MicrostructureProperties: II Martensitic Transformations

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Microstructure-Properties II Martensitic
Transformations

• Prof. A. D. Rollett of CMU Presentation

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Objective

• 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.

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References

• 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
  martensites.
• 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.

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Notation

• 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

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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
  transformations.

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Massive vs. Martensitic Transformations

• There are two basic types of diffusionless
  transformations.
• 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.

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Classification of Transformations
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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.

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Free Energy - Composition T0
a,product
T1
?Gg?a
g,parent
G
Commontangent
T1gtT2
?Gg?a
T2
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.
X
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Driving Force Estimation

• The driving force for a martensitic
  transformation can be estimated in exactly the
  same way as for other transformations such as
  solidification.
• 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.

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Phase relationships
T near T0
equilibrium
diffusionless
Note that the Msline is horizontalin the TTT
diagramalso, the Mf line.
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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
  applies.
• ?G 16pg3 / 3(?GV - ?GS)2
• Why does martensite require heterogeneous
  nucleation? The reason is the large critical
  free energy for nucleation outlined above.

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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.

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Microstructures
Martensite formationrarely goes to completion
becauseof the strain associatedwith the
productthat leads to back stresses in
theparent phase.
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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.

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Mechanisms

• 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
  phases.
• This is analogous to slip (dislocation glide) and
  twinning, especially the latter.

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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.

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Bain model

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

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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.

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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
  nucleation.
• 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.

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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.

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Interstitial sites for C in Fe
fcc carbon occupies the octahedral sitesbcc
carbon occupies the octahedral sites
Leslie
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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.

PE
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Shape Memory Effect (SME)

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

Shape Memory Materials
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Temperatures
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
energy.
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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).

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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.

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Super-elasticity

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

Shape Memory Materials
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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.

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Self-accommodation

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

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Shape Memory Effect

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

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SurfaceRelief
Micrographs show a sequenceof temperatureswith
surfacerelief from themartensite plates.
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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
  Superelasticity

CriticalStress forMartensiteFormation
d?/dT ?S/? ?H/(Te??
As
Mf
Stress
SME
SE
Critical Stress forSlip
Temperature
Af
Ms
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Ni-Ti Alloys
Wasilewski, SME in Alloys, p245
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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
  exist.)

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Photo-stimulated SME!
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Summary

• 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)
  crystallography.
• Technological applications abound - quenched and
  tempered steels, Nitinol shape memory alloys etc.