lattice, i.e., the {111}- and

the {0001}-plane, respectively, with the most closely packed plane {110} of the bcc lattice, it

is evident that the close packed planes of the fcc and hcp lattices can be transformed into the

{110} bcc-plane through little distortion. The lattice transformation can, e.g., be described

through the Bain transformation, which transforms the fcc lattice through buckling and

straining into the bcc lattice. The crystallographic orientation relationship between the γ and

the α’ phase obeys the Bain transformation relationship described by γ{111}|| α’{001} and

γ<100>|| α’<110> . Another commonly observed transformation orientation relationship is the

Kurdjumov-Sachs transformation, where close-packed planes of the fcc structure transform

into the most closely packed planes of the bcc crystal structure, and close-packed directions

into close-packed directions, i.e., γ{111}|| α’{110} and γ<110>|| α’<111>.

Many researchers have reported that the nucleation of α’-martensite takes place at the

intersections of shear bands, while others have reported nucleation within a single shear band.

Since in many cases shear bands consist of ε-martensite, it is often considered an intermediate

phase in the γ fcc → α bccMs phase transformation, which can then be written as γ fcc → ε hcp

Ms → α bccMs.

Whether the crystal structure of the α’-martensite should be considered bcc or slightly

tetragonally distorted bcc (bct), depends on the carbon content6.

2.2.3 Deformation Twins

The classical definition of twinning requires that the lattices of the twin and the matrix are

related either by a reflection in some plane, called the twin plane, or by rotation of 180° about

some axis, called the twin axis2. In crystals of high symmetry, such as fcc, these orientations

are equivalent. Deformation twins in fcc crystals form, at least in principle, by a homogeneous

shear of the parent lattice along the {111} plane in the <112> direction. Frank proposed a way

of creating a twin by stacking or overlapping of intrinsic stacking faults, i.e., by the glide of

Shockley partials with identical Burger’s vectors on successive {111} planes. The case of two

intrinsic stacking faults overlapping on successive {111} planes is referred to as an extrinsic

14

stacking fault, which can also be considered as the special case of a twin, two atom-layers in

thickness. If the overlapping of intrinsic stacking faults proceeds on successive {111} planes,

the twin grows in thickness. The thickness of single twins is therefore only of nanometer

scale, but stacks of nano-twins can add up to twin bands micrometers in thickness. The actual

substructure in twin bands is lamellae like, where arrays of twins and matrix alternate6.

Figure 2.3 is a schematic representation of the formation of mechanical twinning. As

explained earlier the sequential movement of close packed layers alongaγ

6[ 1 12 ] on (111)

plane forms a twin plate. It is obvious that movement along the opposite direction of bp1 is

unfavourable because the translation required would be -2bp1 which doubles the shear and

hence is not favoured from an energy point of view. Thus the shear displacement during twin

formation can take place only in a definite direction but cannot be reversed. The direct

consequence of this fact is the polarization of twinning direction which leads to: on each

{111} twinning plane, only three <112 > directions out of six can be the twinning direction.

Consequently there are 12 twinning systems in FCC, as listed in Table 2.24. The directional

character of twins does not manifest itself in isotropic materials. However, in the presence of

texture the twinning stresses in compression and tension can be different6.

15

Figure 2.3 Schematic representation of the formation of twinning in FCC4

Table 2.2 Twelve possible twinning systems in FCC materials4

Twinning Plane (111) ¿) ¿) ¿)

Twinning Directions

[112] [112] [112] [112][ 12 1 ] [121] [121] [112][ 21 1 ] [211] [211] [ 21 1 ]

In most cases the critical event in the twinning process is nucleation, while growth can occur

at stresses much lower than the nucleation stress. The critical twinning stress can, at least in

theory, be formulated in analogy to the critical resolved shear stress τCRSS for dislocation glide.

However, the experimental evidence supporting this theory suffers from large scatter in

measured twinning stresses. Several critical factors affecting the experimental results can be

the reason for this large scatter. On the one hand, the incidence of twinning as well as the

twinning-slip competition are very sensitive to orientation and therefore require that very

accurate and reproducible orientations in the test specimens are guaranteed. On the other

hand, impurity levels and defect structures giving rise to local stress concentrations can have a

great effect on the twin nucleation in polycrystals, while in single crystals stress concentration

sites of different nature can have a similar effect (e.g. surface notches, internal flaws, etc.).

16

Twinning in fcc metals often nucleates at microscopic defect structures and the local stress at

which twinning initiates is considerably higher than the externally applied stress6.

When an appropriate external shear stress is applied, the width d of the stacking fault may

increase or decrease, depending on the type of stress. The equilibrium width when it increases

is given by35

d=Gb p

2

8 π (γ¿¿ SFE−τ b p)¿

where τ is the applied shear stress. Therefore, the split distance is a function of the applied

stress and the value of SFE. SFE is the intrinsic factor of the materials, while the applied

stress represents the corresponding external deformation conditions. It can be seen that the

split distance increases with increasing applied shear stress. If the applied stress increases to a

critical value, the split distance will approach infinity. A critical value of shear stress clearly

exists, above which the propagation of SF is catastrophic. In general, forming a wide SF is the

prerequisite step of nucleation of a deformation twin. Therefore, the required twinning stress

must be greater than this critical value. This value can be found out since as d→∞; (

γ SFE−τ bp ¿→0

Thus from the above equation we get critical stress τC as35;

τC=γ SFE

bp

Thus τC increases with increasing γSFE. This has proven to be true mostly for fcc metals.

Venables found a linear relationship for the twinning stress as a function of the square root of

γSFE. Narita et al. have confirmed that τCCu>τC

Ag>τCAu in accordance withγ SFE

Cu >γSFEAg >γ SFE

Au , and

Narita and Takamura found a proportional relationship for Ni-Ge alloys, Cu, Au, and Ag

according to γ SFE=2bS τC, where bS is the Burger’s vector of a Shockley partial6.

17

The effect of grain size on the twinning stress obeys in most cases the Hall-Petch

relationship,

σ T=σT 0+kT d−1 /2

where the slope kT is larger than the slope kS for slip, i.e., the twinning stress is more sensitive

to grain size than the slip stress. The reason for the difference is still not fully understood, but

Armstrong and Worthington attributed the higher grain size sensitivity of the twinning stress

to microplasticity, i.e., to localized dislocation activity at stress levels where the metal is

globally in the elastic domain, whereas the yield stress is associated with the onset of global

plastic deformation636.

2.3 Correlation between Deformation Mechanism & Stacking-Fault Energy

The deformation mechanisms and mechanical properties of fcc metals are strongly related to

their stacking fault energy (SFE) γSFE. The dimensionless parameter γSFE /Gb, where G is the

shear modulus and b the slip distance, is a measure for the ease of cross slip of screw

dislocations and therefore determines the work hardening behaviour during deformation. To

fully exploit the twinning and/or phase transformation mechanisms in austenitic steels, the

magnitude of γSFE has to be properly adjusted by choosing the right amount of chemical

alloying elements. At low γSFE, wide dissociation of dislocations into Shockley partials can

hinder dislocation glide and thus favour mechanical twinning (γ→γT) or martensitic phase

transformation (γ fcc → α bccMs or γ fcc → ε hcp

Ms → α bccMs ). The γ→ α` transformation occurs in steels

whose with γSFE ≤ 12 mJ/m2 and generally at low temperature1637.

There is a wide variation in the SFE values proposed for martensitic transformation from

about γSFE ≤ 16 mJ/m2 to γSFE ≤ 20 mJ/m2. For stacking fault energies of the order γSFE = 25

mJ/m2 twinning becomes the dominant deformation mechanism. At even higher stacking fault

energies of approximately γSFE ≥ 45 mJ/m2, plasticity is controlled solely by dislocation

glide638.The data from numerous references relating the deformation mechanism/

18

deformation microstructure observed for different steels at various SFE values is tabulated in

Table 2.3. The deformation mechanism & deformed microstructure are generally

characterized by XRD & TEM.

19

Table 2.3 Stacking fault energy & deformation behaviour

Base Composition Temp.

(K)

SFE

(mJ/m2)

Metho

d

Deformation

Mechanism/Microstructur

e

RemarksRef

.Fe Mn Si Ni Cr Al C Nb Cu N

Bal.

at%

22 0 0.6

300

21.5

36.5

50.7

TPlanar glide followed by

mechanical twinning

↑SFE→↑τC→↑

Strain for onset of

twinning

3022 3 0.6

22 6 0.6

Bal.

at%

280.2

8+ Mo

<0.0

1

1.6 0.08<0.00

1

300

27

T

Mechanical twinning

21250.2

41.6 0.08 0.05 20.5 Mechanical twinning

Below 225K ε-

martensite

270.5

24.1 0.08 0.05 42 Mechanical twinning

Above 350K

dislocation slip

Bal.

Mas

s

%

21.9 0.45

300

15

T

Mechanical twinningTwinning frequency

more

3921.9 0.59 20 Mechanical twinning

24.6 0.59 25 Mechanical twinningTwinning frequency

less

Bal.

wt.

%

13 0.3

300

~0

T

Deformed ε & α’ martensite

4022 0.1 7 ε & deformed ε martensite

18 0.6 19 Mechanical twinning

24 0.7 35 Mechanical twinning

Bal. 22 0.6 77 10 T ε martensite ↑Temp.↑ SFE 41

20


(K)

SFE

(mJ/m2)

Metho

d

Deformation


e

RemarksRef


wt.

%

22 0.6 293 19 Mechanical twinning

22 0.6 693 80 Dislocation Gliding

Bal.

wt.

%

1.490.43

8.2

18.20.00

3

0.04

9 0.430.04

7

300

30

T

Mechanical twinning

In the temperature

range 50≤T≤600 K

↑Temp.↑ SFE

42

1.710.33

8.1

18.20.04

1 0.370.05

429.2

1.221.12

6.4

16.70.00

2

0.09

3 0.250.07

426.6 Mechanical twinning

6.970.35

4.5

17.60.00

5

0.04

5 0.250.19

824.6

1.230.50

6.6

17.40.03

00.16

80.16

823.7

1.610.48

6.6

17.60.01

9 0.220.09

423.2

1.340.51

6.6

17.40.01

7 0.140.14

522.6

28.00.28

<0.01

1.6 0.08 27 Mechanical twinning

5.700.29

4.7

17.30.00

1

0.04

7 2.390.10

724.9 Mechanical twinning

9.000.40

1.1

15.20.00

2

0.07

9 1.680.11

516.8 ε mart. & mech. twinning

21


(K)

SFE

(mJ/m2)

Metho

d

Deformation


e

RemarksRef


Bal.

wt.

%

9.730.24

17.83 0.03 0.39

300

10.4

ND

Deformed ε martensite

15

9.70.24

18.06 0.03 0.44 12.2

9.580.26

17.65 0.03 0.51 17.1ε martensite & mechanical

twinning

9.820.17


10.19

0.25

18.02 0.15 0.42 20.1ε martensite & mechanical

twinning

9.660.22


Bal.

wt.

%

~10 0.6 2

300

10

T


31~13 0.6 2 12 Deformed ε & α’ martensite

~16 0.6 2 15 Deformed ε martensite

~20 0.6 2 17 Deformed ε martensite

Bal.

wt.

%

20.24

2.44

1.95 0.01 0

300 XRD


43

22.57

2.46

1.18 0.010.01

1Deformed ε

21.55

3.00

0.69 0.010.05

2Deformed ε & α’ martensite

20.72

2.00

2.46 0.010.02

2

Mechanical Twinning

Bal.

wt.

19.84

1.3300

24.36T Mechanical Twinning 44

19.8 1.31 1.5 26.56 Mechanical Twinning

22


(K)

SFE

(mJ/m2)

Metho

d

Deformation


e

RemarksRef


%

7

19.87

1.31 3.04 28.74 Mechanical Twinning

Bal.

wt.

%

19 5 0 0.25

300

~9

XRD

Deformed ε & α’ martensiteAl acts as γ

stabilizer at low

conc. And as δ

stabilizer at high

conc.

45

19 5 1 0.25 ~20 Mechanical twinning

19 5 2.5 0.25 ~30 Mechanical twinning


19 5 4 0.25 ~45 Mechanical twinning


T- Thermodynamic Calculations, ND- Neutron Diffraction, XRD- X-Ray Diffraction Line Profile Analysis

23

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x

26

ACKNOWLEDGEMENT

I would like to express my warm gratitude and thanks to Prof. Prita Pant, my seminar supervisor, without whose enterprise and endeavour this seminar report would not have been a possibility.I would also like to express my sincere gratitude to Abhinandan Gangopadhyay and Srijan Sengupta for their support during the course of the present work.

Karthik Iyer

Roll no. – 123114004

27

deformation behaviour of steels having different stacking fault energies - mm694 seminar report...

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