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Martensite

Lecture Series –B-2

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Displacive decomposition of Austenite

log{time}

Tem

pera

ture

/ °C

Ms

ferritepearlite

bainite

martensite

Ae3

upper bainite

lower bainite

Widmanstatten ferriteBs

Ws

Reconstructive

Displacive

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• The “displacive transformation products” are very important form engineering point of view, because the volume fraction of these products directly affects the mechanical properties of the steels.• For example steels in bainite conditions show a

remarkable combination of strengthand toughness [Nakasugi et al. 1983] • and the large volume fraction of acicular ferrite

enhances the toughness [Garland and Kirkwood, 1975].

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Martensite (in steel)

• Plate• Lath• Lenticular

• α‘ = Alpha Prime Martensite(bct-hard)

• ε = Epsilon Martensite (hcp-soft) e.g Maraging Steel (Zero Carbon)

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Introduction• The name Martensite is after the German scientist

Martens. • The quenching to room temperature of austenite in a steel

can lead to the formation of martensite, a very hard phase in which the carbon, formerly in solid solution in the austenite, remains in solution in the new phase.• Unlike ferrite or pearlite, martensite forms by a

deformation of the austenite lattice without any diffusion of atoms.• The deformation causes a change in the shape of the

transformed region, consisting of a large shear and a volume expansion

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• Martensite is, therefore, often referred to as a diffusionless, shear transformation, which is highly crystallographic in character because it is generated by a specific deformation of the austenite.

• Martensite remains of the greatest technological importance in steels where it can confer an outstanding combination of strength (> 3500MPa) and toughness (> 200MPam1/2 )

• Martensite forms in many material, for example, nonferrous alloys, pure metals, ceramics, minerals, inorganic compounds, solidified gases and polymers (Table 1 slide No 8).

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Characteristics Of Martensite

Lenticular

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1- Diffusionless Character:

• Martensitic transformations are diffusionless.

Evidence 1.

Martensite can form at very low temperatures, where diffusion, even of interstitial atoms, is not conceivable over the time period of the experiment.

Rejection of the Evidence 1.

Table 1 gives values of the highest temperature at which martensite forms in a variety of materials; It is obvious that although martensite can form at low temperatures, it need not do so. Therefore, a low transformation temperature is not sufficient evidence for diffusionless transformation.

but Q: what evidence is there to support this?

χ

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Evidence 2.

• Martensite can form extremely rapidly.• Martensite plates can grow

at speeds which approach that of sound in the metal.• Speed of Sound in metal =

1100ms−1 compare with fastest solidification rate = 80ms−1 in pure nickel. (b/c solidification involves diffusion)

Rejection of the Evidence 2.

It can grow slowly as in case of shape–memory alloys the interface velocity is small enough to observe. Where growing an un-growing the Martensite at a slow rate.Therefore, martensite need notgrow so rapidly.

χ

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Evidence 3.

• The chemical composition of martensite can be measured and shown to be identical to that of the parent austenite.

Acceptance of the Evidence 3.

The entirety of these observations demonstrate realistically that martensitic transformations are diffusionless.

√

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2. The Habit Plane.• This is the interface plane between austenite (γ) and martensite (α’) as

measured on a macroscopic scale.• For unconstrained (free/unhindered) transformations this interface

plane is flat,

Single CrystalSingle Crystal in air

Supposing Nothing

surrounding it

Habit Plane

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• when the transformation is constrained (Forced) by its surroundings the minimization of strain energy introduces some curvature.

Habit Plane

Forced by its surroundings Like polycrystalline (many grains)

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• Steels of much different chemical composition can have martensite with the same habit plane (Table 2), and indeed, other identical crystallographic characteristics.

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3. Orientation Relationships.• Formation of martensite involves the coordinated movement of

atoms it means the austenite and martensite lattices are closely related.

• close–packed planes in the ferrite and austenite are parallel or nearly parallel, and corresponding directions within these planes are roughly parallel:

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Note: The body–centred cubic lattice does not have a close–packed plane but {0 1 1}α is the most densely packed plane.

• Note that; these have been stated approximately: • the true relations are irrational, meaning that the indices of the parallel planes

and directions cannot be expressed using rational numbers (the square root of 2 is not a rational number).

Close packed Plane and

Direction are approximately

parallel

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4. Athermal Nature of Transformation• Athermally, i.e. the fraction (portion) transformed depends on the

undercooling below a martensite-start temperature, Ms.• The Koistenen and Marburger equation which describes the progress

of transformation below Ms:

• Vα is the fraction of martensite and Tq is a temperature below M′ S.• This athermal character is a consequence of very rapid nucleation and

growth, so rapid that the time taken can be neglected.

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the amount of reaction is found to be virtually independent of time.

1%

50%

95%

Volume fraction of Martensite Vα’ is a function of Temperature not time. no matter how long hold you at that temperature

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What is To ?

Driving force for the nucleation of Martensite at the Ms temperature:

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• From Equation; it is evident that some austenite remains untransformed when Tq is set to room temperature. This is referred to as retained austenite.

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• The relative effect of other alloying elements is indicated in the following empirical relationship due to Andrews (concentrations in wt%): The equation applies to a limited class of steels

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5. Structure of the Interface b/w γ & α’:• What is Interface: is simple a set of dislocation that allow to connect

two crystals.

• The formation of martensite cannot depend on the thermal activation. There must be a high level of continuity(link) across the interface, which must (may) be coherent and semi–coherent.

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• Ans is : It must be Glissile. • But Fully coherent or semi

–coherent??????

Migration of atoms by dislocation glide that results in the shearing of the parent lattice into the product.

Migration of atoms by the random jumps of individual atom/atoms across the interface.(Climb)

Q: What kind of interface must be present b/w austenite γ & martensite α’?

Hint: It must be special interface that allow rapid transformation without any diffusion.

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• Fully coherent interface is impossible for the γ → α transformation ′because, the lattice deformation BR is an invariant–line strain.

WhereB = Bain StrainR = Rigid Body Rotation

• Invariant-Line: there is no distortion and rotation b/w γ & α ′along that line.

• Means Austenite and martensite match perfectly along that line.• Therefore, the interface b/w γ & α ′

must be semi coherent in a special way.

Fig: Fully Coherent

Fig: A semi-coherent interface

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semi coherency in a special way that there is one set of dislocation:

1. A semi– coherent interface must be such that the interfacial dislocations can glide as the interface moves (climb is not permitted)

2. There is an additional condition for a semi–coherent interface to be glissile.

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• Fig. Atomic matching across a (lll)fcc /(ll0)bcc interface bearing the NW orientation relationship for lattice parameters closely corresponding to the case of fcc and bcc iron (M.G. Hall et al., Surface Science, 31 (1972) 257).

• K-S and N-W orientation can be found approx. in this type of semi-coherency.

Complex Semi-coherent Interfaces

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6. The Shape Deformation: • The shape deformation can be

observed by “Interference Microscopy”• Color represents “HIGHT”• It shows real physical deformation

like plastic deformation by twining & Slipping (shows only change in shape)• In Martensite : Deform (Shape

change) + Crystal structural change.Austenite Sample transformed to Martensite. It is not etched sample.

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• Any scratch which is crossing the transformed region is

similarly deflected though the scratch remains

connected at the α′/γ interface.

Deflection of surface scratch

Figs. – Deflection of surface scratch in Fe-0.31C-30.5%Ni steel due to Martensite formation

Surface Relief

Figs. - Surface relief due to martensitic trasnformation

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• (a, b) Step caused by the passage of a slip dislocation.• (c, d) Many slip

dislocations, causing a macroscopic shear.

Wrong Shape because there is only volume change not crystal structure change.

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(a) Uniaxial dilatation: (Volume change)

Suppose Beryllium-Crystal having Possion ratio =Zero; if it is pulled there is only change in length not contraction i.e. volume change = a3 of Square ≠ a3 of Rectangle.(b) Simple shear:If something is shear there is only shear not volume change.(c) If we add (a) + (b) = Volume + Shear, we get Martensitic shape, which is actually form in Martensite.

Fig: shape deformation is an invariant–plane strain

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• The observations confirm that the measured shape

deformation is an invariant–plane strain with a

large shear component (≃ 0.22) and a small dilatational

strain (≃ 0.03) directed normal to the habit plane.

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7. Bain Strain. (Bain Distortion Model)

• Bain deformation(Strain):

There is a compression along the z axis and a uniform expansion along the x and y axes.

No deformation just arrangement of atoms in bct but still fcc.

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Drawback (inconsistency) of Bain Model:• Although Bain Model has been accepted but, 1. This model neither involve- shear transformation- an important

feature of martensitic transformation2. It does not explain orientation relationship.3. It does not explain a well established Habit Plan.4. No undistorted plane is available in Bain Distortion Model.5. It is not possible to explain IPS associated with martensitic

transformation.

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• The Bain strain implies the following orientation relationship between the parent and product lattices:

• but in fact, the experimentally observed orientation relationships are irrational not exactly like that.

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Q: Is Bain strain leaves at least one line invariant?

• Yellow sphere = Austenite• If it is compressed = Elliposed is

formed (Expansion along x-axis)• So, oa become oa’ and ob become

ob’ are all equal length, means length of oa and ob did not change by the BAIN STRAIN.• Now, are these invariant line?No, b/c they are undistorted but they are rotated.

So, the problem with Bain Strain, B: it does not leave any line invariant..

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• Supposing Austenite (Yellow sphere) and we apply Bain Strain and generated (Ellipsoid) Martensite. • And then we rotate Martensite with

respect to the austenite so one of these lines are connected.• So the combination of Bain strain (B) and

rigid body rotation (B) gives an Invariant-line strain (ILS).• Bain strain is one-part of the deformation

the other part is rotation which generates this invariant line. But there is no rotation which will give two invariant line b/c we need two invariant line to define invariant plane.

(still in-consistency with this)

But this extra rotation that we have put it, that’s predicts the irrational orientation relationship. (so as a result one problem has been solved)

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Phenomenological Theory of Martensite

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• Single crystal of Austenite

• Transformed into Martensite. • We get a shape change which is like a shear,

observed shape is correct but wrong crystal structure b/c we can not form austenite into Martensite by simple shear.

• The observed shape deformation is an invariant-plane strain .

• If a second homogeneous shear P2 is combined with P1 (step b to c), then the correct structure is obtained but the wrong shape since: P1P2 = RB.

• The Problem did not solve, we need to correct shape without change crystal structure.

Phenomenological Theory of Martensite Two-shear theory of Martensite formation

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• These discrepancies are all resolved if the shape changing effect of P2 is cancelled macroscopically by an inhomogeneous lattice-invariant deformation, which may be slip or twinning

• The theory predicts a substructure in plates of martensite (either twins or slip steps) as is observed experimentally.

• The transformation ensure that the shape deformation is macroscopically an invariant-plane strain because this reduces the strain energy when compared with the case where the shape deformation might be an ILS.

Conclusion

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• Figure shows schematically the two types of lattice invariant deformation occurring within a martensite plate. (Slipping & Twining)

It should be noted that the block of martensite formed has produced a surface tilt and that the observed habit is preserved by the accommodation provided by either slip (Fig. 5.10a) or twinning (Fig. 5.10b)

(Fig. 5.10a)

(Fig. 5.10b)

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Q: When do we get slipped Martensite and Twinned Martensite?

When steel deform at normal strain rate-

When steel blasted

produces lots of mechanical

twin.-

• Martensite forms extremely rapidly will be twinned.

• Martensite which has dislocated interface and produces slip steps it tends to be slipped.

• If both of these processes happen perfectly no one can find dislocation in the Martensite.

• Zero Dislocation density in the Martensite.(If processes happen perfectly )

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Fig. - Schematic of shear and surface tilt associated with formation of amartensite plate.

Dislocation density is due to plastic relaxation of shape change.

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• For FCC to HCP • B = P1• Habit Plane is Rational {111}γ

Why ε-Martensite Forms exactly {111}γ ?

Lath (Fe-9%Ni-0.15%C)

Lenticular(Fe-29%Ni-0.26%C)

Thin plate(Fe-31%Ni-0.23%C)

Substructure/Mechanism

Dislocation/Slipped

DislocationTwin (midrib) /Both

Twin/Twining

Habit plane {111}A

{557}A

{259}A

{3 10 15}A{3 10 15}A

Orientation Relatioship K-S N-W

G-T G-T

Ms -Temperature high low

8. Morphology and crystallography of a’ (bcc or bct) Martensite in ferrous alloys

Fig. - Ms temperatures as a function of carbon content in steels. Composition ranges of lath and plate martensite in Fe-C alloys are also shown.

Fig. – Retained austenite as a function of carbon content in Fe-C steels.

Lath Martensite

Fe-31%Ni-0.28%C (Ms=192K)

Lenticular Martensite (Optical micrograph)

Fe-29%Ni-0.26%C (Ms=203K)

Thin plate Martensite

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End Of Martensite

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Invariant-Plane Strain: If the operation of a strain, leaves one plane of the parent crystal completely unrotated and undistorted; this is known as an invariant-plane strain (IPS).