Transcript Microstructure-Properties: II Lecture 12: Martensitic Transformations

1
Objective
Basics
Microstructure-Properties: II
Martensitic Transformations
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
27-302
Lecture 6
Fall, 2002
Prof. A. D. Rollett
2
Materials Tetrahedron
Processing
Performance
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
Microstructure
Properties
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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
Objective
diffusion for the change in crystal structure to occur.
Basics
• Why study martensitic transformations?! They occur in many
T0 concept
different metal, ceramic & polymer systems, and are generally
important to understand. Steels represent the classical
Microexample (and a rate case of a mechanically hard martensite).
structures
Also, there are remarkable devices that exploit the shape
Bain
memory effect (a consequence of martensitic transformation)
model
such as stents that open up once at body temperature. The
Carbon
martensites in this case are generally soft, mechanically
in Fe
speaking.
SME
4
References
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
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 strain
g := Interface energy
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Military Transformations
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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
Objective
product phases) migrates so as to allow the new phase to
Basics
grow. It is, however, a civilian transformation because the
T0 concept
atoms move individually.
Micro• The other is the martensitic transformation. In this type, the
structures
change in phase involves a definite orientation relationship
Bain
because the atoms have to move in a coordinated manner.
model
There is always a change in shape which means that there is a
strain associated with the transformation. The strain is a
Carbon
in Fe
general one, meaning that all six (independent) coefficients
can be different.
SME
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Classification of Transformations
Civilian
Military
Precipitation,
Spinodal
Decomposition
?
Massive
Martensitic
Transformations
Transformations
Objective
Basics
T0 concept
Microstructures
Diffusion
Required
Bain
model
Carbon
in Fe
SME
Diffusionless
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Driving Forces
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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,
Objective
parent
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
G
∆Gga
Common
tangent
T2
Diffusionless transformation impossible at T1,
Diffusionless transformation possible at T2;
“T0” is defined by no difference in free
energy between the phases, ∆G=0.
T1>T2
T2 corresponds to
figure 6.3b in P&E.
X
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Driving Force Estimation
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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 P&E estimate the driving force at the
temperature at which martensite formation starts in
Eq. 6.1 using this relationship.
Phase
relationships
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equilibrium
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
T near T0
Note that the Ms
line is horizontal
in the TTT diagram;
also, the Mf line.
diffusionless
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Heterogeneous Nucleation
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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* = 16πg3 / 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
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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 P&E 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
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
Martensite formation
rarely goes to
completion because
of the strain associated
with the product
that leads to back
stresses in the
parent phase.
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Self-accommodation by variants
Objective
Basics
T0 concept
Microstructures
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model
Carbon
in Fe
SME
• 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
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• Orientation relationships in the Bain model are:
(111)g <=> (011)a’
[101]g <=> [111]a’
[110]g <=> [100]a’
[112]g <=> [011]a’
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Crystallography, contd.
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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
Objective
(& brittle). Most martensites are not significantly stronger than
Basics
their parent phases.
T0 concept • Interstitial sites:
fcc: octahedral sites radius= 0.052 nm
Microtetrahedral sites radius= 0.028 nm
structures
bcc: octahedral sites radius= 0.019 nm
Bain
tetrahedral sites radius= 0.036 nm
model
• Carbon atom radius = 0.08 nm.
Carbon
• Surprisingly, it occupies the octahedral site in the bcc Fe
in Fe
structure, despite the smaller size of this site (compared to the
tetrahedral sites) presumably because of the low modulus in
SME
the <100> directions.
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Interstitial
sites for C in
Fe
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
fcc: carbon
occupies the
octahedral sites
bcc: carbon
occupies the
octahedral sites
SME
[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.
Objective • Each carbon atom therefore distorts
the iron lattice in its vicinity.
Basics
• The distortion is a tetragonal
T0 concept
distortion.
Micro• If all the carbon atoms occupy the
structures
same type of site then the entire
lattice becomes tetragonal, as in the
Bain
martensitic structure.
model
• Switching of the carbon atom
Carbon
between adjacent sites leads to
in Fe
strong internal friction peaks at
SME
characteristic temperatures and
frequencies.
[P&E]
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Shape Memory Effect (SME)
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
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
Ms
Objective
Af
T0
Basics
T0 concept
Ad As
Microstructures
Bain
model
Md
Mf
Carbon
in Fe
SME
The Md and Ad temperatures bracket T0 because they define the oncooling and on-heating temperatures at which the transformation is
possible with allowance for the effect of strain energy.
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SME Definitions
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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.
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• Stress for SIM must be less than yield stress for
plastic deformation.
• SME depends on incomplete transformation and
elastic back stresses to provide memory (>MS).
– 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
Objective
Basics
• Super-elasticity is simply reversible (therefore
“elastic”) deformation over very large strain ranges
(many %).
• Example: Ti-50.2%Ni.
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
[Shape
Memory
Materials]
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Role of Ordering
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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
Objective
(SME) in a spring
Basics
• Mechanism of SME:
1) transformation;
T0 concept
2) martensite, selfMicroaccommodated;
structures
3) deformation by
Bain
variant growth;
model
4) heating causes
Carbon
re-growth of parent
in Fe
phase in original
SME
orientation
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Surface
Relief
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
Micrographs
show a sequence
of temperatures
with surface
relief from the
martensite plates.
34
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 recoverable;
SME= Shape Memory Effect; SE = Superelasticity
Objective
Basics
d/dT = ∆S/e = ∆H/(Tee
T0 concept
Microstructures
Bain
model
Mf
Stress
SME
Critical
Stress for
Martensite
Formation
As
SE
Carbon
in Fe
SME
Ms
Af Temperature
Critical
Stress for
Slip
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Ni-Ti Alloys
[Wasilewski, SME in Alloys, p245]
X
Ms
Mf
As
Af
V
> 25
< -140
< -64
> 25
Cr
-100
< -180
< -58
> 25
Mn
-116
< -180
< -63
> 10
Fe
No
information
< -180
-30
> 25
Bain
model
Co
No
information
No
information
0
> 25
Carbon
in Fe
Cu
> 25
< -100
?
> 25
TiNi0.95
70
60
108
113
TiNi
60
52
71
77
Ti0.95Ni
-50
< -180
?
20 (?)
Objective
Basics
T0 concept
Microstructures
SME
36
SME Requirements
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
SME
• 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.)
37
Photostimulated SME!
Objective
Basics
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Microstructures
Bain
model
Carbon
in Fe
SME
38
Summary
Objective
Basics
T0 concept
Microstructures
Bain
model
Carbon
in Fe
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) crystallography.
• Technological applications abound - quenched and
tempered steels, Nitinol shape memory alloys etc.