Martensitic Transformation Analysis and Transformation Toughness on Zirconia(ZrO 2 ) Ceramics. Panagiotis Floratos AM 1323 Angelos Goulas AM 1483 Department of Mechanical Engineering, University of Thessaly, Volos, Greece.
Martensitic Transformation Analysis
and Transformation Toughness on
Zirconia(ZrO2) Ceramics.
Panagiotis Floratos AM 1323
Angelos Goulas AM 1483
Department of Mechanical Engineering, University of
Thessaly, Volos, Greece.
Contents Abstract .......................................................................................................................... 3
Introduction .................................................................................................................... 4
1. Martesitic Transformation ......................................................................................... 4
1.1 Martensitic transformation in ceramics ................................................................ 5
2. Analysis On Martensitic transformations .................................................................. 6
2.1 Transformation toughening ................................................................................ 12
2.2 The shape strain, stress-induced transformation and self-accommodation .... 13
3. Tetragonal to monoclinic transformation in zirconia............................................... 19
3.1 Yttria-zirconia (Y-TZP) ..................................................................................... 20
Conclusions .................................................................................................................. 21
References .................................................................................................................... 22
Abstract
Zirconia ceramics are high-performance materials with excellent mechanical
properties. Zirconia containing ceramic is one of only two classes of materials
exhibiting transformation toughening. The other one is transformation induced
plasticity/TRIP steels. In this paper a brief review of the martensitic transformation is
made. In the first part of the review, the phenomenological theory of the
transformation is analyzed while on the second part we decompose the transformation
on zirconia ceramics. A lot of attention was given on transformation toughness
happening on Ytrria Stabilized Zirconia.
Introduction In this work, a brief review over martensitic transformation in ceramics was done. In
particular, we studied the martensitic transformation in zirconia ceramics. This
transformation is the key to transformation toughening in ZrO2 ceramics. Over the
last three decades a large amount of experimental data was gathered and is now
available. Based on this information the theoretical predictions that can be made using
the phenomenological theory are really accurate. Τransformation toughening is one of
the characteristics that make ceramics a really useful material. Zirconia containing
ceramics are materials of imparting toughness while maintaining strength and
chemical inertness, and exhibiting new functions such as shape memory effect by
manipulating the microstructure. These properties are mainly dominated by the
structure transformation from tetragonal (t) to monoclinic (m). Zirconia containing
ceramics can be classified into three categories: tetragonal zirconia polycrystalline
(TZP), partially stabilized zirconia (PSZ) and zirconia toughened/ dispersed ceramics
(ZTC/ZDC). Tetragonal zirconia polycrystalline (TZP) is a material with nearly 100%
t-ZrO2 phase, stabilized by yttria or ceria additions. An alternative way to stabilize the
tetragonal phase is to decrease the grain size of tetragonal phase to nanoscale.
1. Martesitic Transformation A martensitic transformation (MT)[1] is a change in crystal structure (a phase
change) in the solid state that is athermal and involves the simultaneous, cooperative
movement of atoms over distances less than atomic diameter, so as to result in a
macroscopic change of shape of the transformed region. It is also a diffusionless
transformation. Diffussion is not prerequisite for the growth of martensitic crystals.
On the contrary, martensitic growth takes place by the migration of glissile interfaces.
These interfaces are composed of dislocations arrays, the glide of which causes the
migration of the interface without the need of atomic diffusion. A consequence of the
diffusionless character is that the martensitic phase inherits the composition, atomic
order and lattice defects of the parent phase (austenite).The diffusionless nature
ensures a high-speed transformation and the dominant deviatoric strain means that the
transformation is readily stress-induced. Diffusion-controlled, reconstructive
transformations, even if they exhibit a shape change, would be far too slow to lead to
transformation in time to effect a growing crack. At the same time, rapid diffusionless
transformations that involve only minor displacive strains are of little use because
they will show a limited ability to be stress-induced. So the two unique features of
martensite transformation, high speed and a change of shape of transformed volume
are both essential, if transformation toughening is to occur.
The interface between the parent and product crystals is a glissile interface, the
migration of which is accomplished by the glide of the dislocations arrays composing
the interface. The shear-dominated strain energy has a major effect on transformation
kinetics and morphology of the transformation product.
1.1 Martensitic transformation in ceramics The worldwide interest in martensitic transformation in non-metallic materials
exploded with the discovery of transformation toughening in zirconia ceramics
(1975). The toughness of a traditionally brittle ceramic could be increased by a factor
of 4 or more.
This held out the prospect of developing engineering ceramics that could be safely
used in structural applications, where their other superior properties like wear
resistance, low density, high melting point , would give them an advantage over their
metallic rivals.
This review is primarily concerned with the important connection between
transformation toughening and the martensite transformation responsible for the
toughening. Attention will be concentrated almost exclusively on the transformation
in zirconia, the main ceramic system that has, to date, exhibited any significant
transformation toughening.
Undoped zirconia exhibits the following phase transitions under ambient during
thermal cycling.[2]
It has been well documented that the t->m transformation is a athermal martensitic
transformation, associated with a large temperature hysteresis (several hundred K), a
volume change or dilation component of transformation strain (4– 5%) and a large
shear strain (14–15%). This leads to disintegration of sintered undoped zirconia parts.
Dopants (yttria, ceria, etc.) are added to stabilize the high temperature tetragonal
and/or cubic phase in the sintered microstructure. In the view of the potential
commercial applications (typically room temperature) of high temperature
polymorphs (tetragonal and cubic) of ZrO2, the issues associated with t->m
martensitic transformation, related mechanism of transformation toughening and
stabilization of metastable tetragonal phase at lower temperatures have drawn much
attention in both ceramic research and martensitic transformation worlds for three
decades.
2. Analysis On Martensitic transformations
The Shape Deformation
The total shape deformation [3] can be described by a 3x3 matrix [F] termed the
deformation gradient tensor, which in case of homogeneous deformation defines the
position vector {y} of a material point after deformation as a function of the
corresponding position vector {x} before deformation
{y}3x1=[F]3x3x{x}3x1 , Fij= 𝜕𝑦𝑖𝜕𝑥𝑖
(2.0)
where the numbers below the matrices indicate their dimensions. It is noted that
during homogeneous deformation the plane surfaces remain plane after deformation.
Figure 1: The shape deformation caused by the invariant plane strain (IPS). ABC is
the habit plane. Line DE is displaced to the new position DF
The shape deformation is revealed macroscopically by the surface tilts, which form
on an originally plane and polished surface (Fig.1) The martensitic transformation is
homogeneous and changes the shape and volume of the transformed region. The
shape deformation can be revealed if we draw a straight line on a polished surface of
the alloy, such as line DE In (Fig.1). After transformation line DE is displaced to the
new position DF, however it remains continuous as it crosses the interface ABC
between the martensite and parent (austenite) phases. Any deformation or rotation of
plane ABC would require deformation of the parent phase in order to maintain
coherency between the martensite crystal and the surrounding matrix. Therefore the
plane ABC remains invariant during MT and is termed the habit plane. The habit
plane is the interface between martensite and parent crystals .It follows that the shape
deformation is an invariant-plane strain, IPS
According to Continuum Mechanics, the deformation gradient [F] in the martensite
crystal can be written as
[𝐹]3X3 = [𝐼]3X3 + 𝜁 ∗ [𝑝]3x1 ∗ [𝑛]1x3
Where [I] is the unit matrix, ζ is a scalar, [n] is the column-vector corresponding to
the unit normal n to the habit plane and {p} is the column-vector corresponding to the
unit vector p, which defines the direction of displacements of all material points
during deformation. If we substitute the above expression for [F] in (2.0) we get
{𝑦} = {𝑥} + 𝜁{𝑝}[𝑛]{𝑥}
The quantity [n]1x3 {x}3x1 is a scalar equal to the distance d of point {x} from the
habit plane . Therefore the last equation can be written as
{𝑦} = {𝑥} + 𝜁𝑑{𝑝}
From the above relation it is concluded that point {x} is displaced in the direction of
{p} and the displacement has a magnitude ζ d proportional to its distance from the
habit plane. In Fig 2 the displacement of a point A to A’ during MT is depicted. A
new set of axes is then introduced, with origin at the habit plane Π,axis 3 is
perpendicular to Π and axis 2 is parallel to the projection of p in Π. Then {p} and [n]
can be written as
{𝑝} = {0
cosωsinω
}
And
[n]= [0 0 1]
Where ω is the angle of p with the habit plane .With reference to the new set of axes
[F] takes the form
[F]=[I]+ζ{p}[n]={1 0 00 1 ζcosω0 0 1 + ζsinω
}={1 0 00 1 𝛾00 0 1 + 𝜀0
} (2.1)
Figure 2: Displacements of a material point A associated with the martensitic
transformation .
Figure 3: Deformation of a unit square during martensitic transformation.
Superposition of shear and normal components of strain.
Where γ0=ζcosω and ε0= ζsinω are the shear and normal components of the
deformation Fig 3 depicts the deformation of a ‘’unit square’’ in the plane defined by
p and n during MT. Points C and D are displaced to C’ and D’ and the initial square is
transformed to the parallelogram ABC’D’ with the superposition of two
displacements: (a) one perpendicular to the habit plane causing a normal strain γ0 and
(b) one perpendicular to the habit plane causing a normal strain ε0.This superposition
can be described analytically if we observe that
[𝐹] = {1 0 00 1 𝛾00 0 1 + 𝜀0
} = {1 0 00 1 00 0 1 + 𝜀0
} ∗ {1 0 00 1 𝛾00 0 1
} = [𝐹𝜀][𝐹𝛾] (2.2)
And
{y}=[F]{x}=[Fε]([Fγ]{χ})
According to the last equation the total deformation can be accomplished in two
stages: (a) shear strain, which brings the material points to an intermediate position
[Fγ]{χ} and (b) a normal strain , which brings the material points to the final position
[Fε]([Fγ]{χ}).The volume change during MT is given by
𝑣
𝑣0= det[𝐹]
Where V0 and V is the material volume before and after transformation and det[F] is
the determinant of [F].Using 2.1 it is concluded that
𝑣
𝑣0= 1 + 𝜀0
Meaning that the volume change is exclusively due to the normal strain ε0.
We will discuss now the components of the shape deformation taking as an example
the transformation →m in Zirconia. According to the phenomenological theory, the
strain component, which causes the change in crystal structure from t→m, is the Bain
strain [B]. The Bain strain reveals the correspondence of lattice points between the
parent crystal tetragonal (t) and the martensitic crystal momonclinic (m).The initial
dimensions of the tetragonal cell are am=0.5126, bm=0.5126,cm=0.5206 and the
dimensions of the product cell are at=0.5181, bt=0.5200,ct=0.5363.Consequently the
bain strain, expressed by the matrix [B] is:
[𝐵] =
{
𝑎𝑚𝑎𝑡
0 0
0𝑏𝑚𝑏𝑡
0
0 0𝑐𝑚𝑐𝑡 }
= {𝑛1 0 00 𝑛2 00 0 𝑛3
} =
{
0.5181
0.51260 0
00.52
0.51260
0 00,5365
0,5206}
= {1.01072 0 0
0 1.01443 00 0 1.03054
}
In position to the above transformation, the Bain strain from FCC->BCC in steels
is:
[𝐵]={𝑛1 0 00 𝑛2 00 0 𝑛3
}={1.136071 0 0
0 1.136071 00 0 0.803324
}
As discussed above, martensitic interfaces are glissile. This requires the presence of
only one array of parallel dislocations, which are capable to glide freely, without any
intersections between them. This requirement means that all dislocations of the array
should be parallel to the same direction on the interface plane. This direction should
remain invariant during the transformation as the interface moves. This means that the
deformation should possess an invariant –line strain, ILS character. As depicted in
Fig.4 we consider a spherical austenite crystal being deformed to an ellipsoid by the
Bain strain. The strain can leave directions such as ab and cd invariant in magnitude ,
however they have rotated to the new positions a’b’ and c’d’. In order to get a real
ILS, the martensite crystal should be rotated by an angle Θ in order to have a
coincidence of lines cd and c’d’. This simply means that it is the combination of the
Bain Strain [B] with a rigid body rotation [R] that can leave an invariant line.
Figure 4:Deformation of a spherical austenite crystal during martensitic
transformation (a) application of the Bain strain (b) application of the Bain strain plus
a rigid body rotation results in ILS
However the deformation [B][R] is much larger than the observable shape
deformation [F]. For this reason an additional deformation takes place, in the opposite
sence, in order to relieve the strain energy caused by [B][R]. This complementary
shear [P] does not change the crystal. As a result the shape deformation can be written
as:
[F]=[R][B][P] (2.4)
Figure 5: Schematic illustration of the steps involved in the phenomenological theory
of martensitic transformation. The changes to the crystal structure are shown on the
left and to the macroscopic transforming volume on the right.
In the following table, there is a comparison between steels and zirconia at the
martensitic transformation.
Table 1: Comparison of the characteristics of the martensite transformation in steels
and zirconia
Characteristic Steels Zirconia
Magnitude of shape
deformation [F] ≅0.200 (±0.025) ≅0.160 (±0.005)
Volume change (ΔV) ≅0.030(±0.025) ≅0.045(±0.005)
Shear Components γ0 ≅0.195(±0.025) ≅0.150(±0.005)
We conclude, that the magnitude of shape deformation [F] and the shear components
are bigger in steels that in zirconia, but the total volume change in zirconia .
2.1 Transformation toughening Transformation toughening in ceramics, is the increase in fracture toughness of a
material that is the direct result of a phase transformation occurring at the tip of an
advancing cracking[4,5]. In particular, tetragonal (t) zirconia (ZrO2) transforms to
monoclinic (m), which is nucleation controlled .In order to achieve the
transformations, there are three essential requirements. First, there must be a
metastable phase present in the material and the transformation of this phase to a more
stable state must be capable of being stress-induced in the crack-tip stress field.
Second , the transformation must be virtually instantaneous and not require time-
dependent processes such as long range diffusion. Third, it must be associated with a
change of shape and/or volume. This deviatoric character is the feature of the
transformation that allows it to be stress induced. It also provides the source of the
toughening because the work done by the interaction of the crack trip stresses and the
transformation strains dissipates a portion of the energy that would normally be
available for crack extension.
An alternative but essentially equivalent , way of regarding the toughening process is
as a form of crack shielding , where the transformation strains generate local stresses
that oppose further crack opening . Finally to ensure that there is a net increase in
toughness of the material, the transformed product must not be significantly more
brittle than the parent phase from which it forms.
The benefit of transformation toughening was effectively compensated by the
intrinsic brittleness of the product phase and in some steels there was little net
toughening. It’s worth mentioning that, the first attempts of making transformation
toughened ceramics led to a transformed product phase that was just as brittle as the
starting material.
Transformation toughening can be illustrated in figure.6. Under an applied load,
stress-induced transformation occurs at the crack tip and produces a transformation
zone. In most of the mechanistic models of transformation toughening this initial
process zone at the tip of a stationary crack has no effect on the toughness of the
material. However, as the crack grows, a wake of transformed material is left behind.
It is the strains remaining in this wake of transformed materials that lead to an
increase in toughness.
The primary deviatoric strain responsible for ‘triggering’ the transformation in the
first place is what governs the height (2h) of the transformed zone. Yet, it is not
essential for this nucleation strain to be the same as the eventually left in the
transformed wake.
It is the first stress-induced martensite unit (plate/nucleus) that is embedded in a
relatively rigid matrix which inevitably leads to the generation of internal stresses,
which will modify the local stress field. Subsequent transformation in the vicinity of
the initial martensite plate will respond to this altered local stress field, provided the
transformation crystallography allows this. As a result, the final assemblage of
martensite plates may well include a component of self-accommodation and have an
overall net transformation strain that differs significantly from the strains associated
with the initial nucleation of a single martensite plate. In this way a large amount of
energy is absorbed and a crack-tip shielding is formed.
So the whole topic of transformation toughening is dominated by a phase
transformation that is associated with a change of shape and/or volume.
Figure 6: Transformation toughening.Under an applied load, stress-induced
transformation occurs at the crack tip and produces a transformation zone.
2.2 The shape strain, stress-induced transformation and
self-accommodation
The shape strain in martensitic-induced transformation is «an invariant plane strain
that consists of a shear parallel to the habit plane, plus a dilatational strain normal to
the habit plane». The above strain leads to volume change (ΔV), either by expanding
or by contracting it. In the case of the t→m transformation in zirconia, the expansion
ranges between 0.04 and 0.05.As regards the shear component (γ) of the shape strain
(s), in this case, is 0.15 -0.16, which is 3 or 4 times larger than the dilatational
component. A significant strain energy can provoke large strains which can be
associated with a martensitic transformation. To appreciate the latter significance, it is
necessary to presume the various energy involved in the transformation.
In order to create a martensite plate by nucleation its vital to overcome a free energy
barrier ΔWn. The total change in energy ΔW that accompanies the formation of a
martensite nucleus or embryo is[6,7]:
ΔW= ΔGc V+ ΔUSTRAIN+ΔUSURFACE (2.5)
Where ΔGc is the chemical free energy change per unit volume (related with the
transformation from the unstable parent phase to the stable product phase and the
energy required to form the nucleus or embryo), ΔUSTRAIN is the strain energy
associated with the shape strain of the martensite plate in proportion to the surface
area of the nucleus. Last but not least ΔUSURFACE is the surface energy of the
interface between the product martensite the parent phase and V ( the volume of the
transformed region). Likewise ΔUSURFACE is in proportion area of the nucleus. In
cases where the transformed region has some form of internal structure it may be
necessary to include an additional term ΔUINTERNAL on the right hand side of Eq. (2.5).
Note that for the transformation to proceed at all ΔGC must be negative.
Christian JW using Eshelby’s[8]analysis derived an expression for the elastic strain
energy SE per unit volume of a thin, oblate of radius R and semi-thickness t (t<<R)
SE =𝜇
(1−𝜈)
𝜋
4(𝑡
𝑅){ΔV2 +
(2−𝜈)
2(𝛾)2} (2.6)
Where μ is the shear modulus and ν is Poisson’s ratio for both the matrix and the
martensite.SE is the product of a term that depends on the shape of the spheroid (t/R)
and a shape independent term that involves the elastic constants and the
transformation strains. Hence, Eq (2.6) can be simplified to SE=(t/R)Ψ, where Ψ is
the right hand side of (2.6) divided by (t/R). Using this expression the value of
USTRAIN is given by the product of the volume of the prolate spheroid (V=4ΠR2t/3)
and the strain energy per unit volume SE –ie (t/R)Ψ.
The surface energy term ΔUSURFACE is given by the surface area of the spheroid
(~2ΠR2 for a thin spheroid) times the surface energy Γ.Hence, for a transformed
spheroid of radius R and thickness t, Eq (2.2) becomes:
ΔW= (4ΠR2t/3)ΔGC+(4ΠR2t/3)(t/R)Ψ +(2ΠR2)Γ (2.8)
When ΔW is plotted as a function of t and R, Eq (2.8) defines a surface with a saddle
point determined by 𝜕ΔW
𝜕𝑡=
𝜕ΔW
𝜕𝑅= 0, from which it follows that the critical saddle
point energy – the energy of nucleation ΔWn – is given by:
ΔWℎ =32πΨ2𝛤3
3ΔG𝐶4 (2.9)
And the critical dimensions of the nucleus tn and Rn by:
𝑡𝑛 =−2𝛤
ΔG𝐶 (2.10)
𝑅𝑛 =4ΨΓ
ΔG𝐶2 =
𝐶𝑛2𝛹
𝛤 (2.11)
For a subcritical spheroidal nucleus or embryo to reach a critical size, pass over the
free energy barrier and grow into a full fledged martensite plate, the most favourable
path to follow is one that minimises ΔW with respect to and R at all stages. This
optimal relationship is given by
𝑡2
𝑅=
𝛤
𝛹 (2.12)
This leads to the ‘classic’ relationship between the free energy change ΔW and the
nucleus radius R.
The difference in free energy between the parent and product phases (ΔGC) is linear
with absolute temperature. At some temperature T0 the energies are equalized
(ΔGC=0). Aiming to nucleate the martensite transformation, the material must be
cooled down to its Ms temperature, when the value of ΔGC is sufficiency large to drive
the transformation Fig.7.This critical value of ΔGC obviously depends on ΔUSURFACE
and ΔUSTRAIN or more importantly on the values of the surface energy Γ and the shape
independent part (Ψ) of the strain energy. The surface energy is not amenable to any
significant externally imposed changes. However, if the strains ΔV and γ that make up
the shape independent part of the strain energy Ψ could be accommodated or
compensated in some way, then the critical value of ΔGC, would be reduced and the
transformation could be occur at a higher MS. For example, if the constraint imposed
by the surrounding matrix could be removed – say by extracting the transformable
particles from the material – then the effective MS temperature would be raised.
Specifically at Ms temperature ΔGC= ΔUSURFACE + ΔUSTRAIN. Decreasing the
ΔUSTRAIN by increasing the stress assistance or reducing the surrounding constraint
raises the MS temperature, while increasing the ΔUSTRAIN lowers the MS temperature.
Fig.7. The relationship between the free energy change ΔGCV for the tetragonal to
monoclinic transformation in zirconia, showing the variation with temperature and the
two energy components ΔUSTRAIN and ΔUSURFACE.
In order to increase the Ms temperature, there is another option by using the
application of an external stress. In the presence of an applied stress σα , the shape-
change can do work in the direction of the stress and this effectively reduces
ΔUSTRAIN.As Patel and Cohen presented[9] , the ΔUWORK done by the shape strain in
a simple two-dimensional situation given by:
ΔUWORK=1/2γςαsin2θ±1/2ξςα(1+cos2θ)
Where γ is the shear component of the shape strain, ξ is the dilatational component
(ξ=ΔV) and θ is the angle between the applied stress and the normal to the habit plane
of the martensite plane. In the more general three-dimensional situation:
ΔUWORK=σαεΖ
where εΖ is the total strain (shear and dilatational components) resolved in the
direction of the applied stress. Regarding the latter, the overall strain energy is now
reduced to (ΔUSTRAIN- ΔUWORK). Consequently, the chemical free energy required to
nucleate the transformation is less and the martensitic transformation can be made to
occur at a temperature higher than Ms.
(- the transformation has been stress-induced.)
In the t→m transformation in zirconia where ΔV=0.045 and γ=0.15, there is a
crucial difference between a dilatational strain and a shear strain. Its worth noting that
a shear strain can change sign, while a dilatational strain cannot. This means that for,
a positive volume change, uniaxial tension will provide positive stress-assistance,
while uniaxial compression will oppose transformation (negative stress-assistance).
Both uniaxial tension and compression will generate the shear stress. These can
interact with the shear component of the shape strain and lead to positive stress-
assistance.
In situations involving externally applied stress, stress-induced martensitic
transformation is not restricted. It is important that stress-induce transformation can
cause internal stresses. In fact, the initial transformation itself will often generate local
internal stresses that influence subsequent transformation in surrounding regions.
Below is presented an example of this behavior that is particularly relevant to
zirconia and to the resulting transformation toughening.This application of the
phenomenological theory shows that, not only the members of these pairs twin-related
to each other, but they have shape strain directions that are essentially equal and
opposite.
Forming the first martensite plate, the shape strain automatically generates opposing
stresses in the surrounding matrix. As the initial plate grows, these stresses increase
and they contribute to the eventual halt in transformation. After this process, the
surrounding matrix is now subject to a local internal stress. This could lead to further
stress-induced martensite plate formation. In addition, the dilatiational component of
the shape strain ΔV is always of the same sign, so it is only the shear components of
the shape strain that will be equal and opposite.
In a transformed volume where the overall shear strain of the pair is effectively zero,
can be produced variants known as self accommodating martensite variants (in
pairs).The formation of self-accommodating variants is particularly likely to occur
when the transforming region is isolated and surrounded by material that cannot
transform. This is the case with the tetragonal precipitates in Mg-PSZ and with
composites containing tetragonal zirconia grains in matrix of some other non-
transformable ceramic. In this situation the process can continue with the formation of
self-accommodating pairs eventually occupying the whole of the now transformed
precipitate or grain.
Despite the fact that the transformed region appears to consist of a stack of these
parallel variants that lead to complete elimination of any long range overall shear, this
arrangement forms via a sequential process. Put very simply, the transformation does
not proceed from the situation illustrated in Fig.8(a) directly to that shown in Fig 8(f).
Fig.8. Schematic diagram illustrating the stages in the transformation of a spherical
tetragonal zirconia particle to self-accommodation monoclinic variants. The double
arrows represent the stresses in the surrounding untransformed material that oppose
continued growth of a particular variant and favour the nucleation of the self-
accommodation variant with an opposing shear strain.
It is not possible a develop a stack of these self-accommodating variants, without
forming a single variant or plate first. The strains associated with the first plate are
dominated by the shear component of the shape strain γ, not the volume strain ΔV.
However, as the transformation proceeds the overall effect of the shear strain is
accommodated – at least on a large scale – and the strains that remain in the
transformed volume are purely dilatational – i.e. ΔV. This is a distinction, which is
particularly important for transformation toughening. The sequential nature of the
formation of these stacks of self-accommodating variants means that the strains (and
hence the nature of the stress-induced transformation) involved in forming the first
variant – the nucleation strains – are quite different from the overall strains associated
with the final stack of self-accommodating variants – the net transformation strains.
The former is shear dominated with a minor contribution from the volume change,
while the latter is essentially pure dilatation - the volume change and no shear. In
other words, the stresses required to trigger the transformation (i.e. from the first
plate) must be separated from those remaining in the material after the transformation
is complete. This is known as ‘decoupling’ the nucleation strain from the net
transformation strain.
Many of the theories of toughening did not do this and instead assumed that the
dilatation-only strains of completely transformed region applied throughout the
process, including the initial nucleation. This physically unrealistic assumption
simplified the mathematics of the models considerably, but probably contributed to
the poor agreement between theoretical predictions and experiment.
3. Tetragonal to monoclinic transformation in zirconia First suggested by Wolten[10] ,that the tetragonal to monoclinic transformation in
zirconia may be martensitic in nature. At the same period, Bailey[11] reported a
transmission electron microscope study of the t→m transformation in thin foils of
zirconia . He observed the appearance of monoclinic twins on (100)m and {110}m.
Since then, the appearance of twinning in the resulting monoclinic phase between
t→m phase has become universal.
Bansal and Heuer [12,13] used a combination of transformation electron
microscopy, optical metallography and X-ray diffraction to study the t→m
transformation in single crystals of zirconia. They found two types of monoclinic
plates. The first is ‘’Type A’’ which formed inside the crystal and had a (671)m or
(761)m habit plane, and ‘’Type B’’ which occurred near the surface of the specimen ,
were often internally twinned on (100)m and had a habit plane close to (100)m . They
reported two orientation relationships. The first, for transformation above
1000⁰C,was:
(100)m~⎹⎹ (010)t
[001]m ͠ ⎸⎸[100]t OR B-2
[001]m ͠ ⎸⎸[001]t
Which implies that correspondence B (in the case correspondence CAB) if followed.
The symbol ‘ ͠ ⎸⎸’ means that that the two plane normals or the two directions are
parallel to each other, at least within ±1⁰ or better. The other reported orientation
relationship, for transformation below 1000⁰C, corresponds to that originally reported
by Bailey [12], namely:
(100)m~⎹⎹ (100)t
[001]m ͠ ⎸⎸[001]t OR C-2
[010]m ͠ ⎸⎸[010]t
In this case it appears that correspondence C is followed.
Several researchers have studied and applied the phenomenological theory of
martensitic transformation ,to t→m transformation . Bansal and Heuer[20], concluded
that they could account for all their experimental observations including the (671)m or
(761)m habit planes, while Choudhry and Crocker[14] concluded that, with their
choice of lattice parameters , they were unable to predict a {671}t habit
plane.Actually, one problem was the lack of experimental evidence that could be used
to verify the theoretical predictions. This led to the subsequent emphasis on the
(671)m habit plane and the fixation with twinning as a lattice invariant shear system,
both of which on occasions tended to obscure the true interpretation of theoretical
predictions. Finally, in the middle of 1980, the discovery of transformation
toughening in zirconia led to increasing amounts of experimental evidence on the
crystallography and other characteristics of the marensitic t→m transformation
became available.
The simplest t→m transformation is Ce-TZP, where single grains of the tetragonal
phase transform to give isolated plates or groups of plates of the monoclinic phase.
This is amenable to treat with the phenomenological theory, since the habit plane and
orientation relationship of a single monoclinic plate embedded in the parent tetragonal
phase can be determined and compared with the phenomenological theory.
As regards the transformation t→m by Y-TZP, the parent phase consists of a series of
internally twinned tetragonal domains parallel to (110)t. In this case, two possible
situations can occur. Either the monoclinic martensitic plates are confined to a single
tetragonal domain or, it is possible for the same martensite plate to traverse two or
more tetragonal domains.
The most complex system, is the t→m transformation within the tetragonal
precipitates produced by ageing of Mg-PSZ. In this case, there is no retained parent
tetragonal phase in association with the monoclinic and it is necessary to use indirect
means to verify the theoretical predictions .Underneath we present the case of Yttria-
zirconia (Y-TZP)
3.1 Yttria-zirconia (Y-TZP) Y-TZP, consists entirely of small tetragonal grains at room temperature. The
microstructure contains the (101)t and (011)t twins arranged in bands, where
Hayakawa [15,16] describe as "herringbone structure". The tetragonal herringbone
structure consists of two alternating bands of tetragonal phase, with each band
containing small twins. The large bands are bounded by (110)t planes, with one
band(band A) having twins on (101)t and the other (band B) having twins on (011)t.
Hayakawa used X-ray diffraction, optical metallography and transmission electron
microscopy to study this version of the t→m transformation in Y-TZP with the
following results. All the variants of the monoclinic phase had a habit plane that was
close to (301)m and obeyed the orientation relationship:
(100)m ⎸⎸(100)t, (010)t or (001)t
[001]m ⎸⎸[010]t, [001]t or [100]t
Conclusions
Characteristics (thermodynamics, kinetics and crystallographics) of t->m martensitic
transformation, related mechanism of transformation toughening and stabilization of
metastable tetragonal phase at lower temperatures have been briefly reviewed. Over
the last three decades a lot of experimental data was gathered. This later provided
more than sufficient information to conduct an extremely rigorous test of the
phenomenological theory of the martensitic transformation as applied to zirconia. The
comparison between theory and experiment demonstrated that the theory is
remarkably successful. In fact the phenomenological theory has proved to be more
successful in zirconia, rather than in steels.
Combination of toughness and new functions makes TZP very attractive. Zirconia is
regarded as the ideal transformation toughened ceramic and thats is mostly because
no-one has been able to find a system that can equal it or, even better, surpass it.
There are some characteristics that make zirconia the best toughening ceramic system.
Those are:
Firstly its ability to suppress the martensitic transformation at the operating
temperature by stabilization (Y-Ce-Mg, Grain size, Particle size,etc)so that the
metastable phase can be made to undergo a stress induced transformation at a
crack tip.
Secondly, the transformation has a positive volume change that provides a
type of crack tip shielding that increases the fracture toughness of the material.
It is also characterized by a relatively large shear component of the shape
strains that ensures the transformaion is easily stress induced at the crack tip.
Additionally the ability to accommodate the shear by providing a mechanism,
that ensures the final strains in the transformed volume can be conformed with
the local conditions of stress and strain. This actually prevents the material
from further cracking or even from completely disintegrating.
At last, probably the most important characteristic is the ability, the material
has, to transform via a large number of possible variants. The possibility of
stress-induced transformation in a particle or a grain regardless of its
orientation is clearly increased. The number of unfavourable orientations of
the parent crystal, in which it may be difficult or even impossible to stress-
induce transformation, is reduced in TZP.
References [1] Christian JW. Physical properties of martensite and bainite. Scarborough (UK):
The Iron and Steel Institute, 1965
[2] Xue-Jun Jin. Martensitic transformation in zirconia containing ceramics and its
applications. School of Materials Science and Engineering, Shanghai Jiao Tong
University
[3] G . Haidemenopoulos,Physical Metallurgy , Tziola
[4] Garvie RC, Hannink RHJ, Pascoe RT. Nature 1975;258:703
[5] Evans AG, Gannon RM. Acta Metallurgica 1986;34:761
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London: Pergamon Press, 1958. p. 165.
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[12] 48 Bansal GK, Heuer AH. Acta Metallurgica 1972;20:1281
[13] 49 Bansal GK, Heuer AH. Acta Metallurgica 1974;22:409
[14] 34 Choundry MA, Crocker AG In: Claussen N, Ruhle M, Heuer AH, editors.
Advances in ceramics-science and technology of zirconia II. Columbus (OH): The
American Ceramic Society, Inc, 1984. p. 46
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[16] 65 Hayakawa M, Tada M, Okamoto, Oka M. Trans JIM 1986;27:750
[17] A. H. Heuer, M. Ruhle On the nucleation of the Martensitic Transformation in
Zirconia ZrO2