shape memory alloys featuring nitinol - pure · shape memory alloys featuring nitinol ... treat the...

Shape Memory Alloys featuring Nitinol

van der Wijst, M.W.M.

Published: 01/01/1992

Document VersionPublisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)

Please check the document version of this publication:

• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differencesbetween the submitted version and the official published version of record. People interested in the research are advised to contact theauthor for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers.

Link to publication

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ?

Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.

Download date: 13. Jul. 2018

https://research.tue.nl/en/publications/shape-memory-alloys-featuring-nitinol(11d42ca3-4cff-44c2-bb53-6f4e468339a7).html


M.W.M. van der Wijst Id.nr: 256199

St ageverslag

Veldhoven, juli 1992

WFW-rapport: 92-085


M.W.M. van der Wijst ID.NR: 256199

Begeleider: Dr.1r. P. J.G. Schreurs

Veldhoven, juli 1992

Stageverslag

TU Eindhoven Faculteit der Werktuigbouwkunde

Vakgroep WFW

And the LORD said unto Moses, "W'hat is that in your hand?" And he said, "A rod. '' Then HE said, "Cast it on the ground." And he cast it on the ground and it became a serpent; and Moses f led from it. And the LORD said unto Moses, "Put forth thine hand and take it b y the tail." And he put forth his hand and caught it, and it became a rod in his hand.

OLD TESTAMENT Exodus, Chapter 4:2-4 [21]

Summary

Shape Memory Alloys are alloys which are able to return to their original shape after being 'plastically' strained up to 8%, just by heating. This Shape Memory Effect is caused by a martensitic transformation, i.e. a change of crystal structure, which can be induced either thermally (cooling) or mechanically (stress), each of which has its boundary temperatures. The formation of variants plays an important role. The general opinion is that only alloys which exhibit thermoelasticity can be Shape Memory Alloys. Most Shape Memory Alloys show pseudoelastic behaviour, but this is not a condition.

Currently there are three main groups of Shape Memory Alloys: Cu-based alloys, which are used commercially, rather recent Fe-based alloys, and Nitinol, a NiTi alloy, the most thoroughly investigated alloy showing the best Shape Memory behaviour.

This report describes the main characteristics of the Shape Memory behaviour and aims at Nitinol in particular.

.. 11

Contents

Summary ii

List of symbols V

1 Introduction 1 1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Shape Memory Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Smart materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Crystals 4 2.1 Introduction to crystallography . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Crystal systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Four important structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Martensitic transformations 10 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1.1 Diffusionless nature of the transformation . . . . . . . . . . . . . . 10 3.1.2 Surface relief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.3 Habit plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Phenomenological description of the martensitic transformation . . . . . . 12 3.2.1 I . The Bain distortion . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2.2 I1 . Simple shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2.3 I11 . Rigid body rotation . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2.4 Total shape change . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3 Slip vs . twinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.4 TheR-phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.5 Martensitevariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.5.1 Crystallographic characteristics . . . . . . . . . . . . . . . . . . . . 21 3.5.2 Variants in NiTi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.6 Self.accomodation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.7 Reorientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.8 The reverse transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.9 Thermoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.10 Transformation thermodynamics and temperatures . . . . . . . . . . . . . 27

4 The Shape Memory Effect 31 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Pseudoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.3 Types of deformation mechanisms . . . . . . . . . . . . . . . . . . . . . . . 33 4.4 One Way Memory Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.5 Two Way Memory Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.5.1 The origin of the TWME . . . . . . . . . . . . . . . . . . . . . . . . 36 4.6 Training processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.6.1 Thermal cycling with a constant stress . . . . . . . . . . . . . . . . 36 4.6.2 Thermal cycling with imposed strain . . . . . . . . . . . . . . . . . 37

4.7 All Round Memory Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.8 Combined mechanical behaviour . . . . . . . . . . . . . . . . . . . . . . . . 40 4.9 Reversal with constant strain . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.10 Influence of stress on thermodynamics and transformation temperatures . . 43

5 Applications 45 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.2 Industrial applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.2.1 Constrained recovery applications . . . . . . . . . . . . . . . . . . . 46 5.2.2 Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.3 Energy applications; heat engines . . . . . . . . . . . . . . . . . . . . . . . 48 5.4 Dental and medical applications . . . . . . . . . . . . . . . . . . . . . . . . 49 5.5 Dynamic control with SMA reinforced plates . . . . . . . . . . . . . . . . . 50

References 52

Appendix A a.1

Appendix B a.2

iv

List of symbols

lattice parameters angles between crystallographic axes

bcc CsC1 structure bcc Fe3Al structure

martensitic phase resulting from a PI resp. P Z structure Parent, austenitic or high temperature phase

Martensitic or low temperature phase starting temperature of P -+ M transformation

finishing temperature of P 3 M transformation starting temperature of M 3 P transformation

finishing temperature of M + P transformation

maximum temperature at which martensite can be induced by stress

starting temperature of P -+ R-phase transformation finishing temperature of P -+ R-phase transformation

starting temperature of R-phase P transformation

finishing temperature of R-phase 3 P transformation

deformat ion temperature

equilibrium temperature

equilibrium temperature

stress necessary to cause transformation at TI stress necessary for reverse transformation at TI free energy

V

1 Introduction

1.1 History

Shape Memory Alloys (SMA's) are all alloys exhibiting the Shape Memory Effect (SME), i.e. if a specimen of these alloys is deformed "plastically" (under well defined conditions), the resulting apparently permanent deformation can easily be reversed by simply heating the specimen up above a specific temperature, returning the specimen to its original shape; Shape Memory Alloys are capable to 'remember' their high temperature shape.

This peculiar behaviour has first been observed by Chang and Read in 1951, concerning the alloy AuCd, although related phenomena like pseudoelasticity had been seen in this alloy by Olander in 1932, and thermoelasticity (these effects will be explainedlater) in CuZn by Greninger and Mooradian in 1938 (however, a detailed study of the latter phenomenon was only published 11 years later by Kurdyumov and Khandros). Some time later, a second alloy, InT1, was found to show the SME too. The discovery of the SME in these two alloys didn't lead to an outburst of scientific interest in this field. Another alloy, consisting of nickel and titanium did.

In 1965, Buehler and Wiley of the U.S. Naval Ordnance Laboratory found Shape Mem- ory behaviour in the less exotic NiTi alloy, or better in a series of alloys. The generic name of the series of alloys for which they requested and received a United States Patent is 55-Nitinol. These alloys have chemical compositions in the range of 53 to 57 weight percent nickel (= 48 to 52 atom percent, i.e. near-equiatomic alloys). NiTi alloys are usually called Nitinol, derived from Ni-Ti-Naval Ordnance Laboratory. Until now, Nitinol is still the alloy showing the best Shape Memory characteristics.

Since 1965, the SME has been observed in a number of alloy systems. Presently the three most important systems are NiTi, Cu-based alloys like Cu-Zn-Al and Cu-Al-Ni, and Fe-based alloys, which have been developed rather recently, like Fept and FePd. NiTi is the most thoroughly studied alloy. Besides the phenomenal Shape Memory behaviour of NiTi alloys, two other favourable properties are their excellent corrosion resistance and stable configuration, which make them the only SME alloys suitable for implantation in human bodies. On the other hand, they are much more expensive than Cu-alloys, and difficult to melt and elaborate.

1.2 Shape Memory Effect

In order to have already an idea of what the Shape Memory Effect is about, before it will be treated more profound, a schematic picture is drawn in figure (1.1).

I I

Austenite L

I -- € - - 1 - - I I +

O max. recovery strain €

Figure 1.1: Shape Memory Effect. a: reversible transformation; a- b-c: Shape Memory Eflect

A Shape Memory Alloy can be in two phases, i.e. a high temperature, 'austenite', or 'parent' phase and a low temperature, 'martensite' or 'product' phase. The terms parent phase and martensite phase will mostly be used. If a specimen at a high temperature, being fully parent phase, is cooled, then at a specific temperature M, (M of Martensite, s of start) martensite starts to form. This transformation proceeds on further cooling until at a temperature M f (f of finish) the specimen is wholly martensite.

On heating again, the reverse transformation takes place, starting at a temperature As ( A of Austenite), which may only be the same as Mf by coincidence, and ending at A f . Both the P(arent) + M and M -+ P transformations are normally not attended by a macroscopic shape change: nothing seems to happen from the outside. As will be seen, a lot does happen on the inside.

In order to show the Shape Memory Effect, the martensite has to be deformed 'plastically'; the resulting permanent macroscopic deformation disappears on heating the specimen above A f . In this way strains of 6-8% allow for full shape recovery. (The maximum value of elastic strain in steel or aluminium is about l%!)

Introduction 3

1.3 Smart materials

In the early days of research on SMA’s scientists were so impressed by the behaviour of these materials that they called Shape Memory Alloys smart materials. Other materials which gained the name smart are electrorheological fluids, which stiffen on application of an electrical potential, piezo-electric transducers and optical fibers. However, there are always scientists who disagree with something or other, and other names like intelligent, sense-able and adaptive were introduced.

Nowadays smart materials (and structures) have to satisfy the following conditions: they have (intrinsic) sensors that recognize and measure a stimulus, actuators to respond to it, a control mechanism to respond in a predetermined manner, and a small reaction time [17]. Although one agrees that this definition doesn’t match the description of ’smart’ in a dictionary, it is still used because the word ’smart’ has found its way into the scientific language for so many years.

In the light of the definition mentioned, Shape Memory Alloys are not smart materials; they can be an important component (as a sensor or actuator) of a smart structure or system.

The Shape Memory behaviour is basically a consequence of a martensitic transformation, which in his turn is a change of crystal structure. For this reason chapter 2 will treat the basic principles of crystallography, after which in chapter 3 characteristics of the martensitic transformation are discussed. After these necessary introductions, the most interesting topic, i.e. the Shape Memory Effect is dealt with in chapter 4. Finally this report will be concluded with some applications of Shape Memory Alloys in chapter 5.

2 Crystals

2.1 Introduction to crystallography

What’s a crystal? An ideal crystal is constructed by the infinite repetition in space of identical structural units [l-51. In the simplest crystals such as cupper, silver, iron, aluminium, the structural unit is a single atom. Often the structural unit is composed of several atoms or molecules up to 10,000 in protein crystals. The structure of all crystals is described in terms of a lattice with a group of atoms attached to each lattice point. A lattice is a regular periodic arrangement of points in space. These points all have exactly the same surroundings. The group of atoms is called the basis; it is repeated in space to form the crystal structure. This can be expressed as

lattice + basis = crystal structure.

In figure (2.1) a (2D) lattice with a two-atom basis forming a crystal structure is shown. If

O O O

O O O 0 0 O O O O

O O O O n n n - - w o w o O 0 0 O O O

+ o 8

O O O O 0 0

Figure 2.1: A crystal structure (c) is formed b y the addition of the basis (6) t o every lattice point of the lattice (a). It doesn’t matter where the basis is put in relation to a lattice point.

the lattice points are connected by straight lines, the space is divided into parallelepepids, the unit cells. The size and shape of a unit cell is specified by means of the lengths a, b and c of the three independent edges, known as the lattice parameters, and the angles cy,

Crystals 5

p and y between these edges. Figure (2.2) shows a unit cell in a 3D lattice (the angles a, and y are not drawn). The three axes a, b and c define a coordinate system appropriate

C

Figure 2.2: Primitive cell of a space lattice in three dimensions [$l.

Figure 2.3: Location of a point with coordinates X , y, Z. Numbers indicate coordinates of unit cell corners [l].

to the crystal, and is therefore often not a Cartesian system. With a crystal dependent system, a point (3, y , z ) is located by starting at the origin (O,O,O), moving successively the distances za, yb, zc in the direction of the respective a, b and c axes (fig. 2.3). In this way every point within the unit cell has coordinates smaller than 1, for if one or more coordinates exceed 1, the point is in one of the surrounding cells. An advantage of basing the coordinate system on lattice vectors is that two points are equivalent if the fractional parts of their coordinates are equal.

The choice of a unit cell is not unique. Any parallelepepid whose edges connect lattice points can be chosen, so there are an infinite number of such possibilities. It's also permis- sible to have lattice points inside a unit cell. In such cases there is more than one lattice point per unit cell: the cell is centered. A unit cell with lattice points only at the corners

Figure 2.4: Centered rectangular lattice; axes are shown for both the primitive cell and for the rectangular unit cell, for which (al # lbl; p = 90" [3].

is called primitive. Figure (2.4) shows two possible unit cells in a rectangular lattice: a

Crystals 6

primitive cell (left) and a centered one (right). Note that the centered cell indicates the rectangularity of the lattice better than the primitive one on the left. A primitive cell contains only one lattice point (the lattice points at the corners are shared with seven other cells). A primitive cell is a minimum-volume cell; no other unit cell of smaller volume can fill all space and form the required crystal structure. The basis associated with a lattice point of a primitive cell may be called a primitive basis. No basis contains fewer atoms than a primitive basis.

2.2 Crystal systems

One feature of crystal structures is symmetry. An object or figure is said to have symmetry if some movement of the figure or operation on the figure leaves it in a position indistin- guishable from its original position. Some lattices possess a large measure of symmetry,

Number Restrictions on

System Lattices Symbols Axes and Angles of Lattice Conventional Cell

Triclinic 1

Monoclinic 2

Orthorhom bic 4

Tetragonal 2

Cubic 3

Trigonal 1

Hexagonal 1

P

p , c

P, c, I , F

p , I

P or sc I or bcc F or fcc R

P

a # b + c f f + B + Y a f b f c ff = y = 90" # p

I

t b a = b # c ff = p = y = go"

a = b = c ff = p = y = 90"

a = b = c C

a = p = y < E O " , # so" a = b # c tr=p=90" y = 120"

Table 2.1: Seven crystal systems and fourteen lattice types [3],

whilst others are symmetric in a much less extent. To be able to make this difference in symmetry between lattices obvious, one usually picks out of the infinite collection of possible unit cells for a particular lattice that unit cell, which expresses the amount of symmetry present in that lattice the best (like in fig. 2.4). The result of choosing unit cells on the ground of symmetry is that restrictions will be imposed on the lattice parameters a, b, c and a, p and y; the restrictions will be greater with increasing symmetry. For example,

a lattice with a cubic unit cell has the highest possible symmetry, but this holds likewise for the mentioned restrictive conditions: a = b = c and a = ,û = y = go", i.e. there is only one degree of freedom left, the length of the cubes sides.

Besides the cubic unit cell there appear to be six other crystal systems. These seven systems are tabled in (2.1). In selecting a unit cell based on symmetry, it may turn out that a non-primitive, or centered, unit cell is obtained. For a particular crystal system everi more than one different, centered cells may be found. For example, the unit cell of steel at roomtemperature is a cube with eight lattice points at the corners and one in the centre of the cube. This is certainly a different structure than the structure of steel at high temperatures, i.e. a cubic unit cell with six points in the middle of the six faces instead of one in the centre. In the former structure each atom has eight nearest neighbours, while in the latter each atom has twelve. Both structures have the same high amount of symmetry and belong to the same cubic crystal system, but still have different unit cells.

If for each of the 7 crystal systems all possible unit cells are searched, the conclusion is that there are apparently fourteen distinct lattice types. These were first deduced by M.A. Bravais in 1848, and they are usually referred to as Bravais lattices. The lattice types are designated by symbols such as P, I, F, C, R:

- P :

- I :

- F :

- c : - R :

Primitive unit cell body centered (symbol Ifrom the German Innerzentrien): a lattice point in the centre of the unit cell Face centered: lattice points in the middle of all 6 faces Centered unit cell: two lattice points in the middle of two opposite faces Rhombohedral unit cell.

2.3 Four important structures

Figure 2.5: Close packing of spheres in two dimensions [l].

Figure 2.6: Two close-packed layers, with upper layer stacked above interstices of lower layer [i].

Crystals 8

Four of these Bravais lattices are very important, especially in metals, and will be discussed here. The atoms (or better ions) of which a metal is constructed may be considered as identical spheres. In a lot of metals (and other elements) these spheres form close- packed arrangements. One layer, A, of such a close-packed crystal structure is shown in figure (2.5); each sphere in this layer has six neighbours. Another layer, B, can be placed on top of A, by positioning the spheres of B in the interstices of A, like In figure (2.6). Half of the interstices in A will be filled with spheres of B, and the other half has holes of B above them. A third layer C can be added in two ways: (I) The spheres of C lay exactly above the spheres of A; if a fourth layer is placed precisely above B, a fifth above A etc., the stacking order will be . . .ABABABA.. . and the structure is called a Hexagonal Close Packed structure hcp. It has a hexagonal primitive cell

Figure 2.7: The hcp primitive cell has a = b, with an included angle of 120'. The c axis is normal to the plane of a and b. In ideal hcp c = 1.633a. The two atoms of one basis are shown as solid in the figure [3].

Figure 2.8: Fcc unit cell; two close-packed layers are shown [4].

(fig. 2.7); the basis contains two atoms: one at (O,O,O), the other at (i, i, f). Metals like Mg, Ti, Zn, Cd and Co have this structure. (11) The spheres of C are placed over the holes in the first layer not occupied by the spheres of B. Repetition of this leads to a different stacking order: . . .ABCABCABCAB.. .. Though it is not very clear, this structure consists of Face Centered Cubes (fig. 2.8) and is consequently called fcc. In terms of Bravais lattices the unit cell is F-cubic. Fcc-metals are Fe (T > 727'C), Ag, Al, Ni, Pt. Several compounds crystallize in fcc form as well, the most well-known of which is NaCl, consisting of equal numbers of sodium and chlorine ions placed at alternate points of a simple cubic lattice, in such way that each ion has six of the other kind of ions as its nearest neighbours (fig. 2.9). The basis consists of a Naf-ion at (O,O,O) and a Cl--ion at the center of the unit cell (i, f , f ) . There are infinitely many other close-packing arrangements, since each successive layer can be placed in either

Crustals 9

Figure 2.9: The NaCI structure. One type Figure 2.10: The CsCl structure r.'. of ion is represented by black balls, the other t ype b y white [4].

-

of two positions; some rare earth metals, for example, take on a structure of the form . . . A BA CA BA CA BA C. . . .

The third structure frequently encountered in the elements is Body Centered Cubic, bcc. Each atom is surrounded by eight other atoms at a distance 2r = $4. The unit cell is I-cubic. This is not a close-packed structure, but several elements prefer to crystallize in this way, like Fe (T < 727"C), Cr, Ba, K, Li and Na.

A structure that looks very similar to the bcc structure is the so-called CsC1-structure (fig. 2.10). The basis consists of a Csf-ion at (O,O,O) and a Cl--ion at the center of the unit cell. There are only lattice points at the corners of the cube, so this structure is of the simple (P) cubic type. No common element crystallizes in a simple cubic structure, but several compounds do, like CsC1, CuZn, A1Ni and NiTi, the main subject of this report, at temperatures far enough above roomtemperature. Other designations of this structure are ,û2 and B2. (This structure is possible when the ions are about the same size; if the radius ratio exceeds 1.366, the NaC1 structure is preferred.)

The fourth structure that is encountered in metals is bct: Body Centered Tetragonal. The unit cell of this structure is a kind of bcc-unit cell which is stretched in one direction. If steel is quenched a structure called martensite comes into existence, which has a bct- structure.

3 Martensitic transformations

3.1 Introduction

Definition Martensitic transformations are displacive, diffusionless transformations during which the atoms execute a small, well-defined and cooperative movement, resulting in a change in lattice structure and a shape change. The lattice structure of the resulting martensite has an orientation relationship to the lattice structure of the parent phase. The martensite phase is separated from the parent phase by an undistorted plane, called the habit plane [16].

Martensitic transformations are nowadays known to occur in a wide variety of metallic and nonmetallic materials (ceramics, polymers, even biological structures). Martensite is the name given to the resultant product phase from a parent phase which undergoes a martensitic transformation. However, the name martensite was originally suggested by Osmond in 1895 to describe the microstructure found in hardened steels, in recognition of the German metallurgist Adolf Martens'. The martensitic transformation which occurs when carbon steels are rapidly cooled from high temperatures is fundamentally responsible for the hardening of steel.

3.1.1

In a martensitic transformation, individual atoms execute well-defined and correlated movements during the course of the transformation, the movement of each atom being some- what less than one interatomic distance [9]. The martensitic structure is the result of a lattice transformation wholly without atomic diffusion. This is entirely different from some diffusion-controlled solid state transformations such as the eutectoid decomposition (e.g. when steel with 0.8% carbon dissolved at temperatures higher than 727"C, i.e. being in the homogeneous austenitic phase, is cooled, then at the eutectic temperature Te=727"C the austenite splits in ferrite, which is poor in carbon, and cementite Fe3C, containing a lot of carbon) in which the atoms undergo random diffusional movements of a relatively long range nature.

Diffusionless na ture of t h e transformation

i

i

IAdolf Martens (1850-1914): one of the founders of metallography in the l g t h century

Martensitic transformations 11

3.1.2 Surface relief

The most obvious geometrical characteristic of a martensitic transformation is a change in shape, shape deformation, or surface relief of a definite value. If the surface of a specimen which begins to transform at M, is, in the parent (P) stage, polished and made planar and then cooled below M, to induce the transformation, some regions where the martensite (M) phase appears on the surface will exhibit relief effects like those shown in figure (3.1): the silrface of the martensite phase is stil! planar Uüt it is tilted. This sha@ charge inay

(a> Surface Relief (b) Bending of Scratch Line

G

Figure 3.1: Formation of surface relief and bending of scratch line accompanying martensitic transformation [í5, 91.

also be observed if a scratch line is constructed on the surface in the parent state: bends will arise in the line at the boundaries between the P and M phases as shown in (b). Figure (3.1~) shows schematically (in three dimensions) how the formation of a martensite plate displaces a reference scratch ABCD. The inclination of the surface relief and the bends in the scratch line will have definite values depending upon the crystal orientation of the P phase.

3.1.3 Habit plane

The martensitic phase takes the form of plates or needles, which appear to be embedded in the matrix along certain will-defined planes. Such a plane, the plane of contact between the two phases or interface plane, is called the habit plane. It separates the parent and martensite phases. In figure (3.1~) the planes EFIJ and GHKL are habit planes. The habit planes which occur in a specimen don’t have arbitrary directions, owing to the well-defined movements of atoms during transformation. These directions are specified by indices of planes in the parent phase (the use of indices is explained in appendix A); there are many cases in which they are irrational, in contrast with ordinary crystal planes which always have rational Miller indices. The scratches mentioned above prove two very important features of habit planes; since the scratches on the surface across the habit plane are continuous, there cannot exist any appreciable deformation in the habit plane, and it must be concluded that the habit plane is essentially an undistorted plane. Moreover,


if the shape deformation caused any significant rotation of the habit plane, the matrix (parent) material adjacent to a martensite plate would be deformed plastically in order to keep the parent en martensite phases together, and this would reveal itself in the form of displacements of the scratches in the parent phase. Since plastic deformation of the adjacent material is not observed, the habit plane must not only be undistorted, but also unrotated.

3.2 Phenomenological description of the martensitic transformation

Historically, research on metals, mainly on steels, has led to the development of the phenomenological crystallography theory of the martensitic transformation. It is very illus- trative for the understanding of the martensitic transformation, and an attempt to involve mathematics. Two examples of this theory are the Bowles-Mackenzie and the Wechsler- Lieberman-Read descriptions. In fact they are the same, though worked out differently [9]. According to this theory there are three phenomenological steps describing the total transformation. It is to be emphasized that it only concerns three mathematical steps, not physical steps. In reality the martensitic transformation is a process that cannot be divided in separate, chronological steps. Though the described theory is applicable to any lattice transformation, e.g. fee -+ fct in InT1, the martensitic transformation in iron alloys will be used as an example.

3.2.1 I. The B a h distortion

In the definition of martensitic transformations it is stated that a lattice change occurs. For example, in iron alloys, the high temperature phase is fee; after quenching the resulting martensitic phase is bct. Figure (3.2a) shows unit cells of these two lattices. E.C. Bain proposed in 1924 a simple mechanism: in fact, a fee-lattice can also thought to be constructed of bet-cells with a c/a-ratio of a. The only thing to do is to distort this tetragonal lattice homogeneously into another one of different (lower) axial ratio, i.e. compress the parent bet-cell in the c = z3-direction and expand it in the a = 21- and b = zz-directions, until the right martensite c/a-ratio is obtained. Such a homogeneous distortion, by means of which one lattice is transformed into another, is termed a lattice deformation. Any point in the parent lattice corresponds uniquely with the point it becomes in the final lattice: this is called a lattice correspondence. Of the many ways to generate a bet-lattice from a fcc-lattice, the Bain correspondence involves the smallest possible atomic displacements.

From figure (3.2a), it can be derived that the direction [ lOO]f becomes the direction [110]b (the subscripts f and b refer to the fee and bet structures respectively), [OlO] f becomes [ l l O ] b and [OOl] f becomes [ O O l I b . This implies that the following lattice correspondence


Figure 3.2: Lattice correspondence and lattice deformation for the fcc to bet transformation in iron alloys [9].

exists between vectors in the parent and martensitic lattices: [":I,= [ 0 1 -1 1 o o ] [ T'] 23 o 1 X i f

The matrix is called correspondence matrix, and belongs to the described Bain correspondence; if another correspondence is assumed to transform a fcc into a bct lattice, then another correspondence matrix results.

Tetragonal martensite in Fe-Ni alloys has a c/a-ratio of 1.0, while in the parent structure this ratio is fi. If the volume of the structural cell doesn't change during transformation (which is true for NiTi 113, p.322]), then the following principal distortions vis 772 and 73 are obtained:

dong xi .vIsa0/2 -$ a vi = &a/ao = 1.12 along xh .vIsa0/2 + a 7 2 = &-i/ao = vi = 1.12 along xi a0 -$ c 773 = c/ao = 0.80

In matrix form, the lattice deformation is:

A clear view of this deformation may be obtained by considering a unit sphere in the parent structure: just as a tetragonal deforms into another tetragonal with lower c/a- ratio, precisely so transforms a sphere into an ellipsoid of revolution. Since the xi and x; directions are similar, a 2D picture of the 2;-xi-plane suffices. This is shown in figure (3.3).


x i out of paper

Figure 3.3: Cones of unextended lines resulting when a unit sphere is homogeneously distorted into an ellipsoid [9].

The ellipsoid intersects the initial sphere in two circles (with the zk-axis as axis and A’, B’ and C’, D’ respectively lying on them). These two circles contain all endpoints of vectors (like OA’ and OB’) which are unchanged in magnitude. The initial position of these vectors is represented by the cones containing OA, OB and OC, O D respectively, the so called initial cones of unextended lines. Vectors lying within the initial cones of unextended lines are shortened, the ones outside these cones are extended.

There is not one single plane that is undistorted: only on two cones vectors are unchanged in length. So it may be concluded that a homogeneous distortion such as the one proposed by Bain is, though it describes the change in lattice structure, inconsistent with at least one of the important crystallographic features of martensitic transformations: an (almost) undistorted habit plane.

3.2.2 11. Simple shear

This condition is satisfied by a second deformation in the form of a simple shear. In figure (3.4) a sphere is sheared on an equatorial plane KI in the direction d. All points of the structure are displaced in the direction of 4 the distance over which a point is displaced is proportional to the distance of the point to the shear plane Kl. Figure (3.5) shows a cross-sectional view of figure (3.4). As a result of the shear, any vector in the plane AK2B is transformed into a vector in the plane AKiB; its magnitude is unchanged, the vector is only rotated. All vectors on the left of AK2B are decreased in length, those on the right are increased. The plane AK2B represents the initial position of the plane AKkB which remains undistorted as a result of shear. Obviously, the relative positions of the planes AK2B and AKkB depend upon the amount of shear: the bigger the shear, the bigger angle CY.

The essential point is that (exclusive of vectors in the shear plane itself), some vectors

I


Figure 3.4: Graphical representation of sim- Figure 3.5: Cross-sectional view of

equatorial plane KI in the direction d [g]. ple shear, whereby a sphere is sheared on an fig. 3.4 191.

-#

are increased in length, some are decreased in length, and some remain unchanged in length as a result of simple shear. A similar result was obtained from a consideration of the lattice deformation and the corresponding cones of unextended lines. Combining these two effects leads to the following conclusion: a simple shear (of a unique amount, on a certain plane, and in a certain direction) can be found such that vectors which are increased in length due to the Bain lattice deformation are correspondingly decreased in length by the same amount due to the simple shear, and vice-versa. Such vectors which remain invariant in length to these operations define potential habit planes. The simple shear can be either a slip shear or a twinning shear (later more), but in either case, the lattice is left invariant, and the simple shear is thus termed a lattice invariant shear, which may be represented by a matrix p.

3.2.3 111. Rigid body rotation

The third additional requirement that the habit plane be unrotated as well has not yet been fulfilled. If in addition to the lattice deformation and the lattice invariant deformation, a rigid body rotation (about a certain axis, over a unique amount $) is supposed to return the undistorted plane to its original position, then an undistorted ánd unrotated plane will exist. This rotation can be described by means of a matrix R.

3.2.4 Total shape change

The features of the total macroscopic shape change, i.e. surface relief and an undistorted and unrotated habit plane, match well to a mathematical model called invariant plane strain. With an invariant plane strain (IPS) the displacement of any point is in a common direction and proportional to the distance from a fixed (i.e., not moved by the strain) plane of reference, which is the invariant plane. Simple examples are simple shear and


uniaxial extension. A general IPS can be represented by the combination of these two, as in figure (3.6), where a martensite plate is formed within phase. The invariant plane is of course the habit plane. An

shape after the

----?&i - _ _ _ _ _ _ ~

parent Q martensite

a single crystal of the parent invariant plane strain Et can

transformation

i I parent #,IJ phase I I I ' phase 3 I c I I

shape prior to transformation

Figure 3.6: Shape deformation accompanying the formation of a single madensite plate [lis].

be represented in matrix notation as:

where : (3 x 3) unit matrix mt : amount of deformation dt : (3 x 1) unit vector in the direction of the shape change pi : (1 x 3) unit vector normal to the invariant plane

As we have seen, the total shape change may also be described by means of three subtransformations, with respective matrices B, p and R. Therefore we can write:

If the lattice parameters of the parent and martensite phases are known (e.g. from X-ray diffraction measurement), then the principal strain in the Bain deformation and, therefore, matrix B is determined. If further assumptions are made concerning the direction and shear plane for the lattice invariant strain, then matrix P can be determined. The matrix

= BP determines the habit plane, i.e. the unit habit plane normal pt is known (in fact, two possible solutions for pt are calculated). From the condition that the habit plane is unrotated, matrix R can be calculated. Now it is possible to determine Pt with equation 3.2. Using equation 3.1 we can see what happens if 0, is applied to pt:

PtPt = pt + mtd t (p tp t ) = pt + m t d t +

PtPt - p t = mtd t (3.3)


This is the last step: with equation 3.3 the amount of shear mt and the shear direction dt are calculated.

In this section, the fcc + bct transformation occurring in steel is used as example. How- ever, most SMA's have a bcc structure in the high temperature state, which transforms into some other structure. The phenomenological theory described above is likewise applicable to any other martensitic transformation.

3.3 Slip vs. twinning

It has already been stated, that the required simple shear may be produced either by slip or twinning; the shear must be permanent. In figure (3 .7 ) this is rendered schematically. Figure (3.7a) shows the initial crystal before transformation. Due to the lattice deformation

shape change

/ Y / (a) Parent Lattice Prior (b) Lattice Deformation Due (c) Lattice Deformation (d) Lattice Deformation and

to Transformation to Transformation and Slip Shear Twinning Shear

Figure 3.7: Slip shear or twinning shear in addition t o lattice deformation is necessary to obtain the actual shape change [1.5].

(Bain distortion), the parent phase lattice is changed to the martensite lattice, resulting in a certain shape change (solid line). The real observed shape change of the crystal is different, indicated with the dashed line. The dashed line in (c) and (d) marks the habit plane, the plane which separates the parent and martensite phase. Comparison of (b) with (c) and (d) makes clear that slip or twinning is necessary to connect the parent and martensite phase along the habit plane.

When slip occurs in a crystal, then crystal planes glide over each other (usually close packed planes in close packed directions). This proces is irreversible; it is not possible to return the crystal into its exact original configuration. Martensitic transformations which are accompanied by slip are therefore irreversible transformations and metals or alloys with this property cannot show the SME, since reversible martensitic transformation is required for this.

Crystal structures which possess very little slip possibilities, have a quite different mechanism to react on shear loads: twinning [6-81. When twinning occurs, atoms in a thin band move over a distance, which is less than an interatomic distance, in such way, that afterwards the atoms are mirrorred-about a mirror plane, called the twinning


C- Spiegelvlak

I

Figure 3.8: Atom movements during twinning; the dot- ted lines give the initial situation [7].

Figure 3.9: Displacements of crystal parts to the left as a result of twinning [9].

plane (fig. 3.8). The thin band is bounded by two parallel twinning planes. The result is a displacement of the crystal part above the twin with respect to the part underneath it, and therefore a deformation of the crystal, as shown in figure (3.9). Twins occurring during deformation are found in all metal lattices. They come into existence either because the deformation takes place so rapidly that the usual deformation process doesn’t appear or because the normal plastic deformation is difficult to be brought about; this is the case when the stress, needed to cause the turning over, is less than the stress giving rise to plastic deformation by slip.

Twinning is in contrast with slip a reversible process. That is why martensites formed in SMA’s are often internally twinned (there are still other ’lattice invariant deformations’ such as stacking faulting, but these will not be treated, first, because there is absolutely no unanimity among scientists what process occurs in which alloy, second because twinning is the main process in NiTi, the subject of this report). It should be noted that the important parameter in twinned martensite is the proportion of the twinned volume to the untwinned volume, i.e. the relative thicknesses of the bands determine the amount of macroscopic shear.

3.4 The R-phase

Until now the impression may have been created that the martensitic transformation is the only interesting transformation to occur in SMA’s. Nevertheless, in some alloys, including NiTi, on cooling the total parent-martensite transformation consists of two or even more steps, i.e. additional phases exist [16]. For NiTi the entire transformation is treated below,

In figure (3.10) the phase diagram of binary NiTi is shown. In this report, with NiTi is meant Ni50Ti50, i.e. the equiatomic composition. The high temperature phase of NiTi is

Mart e nsitic transform at ions 19

Weight Percent Nickel O 10 20 30 40 50 80 70 80 90 I

1800

L 145S01

o Ti Atomic P e r c e n l Nickel N i

Figure 3.10; The phase diagram o f NiTi [16].

the B2 (CsC1) structure. This phase is formed directly from the liquid phase and is stable down to about room temperature. It is an ordered alloy, which means that the structure of the unit cell, i.e. the positions of Nickel and Titanium atoms in the unit cell relative to each other (each Ni atom has eight next neighbouring Ti atoms, and vice versa) is maintained over considerable distances; this is called a superlattice structure. The general opinion is that ordering is a condition in most alloys to show the SME (see also 3.8).

At least two transformations are involved when going from the high temperature B2 phase to the low temperature B19’ phase, due to the formation of a so-called intermediate or R-phase (this transformation is according to some scientists also a two stage process). Especially in binary NiTi alloys with high nickel content or in Niso_,TisoFe,?: alloys this

I .G

1

z

ln

0.4

0.0 -200 -150 -100 -50 O 50 100

TEMPERATURE PC]

Figure 3.11: Deformation-temperature curve of a NiTi alloy showing a two stage transformation [lJ].


additional phase is apparent present. Figure (3.11) shows a temperature-strain curve from which it is obvious that the transformation proceeds in two steps both in heating and cooling, because there are two steep parts in the curves. The structure of the R-phase is Rhombohedral (or trigonal: a = b = c, a = ,û = y # 90"); it exhibits but little distortion from the austenitic B2 phase (fig. 3.12). On the other hand, the R-phase to martensite

Ni A: ( B2 1 a=b=c=3.015

p =90grad V=27.41

Ni

Figure 3.12: Austenite unit cell with B2 structure (left) and R-phase unit cell (right) [13].

transformation involves a much bigger change in lattice. This explains the difference in the size of the hysteresis of both transformations: the measure of hysteresis is determined by the interfacial energies of the phase boundaries and these will be big, if the lattice distortion is big.

Although it is still a matter of debate whether the R-phase must form before the martensitic transformation can take place or not, the common opinion is that the B2 + R transformation is not a precursor to the martensitic transformation, but an independent phase transition which just happens to set in ahead of the martensitic transformation. In fact, with the addition of some 5% Fe, the martensitic transformation no longer occurs although the R-phase still forms. The direct B2 -+ B19' transformation, seemingly without R-phase forming, is explained by the two transformations B2 -+ R and R -$ B19' occurring at about the same temperature range.

However, because of the relatively small influence on general characteristics, the R- phase will not be mentioned anymore, exceptions leaving aside, and only the direct B2 + B19' transformation is considered to be the important martensitic transformation.

3.5 Martensite variants

Figure (3.6) shows the shape deformation occurring when one martensite plate is formed within'a single crystal of the parent phase, and indicates that when a martensitic transformation occurs, the external shape of the specimen changes significantly. In reality such drastic shape change is not observed; nothing seems to happen from the outside. This contradiction is explained as follows [15]:

Martensitic trans-formations 21

The parent phase is often not a single crystal, but polycrystalline. A lot of grains with different orientations exist in a polycrystalline material. This will cause constraining effects at the grain boundaries; if a particular grain wants to change its shape, then the surrounding grains prohibit this shape change to a large extent.

But even when we are dealing with a parent phase consisting of a single crystal, still no macroscopic shape change will occur. This is due to the formation of so- called martensite variants. The following will describe the way in which variants are generated.

3.5.1 Crystallographic characteristics

Most Shape Memory Alloys have basically superlattices with bcc structures in the high temperature state. Alloys with bcc structures are classified as ,8 phase alloys. Regardless of the type of alloy, ,8 phases of alloys which have about 50:50 composition ratios (like NiTi) and are ordered like CsC1 are denoted by ,f?z or B2. ,8 phases of alloys which have about 75:25 composition ratios and are ordered like Fe3A1 are denoted by or D03. The martensitic phases obtained from

Figure (3.13) illustrates the crystal structure of a B2 parent phase; (a) shows the three- and ,f?2 are respectively ,Bi and p;.

(a) unit cell

e cs o c1

[ l i l ] [i1 13 \ AZ / 32

O u ~ ' ~ ' O

t - [Ti01

(b) (110) plane (C) the (110) Plane above and below the plane in (b)

Figure 3.13: Crystal structure of a CsCl-type B2 lattice (a); the planes in ( b ) and (c) are alternately stacked [15].

dimensional structure, (b) shows the arrangement of the atoms within the (110) close packed plane, and (c) shows the arrangement in the (110) plane that lies above (b) (in front of the page) or below (b). The cubic structure may therefore be viewed as the result of alternately stacking the planes pictured in (b) and (c), resulting in afct cell, as shown in figure (3.14atb). In spite of the fact that NiTi is the most popular and best studied SMA, the precise structure of the martensitic phase is still a matter of debate. The structure discussed in [16] will be presented here. It is thought that the martensitic transformations which occur in ,û phase alloys are due to: (I) an orthorombic distortion, resulting in different values of the lattice parameters, but still right angles (fig. 3.14~); (11) shearing,

Mart e nsit ic transformations 22

0 Ni ATOMS

.Ti ATOMS

Figure 3.14: Crystallographic ’steps’for the B2 -+ Bl9’ transformation in NiTi. (a) B2 cells; (b) B2 f f c t cell; (c) orthorombic distortion; (d) (loo)B2[oII]B2 shear to monoclinic; (e) ( û i í ) m [ û 1 i ] m planar shuffle.

which is for NiTi in the [01I]B2 direction along the (100)B2 plane (fig. 3.14d), and (111) a planar shuffle: the atoms in alternate (011)Bz planes shift about 1/3 in the [ O l i ] ~ ~ direction (fig. 3.14e). These three ’steps’ just describe what kind of subdeformations the total B2 + B19’ deformation is composed of; they are not really occurring discrete stages. These three stages, which visualize the change from one crystal structure into another, should not be confused with the three mathematical steps in 3.2, which are three mathematical operations in order to calculate habit planes.

3.5.2 Variants in NiTi

In the section above the (100) plane was taken as the shear plane; however, the (010) and (001) planes will give rise to martensitic structures that are actually the same, i.e. crystallographic equivalent structures are obtained. The same holds for the shear directions. The conclusion is that even though the parent phase consists of a single crystal, a number of different martensites, i.e. with different lattice correspondences and with different habit plane indices (but nonetheless crystallographically equivalent), will appear scattered throughout the specimen. These martensites with different habit plane indices are called variants. In bee SMA’s, 24 variants are possible. Accordingly, deformations such as shown

Mart ensitic transformations 23

in figure (3.6) do not actually occur. The 24 habit planes are of course for every Ni,Tiloo-,, with x the atomic percentage

in the alloy, different: each particular alloy has its own set of 24 variants. Nevertheless, some general properties are observed in all (NiTi) alloys. In figure (3.15) the 24 variants belonging to Ni50.2Ti alloy are represented in a stereographic projection. The number

Figure 3.15: Habit planes of the 24 variants in a Ni50.2 T i alloy in a Stereographic projection [12].

designation of each habit plane variant indicates the dominant (major) correspondence variant: variant 1 or 1’ is more dominantly present then variant 2, while variant 6 and 6’ are minor variants. The same number appears with and without a prime (’); this indicates that the pair are variants with oppositely directed shears. Finally, for a given shear plane and direction, there are two possible solutions for the habit plane indices (see section 3.2.4); this is indicated by a (+) and (-).

3.6 Self-accomo dat ion

The 24 variants do not come into existence randomly. Figure (3.16) are two micrographs showing surface relief in a Ni49.5Ti alloy; (a) has been taken during cooling (and thus during transformation) between M8 and M j , while in (b) the transformation is completed below M f . It is very striking that properly but three variants are present: 1(-), i,(+) and 2’(-). Especially in (b) it is seen that these three variants form triangles. Why should the martensitic phase display such a triangular morphology? The answer is properly rather obvious. A martensitic transformation like in figure (3.6), i.e. resulting in a single variant, is accompanied by shape strains, which may be represented in a shape strain matrix T. The principal distortions (diagonal elements) often differ from unity by some 10-20%. If three variants are formed, the average shape strain matrix may be calculated. In this


Figure 3.16: Surface relief micrographs showing typical triangular self-accomodating NiTi after diflerent degrees of transformation. (a) between Ms and M j ; (b) below M j [12].

example:

T = 1/3(T{I(-)} + T{l’(+)} + T{2’(-)}) 0.950 0.008 0.019

-0.019 1.023 0.005 0.067 0.013 KO24 1

In the average shape strain matrix, the off-diagonal elements are nearly zero, while the principal distortions are about unity. This means that very little shape change occurs, as is observed.

Since martensite variants are created side by side in this way, they mutually reduce the transformation strain accompanying the formation of the martensite variants. This effect is called self-accomodation.

3.7 Reorient at ion

The formation of (up to 24) internally twinned variants occurs under normal conditions, i.e. on cooling and zero external stress. What happens if an external stress is applied? There are two different situations: (1.): the starting material consists of a single twinned martensite plate, i.e. only one variant (fig. 3.17a, dashed lines). (This picture is about the same as fig. 3.7). By applying a shear stress, the internal interfaces, mostly twin boundaries, will move. One of the two twin variants will shrink (2) while the other (1) is growing resulting in the shown macroscopic shape change. On further stressing, eventually the plate will be totally detwinned, and plastic deformation like slip will commence. Possibility (2.): the material consists of several variants like in figure (3.17b), which is an idealized situation, where two out of the twenty-four martensite plate variants have grown together as a self-accomodating martensite plate group in order to minimize the strains and stresses. The parent phase above and below the martensite plates is kept fixed. If the sample is not kept fixed but strained by a shear stress as shown in figure (3.17c), the martensite plate

Mart ensit ic transformations 25

D

A

t_

r f i 4 M I c)

Figure 3.ï7: Changes introduced upon application of external stress. (a) movement of the boundaries in between the digerent twin related variants; ( b ) two variants formed in a self-accomodating manner; (e) growth of one variant a t the expense of the other caused by an external stress [22].

group tends to minimize the internal stresses by changing the amount of the two variants present. This means that the boundary CD between the two martensite plates moves or that the habit plane AB moves faster than the habit plane EF. So in this case certain variants grow at the expense of others by means of moving interfaces, and eventually only one variant persists (after which possibility (1.) may occur). This process is called reorientation of martensite variants. At this point the specimen surface is featureless, showing no reliëf effects. Theurviving variant is thatwhöse shape strain directiön is most parallel to the tensile axis, thus permitting maximum elongation of the specimen. -

The maximum strain that may occur is the Bain strain. In figure (3.18) an example of

Figure 3.18: Reorientation of martensite b y movement of already existing martensite plate boundaries while applying an external stress in a CuZnAlNi alloy [22].

reorientation in a CuZnAlNi alloy is shown (the big white part moves to the right).

3.8 The reverse transformation

The important feature of the Shape Memory Effect is that on heating a specimen regains its original macroscopic form. But does this hold for the inside as well, i.e. is the crystal

Martensitic transformations 26 ~ ~ ~~

structure of the parent phase after heating exactly the same as its initial structure? In most alloys it is, especially the ordered ones. Figure (3.19) illustrates why the crystallographic reversibility is automatically guaranteed by superlattice structures. In this figure the re-

e +&jz O O

Figure 3.í9: (a ) Three possible lattice correspondences in the reverse transformation of the B2 += BI9 transformation; ( b ) parent phase crystal síructure resulting from lattice correspondence A: a B2 superlattice the same as the pre;transformation-structure; (c) parent phase crystal struc7ure resulting from lattice correspondence B: completely different from a B2 structure [lrS].

verse transformation of a B2 + B19 transformation is taken as example. Figure (3.19a) is a projection of the crystal structure of the B19 martensite onto its basal plane. The black and white circles represent the two alloying elements; the big circles lie in the basal plane, while the little ones form the plane above. If we ignore the ordered arrangement of the atoms, the structure is Hexagonal Close Packed.

Generally, the crystal structure of martensite is relatively less symmetric compared to that of the parent phase. For this reason, the kinds of lattice correspondences between the phases involved in the reverse transformation are restricted. In the example in figure (3.19a) there are, if we ignore the ordered arrangement of the atoms, three equivalent lattice correspondences, represented by the rectangles marked A, B and C. If the reverse transformation occurs along path A in the figure, then the crystal structure of the product phase will be as shown in (b), and the B2 superlattice structure of the parent phase will be preserved in both the forward and reverse transformations. However, if the reverse transformation occurs along either the B or C paths, the crystal structure of the resultant parent phase will be as shown in (c), and will markedly differ from the original B2 structure: in the B2 structure the nearest neighbour atomic bonds are all between different types of atoms, whereas in (c) half of those bonds are between atoms of the same type.

Since the changes in crystal structure shown in (c) would raise the free energy, reverse transformations along path B or C are impossible. Thus the orientation of the parent phase crystal is automatically preserved by its ordered structure.

Mart e nsit ic transformations 27

The crystallographic reversibility of Shape Memory Alloys is a characteristic of thermoelastic transformations. This phenomenon will be discussed in the next section.

3.9 Thermo elast kity

Definition The therm-oelastic transformation is a transformation in which a given plate or domain ~f martensite grows or shrinks as the temperature is respectively lowered or raised, and the growth rate appears to be governed only by the rate of change in temperature [14].

This definition implies a fundamental distinction between the thermoelastic and other (e.g. burst) types of transformation; therefore also the existence of at least two, and possibly more, different types of martensitic transformation. The first observed and most well-known martensitic transformation occurs during the hardening of steel. In pure iron, the high temperature austenitic fcc lattice transforms into a bcc lattice. In quenched steel (Fe-C alloy), this transformation is prevented by the carbon atoms dissolved in the fcc lattice of iron. The structure that results is the martensite bct structure. The quenching 0200 deg/sec) is essential to prevent diffusion of C atoms out of the fcc lattice to form cementite (Fe3C), while the remaining fcc lattice can transform into ferrite, which has a bcc lattice. This clearly shows the diffusionless character of the martensitic transformation. However, short distance diffusions, which always occur, and diffusion during heating cause the irreversibility of the martensitic transformation in steel. This kind of transformation is obviously non-thermoelastic.

NiTi does show thermoelastic behaviour. Quenching is not needed to achieve a martensitic transformation: the transition from a B2 to a B19’ lattice also takes place during slow cooling near room temperature. Upon heating again the reverse B19’ -+ B2 transformation takes place; this reversibility of the transformation requires a total absence of short or long diffusion.

A significant difference between martensitic transformations in steel and NiTi and other SMA’s is therefore that a minimum cooling rate is required for the formation of martensite in steel, while this formation in SMA’s is independent of the cooling rate. Only alloys that exhibit thermoelastic martensitic transformation can be Shape Memory Alloys.

3.10 Transformation thermodynamics and temperatures

Like all processes in nature the martensitic transformation is ruled by the striving for a minimum in free energy. The total energy change during transformation is:

AG(T)‘ + = AG: + M(T) + 6(AGtc+ M, + AG,

while for the reverse transformation:

AG( T ) ~ + +’)+


where AG, : change in the chemical free energy, &(AG,,) : change in the non-chemical free energy, consist-

ing primarily of elastic energy accumulated in the thermoelastic transformation,

: this term corresponds to the forces resisting either the growth and shrinkage of existing M crystals or the creation and annihilation of new M crystals.

AG,

At a certain equilibrium temperature To the chemical free energy of the parent phase is equal to the chemical free energy of the martensitic phase, i.e. AG: -$ M(TO) = O. Trans- formation doesn't take place at this temperature because there is an activation energy or driving force necessary to overcome resisting forces like friction, forming AG,. At T=Ms, which is independent of the cooling rate (but dependent on other variables like the composition of the alloy, including alloy element additives, thermal history and treatment, and the applied stress, as will be seen later), AG(T)' -* = O, and the transformation starts; the difference between To and Ms is called the degree of supercooling. When the temperature is lowered further, the difference between the chemical free energies of the parent and martensite phases increases (negative sign), but as a result of the growing martensite plates, the elastic strain energy increases too (positive sign). In this way there exists a certain size of the martensite plates at every temperature below Ms which yields a minimum in total free energy. At T=Mj, reaches saturation, and the entire specimen consists of martensite variants. In case of non-thermoelastic martensitic transformations, the same kind of story holds for the reverse transformation; there is only one equilibrium temperature To.

P P

Figure 3.20: Schematic representation of free energy-temperature relationship for a thermoelastic transformation, showing two characteristic temperatures, To and TO' . [id].

However, in thermoelastic transformations, there is another equilibrium temperature TA. This is caused by the stored elastic energy. For the P + M transformation holds,


because there is not any elastic energy stored yet:

AG^ - M = A@' - M = 0

In the reverse transformation the nonchemical term must be considered too; at T=TA the following is satisfied:

In other words, the nonchemical term lifts the chemical energy graphs to a higher ievel, as illustrated in figure (3.20); the stored elastic energy assists the chemical driving force gained by heating. The result is that the reverse transformation starts at a temperature A, which is for some alloys lower than M,. (A, -TA ) is called the degree of superheating. The reverse transformation is completed at T=Aj. Figure (3.21) illustrates this thermoelastic

A G M - + P = AG:+~+AG;+~= O

. __-__-- I \

'. \ \

Í

I Y

I

0 10 t' 20 25 Kt 35 -o.? '

Tempcrature

Figure 3.21: Martensite fracture vs. temperature [ZO],

behaviour schematically. Since the two equilibrium temperatures To and Ti cannot be measured, they are often

calculated as follows, starting from the idea that the degrees of supercooling and superheating are about equal:

If the R-phase transformation occurs, then in accordance with the already discussed transformation temperatures, the relevant P t) R temperatures are MJ, M l , Ai and Af.

To conclude this section about thermoelasticity, figure (3.22) shows micrographs of the growth and shrinkage of two martensitic variants in a self-accomodating way due to cooling and heating in CuAlNi.


-+ Cooling (growth)

4 Heating (shrinkage)

Figure 3.22: Optical micrographs of the growth and shrinkage of thermoelastic martensite crystals due

to cooling and heating in CuAlNi [lis].

4 The Shape Memory Effect

4.1 Introduction

Now the (crystallographic) backgrounds of the Shape Memory Effect are known, this effect is treated in this chapter in general, but especially concerning NiTi. Before 1969 the SME was thought to be a characteristic peculiar only to AuCd, InT1 and NiTi. Since then a number of SMA’s have been discovered; table (4.1) gives some information about the most well-known alloys. When tensile tests are performed on a SMA at various temperatures,

Alloy Composition

AgCd 44-49at.%Cd AuCd 46.5-50at.YXd CuAINi 14-14.5wt.%AI

3-4.5wt.%Ni CuAuZn 23-28at %Au

45-47at.YoZn CuSn -I5at.%Sn CuZn 38 5-41 5wt.%Zn CuZnX few wt.% x (X=Si, Sn, AI, Ga) I n n 18-23at. %TI NiAI 36-38at. %Al TiNi 49-51at.YoNi Fept -25at.%Pt FePd -30at. %Pd MnCu 5-35at.%Cu

M, (“C)

- 190--50 30-100

-140-100

- 190-40

- 120-30 -180- 10 -180-100

60-100 -180-100 -50-100

--13( --lo(

- 250- 180

Transformation Temperature

Hysteresis (“C)

-15 -15 -35

- 6

-10 -10

- 4 -10 -30 - A

-25

Type of Transformation*

B2-M2H B2-tM2H D0,+2H

L21-+M18R

DO,+2H orl8R B2-9R or M9R B2-9R or M9R DO,-tlSR or M18R FCC-tFCT B2-M3R B2-tB19 L1,- ordered BCT FCC-FCT-tBCT FCC-FCT

Ordered or

Disordered

ordered ordered ordered

ordered

ordered ordered ordered

disordered ordered ordered ordered

disordered disordered

Volume Change ~

-0.16 -0.41 -0.30

-0.25

-0.5

-0.2 -0.42 -0.34

0.8--0.5

* FCT means face centered tetragonal lattice; BCT means body centered tetragonal. For other symbols see section 1.2.5.

Table 4.1: Data for alloys which exhibit a complete SME [15].

stress-strain curves with very different shapes are obtained. The transformation temperatures appear to play an important role. In figure (4.1)’ such stress-strain curves for Ni49Ti are given. At 5% strain the stress was relieved. Though it is not very clear form these graphs, the stress-strain curves of NiTi-based alloys can be classified into the five types shown in figure (4.2) according to the temperatures at which measurements were made. Each type is associated with a certain deformation mechanism. It is striking that for de-

The Shape Memory Egeet 32

O v1 v1

2 tj

Ms = - 114'C A,= -89'C

200 Mi= - 153'C 4ol!LzLl O 5 A,= -4O'C

5 0 Strain E (YO)

- 27°C P P J,,,,,

~~

Figure 4.1: Stress-strain curves for Ni49Ti at various temperatures [15].

formation temperatures Td >Af (type IV) the strain is entirely regained when the stress is released, although the deformation seems to be rather plastic. This behaviour, which is related to the Shape Memory Effect, but not a condition for this (i.e. some SMA's don't show this behaviour), is called pseudoelasticity. Before the mechanisms of the other types are discussed, first pseudoelasticity is explained.

c

Strain

Figure 4.2: Five types of stress-strain curves for NiTi systems [15].

The Shape Memory Eflect 33

4.2 Pseudoelasticity

The pseudoelastic behaviour is a complete mechanical analogue to the thermoelastic transformation. Other expressions meaning about the same are superelasticity and rubberlike behaviour. While in the thermoelastic case the martensitic transformation proceeds continuously with decreasing temperature, in the pseudoelastic case this transformation proceeds continuously with increasing applied stress O, and is reversed continuously when the stress is decreased (only in a certain temperature range, i.e. T >Af j.

The stress-strain curve in figure (4.3), which is obtained at a temperature > A f , shows this behaviour schematically. Section AB represents purely elastic deformation of the

P-+M Figure 4.3: Schematic representation of a stress-strain curve showing the pseudoelastic behaviour; CT, = stress necessary t o cause transformation at TI; aE-IP = stress necessary for reverse transformation at TI; ai = plastic yield stress of martensite a t TI; E = total strain achieved [22].

P - I M parent phase. At point B, corresponding to a stress level uT, , the first martensite plates start to form. The transformation is essentially complete when point C is reached. The slope of section BC reflects the ease with which the transformation proceeds. On continued stressing, the material which is in the completely transformed condition, deforms elastically as represented by section CD of the curve. At D, the plastic yield point, O. of the martensite is reached and the material deforms plastically until fracture occurs. If the stress is released before reaching point D, e.g. at point C’, the strain is recovered in several stages. Part C’F of the curve corresponds to elastic unloading of the martensite.

at F, the reverse martensitic transformation starts and the On reaching a stress fraction of martensite decreases until the parent phase is completely restored at point G. Section GH represents the elastic unloading of the parent phase. If no irreversible deformation has taken place either during loading or unloading, then the total strain is recovered. If so, a partial recovery occurs. The area enclosed by the loading and unloading curves gives the amount of dissipated energy.

M - I P

The Shape Memory Egeet 34

4.3 Types of deformation mechanisms

The four other types in figure (4.2) are still to be discussed:

Type17 Td<Mj : Even before deformation, the specimen is entirely martensitic (variants formed on cooling). Consequently, the deformation proceeds according to the migration of twinniiig ifiterfaces within the martensite phase and the coalescence of variants.

Type 11, M j <Td < M s : The specimen deforms because of stress-induced growth within the existing martensite phase, growth of new stress-induced martensite, as well as continuation of the mechanisms of type I.

Type 111, Ms <Td <Af : The deformation is due only to growth of stress-induced mart ensi t e.

Type IV, A f <Td : As explained in the previous section, pseudoelasticity makes that the martensite phase exists only under stress.

Type V, A f <Td : The yield stress of the parent phase is lower than the stress necessary to induce martensitic transformation, so plastic deformation of the parent phase occurs before the stress-induced martensite is formed.

The strains in graph type I, I1 and 111, in other words if Td <Af , are not (completely) recovered after the stress is removed. However, the residual strain can be (almost) completely eliminated by heating the specimen above A f . This phenomenon is nothing but the Shape Memory Effect itself: a specimen ’plastically’ deformed below A f , resulting in martensite formation or reorientation (depending on temperature), regains its initial size and form by heating it up above A f .

4.4 One Way Memory Effect

When the specimen in the previous section is cooled again, it will not deform like before; if a new deformation is to take place, it has to be achieved by stressing again. So successively heating and cooling doesn’t have any macroscopic effect, only the first heating after loading.

One-way memory

--t -* +

Below M f Below Mf Above A , Below M,

Figure 4.4: Coil spring example showing the One Way Memory Efect [lil].


Figure (4.4) illustrates this behaviour, using a coil spring. For this reason this Shape Memory Effect is called the One Way Memory E’ect. As the name suggests, there are other Memory Effects. They are called the Two Way Memory Eflect and the AZ2 Round Memory Egeet. The following two sections will consecutively treat these effects.

Figure (4.5) illustrates the One Way Memory Effect. The upper part of the figure

Figure 4.5: Schematic representation of a stress-strain curve showing the Shape Memory Eflect; (a) the deformation stage; (b ) the shape recovery while heating the specimen [22].

represents the deformation stage, while the bottom part shows the shape recovery. Note that this graph may be three-dimensional if the temperature axis is perpendicular to the strain and stress axes (see fig. 4.12).

4.5 Two Way Memory Effect

In the Two Way Memory Effect (TWME) the object changes shape upon both cooling and heating. It doesn’t only remember its parent phase shape, but also its martensitic shape. Figure (4.6) shows the TWME in a coil spring. It differs from the One Way Memory Effect (OWME) in two respects:

1. a shape change during cooling

2. indefinite repeatability of the Shape Memory Effect by thermal cycling (=heating and cooling)

The Shawe Memoru Effect 36

Two-way memory

3

a-

Below Mf Above A f

Figure 4.6: Coil spring example showing the Two Way Memory Effect [ll].

In the alloys which exhibit a thermoelastic transformation, the OWME is always effective, it is inherent to the martensitic transformation. However, the TWME must be induced by some thermomechanical treatment , called training: it is an acquired property. The degree of shape change in NiTi is small compared to e.g. CuZnAl, while its control is not easy. The recoverable strain depends on the number of cycles the sample has to withstand.

4.5.1

The principle involved in all training techniques is that sites of internal stress are created by some mechanism inside the high-temperature phase. The sites are either irreversibledefects such as dislocations caused by the deformation, or they consist of stable stress-induced martensite, which doesn’t undergo a reverse transformation when heated, or precipitates. These sites cause an internal stress field, which in his turn influences on the nucleation of a limited number of particular variants; the other variants don’t appear. When these existing variants grow on cooling, a macroscopic shape strain is observed.

The origin of t h e TWME

4.6 Training processes

Several training methods are used which generally involve repeated cycles combining temperature, stress and strain variations. They have in common that they are diffusionless processes. Two methods will be treated here.

4.6.1

When a constant stress (e.g. torsion) 7, which is insufficient to induce the martensite, is applied at a temperature T > A f , then during cooling the Afs7 temperature is attained for one particular variant, giving rise to a large strain 7. On heating the specimen will ordinarily return into its austenitic state. When such thermal cycles are repeated a number of times (N>10 to stabilize the hysteresis loop), it is consequently observed that, without any external applied stress, a spontaneous strain occurs in the same direction as with the stress; its amplitude depends on the number of cycles and on the applied stress during training. Figure (4.7) shows the successive training cycles, resulting in the TWME behaviour in figure (4.8). This type of training is the most efficient one. It also allows to

The rma l cycling wi th a constant stress


4

Y,

predict the high and low temperature shapes with good accuracy.

Y / ( % I Z = 25 MPa

Figure 4.7: Successive temperature-strain cycles in CuZnAI (torsion). For N>10 t t b z cycles are quasi- closed; ye=elastic strain induced by the constant stress T in the austenitic state; yp=plastic strain induced by thëtraining [lJ].

~ -

Y

4

2

O

(%I z = o

Figure 4.8: Temperature-strain cycle with zero stress after training with a constant stress of 25MPa; yv is the reversible pari of the strain and the amplitude of the TWME [I$].

4.6.2

The sample in the austenite state is submitted to an elastic strain in such a way that the corresponding elastic stress is not enough to generate the martensite or plasticity. By cooling the stress induces the favoured variants; this relaxes the stress itself because the

The rma l cycling with imposed strain


strain remains constant. On further cooling the sample strain surpasses the imposed strain, which is a proof that the favoured variants, once created, carry on to increase even with zero stress (fig. 4.9). By heating, the sample recovers its initial shape and stress. When

no strain imposed strain (purely elastic)

Figure 4.9: Training process with imposed strain [13].

this cycle is repeated a number of times, it will also lead to the TWME, but with less efficiency than the former method.

4.7 All Round Memory Effect ~~ - ~ ~ ~~

We have seen that diffusionless training processes induce the TWME. Training methods with some diffusion process lead to a third kind of Shape Memory Effect, the All Round Memory Effect (ARME), in Ni rich NiTi. These methods make use of a heat treatment called aging [23]. Aging means keeping the sample at a high temperature during a certain time. Aging may take place in one or more steps. As a result of aging treatments precipitates form from the supersaturated matrix. A precipitate is a metastable intermediate state of a segregation. In Ni rich NiTi the precipitates are mainly TiSNi4. Figure (4.10)

I 0 7 3 K + q u e n c h iMs =BOK

l h 773K M’s = 310K MS = 230K M f = 205K

J

77K 230K 273K 373K

Figure 4.10: Thermomechanical treatment leading t o the All Round Memory Effect in Ni rich NiTi [ lJ ] .


summarises the training process and resulting behaviour: the first step is heating the sample (a straight ribbon) at a high temperature (800°C) and then quenching it; this is called a solution treatment, probably executed to maintain the high ordering which is present at high temperatures. After this the sample is constrained in a stainless steel tube and heated at moderate temperature (400-500" C). During this thermomechanical treatment, some precipitation of the Ti3Ni4 phase occurs. As has been seen, in NiTi with high oickel content, two transformations occur, the first one being P 4 R-phase and starting at !di. The third step of the training process is cooling the sample at T >Mi after which it is released; it is partially curved in the way imposed by the tube. On further cooling, between 30°C and -70°C a spontaneous shape change, opposite to the one imposed during the aging, is observed during the R-phase and martensitic transformations, i.e. the ribbon curls to the other side. On heating above 30"C, the after aging shape is recovered and the All Round Memory Effect cycle can be repeated.

The ARME is just a TWME in which the shape changes are greater than in a normal TWME, and the shapes at high and low temperatures are exact inverses. The reversible strain is limited to f 2 % . Another problem common to diffusion controlled processes is the fact that the high and low temperature shapes seem to be very hard to define in advance.

The ARME is explained as follows: when the sample is constrained in the tube, tensile stresses will occur in the outside part of the sample and compressive stresses in the inside part (with reference to the neutral axis) because of the bending. The precipitationöccurs in such a way that the normal ~~ to the plate shape precipitates is perpendicular to the tension axis, as shown in figure (4.11), which could be a detail of the outside part. As a result

tensile stress field due to the precipitate matrix (TiNi)

precipitate

(Til 1 Ni i 4 1 Y

tensile stress

planes

Figure 4.11: Schematic illustration of the precipitation of Ti3Ni4 orientated b y the external tensile stress and providing an internal perpendicular tensile stress field [i$].

of the plate the lattice is locally distorted, yielding tensile stresses perpendicular to the external stress. These local stresses still exist after the external stress has been removed, and on cooling they make those martensite variants form, which extend in the direction of the internal stresses, i.e. a contraction in the direction of the initial imposed stress occurs, causing the sample to curl to the other side.

The Shape Memory Efect 40

4.8 Combined mechanical behaviour

The mechanical behaviour of NiTi is summarized in figure (4.12), which is a stress-strain- temperature diagram. At the extreme rear the stress-stsain curve shown in the €-CT plane

Figure 4.12: Stress-strain-temperature diagram for a NiTi Shape Memory Alloy showing Shape Mem- ory and pseudoelastic characteristics, and the deformation behaviour of the parent phase above the A.4, temperature [ll].

corresponds to the deformation of martensite below A l f . The induced strain, about 4%, recovers between A, and A f , when the specimen is heated, as seen in the E-T plane; this loop corresponds to the OWME.

At a temperature above Af pseudoelasticity occurs, shown by the second graph. At a still higher temperature above k f d , no stress-induced martensite is formed. Instead, the parent phase undergoes ordinary plastic deformation.

A number of forward stress-strain curves (increasing strain) obtained at various temperatures form a O-GT surface like the one in figure (4.13). The arrowed route may be obtained by first executing a tensile test at a temperature f - 60°C until 7% strain, and then heating the specimen up to &lOO°C, while keeping the strain at 7%. If the temperature, stress or strain is lowered, then this surface doesn’t describe the mechanical behaviour anymore.


Figure 4.13: Stress-strain-temperature surface for NiTi achieved from stress-strain curves a t various temperatures [ld].

4.9 Reversal with constant strain

Until now only free recovery has been looked at, i.e. if a specimen after being loaded below M f is unloaded, so that it consists fully of martensite and then is heated, it is not prevented from returning into its original shape; the internal stress is zero. However, if during the heating the sample is kept at the strain before heating, i.e. it cannot shrink, then large recovery stresses will occur (this can be derived from figure (4.13): the second step of the arrowed route gives the stress with increasing temperature at constant strain). When after the heating the constraint is removed, the sample in the austenitic state, returns (elastically) to its initial form. In figme (4.14) such cycles are shown at different temperatures.

The recovery stresses may be measured as a function of temperature for various initial strains. Figure (4.15) shows these graphs for NiTi, obtained during heating; the recovery stress is maximal for an initial strain of 8%. When the sample in the high temperature state, still constrained, is cooled again, a hysteresis occurs, i.e. the recovery stress-temperature


50

o .5 o .s n

STRAIN. 9:

Figure 4.147 Eflect of heating a specimen above A f at constant strain and then releasing the l o a d [ q ] .

relations for heating and cooling are different (fig. 4.16).

80

70

60

50

40

30

20

1 0

O

d

60 100 140 180 220 260 300 340 380

T E M P E R A T U R E , O F

Figure 4.15: Recovery stress vs. temperature for different initial strains [18].


Figure 4.16: Hysteresis of SMA [20].

4.10 Influence of stress on thermodynamics and transformation temperatures

The fact- that martensite transformations can be induced by temperature as--well as by stress, i.e. temperature and stress are replacable, is principally a thermodynamic matter, It can be proved that an imposed stress always operates to assist the transformation, whatever its sign or kind. Therefore the work that the stress does, AG", is always positive. Figure (4.17) gives the contribution of AG" to the transformation driving force AGP -.) M. As a result of an applied stress ~ , = û j , the AGP -+ M-T plot with 0,=0 is pushed down as a whole by the amount AG"(a1); the nucleation of the martensite can commence at a higher temperature Msui, because the necessary driving force AGnuc1 is reached at this temperature. Consequently, as a result of stress, Ms rises from Ms (O) (zero stress) to Msu, . Such rises in M, due to the application of stress have been verified in many alloys. Figure (4.18)

Figure 4.17: Thermodynamical effects of stress on martensitic transformations [15].

~~

The Shape Memory Effect 44

Austenite

Figure 4.18: Schematic phase diagram as a function of temperature and uniaxial stress [13].

shows this dependence of M, on stress schematically. For M f ? A, and A f often comparable graphs may be obtained.

~~ ~

5 Applications

I I r n a

5.1 Introduction

Despite great scientific efforts to understand, improve and practically use Shape Memory Alloys, which can roughly be divided in NiTi-, Cu- and Fe-based alloys, only two among them are presently suitable enough for wide spread applications: NiTi and CuZnAl. Ta- ble (5.1) gives some information about these two. Other alloys are ill-suited to industrial

&king point Density Specific Electrical resi stance Them1 conductivity (room temperaturet mermal d i la t ion coefficient

Specific heat Them-electric power

Transformation heat

Emodulus Yield-strength

Tensile strength (mart.) . Fracture s t ra in (mart. 1 Fatigue l i m i t Grain size

Transformation temperatures Hysteresis (A,-Af) H a x a - one-way shape memory Max. two-w$y shape memory

N = 10

N I 107 N = 105

Super heating teinperûrure (1 hl Specific Darnpins Capacity Max. pseudoelastic strain-sigplr crys - polycrysta'

'C kg/m3 10-6fh Wlm*C

10-6:c-'

J (kgoC1-' 10-6 V.Y-1

Jfkg

GPa MPa

MPa X strain MPa 10-6 m

"C "C X strain X strain

*C SOC-x

X strain X . strain

Hi-Ti

1240-1310 6400-6500 0.5-1.10

(10-118

10 (Aust.) 6.6 (Mart.)

9-13 (mart.) 5- 8 taust.) 3200

470(-620)

98 150-300 (Mart.) 200-800 (Aust. 1 800-1100 40-50 350. 1-10

-50 to t +lOO°C 30 8

6 2 0.5 400 15

10 4-

Cu-Zn- Al

950-1020 7800-8000 0.07-0.12 120 ( b i j 20°C)

16-18 (Mart.) 390

7000-9000

70- 1 O0 150-300

700-800 10-15 270 50-100

-2000 t o t +12ooc 10-20 5

1 0.8 ~~

0.5 160-200 30

10 2

Table 5.1: Comparison between NiTi and Cu-based alloys [13].

Cu-Al-Ni

1000- 1050 7100-7200 0.1-0.14

75

16-18 (Mart.) (400-)480

7000-9000

80-100 150-300

1000- 1200 8-10 350 25-60

~

-200" to t +17OoC 20-30 6

1.2 0.8 0.5 300 10

10 2

manufacturing either because of their price because they are difficult t o fabricate; their price/quality ratio is too high.

Awwlications 46

SMA’s are used for the following applications [11,13-15,17-19,21,24]: - industrial, - energy, - dental/medical.

In each of these fields specific characteristics of SMA’s are utilized: - constrained recovery; the SME is used only once, - actuator or work production; the SME is used a number of times, - pseudoelasticity or superelasticity.

5.2 Industrial applications

5.2.1 Constrained recovery applications

Industrial applications in which the SME is used only once are for instance tubing or pipe couplings (fig. 5.1). In these products a NiTi (or ~ Cu-based) alloy which has a transforma-

heating insert pipes after expanding the coupling

Figure 5.1: Shape M e m o r y A l l o y pipe coupling [15].

tion temperature far lower than room temperature (about -150°C) is formed into tubing with an inner diameter about 4% smaller than the nominal outer diameter of the pipes to be joined. When the connection is to be made, the coupling is first immersed in liquid nitrogen and maintained in a low (martensite) state; then a tapered plug is forced inside the coupling so that its innner diameter is expanded by about 7-8%. While keeping the coupling at the low temperature, the two pipes are inserted at both ends of the coupling. When the coupling’s temperature rises to room temperature, its inner diameter reverts to the size before the expansion, and the ends of the two pipes are strongly bound together.

More than one hundred thousand of these couplings have been installed in the hydraulic systems of F-14 jet fighters, atomic submarines and warships as well as in subsea piping, and are reported to be completely free of oil leaks and other such troubles. The most important advantages are their high reliability, their capability to withstand all kinds of severe environmental influences, and, since there is no need of high temperatures for conventional welding, no thermal damage to surrounding materials occurs.

Fasteners and clamps have likewise applications. Shape Memory fasteners are used e.g. if the far side of the fastened objects cannot be accessed. Figure (5.2) shows this principle. Figure (5.3) shows two plates being clamped by use of a Shape Memory Alloy clamp.

Applications 47

SMA clamp

Figure 5.2: Shape Memory Alloy fastener; (a) original Figure 5.3: Shape Memory Alloy shape; (b) straighten ends; (e) insert; (a) heating and fas- tening [15].

clamp [15],

5.2.2 Actuators

For actuators a two way operation is needed. There are two methods for achieving two-way operation properties: - induce the TWME by training processes; since this is still a rather difficult matter, it has not been used yet extensively. - combine a OWME alloy with springs, weights, or other parts so that the component as a whole has two way characteristics.

shape memory coil coil spring

5

7t

Deflection (mm)

Figure 5.4: Bias-type Two Way Shape Mem- ory component (a spring is used for the bias force) [í5].

Figure 5.5: Principles of a Two Way Shape Memory component using a bias spring [15].

In figure (5.4) a simplified actuator is shown. Most actuators are of the so-called bias- type: it consists of a shape memory coil and an ordinary coil spring. They are inexpensive and simple to construct. Figure ( 5 . 5 ) presents the involved relationships. The point where the load on the SMA coil is zero is the origin; the zero load point of the coil spring is 50 mm to the left. At room temperature, the SMA follows the lower force-deflection curve and an equilibriium sets in at 34 mm from the origin. When the SMA coil is heated above A f , it stiffens (note that this is quite different from steel, where the austenitic phase is the weak phase) so that the upper graph is valid: the equilibrium is disturbed and a displacement of 18 mm is obtained. If the actuator is used to perform external work, the stroke length

TiNi

Applications 48

is effectively shortened; if for example a force of 0.5 N works opposite to the displacements at both high and low temperatures, the stroke length would be reduced t o 10 mm. The stroke may be extended by utilizing rotational movements and moments.

Actuator devices are driven either electrically or by changes in ambient temperature. Applications in robotics belong to the first group; SMA actuators are far more compact than conventional ones, like servo-motors. An example of a microrobot is shown in figure (5.6). Another application is a safety switch i2 electrical circcits: if the curred becomes

9

elbow elbo

height: 160 mm idler

alloy wire

idler

alloy wire

Figure 5.6: Memory Alloys [15].

Microrobot actuated b y Shape Figure 5.7: The first thermal actuator used a large CuZnAl spring t o open and close greenhouse windows [ll].

-

too large, the SMA is heated and interrupts the circuit. Thermal actuators have been far more successful than electrical. The first thermal

actuator of note was a greenhouse window opener (fig. 5.7) which used a CuZnAl spring to open windows when the inside temperature became too high, and would close them when the temperature dropped. Other examples are a thermostatic radiator valve, a thermostat, an automotive clutch fan, a fuel jet orifice in a carburator which reduces in size with warming and thus less viscous fuel, which minimizes atmospheric pollution and optimizes fuel consumption.

5.3 Energy applications; heat engines

A special application which uses the ability to do work by means of recovery forces is the heat engine. The principle is as follows: below M j the martensitic specimen is deformed by means of a relatively small force. This force is replaced by a large force. On heating

Applications 49

large recovery stresses occur doing external work. The large force is again replaced by the smaller one, after which the temperature is lowered; the cycle is completed (fig. 5.8). Since only small differences in temperature are necessary, these heat engines are well suited

-- HEAT ENGINE APPLICATION CF %: below MI below MI below M.

- & & Wl

Opply lood a, specimen bends

/ opply odditionoi lood

W,li.iO w,

~~

Figure 5.8: Schemaiic of heat engine application of a SMA [21].

to extract heat from ”low-grade” energy sources like industrial coolant water, discharge water from nuclear reactors, geothermal sources and solar heated masses. However, their efficiency of 4-6% is rather low.

5.4 Dental and medical applications

An application in the dental field is the orthodontic wire, a wire which is fastened to malposed teeth. The previously used stainless steel and CoCr wires have an elastic range which is much smaller than superelastic NiTi has. By means of a special work-hardening treatment in advance, plastic deformations are not induced even at strains of 10%. The stress on unloading is nearly constant. Consequently, the need to retighten and adjust the wire is reduced, which saves both time and comfort.

An important condition for materials used inside the body is their biochemical stability, i.e. no metallic ions may dissolve in bodily fluids, and biocompatibility, i.e. the acceptance of the alien material by the body. This makes NiTi the only applicable SMA in the medical field. One of various applications is the NiTi bone plate, used for healing fractures in bone shafts. The bone plate is fastened to both bone parts and then heated a few degrees above body temperature, making the plate shrink and thus firmly securing the fracture area, without applying undue forces during the operation itself.

Applications 50

5.5

Besides commercial applications of which a survey has been given, SMA's are investigated in laboratories for all kinds of purposes. Rogers C.S. [17] study the capabilities of SMA's to

Dynamic control with SMA reinforced plates

>- -100 -20

n HEATING -1 10

>- -100 -20 60 140 220 300 I I

A MODULUS 0.2 PERCENT YIELD

MS

TEMPERATURE, OF

Figure 5.9: Yield stress and elastic modulus us. temperature [I7].

modify the configuration and modal response of-a plate. For this purpose,- pre-elongated (2%) Nitinol fibers are embedded in an epoxy plate, e.g. under various angles, so that a laminate is built. The configuration of the plate may be modified by heating certain fibers, which will contract, causing a uniformly distributed shear load along the entire length of the fibers. Because of this shear load offset from the neutral axis, the structure will bend in a known and predictable manner.

E, IE: = 1.0

Activoled Lominoe

k = 19.9

2"dMoae E3 k = 49.9

3rd Mode m k- 49.6

4Ih Mode

k = 79.5 ea

E, /E f -4.0

f450 -45" +O" +90° o I I

25 2 228 20 o 20 6 28 5

a m a r n m 60 I 55 4 49 7 50 3 68 2

C i E I U H D 53 2 704

a m E ! a E a m I O 0 91 2 799 81 5 1140

629 56 8 5 0 0

Figure 5.10: Comparison of mode shapes for [45,-45,0,90], SMA reinforced p la te [17].

The important property in active modal modification is the change in elastic modulus

Applications 51

during heating or cooling (fig. 5.9); the elastic modulus of Nitinol in the austenitic state is 3- 4 times larger than in the martensitic state. This offers the opportunity to change the total plate’s stiffness, and consequently, since the modal response of an object depends on its stiffness, to modify the modes and natural frequencies. Figure (5.10) shows schematically the first 4 modes by means of their nodal lines of a [45,-45,0,90], SMA reinforced plate; underneath every modal picture is the natural frequency. The conclusion is that the natural frequencies of all modes may be shifted some 40%; this is a very useful tool t o avoid large displacements resulting from occurring ” dangerous” external frequencies.

References

Sands, Donald E.: Introduction to crystallography. W.A. Benjamin, New York, 1969

Brick, Robert M., Gordon, Robert B. & Phillips, Arthur: Metaallegeringen structuur en eigenschappen, Het Spectrum, Utrecht/Antwerpen, 1967

Kittel, Charles: Introduction to solid state physics 5th edition. John Wiley & Sons Inc., New York, 1976

Ashcroft, Neil W. & Mermin, N. David: Solid state physics. Saunders College, Philadelphia, 1976

Metselaar, R.: Struktuur en eigenschappen van de vaste stof. dictaat 6696 van de T U Eindhoven, faculteit scheikundige technologie, 1989

Landheer, D. & Zaat, J.H.: Materiaalkunde, trimester 1.2. dictaten 4560,4561 van de TU Eindhoven, faculteit werktuigbouwkunde

Zaat, J.H.: Technische metaalkunde, deel 1 basiskennis. Agon Elsevier, Amsterdam/Brussel, 1974

Zaat, J.H.: Technische metaalkunde, dee l 2 algemene metaalkunde. Agon Elsevier, Amsterdam/Brus- sel, 1974

Wayman, C.M.: Introduction to the crystallography of martensitic transformations. The Macmillan Company, New York, 1964

Nishiyama, Zenji: Martensitic Transformation. Academic Press, New York, 1978

Muddle, B.C.: Martensitic Dansformations Part I & II Proceedings of the 6th International Conference on Martensitic Transformations held in Sydney, Aus- tralia, 3-7 July, 1989. Trans Tech Publications Ltd, Zurich, 1990

Doyama, M., Sömiya, S. & Chang, R.P.H.: Shape Memory Materials vol 9 Proceedings of the MRS International Meeting on Advanced Materials, held in Sunshine City, Japan, May 31-June 3, i988. Materials Research Society, Pittsburg, 1989

Hornbogen, E. & Jost, N.: The martensitic transformation in science and technology. DGM Informa- tionsgesellschaft m.b .H., Bochum, 1989

Perkins, JefE Shape memory effects in alloys. Plenum Press, New York, 1975

Funakubo, Hiroyasu: Shape memory alloys. Gordon and Breach science publishers, New York, 1987

Huisman-Kleinherenbrink, Patricia M.: On the martensitic transformation temperatures of NiTi and their dependence on alloying elements. Offset-drukkerij FEBO, Enschede, 1991

References 53

[17] Rogers, Craig A.: Smart materials, structures, and mathematical issues. Technomic publishing company Inc., Pennsylvania, 1989

[18] Rogers, Craig A., Crawley, Edward F. & Claus, Richard O.: Intelligent material systems €4 structures; two-day seminar.

[19] Ahmad, I., Crowson, A., Rogers, C.A. & Aizawa, M.: U.S.-Japan workshop on smart/intelligent materials and systems, held in Honululu, Hawaii, March 19-23, 1990. Technomic publishing company Inc., Pennsyivania, i990

[20] Liang, C. & Rogers, C.A.: One-dimensional thermomechanical constitutive relations for Shape Mem- ory materials. J. Intell. Mater. Syst. and Struct., vol. 1, p.207-234, July 1990

[21] Wayman, C.M.: Some applications of Shape Memory Alloys. J . of Metals, p.129-137, June 1980

[22] Delaey, L., Krishnan, R.V., Tas, H. & WarIimont, H.: Thermoelasticity, pseudoelasticity and the memory effects associated with martensitic transformations. J . of Mat. Sc., vol. 9, p.1521-1535, 1974

[23] American Society for Metals: Metals Handbook Ninth edition, vol. 4 Heat Treating.

[24] Technieuws Washington: Intelligente materialen, materiaalsystemen en -constructies. Publicatie van het Ministerie van Economische Zaken, jaargang 29, nr. 1, feb. 1991

Appendix A

Miller indices

Since planes are very important in crystals, a simple and clear way of describing planes is necessary, The orientation and position of a crystal plane may be specified by the intercepts on the axes a , b and c in terms of the lattice constants. For instance, if a plane intersects the three crystal axes in (4,0,0), (0,1,0) and (0,0,2), then this plane could be designated

by the numbers (4,1,2). In crystallography the reciprocals of these numbers are taken and these reciprocals are multiplied or divided by an integer, so that the smallest possible integers remain. The result is enclosed in parentheses (hkZ); the earlier mentioned plane is therefore indicated as (142). The indices h, k, I

Suppose another plane parallel to the first has intersection points (12,3,6). According to the above, this plane is also denoted as (142); parallel planes have the same Miller indices. That is because in crystals only angles between planes are important, not mutual distances.

An intersection at infinity yields an index zero. If a plane cuts an axis on the negative side of the origin, the corresponding index is negative and is indicated by placing a minus sign above the concerned index, e.g. (170). Planes which are equivalent because of symmetry may be denoted using braces. For example, in a cubic structure (110) means the collection of the planes (110)) ( O l l ) , ( l o l ) , ( T i O ) , (011) and (101).

Directions can be described by means of Miller indices likewise. They are just the set of smallest integers having the ratio of the components of a vector in the desired direction, referred to the axes, and are written between square brackets: [uvw]. The u-axis becomes the [loo] direction. In cubic crystals the direction [ A M ] is perpendicular to a plane (hkZ) having the same indices, but this is not generally true in other crystal systems.

I I b

Y

5 are called Miller indices.

Appendix B

Stereographic pro ject ion

Since only directions of planes are of importance, a crystal may be represented on a flat plane. One method to project crystal planes and directions on a flat plane is the stereographic projection. A tiny crystal is considered to be in the centre M of a sphere. This

M

The little cross x in the equatorial plane is the

stereographic projection of

~

A ~51-

z sphere is cut by a horizontal plane through M, the base, with a circle as result. An arbitrary crystal plane is projected in the following way: draw a straight line, perpendicular to the crystal plane (the plane normal), through M. This line intersects the sphere in a point, say A. If A is on the northern hemisphere, A is connected with the south pole S; likewise, if A is on the southern hemisphere, it is connected with the north pole N. The point of intersection of AZ (or AN) with the base is the projection of A, and therefore of the considered plane. Planes as well as directions are represented as points in the stereographic project ion.

shape memory alloys featuring nitinol - pure · shape memory alloys featuring nitinol ... treat the...

Documents