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Microstructure-Properties: II Martensitic Transformations


Microstructure-Properties: II Martensitic Transformations 27-302 Lecture 6 Fall, 2002 Prof. A. D. Rollett Materials Tetrahedron Objective The objective of this ... – PowerPoint PPT presentation

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Title: Microstructure-Properties: II Martensitic Transformations

Microstructure-Properties II Martensitic
  • 27-302
  • Lecture 6
  • Fall, 2002
  • Prof. A. D. Rollett

Materials Tetrahedron
  • The objective of this lecture is to explain the
    basic features of martensitic transformations.
  • Martensitic transformations are the most
    important type of military transformations, i.e.
    transformations that do not require diffusion for
    the change in crystal structure to occur.
  • Why study martensitic transformations?! They
    occur in many different metal, ceramic polymer
    systems, and are generally important to
    understand. Steels represent the classical
    example (and a rate case of a mechanically hard
    martensite). Also, there are remarkable devices
    that exploit the shape memory effect (a
    consequence of martensitic transformation) such
    as stents that open up once at body temperature.
    The martensites in this case are generally soft,
    mechanically speaking.

  • Phase transformations in metals and alloys, D.A.
    Porter, K.E. Easterling, Chapman Hall. Porter
    Easterling concentrate on the geometrical and
    crystallographic characteristics of Fe-based
  • Materials Principles Practice, Butterworth
    Heinemann, Edited by C. Newey G. Weaver.
  • Otsuka, K. and C. M. Wayman (1998). Shape Memory
    Materials. Cambridge, England, Cambridge
    University Press. This book provides a very
    thorough description of the scientific and
    technological basis for the shape memory effect.

  • T0 Eq. Temp. for 2 phases at same
    composition?T undercooling?S entropy of
    transformation?H enthalpy of
    transformation?G Gibbs free energy e
    transformation straing Interface energy

Military Transformations
  • What is a martensitic transformation?
  • Most phase transformations studied in this course
    have been diffusional transformations where long
    range diffusion is required for the (nucleation
    and) growth of the new phase(s).
  • There is a whole other class of military
    transformations which are diffusionless
    transformations in which the atoms move only
    short distances in order to join the new phase
    (on the order of the interatomic spacing).
  • These transformations are also subject to the
    constraints of nucleation and growth. They are
    (almost invariably) associated with allotropic

Massive vs. Martensitic Transformations
  • There are two basic types of diffusionless
  • One is the massive transformation. In this type,
    a diffusionless transformation takes place
    without a definite orientation relationship. The
    interphase boundary (between parent and product
    phases) migrates so as to allow the new phase to
    grow. It is, however, a civilian transformation
    because the atoms move individually.
  • The other is the martensitic transformation. In
    this type, the change in phase involves a
    definite orientation relationship because the
    atoms have to move in a coordinated manner.
    There is always a change in shape which means
    that there is a strain associated with the
    transformation. The strain is a general one,
    meaning that all six (independent) coefficients
    can be different.

Classification of Transformations
Civilian Military
Diffusion Required Precipitation, Spinodal Decomposition ?
Diffusionless Massive Transformations Martensitic Transformations
Driving Forces
  • These transformations require larger driving
    forces than for diffusional transformations.
  • Why? In order for a transformation to occur
    without long range diffusion, it must take place
    without a change in composition.
  • This leads to the so-called T0 concept, which is
    the temperature at which the new phase can appear
    with a net decrease in free energy at the same
    composition as the parent (matrix) phase.
  • As the following diagram demonstrates, the
    temperature, T0, at which segregation-less
    transformation becomes possible (i.e. a decrease
    in free energy would occur), is always less than
    the solvus (liquidus) temperature.

Free Energy - Composition T0
T2 corresponds to figure 6.3b in PE.
Diffusionless transformation impossible at
T1, Diffusionless transformation possible at
T2 T0 is defined by no difference in free
energy between the phases, ?G0.
Driving Force Estimation
  • The driving force for a martensitic
    transformation can be estimated in exactly the
    same way as for other transformations such as
  • Provided that an enthalpy (latent heat of
    transformation) is known for the transformation,
    the driving force can be estimated as
    proportional to the latent heat and the
    undercooling below T0. ?Gg?a ?Hg?a ?T/T0.
  • Thus PE estimate the driving force at the
    temperature at which martensite formation starts
    in Eq. 6.1 using this relationship.

Phase relationships
T near T0
Note that the Msline is horizontalin the TTT
diagramalso, the Mf line.
Heterogeneous Nucleation
  • Why does martensite not form until well below the
    T0 temperature? The reason is that a finite
    driving force is required to supply the energy
    needed for (a) the interfacial energy of the
    nucleus and (b) the elastic energy associated
    with the transformation strain. The former is a
    small quantity (estimated at 0.02 J.m-2) but the
    elastic strain is large (estimated at 0.2 in the
    Fe-C system), see section 6.3.1 for details.
    Therefore the following (standard) equation
  • ?G 16pg3 / 3(?GV - ?GS)2
  • Why does martensite require heterogeneous
    nucleation? The reason is the large critical
    free energy for nucleation outlined above.

Microstructure of Martensite
  • The microstructural characteristics of martensite
    are- the product (martensite) phase has a well
    defined crystallographic relationship with the
    parent (matrix).- martensite forms as platelets
    within grains.- each platelet is accompanied by
    a shape change- the shape change appears to be
    a simple shear parallel to a habit plane (the
    common, coherent plane between the phases) and a
    uniaxial expansion (dilatation) normal to the
    habit plane. The habit plane in plain-carbon
    steels is close to (225), for example (see PE
    fig. 6.11).- successive sets of platelets form,
    each generation forming between pairs of the
    previous set.- the transformation rarely goes
    to completion.

Martensite formationrarely goes to completion
becauseof the strain associatedwith the
productthat leads to back stresses in
theparent phase.
Self-accommodation by variants
  • A typical feature of martensitic transformations
    is that each colony of martensite laths/plates
    consists of a stack in which different variants
    alternate. This allows large shears to be
    accommodated with minimal macroscopic shear.

  • The mechanisms of military transformations are
    not entirely clear. The small length scales mean
    that the reactions propagate at high rates -
    close to the speed of sound. The high rates are
    possible because of the absence of long range
    atomic movement (via diffusion).
  • Possible mechanisms for martensitic
    transformations include(a) dislocation based
    (b) shear based
  • Martensitic transformations strongly constrained
    by crystallography of the parent and product
  • This is analogous to slip (dislocation glide) and
    twinning, especially the latter.

Atomic model - the Bain Model
  • For the case of fcc Fe transforming to bct
    ferrite (Fe-C martensite), there is a basic
    model known as the Bain model.
  • The essential point of the Bain model is that it
    accounts for the structural transformation with a
    minimum of atomic motion.
  • Start with two fcc unit cells contract by 20 in
    the z direction, and expand by 12 along the x
    and y directions.

Bain model
  • Orientation relationships in the Bain model
    are(111)g ltgt (011)a 101g ltgt 111a
    110g ltgt 100a 112g ltgt 011a

Crystallography, contd.
  • Although the Bain model explains several basic
    aspects of martensite formation, additional
    features must be added for complete explanations
    (not discussed here).
  • The missing component of the transformation
    strain is an additional shear that changes the
    character of the strain so that an invariant
    plane exists. This is explained in fig. 6.8.

Role of Dislocations
  • Dislocations play an important, albeit hard to
    define role in martensitic transformations.
  • Dislocations in the parent phase (austenite)
    clearly provide sites for heterogeneous
  • Dislocation mechanisms are thought to be
    important for propagation/growth of martensite
    platelets or laths. Unfortunately, the
    transformation strain (and invariant plane) does
    not correspond to simple lattice dislocations in
    the fcc phase. Instead, more complex models of
    interfacial dislocations are required.

Why tetragonal Fe-C martensite?
  • At this point, it is worth stopping to ask why a
    tetragonal martensite forms in iron. The answer
    has to do with the preferred site for carbon as
    an interstitial impurity in bcc Fe.
  • Remember Fe-C martensites are unusual for being
    so strong ( brittle). Most martensites are not
    significantly stronger than their parent phases.
  • Interstitial sitesfcc octahedral sites radius
    0.052 nm tetrahedral sites radius 0.028
    nmbcc octahedral sites radius 0.019 nm
    tetrahedral sites radius 0.036 nm
  • Carbon atom radius 0.08 nm.
  • Surprisingly, it occupies the octahedral site in
    the bcc Fe structure, despite the smaller size of
    this site (compared to the tetrahedral sites)
    presumably because of the low modulus in the
    lt100gt directions.

Interstitial sites for C in Fe
fcc carbon occupies the octahedral sitesbcc
carbon occupies the octahedral sites
Carbon in ferrite
  • One consequence of the occupation of the
    octahedral site in ferrite is that the carbon
    atom has only two nearest neighbors.
  • Each carbon atom therefore distorts the iron
    lattice in its vicinity.
  • The distortion is a tetragonal distortion.
  • If all the carbon atoms occupy the same type of
    site then the entire lattice becomes tetragonal,
    as in the martensitic structure.
  • Switching of the carbon atom between adjacent
    sites leads to strong internal friction peaks at
    characteristic temperatures and frequencies.

Shape Memory Effect (SME)
  • General phenomenon associated with martensitic
  • Characteristic feature strain induced
    martensite (SIM), capable of thermal reversion.
  • Ferroelasticity and Superelasticity also
  • Md,Af,As,Ad,Ms,Mf temperatures.

Shape Memory Materials
The Md and Ad temperatures bracket T0 because
they define the on-cooling and on-heating
temperatures at which the transformation is
possible with allowance for the effect of strain
SME Definitions
  • Md SIM possible below Md.
  • Af reversion of SIM complete above Af (heating).
  • As reversion of SIM starts above As (heating).
  • Ad formation of parent phase possible above Ad.
  • Ms martensite start temperature (cooling).
  • Mf martensite finish temperature (cooling).

SME, contd.
  • Classic alloy Nitinol NiTi
  • alloying for control of Ms.
  • Stress for SIM must be less than yield stress for
    plastic deformation.
  • SME depends on incomplete transformation and
    elastic back stresses to provide memory (gtMS).
  • SME more effective in single xtals.
  • Alloying permits variations in the equilibrium
    transformation temperature, for example (critical
    for bio applications, for example). Also
    variations in the maximum strain that can be
    recovered are possible.

  • Super-elasticity is simply reversible (therefore
    elastic) deformation over very large strain
    ranges (many ).
  • Example Ti-50.2Ni.

Shape Memory Materials
Role of Ordering
  • A key feature of the Ni-Ti alloys for shape
    memory applications is that their compositions
    are all in the vicinity of 50Ni-50Ti and that the
    high temperature phase is an ordered B2
    structure. The low temperature B19 monoclinic
    structure is therefore also ordered (as is the
    other, intermediate R phase which is trigonal).
  • The ordered structure (recall the discussion of
    ordered particle strengthening) means that there
    is an appreciable resistance to dislocation
    motion. This is critical for favoring strain
    accommodation via transformation and twinning as
    opposed to dislocation glide.

  • Micrograph with diagram shows how different
    variants of a given martensitic phase form so as
    to minimize macroscopic shear strains in a given

Shape Memory Effect
  • Demonstration of shape memory effect (SME) in a
  • Mechanism of SME 1) transformation2)
    martensite, self-accommodated3) deformation by
    variant growth4) heating causes re-growth of
    parent phase in original orientation

Micrographs show a sequenceof temperatureswith
surfacerelief from themartensite plates.
Stress versus Temperature
  • The stress applied to the material must be less
    than the critical resolved shear stress for
    dislocation motion, because the latter is not
    recoverableSME Shape Memory Effect SE

CriticalStress forMartensiteFormation
d?/dT ?S/? ?H/(Te??
Critical Stress forSlip
Ni-Ti Alloys
Wasilewski, SME in Alloys, p245
X Ms Mf As Af
V gt 25 lt -140 lt -64 gt 25
Cr -100 lt -180 lt -58 gt 25
Mn -116 lt -180 lt -63 gt 10
Fe No information lt -180 -30 gt 25
Co No information No information 0 gt 25
Cu gt 25 lt -100 ? gt 25
TiNi0.95 70 60 108 113
TiNi 60 52 71 77
Ti0.95Ni -50 lt -180 ? 20 (?)
SME Requirements
  • For achieving a strong or technologically useful
    SME, the following characteristics are required.
  • High resistance to dislocation slip (to avoid
    irreversible deformation).
  • Easy twin motion in the martensitic state so that
    variants can exchange volume at low stresses.
  • Crystallographically reversible transformation
    from product phase back to parent phase. Ordered
    structures have this property (whereas for a
    disordered parent phase, e.g. most Fe-alloys,
    multiple routes back to the parent structure

Photo-stimulated SME!
  • Martensitic transformations are characterized by
    a diffusionless change in crystal structure.
  • The lack of change in composition means that
    larger driving forces and undercoolings are
    required in order for this type of transformation
    to occur.
  • The temperature below which a diffusionless
    transformation is possible is known as T0.
  • Martensitic transformations invariably result in
    significant strains with well defined (if
    irrational, in terms of Miller indices)
  • Technological applications abound - quenched and
    tempered steels, Nitinol shape memory alloys etc.
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