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

[6] Kaufman L, Cohen M In: Chalmers B, King R, editors. Progress in metal physics.

London: Pergamon Press, 1958. p. 165.

[7] Cohen M. Transactions of the Metallurgical Society of AIME 1958;212:171

[8] 42 Eshelby JD. Proceedings of the Royal Society of London A 1957;241:376

[9] 44 Patel JR, Cohen M. Acta Metallurgica 1953;1:531

[10] 47 Wolten GM. Journal American Ceramic Society 1963;46:418

[11] 31 Bailey JE. Prov Roy Soc A 1964;279:395

[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

[15] 28 Hayakawa M, Kuntani N, Oka M. Acta Metallurgica 1989;37:2223

[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