Document [original]

Thermomechanical and Microstructural

Characterization of Co49Ni21Ga30 and

Co38Ni33Al29 High-temperature Shape Memory

Alloy Single Crystals

zur Erlangung des akademischen Grades eines

DOKTORS DER INGENIEURWISSENSCHAFTEN (Dr.-Ing.)

der Fakult¨at f¨ur Maschinenbau

der Universit¨at Paderborn

genehmigte

DISSERTATION

von

Jayaram Dadda

aus Indien

Tag des Kolloquiums: 09.04.2009

Referent: Prof. Dr.-Ing. H.J. Maier

Korreferent: Prof. Dr. D. Canadinc

Dedicated to my parents.

Abstract

In this study, functional behavior of newly developed Co-base Co49Ni21Ga30

and Co38Ni33Al29 high-temperature shape memory alloys (HTSMAs) is reported.

A thorough experimental programme addressing the mechanical and functional

properties of Co49Ni21Ga30 and Co38Ni33Al29 (in at.%) single crystalline alloys

was executed in order to understand the effects due to crystallographic orienta-

tion and thermomechanical treatments.

The Co38Ni33Al29 single crystals investigated in this work demonstrate a large

pseudoelastic (PE) window of more than 250 ◦C, good cyclic stability and train-

ability with a maximum two-way shape memory effect (TWSME) strain of 2.7%.

The results emphasize the need for texturing polycrystalline aggregates of the

current material near the <001>and <110>poles with an optimum γ-phase

volume fraction to achieve high functional performance in Co38Ni33Al29 alloys.

In as-grown Co49Ni21Ga30 specimens, the low critical transformation stress

due to the high resolved shear stress factor (RSSF) value, i.e. low Clausius-

Clapeyron (CC) slope, high slip resistance in the austenite due to zero Schmid

factor and B2 atomic ordering allow for excellent transformation recoverability

with a large PE temperature range of about 325 ◦C when loaded in the [001]

direction. The thermomechanical training resulted in a stable microstructure im-

proving the transformation recoverability, which in turn resulted in a large PE

window of 400 ◦C in the temperature range of 40-425 ◦C, and also in a stable cyclic

behavior. In addition, the employed high-temperature aging treatments at 900

◦C for 24 hours on Co49Ni21Ga30 alloys brought about a stable cyclic stress-strain

response at elevated temperatures as high as 300 ◦C. The martensite stabiliza-

tion due to pinning of moving interfaces, detwinning and diffusion of point defects

in Co49Ni21Ga30 alloys especially at elevated temperatures (>120 ◦C) is macro-

scopically reflected by the shift of the unloading curve to lower stress levels and

consequently resulted in a large stress hysteresis of about 350 MPa. Along with

the in-situ microscopy, the spatial visualization of strain localization obtained

by using digital image correlation (DIC) revealed heterogeneous transformation

characteristics at temperatures below 120 ◦C, beyond which the nucleation and

growth characteristics of SIM transformation are quasi-homogeneous resulting in

a multi-variant configuration, which was later inherited by the trained crystal.

An insight into the evolution of the microstructure and stress-strain behavior in

terms of stress hysteresis with test temperatures is provided, and the possible

operant mechanisms are presented.

Contents

Nomenclature viii

Introduction and Scope of Research 1

1 Theoretical Background 3

1.1 Shape Memory Alloys . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Reversible Martensitic Transformation . . . . . . . . . . . . . . . 4

1.3 Thermodynamic Aspects of the Martensitic Transformations . . . 5

1.4 Shape Memory Effect (SME) . . . . . . . . . . . . . . . . . . . . . 8

1.5 Pseudoelasticity (PE) . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.6 Two-way Shape Memory Effect (TWSME) . . . . . . . . . . . . . 12

1.7 Cyclic stress-strain response (CSSR) of Shape Memory Alloys . . 12

1.8 Co-baseAlloys ............................ 13

2 Material and Experimental Procedures 19

2.1 Material and Sample Preparation . . . . . . . . . . . . . . . . . . 19

2.2 Thermo-mechanical Experiments . . . . . . . . . . . . . . . . . . 20

2.3 Microscopy and Digital Image Correlation . . . . . . . . . . . . . 21

2.4 Electron Microscopy, DSC and SQUID . . . . . . . . . . . . . . . 23

3 Characterization of Shape Memory Behavior in Co38Ni33Al29 and

Co49Ni21Ga30 Alloys 25

3.1 Introduction.............................. 25

3.2 Analysis of Results and Discussion . . . . . . . . . . . . . . . . . 26

3.2.1 Stress-assisted Shape Memory Effect . . . . . . . . . . . . 26

3.2.2 Pseudoelasticity........................ 38

3.3 ChapterSummary .......................... 48

4 Co49Ni21Ga30-alloys as a High-temperature Pseudoelastic Mate-

rial 51

4.1 Introduction.............................. 51

4.2 Microstructure-pseudoelastic property relationships . . . . . . . . 52

4.2.1 Mechanical property variation with temperature . . . . . . 52

4.2.2 Evolution of microstructure with temperature during SIM

transformations........................ 54

4.2.2.1 Region I - Constant low stress hysteresis . . . . . 54

4.2.2.2 Region II - Increasing stress hysteresis . . . . . . 58

4.3 Effect of Training on the Pseudoelasticity . . . . . . . . . . . . . . 60

4.4 ChapterSummary .......................... 72

5 Cyclic Stability of Co49Ni21Ga30 Single Crystals 74

5.1 Introduction.............................. 74

5.2 Cyclic Stress-Strain Response at Ambient Temperatures . . . . . 75

5.3 Cyclic deformation behavior at elevated temperatures . . . . . . . 80

5.4 ChapterSummary .......................... 89

6 Summary & Future Research 91

References 105

Vita 106

Nomenclature

Greek Symbols

σF or

crit Critical stress for forward transformation

CV P CVP formation strain

det Detwinning strain

Engineering strain

ps Permanent strain

res Residual strain

σEngineering stress

σRev

crit Critical stress for reverse transformation

∆Strain Range

∆σStress Hysteresis

TTransformation strain

Superscripts

For superscript Forward Transformation

Rev superscript Reverse Transformation

Subscripts

crit subscript Critical Value

fsubscript Finish

ssubscript Start

Acronyms

AAustenite

AC Air-cooled

AfAustenite Finish

AsAustenite Start

CC Clausius-Clapeyron

CSSR Cyclic Stress-Strain Response

CV P Corresponding Variant Pair

DIC Digital Image Correlation

DSC Differential Scanning Calorimetry

EBSD Electron Back-scattered Diffraction

HTPM High-temperature Pseudoelastic Material

HTSMA High-temperature Shape Memory Alloy

IST Incremental Strain Test

MMartensite

MfMartensite Finish

MFIS Magnetic Field-Induced Strain

MR Martensite Reorientation

MsMartensite Start

vii

MSMA Magnetic Shape Memory Alloy

MSME Magnetic Shape Memory Effect

MT Martensitic Transformation

OM Optical Microscopy

OQ Oil-quenched

OWSME One-Way Shape Memory Effect or Shape Memory Effect

PE Pseudoelasticity

SADP Selected Area Diffraction Pattern

SC −SRO Symmetry Conforming-Short Range Ordering

SCV Single Correspondence Variant

SEM Scanning Electron Microscope

SIM Stress-induced Martensite

SMA Shape Memory Alloy

SME Shape Memory Effect

TEM Transmission Electron Microscope

TWSME Two-Way Shape Memory Effect

WQ Water-quenched

viii

Introduction and Scope of Research

In recent years, search for new shape memory alloys (SMAs) that can undergo

phase transformations at high temperatures has been the focus of many re-

searchers around the world owing to poor thermal stability, workability and

pseudoelasticity (PE) of existing SMA systems. This is necessary for robotic,

automotive, aerospace, turbine engine and air-conditioning industries where the

operating temperatures are often well above 100 ◦C. In this study, the results

related to different investigations carried out on new class of Co-Ni-Al and Co-

Ni-Ga high-temperature shape memory alloy (HTSMA) material are presented.

In particular, using proper experimental procedures, the thermomechanical be-

havior of the material was investigated under static and cyclic loading conditions

to better understand the deformation mechanisms involved in the shape memory

effect (SME) and PE.

Thermomechanical characterization of Co49Ni21Ga30 and Co38Ni33Al29 alloys

was undertaken on their single crystals with the loading axis along the [001], [123],

[235] and [110] crystallographic orientations. The use of single crystals allows a

systematic bias of operant deformation mechanisms such as martensite variant

reorientation, detwinning and dislocation slip, which facilitates the fundamen-

tal understanding of the phase transformation and the stress-strain response in

Co49Ni21Ga30 and Co38Ni33Al29 alloys. Several appropriate heat-treatments were

also performed to optimize the shape memory characteristics of these alloys. In

addition, to gain an understanding of the other orientation dependence of the

transformation stress and transformation strain levels, theoretical values for the

resolved shear stress factors (RSSFs) and transformation strains were calculated

using the energy minimization theory. This information is needed to fabricate a

textured polycrystalline material already optimized for desired functional prop-

erties that are necessary for the envisaged applications.

In addition, high-temperature in-situ optical microscopy (OM) was carried

out at various stages during the PE experiments to follow the evolution of the

stress-induced phase transformation and to track the propagation of phase bound-

aries. Along with these investigations, a full-field digital image correlation (DIC)

was also employed to obtain the local strain fields during loading and unload-

ing. This information is essential for the constitutive modeling of inhomogeneous

and homogeneous deformation regimes in SMAs. The present Co49Ni21Ga30 and

Co38Ni33Al29 alloys displayed pronounced cyclic stability at elevated tempera-

tures under compressive loading conditions indicating their potential as promis-

ing HTSMAs for PE applications that involve high stress levels. Part of the data

presented herein has already been published elsewhere Canadinc et al. (2007);

Dadda et al. (2006a,b,2008,2009); Meyer et al. (2006); Niklasch et al. (2008)

due to the rapid evolution in the field.

Chapter 1

Theoretical Background

1.1 Shape Memory Alloys

Smart Materials are able to note an external stimulus responding in a predeter-

mined and repeatable manner; this capacity permits the material to change its

geometrical and thermomechanical conditions. In this field, SMAs are a class of

materials able to remember a predetermined configuration and to recover it as

consequence of thermal or mechanical loads. NiTi, Cu-base and Au-Cd alloys are

the most commonly used and widely studied SMAs due to their abundance and

inexpensive constituent elements especially in Cu-Zn-Al, Cu-Al-Ni alloys Duerig

et al. (1990); Otsuka & Wayman (1999). The special functional properties exhib-

ited by these alloys, namely one way or two way shape memory effect (OWSME,

TWSME) and pseudoelasticity are the phenomena being exploited in a number of

industrial fields such as biomedical, automotive, aerospace and turbine engines.

The use of SMAs seems to be very useful in applications where it is necessary

to use smart components with small dimensions. Many conventional actuators

and sensors could be substituted with SMAs, obtaining high advantages in terms

of reduction of weight and dimensions, reliability and costs. Furthermore, in the

last years, their use for the realization of smart composites, as an example for

vibration and shape control, is becoming very interesting.

Unfortunately, there are still some difficulties with SMAs that must be over-

come before they can live up to their full potential. For example, these alloys

are still relatively expensive to manufacture compared to other materials such

as steel and aluminium. These difficulties regard the high sensibility to the pro-

duction parameters. Furthermore, the non-linear characteristics of their behavior

increases the difficulties related to the control of their functional properties. For

this reason, in the last decades, many research activities have been addressed

to the investigation of the influence of different working processes on the SMA

behavior and to develop simple numerical models able to simulate it.

1.2 Reversible Martensitic Transformation

Martensitic transformations (MTs) are diffusionless, solid-to-solid phase transi-

tions, and have been observed in metals, alloys, ceramics and polymers Otsuka

& Wayman (1999). MTs can be irreversible, as seen in steels upon quenching,

or they can be reversible (often termed ’thermoelastic’), such as those observed

in SMAs. In the latter case, the microstructures formed on cooling can easily

be manipulated by external loads and disappear upon reheating causing large

reversible shape changes in SMAs. As the MT is associated with a shape change,

a large strain develops around the martensite when it is formed in the parent

phase (high temperature phase) Otsuka & Wayman (1999). This will increase

the strain energy at the interface between austenite and martensite and conse-

quently raises the total energy of the system. In order to minimize this energy the

MT involves a pure shear that occurs either by internal slip or internal twinning

as shown in Figure 1.1 Duerig et al. (1990); Otsuka & Wayman (1999). These

two mechanisms are known as the lattice invariant shear, since neither process

changes the structure of the martensite. The selection of either slip or twinning

depends on the kind of alloy, but twinning is usually preferred to slip in SMAs.

Schematic in Fig. 1.1c shows the twinned morphology where a twin boundary

separates two martensite domains V1and V2. It should be noted that V1and

V2have the same structure, but the orientations are different as they are mirror

reflections of each other across the twin boundary. Thus, these are also known as

a corresponding variant pair (CVP) of the martensite. When a CVP is exposed

to external stimuli such as magnetic or electric fields (in certain ferroelectric ma-

terials) or stress fields, the martensitic domains, V1in the present case, which are

more favorable to external forces will grow in expense of others via twin boundary

Figure 1.1: Schematics demonstrating the formation of martensite through a

shear process from a single crystalline austenite

motion as illustrated in Fig. 1.1c, i.e. detwinning occurs giving rise to a large

transformation strain. Based on these mechanisms, SMAs exhibit several phe-

nomena accompanied with reversible MT coupled with external stresses, namely

SME, PE and TWSME. It is worth to mention the thermodynamics of MT in

SMAs before elucidating these phenomena in brief.

1.3 Thermodynamic Aspects of the Martensitic

Transformations

In SMAs, martensitic transformations are characterized by the non-equilibrium

transformation temperatures, namely Ms, martensite start, Mf, martensite finish,

As, austenite start, and Af, austenite finish temperature. Afis the temperature

above which the martensite becomes completely unstable. These transformation

temperatures can be determined by measuring some physical properties such

Figure 1.2: Magnetization-temperature response of Co38Ni33Al29 alloy under a

constant magnetic field of 200 Oe. The arrows indicate the cooling and heating

paths of the curves.

as electrical resistance, magnetization, heat change as a function of tempera-

ture, since these properties drastically change upon reaching these temperatures.

This is illustrated with help of a magnetization curve shown in Figure 1.2 for a

Co38Ni33Al29 system. Since the austenite and martensite phases have different

magnetic properties, magnetization of the material changes upon thermal cycling

clearly indicating the both forward and reverse transformations reflecting as slope

changes as seen in the figure. The inflection points are considered as transfor-

mation temperatures as marked in Fig. 1.2. The minima on the curve obtained

by plotting the change in magnetization with respect to temperature (dM/dT)

is considered as the Curie temperature (Tc) above which the material becomes

paramagnetic.

As the martensitic transformations are not associated with a compositional

change, the free energy curves of both parent and martensite phases as a function

of temperature may be represented schematically as shown in Figure 1.3. Fig. 1.3

shows that the forward transformation (A →M) occurs at the Mstemperature

Figure 1.3: Schematic representation of free energy curves for both austenite (GA)

and martensite (GM) phases, and their relation to the Msand Astemperatures.

∆T1and ∆T2are the under-cooling and over-heating required for forward and

reverse transformations, respectively.

(where ∆GA→M

ch |Ms=GM−GA<0) instead of thermodynamic equilibrium

temperature T0at which the free energies of the two phases are equal. This

brings about an under-cooling ∆T1that is necessary for the onset of MT. The

same arguments apply for the reverse transformation (M →A) as well at the As

temperature resulting in an overheating ∆T2(Fig. 1.3). An additional chemical

driving force ∆Gch to overcome energy barrier that is due to the generation of

elastic energy (∆Gel) and a surface energy (∆Gs), and to the frictional work spent

during the growth of martensite and dislocation formation (∆Gfr) is responsible

for this shift Otsuka & Wayman (1999); Panchenko et al. (2008); Patoor et al.

(2006); R¨osner et al. (2001). Thus, the energy balance for the onset of MT can

be written as Panchenko et al. (2008); R¨osner et al. (2001):

−∆GA→M

ch + ∆GA→M

rev + ∆GA→M

fr =−∆GA→M

ch + ∆GA→M

nc = 0 (1.1)

Here ∆Grev = ∆Gel + ∆Gsis the reversible component of the non-chemical

free energy (∆GA→M

nc ), which increases with the volume fraction of martensite.

∆GA→M

fr is the irreversible component of ∆GA→M

nc , which characterizes the energy

dissipation during forward transformation. It is clear from Eq. 1.1 that ∆Gnc is

as large as ∆Gch, which is valid for the most of MTs and is also rationale behind

the aforementioned under-cooling ∆T1. This can be shown as follows: At T0,

the chemical Gibbs free energy change , ∆Gch = ∆H−T∆S, equals zero, i.e.

T0= ∆H/∆S(Fig. 1.3). ∆Hand ∆Sare the change in chemical enthalpy and

entropy, respectively. Re-arranging Eq. 1.1 leads to the following expression for

the Mstemperature:

Ms=T0−∆GA→M

rev + ∆GA→M

∆S(1.2)

From Eq. 1.2, the under-cooling ∆T1(Ms-T0) can be described by the second

term, which is proportional to non-chemical Gibbs free energy term. Similarly,

further undercooling Mf−Msis needed to complete MT as the elastic energy

around martensite resists the growth of the martensite unless a further driving

force (i.e. cooling) is provided externally. By the same token, Asis not the

same as Afgiving way to the necessary overheating for the completion of reverse

transformation in many alloys.

1.4 Shape Memory Effect (SME)

Since the MT lowers the symmetry of a crystal without involving atomic exchange

or diffusion, a single crystal of the parent phase is split into many twin-related

domains called CVPs as said earlier. Figure 1.4 illustrates that, when the above-

mentioned alloy is deformed below the Mstemperature, i.e. when the twinned

martensite is prevailing, the strain can be accommodated by the easy reversal of

some of the domains into new ones i.e. detwinned or reoriented variants. Since

the stress-induced domains have the same martensitic structure as before and the

Figure 1.4: A schematic demonstrates the occurrence of the shape-memory effect

with the help of a stress-strain-temperature diagram.

martensite is the stable phase below Ms, which is the working temperature, the

original domains cannot be restored even after the stress is released as shown in

the figure. This leads to an irrecoverable strain for the reoriented martensite.

This strain can be restored, when the alloy is heated sufficiently to reach Af

such that austenite is induced and then a subsequent cooling is needed to obtain

the original state of the alloy (Fig. 1.4). These processes in the aforementioned

sequence result in a phenomenon commonly known as the shape-memory effect

(SME), as the alloy remembers its original shape/dimensions upon heating and

subsequent cooling from its deformed condition.

1.5 Pseudoelasticity (PE)

Pseudoelasticity is a phenomenon that generally occurs when an SMA is de-

formed at temperature sufficiently above Afand is associated with the stress-

induced martensite (SIM). The schematic in Figure 1.5 represents the typical

stress-strain behavior of an SMA at temperatures above Af. As austenite is

the stable phase above Af, initial loading results in linear elastic deformation of

Figure 1.5: A schematic illustrating a typical pseudoelastic stress-strain curve.

austenite. The initial departure from linearity indicates the onset of SIM and the

corresponding stress level is known as the critical stress levels for SIM or forward

transformation (σF or

crit ) as marked in the figure. As the loading continues, the level

of strain continues to increase pointing out the transformation of untransformed

austenitic regions in the sample. Further loading leads to an apparent hardening

behavior, which indicates the elastic deformation of martensite as well as de-

twinning of twinned martensite. Note that this second linear loading curve does

not reveal the completeness of the stress-induced austenite to martensite trans-

formation. Finally, as the martensite is unstable at this test temperature, SIM

will transform back to austenite on unloading, thereby completely recovering the

large strain accompanying a stress hysteresis, ∆σ, as marked in the figure. Thus,

this phenomenon is referred to as pseudoelasticity. In addition, the unloading

curve also shows the same trend as the loading curve, where the first deviation

from linearity corresponds to the onset of reverse transformation, and is called

the critical stress for the reverse transformation, σRev

crit , as indicated in Fig. 1.5.

Moreover, the effect of temperature, T, on PE can be understood based on

the Clausius-Clapeyron (CC) relationship as follows:

dσF or

crit

dT =−∆S

0

=−∆H

0T0

(1.3)

where 0is the transformation strain, ∆Sis the entropy of transformation per

unit volume, and ∆Hthe enthalpy of transformation per unit volume. It is clear

from Eq. 1.3) that σF or

crit follows a linear relationship with test temperature, T,

for a constant ratio between ∆Sand 0at all temperatures. In other words, the

left-hand term in Eq. 1.3,i.e. the CC-slope, is constant for a given SMA system

producing a linear relationship between critical stress and temperature.

In Figure 1.6, the straight line with positive slope represents the critical stress

to induce SIM with temperature. This is in accord with the CC relationship

in Eq. 1.3, since ∆His exothermic for SIM in the equation. The reason for

Figure 1.6: Stress-Temperature diagram that shows the region of the shape-

memory effect and pseudoelasticity in temperature-stress coordinates.

the increase in critical stress levels with increasing test temperature is that the

austenite becomes more stable at higher temperatures, and thus a higher stress

level is needed to induce SIM. Fig. 1.6 also demonstrates that both PE and SME

are observable in the same sample, depending upon the test temperature, as

long as the critical stress for slip is high enough. A straight line with negative

slope represents the critical stress for slip. Since slip is irreversible upon heating

or unloading, the stress must be below this line to realize either SME or PE.

It should be noted that, in the temperature regime between Msand As, both

phenomenon may take place partially. The temperature above which no more

SIM can be observed is defined as Mdon the abscissa as shown in the figure.

In addition, the temperature difference Md−Msis also considered as the PE

temperature window/range in which an SMA can exhibit pseudoelasticity. This

is a very important parameter for an SMA system, as it determines the working

temperatures at which the alloy can be exploited for PE applications.

1.6 Two-way Shape Memory Effect (TWSME)

The TWSME is generally resulted in SMAs by repeating the forward and re-

verse transformations. This can be achieved either by isobaric thermal cycles

or through isothermal stress-strain cycles. This will induce and increase the

dislocation density in the matrix as MTs are commonly accompanied by defect

formation. This causes the nucleation and growth of most favorable martensitic

variants due to the stress fields generated around the dislocations. This makes

the alloy to remember the shape of the sample in the martensitic state every time

when the sample is cooled to below Ms. The subsequent heating will revert the

specimen to its original austenitic state/shape. In this way, if heating and cooling

is repeated even in the absence of external forces, the specimen changes its shapes

between martensite and austenite. This is called two-way shape memory effect.

1.7 Cyclic stress-strain response (CSSR) of Shape

Memory Alloys

SMAs can yield large forces in actuators Duerig et al. (1990); Otsuka & Wayman

(1999), and possess high damping capacity both in the austenitic state, where the

SIM transformation takes place, and in the martensitic state because of the SIM

variant reorientation Liu et al. (1999). In many applications, a thermomechanical

loading path utilizing the PE effect is repeated often involving a large number

of loading and unloading cycles above the Aftemperature. Irrecoverable strains

accumulated during cyclic loading may result in loss of the pseudoelastic material

response, thus, good cyclic stability is an essential criterion for SMAs. Therefore,

it is important to comprehend the evolution of the cyclic stress-strain character-

istics and the associated operant mechanisms that cause the degradation of the

functional properties in SMAs.

For the widely studied NiTi and Cu-Zn-base SMA systems, it has been re-

ported that cyclic deformation initially results in an increase in the residual strain,

a decrease in the critical stress for inducing SIM and a decrease in the stress

hysteresis Gall & Maier (2002); Kato et al. (1999); Miyazaki et al. (1986); Se-

hitoglu et al. (2001a). However, with increasing number of cycles, the effects

become less pronounced and finally steady state PE characteristics may be at-

tained Eggeler et al. (2004); Gall & Maier (2002); Gall et al. (1999); Kato et al.

(1999); Liu et al. (1999); Miyazaki et al. (1986); Nemat-Nasser & Guo (2006); Se-

hitoglu et al. (2001a); Strnadel et al. (1995); Yawny et al. (2005). The changes in

stress-strain characteristics are attributed to the introduction and accumulation

of dislocations during the repeated SIM transformations Miyazaki et al. (1986).

Therefore, it is necessary to raise the critical stress for slip in order to stabilize

the PE characteristics during cyclic loading. Strengthening against dislocation

slip can be achieved through precipitation hardening or by reducing the grain

size in polycrystalline material. Thus, several studies have focused on precipi-

tated NiTi single crystals Gall & Maier (2002); Gall et al. (1999); Sehitoglu et al.

(2001a), and ultra-fine grained NiTi wires and bulk material Yawny et al. (2005)

in an attempt to capture the inherent orientation dependent cyclic pseudoelastic

properties and to provide the parameters needed for constitutive modeling.

1.8 Co-base Alloys

The magnetic shape memory alloys (MSMAs) are a new class of smart materials

that exhibit magnetic shape memory effect (MSME), which involves the mag-

netic field-controlled reversible shape changes resulting in faster response time

than the temperature driven reversible shape changes in conventional SMAs.

Heusler Ni2MnGa alloys are widely studied MSMAs since the pioneering work

of Ullakko et al. (1996). This alloy in its single crystalline state is well-known

for its superior MSMA properties such as large magnetic field-induced strains

(MFIS) of about 9.5 % via a rearrangement of martensite twin variants induced

by an external magnetic field Sozinov et al. (2002). However, the poor ductility of

Ni2MnGa in the polycrystalline state Oikawa et al. (2001) and low blocking stress

levels Karaman et al. (2006) limits its applications. Therefore, in the pursuit of

fabricating an alternative to Ni2MnGa alloys, the new Co-base alloys have been

developed because of their natural ferromagnetism and ability to undergo ther-

moelastic maratensitic transformations Craciunescu et al. (2002); Oikawa et al.

(2001); Sato et al. (2003). Some other attributes that make CoNiAl and CoNiGa

alloys interesting MSMA candidate materials are: better ductility compared to

NiMnGa due to secondary γ-phase in the matrix Sato et al. (2003), wide range

of transformation temperatures Craciunescu et al. (2002); Oikawa et al. (2001,

2006), and higher Curie temperature, Tc>150 ◦C, thus giving way to higher

magnetization at operating temperatures below Tc. In addition, there are sev-

eral studies that investigated thermo-mechanical characteristics of Co-Ni-Al and

Co-Ni-Ga systems in relation to the expected MSME in these alloys Canadinc

et al. (2007); Dadda et al. (2006a); Efstathiou et al. (2004); Hamilton et al. (2004,

2005); Li et al. (2004); Zhang et al. (2005). However, reports on the any observed

MSME phenomenon of these Co-base alloys are very scarce in the literature, ow-

ing to their high twinning stresses that require relatively large magnetic fields

to exhibit any MFIS Chernenko et al. (2004); Niklasch et al. (2008); O’Handley

(1998). Nevertheless, recent studies Canadinc et al. (2007); Dadda et al. (2006a,b)

have shown that these alloys are promising HTSMAs, therefore, the current study

mainly focused on their high-temperature characterization.

Several other HTSMA systems reported to date are CuZnAl, CuAlNi, ZrCu-

base, NiTiHf, NiTiZr, NiTiPd, NiTiPt, NiMnGa and NiAl Firstov et al. (2004b);

Otsuka & Wayman (1999); Segui et al. (2005). However, these SMAs suffer from

several problems, for instance, Cu-based alloys are considered unstable, as they

tend to decompose into other non-transformable phases Duerig et al. (1990);

Otsuka & Ren (1999). The NiTiHf, NiTiZr and NiMnGa alloys, on the other

hand, are too brittle for practical use Otsuka & Ren (1999). As for the NiTiPd

and NiTiPt alloys, the high cost of Pd and Pt elements and poor pseudoelasticity

of ZrCu-base alloys hinders their widespread use Firstov et al. (2004a). The NiAl

alloys received considerable attention for HTSMA as well as high temperature

structural applications, since they are relatively inexpensive, their martensite

start (Ms) temperature may be raised up to 900 ◦C depending upon composition

Otsuka & Ren (1999), and they possess a high melting temperature, relatively

low density and good resistance to oxidation Tian et al. (1998). Nevertheless,

they still suffer from a lack of low temperature ductility, lack of high temperature

creep strength, and are unstable at high temperatures Otsuka & Ren (1999);

Tian et al. (1998). Researchers have succeeded in improving workability of NiAl

alloys by the addition of Fe, Mn and Co as ternary elements Otsuka & Wayman

(1999). Thus, the CoNiAl system acquired hot workability and room-temperature

ductility by incorporating a small amount of disordered γ(Ni,Co,Al: A1) within

the β((Ni,Co)Al: B2)-matrix Oikawa et al. (2001); Tian et al. (1998).

Figure 1.7 shows the phase constitution of Co-Ni-Al system taken from Kainuma

et al. (1996) and equilibria among the β,γand γ0((Ni,Co)3Al: L12) phases. The

phase relations concerned with these phases play a key role on the practical de-

sign of high temperature Co-Ni-Al material. In particular, the γ0phase shows

the anomalous positive temperature dependence of strength, while the βphase is

used for the surface coating because of its excellent oxidation resistance Kainuma

et al. (1996). Moreover, the βphase appears in a wide range of compositions

(the shaded region) as shown in Fig. 1.7 and undergoes a thermoelastic marten-

sitic transformation to L10in structure and exhibits the shape memory effect

Kainuma et al. (1996) and pseudoelasticity at elevated temperatures as high as

200 ◦CKaraca et al. (2003). Another important feature of these alloys is the

absence of highly volatile alloying elements, such as Mn in the case of high-

temperature NiMnGa alloys, so that one can control the chemical composition

more accurately. This is necessary for adjusting the transformation temperatures

as they are very sensitive to the content of Nickel Oikawa et al. (2001). Further-

more, in continuing efforts made to provide some ductility to various intermetal-

lic compounds, there has been an attempt by Kimura et al. (1994) to make B2

CoAl, an intrinsically brittle high temperature material, ductile by controlling

Figure 1.7: Phase equilibria in Co-Ni-Al system Kainuma et al. (1996)

the two-phase β/γand β/γ0microstructures in the CoNiAl system. Similarly, a

new Co-Ni-Ga β-base alloy system was developed and expected to have similar

characteristics as the Co-Ni-Al β-base alloy, because: a) Ga and Al belong to

column IIIb in the periodic table; and b) the βphase appears in a wide range of

compositions in the Ni-Ga and Co-Ga binary systems and is in equilibrium with

the γphase in Co-rich and Ni-rich regions as shown in Figure 1.8. Fig. 1.8 shows

the conjectural ternary phase diagram pieced by the Co-Ni, Co-Ga and Ni-Ga

binary phase diagrams reported elsewhere Liu et al. (2006). Most importantly,

the β+γtwo phase CoNiGa alloys, which exists over a large composition range

Figure 1.8: The designed two composition series in the CoNiGa schematic ternary

diagram and crystal structure for each phase. The B2 ordered parent phase

undergoes to the L10martensite based on the Bain distortion model Liu et al.

(2006)

(Fig. 1.8), are characterized by good ductility and wide range of transformation

temperatures Oikawa et al. (2001,2006). Moreover, the recent reports on CoNiGa

alloys suggested that these alloys are promising HTSMA systems with Msand

Aftemperatures reaching as high as 200 and 350 ◦C, respectively, by adjusting

the composition Liu et al. (2006); Ma et al. (2007); Schlagel et al. (2004).

From Figs. 1.7 and 1.8 and previous reports Brown et al. (2005); Oikawa

et al. (2001), it can be understood that other than the austenitic and marten-

sitic crystallograhpic structures, the solid-state transformations and the magnetic

properties of Co-Ni-Ga alloys are similar to those in CoNiAl alloys. However, the

resultant microstructures upon solidification of Co-Ni-Ga and Co-Ni-Al alloys are

quite different according to the recent studies by Liu et al. (2005,2006) and they

attributed this behavior to different equilibrium reactions; Co-Ni-Ga system un-

dergoes peritectic reaction (L + γ→β), while Co-Ni-Al eutectic reaction (L →

β+γ). In addition, there are several studies describing the fundamental shape

memory and pseudoelastic properties as a function of temperature and stress

such as the transformation strains, Clausius-Clapeyron relation, stress and ther-

mal hysteresis, and the influence of deformation history on the transformation

behavior and cyclic stability at ambient temperatures Canadinc et al. (2007);

Chernenko et al. (2004,2007); Dadda et al. (2006a,b,2008,2009); Efstathiou

et al. (2004); Hamilton et al. (2005,2006); Karaca et al. (2003,2004); Meyer

et al. (2006).

Chapter 2

Material and Experimental

Procedures

2.1 Material and Sample Preparation

Ingots of CoNiGa and CoNiAl with a nominal composition of 49Co-21Ni-30Ga

and 38Co-33Ni-29Al (in at. %) were prepared using vacuum induction melting in

an inert gas environment1. The composition of these alloy system was chosen in

order to obtain a two phase β+γmicrostructure with β-matrix as the stable phase

at high temperatures as shown in the phase diagrams in Figs. 1.7 and 1.8 on

page 16 and17 in Chapter 1. The single crystals were grown using the Bridgman

technique in a He environment. For compression experiments, specimens with

dimensions of 4 ×4×8 mm3were electro-discharge machined from the bulk single

crystals such that their longer, i.e. compression axes, were along the [001],[123],

[110] and [235] crystallographic orientations.

For the heat-treatments, the samples were kept in evacuated and argon filled

quartz tubes in order to avoid oxidation and evaporation of any constituent ele-

ments. Solutionization of Co38Ni33Al29 and Co49Ni21Ga30 alloys was carried out

at 1350 ◦C for 24 hours and 1200 ◦C for 4 hours followed by quenching in cold

water, respectively. The aging of the Co49Ni21Ga30 alloys was conducted at 900

◦C for 24 hours and 1100 ◦C for 4 hours and then water quenched. Samples for

1This was carried out under the supervision of Prof. Y. Chumlyakov.

optical microscopy (OM) were prepared using standard silicon carbide grinding

down to 4000 grit, followed by mechanical polishing with 1 µm diamond paste

using Struers Red lubricant, and 0.02 µm OPS (Oxide (silica) polishing suspen-

sion) solution. Sometimes samples were etched to better bring out the γ-phase

distribution in the β-matrix of both CoNiAl and CoNiGa alloys utilizing the

etchant HCl (75 ml), ethanol (75 ml), 15 gr CuSO4and 15 ml water solution.

Samples for Electron Backscattered Diffraction (EBSD) were first mechanically

polished to 0.02 µm OPS as describe above, and subsequently twin-jet electro-

polished with a 5 % perchloric acid and 95 % ethanol solution cooled to -25 ◦C;

electro-polishing was carried out at 30 V for about 120 seconds. The removal of

few microns (20-30 µm) of the surface layer by electro-polishing is necessary to

remove any preparation-induced artifacts. For Transmission Electron Microscopy

(TEM), 1 mm thick disks were sliced normal to the loading axis of the compres-

sion samples. Final thinning of mechanically polished 3 mm diameter disks was

carried out by twin-jet electro-polishing with a 5 % perchloric acid and 95 %

ethanol solution.

2.2 Thermo-mechanical Experiments

Two main types of thermo-mechanical tests were conducted to study the trans-

formation behavior of Co38Ni33Al29 and Co49Ni21Ga30 alloys: i) isostress temper-

ature variation experiments, and ii) isothermal monotonic or cyclic stress-strain

tests. In the first case, depending on the test temperature range, heating/cooling

was either achieved by direct flow of hot/cold nitrogen gas onto the samples

or by induction heating for test temperatures above 200 ◦C (Figure 2.1). The

heating/cooling rate was limited to 10 K/min, and thus, temperature variation

along the sample could be restricted to a maximum of ±2◦C. The isother-

mal stress-strain experiments that involved many cycles were conducted using an

MTS servo-hydraulic load frame in displacement control with a fixed maximum

strain upon loading and a fixed minimum stress for unloading at a strain rate of

1×10−3s−1, while those involved only one loading-unloading cycle (a monotonic

test) were performed at a quasi-static rate of 6×10−5s−1. Strains were mea-

Figure 2.1: Experimental setup adopted for thermomechanical characterization

under compressive loading conditions. This setup also allows one to perform

in-situ microscopy at elevated temperatures when it is used without the mini-

chamber shown in the schematic.

sured with a high-temperature MTS extensometer having a 12 mm gauge length

attached to the compression grips.

2.3 Microscopy and Digital Image Correlation

In-situ microscopic observations were made to investigate the evolution of trans-

formation at various stages during pseudoelasticity. Images were captured with

a Keyence digital microscope model VH-500 with a resolution of 500 nm. A tele-

zoom lens was used at 50 times magnification covering 5×4 mm2surface area. A

full-field optical technique called digital image correlation (DIC) was carried out

on the images of size 5×4 mm2to determine the local strain fields during loading

and unloading. The DIC technique measures the displacement fields by tracking

features on the specimen surface and to achieve this a surface with a random

speckle patterns is the most common approach, which works well for DIC Chu

et al. (1985). Speckle patterns with a speckle size in the range of 5 - 40 µm on

a polished surface were achieved using an Efbe-Airbrush with the nozzle size of

0.15 mm from Friedrich Boldt GmbH. Commercially available Vic-2D software

from LIMESS Messtechnik und Software GmbH was used to perform the image

correlation and strain calculations.

To perform DIC, a region of interest is selected in the reference image and

divided into small square regions with a defined number of pixels called subsets

or subimages. Here the reference image stands for an image that is recorded in

an undeformed state of the sample. An array of pixel intensities in each subset

typically of size (2M + 1)×(2M + 1) pixels is registered and the regions with the

same intensities are sought after in the deformed image. Here M is an integer

referring to the given subset size. In order to find the location of a deformed

subset, nonlinear optimization techniques are used in which displacements and

displacement gradients are assumed. An iterative approach is used to adjust these

assumed values until the difference in pixel intensity between the undeformed and

deformed subsets is a minimum. In other words, a 2D cross correlation coefficient

as a function of pixel intensity maps is defined and minimized in order to find the

position of a corresponding deformed subset. This can be represented as follows:

rij = 1 −Pi=M

i=−MPj=M

j=−MF(xi, yj)−¯

FGx∗

i, y∗

j−¯

G

rPi=M

i=−MPj=M

j=−MF(xi, yj)−¯

F2Pi=M

i=−MPj=M

j=−MGx∗

i, y∗

j−¯

G2

(2.1)

Here F(xi,yj) and G(x∗

i,y∗

j) are the grey values or the pixel intensities of the subset

centered at the source and target point located in the reference and deformed

images, respectively; ¯

Fand ¯

Gare the ensemble averages. The coordinates or grid

points (xi,yj) and (x∗

i,y∗

j) are related by the deformation that occurs between

the two images. If the motion is perpendicular to the optical axis of the camera

and a subset is chosen small enough, then the deformation can be assumed to be

homogenous within the region, thus, the relation between (xi,yj) and (x∗

i,y∗

j) can

be approximated by a 2D affine transformation such as:

x∗=x+u+∂u

∂x∆x+∂u

∂y ∆y(2.2)

y∗=y+v+∂v

∂x∆x+∂v

∂y∆y(2.3)

Here u and v are the admissible translation fields of the center of the subset in the

X and Y directions, respectively (capital X and Y refer to the coordinate system

in the deformed reference system). The distances from the center of the subset

to the point (x, y) are denoted by ∆x and ∆y. Thus, the correlation coefficient

rij is a function of displacement components (u, v) and their gradients, i.e. strain

fields. These deformations of the reference subset commonly include rigid body

motions and deformations as outlined in Figure 2.2. It should be noted that

the aforementioned admissible deformation fields are referred only to the subset

deformation not to the applied deformation of the sample. Further details of data

analysis and general background on DIC can be found in Chu et al. (1985).

Figure 2.2: The pixels in the undeformed subset undergoing a variety of homo-

geneous deformations according to the deformation gradients shown above.

2.4 Electron Microscopy, DSC and SQUID

The samples were examined with a Philips CM 200 Transmission Electron Mi-

croscope (TEM) operated at a nominal accelerating voltage of 200 kV. An EBSD

system in a Philips- XL 40 ESEM- scanning electron microscope (SEM) oper-

ated at nominal voltage of 20 kV was used to obtain orientation maps. EBSD

measurements have been realized with an orientation imaging microscopy (OIM)

system provided by TexSEM-Laboratories (TSL).

Differential scanning calorimetry (DSC) was performed on virgin and trained

samples in order to determine the transformation temperatures and their evo-

lution under stress-free conditions. A Perkin Elmer DSC cell was used in the

temperature range of -100 to 300 ◦C at cooling/heating rates of 10 K/min, and

all DSC measurements started by cooling until temperature reached -100 ◦C in

order to ensure the sample was completely in martensitic state.

The phase transformation temperatures were also obtained through a Quan-

tum Design Superconducting Quantum Interference Device (SQUID) magnetome-

ter that utilizes the principle of magnetization change upon martensitic transfor-

mation Oikawa et al. (2001); Ullakko et al. (1996). A 3 ◦C/min heating/cooling

rate was utilized during the SQUID experiments, in order to avoid rate effects.

Chapter 3

Characterization of Shape

Memory Behavior in Co38Ni33Al29

and Co49Ni21Ga30 Alloys

3.1 Introduction

In Section 1.8 of Chapter 1the motivation for the development of new Co-Ni-

Al and Co-Ni-Ga HTSMA and MSMA systems has been described. However,

their successful incorporation into industry requires a full comprehension of their

thermoelastic martensitic transformation behavior and the resultant shape mem-

ory and pseudoelastic phenomena. In this chapter some of the results of the

experimental investigations that involve isobaric thermal cycling and isothermal

stress-strain experiments and incremental strains tests (ISTs) on Co38Ni33Al29

and Co49Ni21Ga30 (in at. %) single crystalline alloys are reported. The results

demonstrate that i) the γ-phase volume fraction can be adjusted to achieve opti-

mum SME, PE and TWSME properties in solutionized Co38Ni33Al29 alloys sub-

jected to different cooling rates and ii) the [001]-oriented as-grown Co49Ni21Al30

single crystals exhibit pseudoelasticity at temperatures high above 300 ◦C mark-

ing them as promising candidates for high-temperature pseudoelastic material

(HTPM).

3.2 Analysis of Results and Discussion

3.2.1 Stress-assisted Shape Memory Effect

Co38Ni33Al29 single crystals solutionized for 24 hours at 1350 ◦C and cooled down

in different media (water, oil and air) were used for this study. The typical mi-

crostructures achieved through utilizing the three cooling methods are illustrated

in Figures 3.1 (a) to (c). The micrographs in the figure demonstrate signifi-

cantly varying distribution and volume fraction of γ-phase in the β-matrix. It

Figure 3.1: Optical micrographs of Co38Ni33Al29 alloys showing the microstruc-

tures obtained through different cooling media following solutionization: (a) wa-

ter quenched (WQ), (b) oil quenched (OQ), and (c) air cooled (AC). Canadinc

et al. (2007).

is observed that the volume fraction of the γphase increases with decreasing

cooling rate for all three orientations studied (Fig. 3.1) as this phase is stabilized

at low temperatures Liu et al. (2005). It should be noted that the γphase is

relatively soft and enhances ductility Ishida et al. (1991); Kimura et al. (1994),

which does not undergo phase transformation, even though it strongly affects the

phase transformation temperatures and the martensitic transformation behavior

as it interacts with the moving phase fronts Efstathiou et al. (2004).

Figure 3.2: Strain-temperature response of Co38Ni33Al29 single crystals under

compressive loading. Three thermal cycles were conducted at each stress level,

yet only the final cycles are shown here for the sake of clarity. Canadinc et al.

(2007).

Results of the thermal cycling experiments carried out under various constant

stress levels (Figure 3.2) brought several important points to attention. Moreover,

thermal cycles shown in Fig. 3.2 were used to evaluate different shape-memory

parameters including shape memory strains, thermal hysteresis and transforma-

Figure 3.3: Schematic showing a typical isobaric strain-temperature curve under

compression illustrating the definition of transformation temperatures (Ms,Mf,

Asand Af) using intersecting slope-line method, and the vertical and horizontal

widths of the loop are considered as transformation strains (SME) and thermal

hysteresis (TH), respectively. The arrows indicate the cooling and heating paths

of the loop.

tion temperatures as defined in Figure 3.3. These values were compared among

the different oriented crystals with different microstructures (Fig. 3.1) to bet-

ter estimate the functional performance of Co38Ni33Al29 alloys. To start with,

the [001]-oriented single crystals exhibit the highest recoverable transformation

strains, which stand close to -yet slightly below- the theoretical CVP formation

strain (CV P ) values, as stated in Table 3.1, which also displays the maximum

transformation strain (SME) for each single crystal and cooling rate, along with

the corresponding Schmid factors for dislocation slip in the {110}<001>and

{100}<001>systems (austenite), the resolved shear stress factors (RSSF), max-

imum recoverable PE strains (P E), and maximum TWSME strains (T W SME).

The [110] orientation in some microstructural conditions, on the other hand,

exhibits recoverable transformation strains exceeding their corresponding CV P

values (Table 3.1). It should be noted that they were calculated considering only

the transformable β-phase Karaca et al. (2004). The γ-phase does not undergo

phase transformation: however, it obstructs the propagation of the phase front.

Hence the reduced volume fraction of transformable phase in a dual phase (β+γ)

microstructure (Fig. 3.1) reduces the maximum transformation strains.

Table 3.1: The resolved shear stress factors (RSFF), Schmid factors (SF), theo-

retical CVP formation strains (CV P ) (from energy minimization theory Karaca

et al. (2003)), maximum transformation strain (SME), maximum recoverable PE

strains (P E), and maximum TWSME strains (T W SME) for each single crystal

orientation and cooling rate. σ: Compressive stress; T: Temperature; N/A: Not

available; AC: Air cooled; OQ: Oil quenched; WQ: Water quenched. Canadinc

et al. (2007).

Crystallographic

orientation [001] [123] [110]

RSSF 0.56 0.38 0.30

SF 0 0.45 0.50

CV P (%) 4.8 3.1 2.4

Cooling method AC OQ WQ AC OQ WQ AC OQ WQ

SME(%)@ 3.1 4.1 4.0 1.8 1.9 2.8 1.0 3.4 4.0

σopt(MPa) 100 50 50 200 200 100 200 50 50

P E(%)@ 4.3 3.8 4.0 2.2 2.5 2.6 3.4

T(◦C) 10 22 170 50 N/A 107 N/A 26 60

T W SME(%)

@4-6MPa 1.3 1.2 0.25 0.8 1.4 2.6 0.15 2.6 2.7

The orientation dependency of recoverable transformation strains is dictated

by the RSSF, such that high RSSF values imply low transformation stresses

and high recoverable transformation strains. Accordingly, the [110] orientation,

which possesses a low RSSF, is expected to yield a low transformation strain.

However, the experimentally determined transformation strain values for the OQ

or WQ [110] samples are well above the CV P values (Table 3.1). This clearly

demonstrates the contribution of martensite detwinning to the overall strain.

Specifically, compression along the [110] direction activates dislocations and the

corresponding local stress fields create preferential nucleation sites for the most

favorably oriented CVPs and help twin boundary motion. This, in turn, promotes

the growth of a favorable single correspondence variant (SCV), giving way to

detwinning strains, and thus increasing the overall transformation strain exhibited

by the material. As for the [001] orientation, its zero Schmid factor theoretically

eliminates the possibility for easy dislocation slip. The matrix resists dislocation

slip and twin boundary motion, suppressing the detwinning in this orientation,

which explains the transformation strains being lower than the corresponding

CV P values (Table 3.1).

Accordingly, the orientation dependence of the transformation strains is brought

about by the orientation dependence of CVP activation and growth of a favor-

able SCV Hamilton et al. (2004); Meyer et al. (2006); Sehitoglu et al. (2000,

2001b). For instance, the [123] orientation in B2 phase NiTi alloys possess only

one active CVP Sehitoglu et al. (2003), which should also be true for the B2

structured Co38Ni33Al29 alloys. In fact, in the strain-temperature experiments,

the [123] orientation Co38Ni33Al29 single crystals exhibited low transformation

strains (Table 3.1). The low RSSF value and dislocation activity coupled with

the presence of the γ-phase in the [123] orientation offer more frictional resistance

to the twin boundary motion, as well as to that of a CVP martensite structure

into a SCV structure. Consequently, higher optimum training stress (σopt)Meyer

et al. (2006) and lower transformation strains were obtained in this orientation.

Furthermore, the results emphasize the need for texturing polycrystalline aggre-

gates of the current material near the [001] and [110] poles with an optimum

γ-phase volume fraction to achieve high transformation strains.

It is speculated that the transformation strains below the theoretical values

displayed by the AC samples stems from the increased matrix strength due to

γ0precipitation. The high matrix strength obstructs twin boundary motion and

detwinning, as observed in peak-aged NiTi alloys Sehitoglu et al. (2000), where

coherent precipitates increase the matrix strength suppressing transformation

and/or detwinning at low stresses. Moreover, the single crystals that demon-

strate higher dislocation activity, such as the [110] and [123] orientations, further

exhibit reduced transformation strains due to increased dislocation density in the

untransformed austenite regions, which in turn increases the matrix strength.

This idea is supported by the lower transformation and TWSME strains, and

high σopt values exhibited by the [110] and [123]-oriented AC single crystalline

samples (Table 3.1). With regards to the AC [001] samples, the higher SME and

T W SME in the AC [001]-oriented single crystals (Table 3.1) can be attributed

to the lack of substantial dislocation slip in the matrix and the nucleation and

growth of specific favorable martensitic variants aided by stress fields around γ-

βboundaries, the presence of γ0precipitates, and the growth of variants trapped

at the γ-βboundaries.

The OQ and WQ samples, which possess a lower volume fraction of ductile γ-

phase compared to AC samples (Fig. 3.1), exhibit higher SME and T W SME. This

is attributed to the high volume fraction of transformable β-phase, offering lower

frictional resistance to the mobility of phase fronts and thereby facilitating growth

of favorable variants. However, the [001] oriented WQ crystals exhibit lower

T W SME despite the high SME they display. The absence of local stress fields

due to dislocation arrays, or secondary phase, such as the γ-phase, is responsible

for this difference in the case of the [001] orientation.

Other important facts revealed by the iso-stress strain-temperature experi-

ments (Fig. 3.2) include a gradual variation in strain at the transformation tem-

peratures at low stress levels in the [123] orientation, abrupt variation in strain at

the transformation temperatures in the same orientation at high stress levels, a

gradual strain-temperature response instead of an abrupt transition in the other

orientations ([001] and [110]) at all stress levels, and a wider thermal hysteresis

in the case of the [123] and [110] orientations than in the [001] orientation. All of

the observations revealed by the iso-stress strain-temperature experiments can be

rationalized on the basis of various energy contributions to the overall free energy

of the system during phase transformation. For instance, at low stress levels the

volume fraction of self-accommodating groups of martensite CVPs grows, and

increases the interfacial energy due to variant-variant interaction. The variant-

variant interaction, γ-martensite phase interaction and elastic strain raise the

stored elastic energy of the system. The elastic strain energy due to various forms

of interactions provides opposition to the forward transformation, and thus, fur-

ther transformation requires additional undercooling, leading to a gradual flow

of the strain-temperature curves as shown in Fig. 3.2. As the stress levels in-

crease, formation of the most favorably oriented CVPs in expense of unfavorable

ones results in a decrease in the stored elastic energy. An abrupt transition oc-

curs when the stored elastic energy is dissipated by relaxing coherency strains of

martensite-austenite interfaces Hamilton et al. (2004) under higher stress levels.

Figure 3.4: Evolution of thermal hysteresis with applied stress. Canadinc et al.

(2007).

In the [123] and [110] orientations, relaxation of coherency strains occur by

introducing dislocations upon the application of stress. Therefore, [110] and [123]

orientations display abrupt transition at high stress levels, whereas the [001] orien-

tation does not respond similarly. As a result of stored elastic energy dissipation

in the [123] and [110] orientations, less elastic energy is available to assist the

reverse transformation. Therefore, increased chemical driving force is necessary

(resulting in an increased As) to initiate and complete the reverse transformation,

which widens the thermal hysteresis (Figures 3.2 and 3.4). In the [001] orienta-

tion, on the other hand, stored elastic energy helps the reverse transformation,

reducing the thermal hysteresis (Fig. 3.4). It should be noted that the thermal

hysteresis of Co38Ni33Al29 alloys studied in this work is greater than those exhib-

ited by NiTi and NiTiCu alloys Hamilton et al. (2004); Sehitoglu et al. (2001b,

2003). Large thermal hysteresis can be exploited in applications that require high

damping capacity and shape stability, while smaller thermal hysteresis is more

essential for actuators Mosley & Mavroidis (2001). Thus, crystals with [001]

orientation would perform better in actuation applications, whereas [110] and

[123] orientations are more suitable for applications demanding higher damping

capacity.

Transformation strain and thermal hysteresis evolutions with stress observed

in the present study are different from what has been reported so far for conven-

tional SMAs such as NiTiCu Sehitoglu et al. (2001b) and NiTi Hamilton et al.

(2004); Sehitoglu et al. (2000,2003). At low stress levels, the martensite mor-

phology is self-accommodating, and imparts low transformation strains. Conse-

quently, CVP interactions and variant-second phase interactions raise the stored

elastic energy contributing to the reversible form of free energy of the system,

which in turn helps reverse transformations, thus lowering the thermal hystere-

sis. As the external stresses are increased, the growth of favorable martensite

variants gives way to reduced interaction energies, and thereby increased trans-

formation strains. The concomitant decrease in stored elastic energy by relax-

ation of coherency strains increases the difficulty of reverse transformation. As a

result, more energy is required, as evidenced by the increase in temperature hys-

teresis. The results in Figs. 3.2 and 3.5 for the [001]-oriented OQ single crystals

demonstrate that both the maximum transformation strain and the maximum

temperature hysteresis occur at approximately the same stress level (σopt). The

maximum transformation strain is obtained when a multivariant martensite (A

and B in schematic of Fig. 3.5) transforms into a single variant martensite (C in

the schematic of Fig. 3.5) in an ideal condition. Therefore, a martensite structure

with a single variant is expected at 4.1% strain (C in the schematic of Fig. 3.5).

With further thermal cycling upon attaining a maximum value, increased stress

levels decrease the thermal hysteresis, as well as the transformation strains. The

decrease in transformation strains is attributed to the formation of a twinned

Figure 3.5: Demonstration of transformation strain evolution with compressive

stress as a function of cooling rate. Potential twinning of variants is not shown

in the schematics of microstructure states A and B. Canadinc et al. (2007).

state of SIM within the thermoelastic martensite to relax strain energy or intro-

duction of dislocations, which interrupt the phase or twin front propagation. This

state of martensite promotes the interaction between SIM and thermally-induced

martensite, or oriented martensite variants due to the internal stresses, and re-

sults in an increased elastic energy, and thus reduces the temperature hysteresis.

In the case of Co49Ni21Ga30 alloys, as-grown crystals were used and whose

general microstructure is shown in Figure 3.6. The micrograph in the figure

displays the uniform distribution of fine γprecipitates in the β-matrix. Owing

to the slow cooling rates that have prevailed during the growth of single crys-

tals using the Bridgman process, one would expect precipitation of γphase in

Co49Ni21Ga30 alloys as the γphase-field stabilizes at lower temperatures Liu et al.

Figure 3.6: A microstructural overview of an as-grown Co49Ni21Ga30 crystal

showing the fine γprecipitates in the matrix.

(2006). The transformation temperatures of as-grown Co49Ni21Ga30 single crys-

tals were determined through differential scanning calorimetry (DSC) as shown

in Figure 3.7. Accordingly, As,Af,Ms,Mfare -2.4, 1.3, -18 and -22.4 ◦C, re-

spectively. A stress-free thermal hysteresis, TH, of only 20 ◦C is present in this

material. Such a narrow hysteresis indicates the high degree of compatibility

between austenite and martensite in these alloys. The strain-temperature

response of [001]-oriented Co49Ni21Ga30 single crystals under constant compres-

sive stress (Figure 3.8) revealed that the phase transformation occurs in a rather

abrupt manner at low stress levels (e.g. -4 MPa), accompanied by a low ther-

mal hysteresis. Yet higher levels of applied compressive stresses bring about

a completely different picture, such that a wider thermal hysteresis is present

(Fig. 3.8). Moreover, substantial undercooling and overheating are indispensable

for the completion of the forward and backward phase transformations, respec-

tively. This difference in strain-temperature response due to change in applied

stress levels stems from the fact that the frictional dissipation during phase trans-

formation increases with increasing external stresses. It should also be noted that

the difference between the transformation temperatures obtained from DSC and

strain-temperature experiments results from a possible heterogeneity in the chem-

Figure 3.7: DSC curve of Co49Ni21Ga30 alloy, showing the As,Af,Msand Mf

temperatures, and the thermal hysteresis (TH) brought about by stress-free ther-

mal cycling. Dadda et al. (2006a).

ical composition. Specifically, the samples utilized in DSC are much smaller in

size compared to the specimens used in strain-temperature tests. While the large

specimens reflect the average response, even a small inhomogeneity in the compo-

sition could lead to large effects in a small DSC sample. Moreover, the material

utilized in this study was as-grown, and this could cause inhomogeneities in the

bulk.

Fig. 3.8 demonstrates that both the transformation strain and temperature

hysteresis evolve with externally applied stress. The increase in thermal hystere-

sis is not drastic above stress levels of 50 MPa, and the saturation is reached

at 150 MPa and higher stresses. The transformation strain of 4.7 % at 4 MPa

applied stress decreases with increasing stress levels, converging to a saturation

value of 3.5% at applied stress levels of 150 MPa and above. Interestingly, the re-

sponse at low stress levels differs significantly from that observed in [001]-oriented

Co38Ni33Al29 single crystals cf. Figs. 3.2 and 3.5, indicating expressively lower

critical stress levels for the Co49Ni21Ga30 alloy in comparison to Co38Ni33Al29.

Figure 3.8: Isostress strain-temperature behavior of [001] oriented Co49Ni21Ga30

single crystals. The scale bar on the strain axis is used instead of a conventional

scale to avoid misunderstanding as the curves were shifted vertically from their

original position for the sake of a clear presentation. Dadda et al. (2006a).

The abrupt phase transformation at lower applied stress levels (-4 MPa) in

Fig. 3.8 suggests the nucleation and growth of a single variant, thereby reducing

the interaction between the CVPs. Moreover, an external stress of about -4 MPa

gives way to a transformation strain of about 4.3 %, which is the transforma-

tion strain from single crystal austenite to single crystal martensite according to

theoretical calculations made elsewhere Dadda et al. (2008).

As for the higher stress levels (150 MPa), however, the transformation does not

occur abruptly, but takes place in a gradual manner (Fig. 3.8) due to the difficulty

in forward transformation brought about by the increased interaction between the

thermally-induced and stress-induced martensitic variants. Figure 3.9 illustrates

martensitic variants grown in several directions, which shows an example to this

statement, where interaction between these differently oriented martensitic vari-

ants takes place. Consequently, the martensite is expected to possess a partial

self-accommodating structure at these stress levels, where thermally- and stress-

Figure 3.9: The residual martensite plates that grew in different directions in a

trained/deformed sample. Dadda et al. (2006b).

induced variants coexist. This is supported by the observed decrease in trans-

formation strain with increasing stress level (Fig. 3.8), which is again consistent

with the microstructural model proposed earlier to understand the variation of

transformation strains with the applied stress in Fig. 3.5 for Co38Ni33Al29 al-

loys. On the other hand, the increase in thermal hysteresis is associated with the

mechanical stabilization of martensite, leading to the reverse transformation at

elevated temperatures Picornell et al. (2001). Further elaboration, such as in-situ

observations of the microstructural changes, is necessary in order to draw a solid

conclusion regarding this point.

3.2.2 Pseudoelasticity

Figure 3.10 shows a typical pseudoelastic response of the Co-base alloys used in

this study. The figure is used to define several pseudoelastic parameters such as

the critical stress levels for the forward, σF or

cr , and the reverse, σRev

cr , transforma-

tions, which were evaluated using the intersecting slope lines method at the inflec-

tion points where the deviation from initial linearity occurs both during loading

and unloading. The stress hysteresis, ∆σ, was measured at the half of the applied

strain range (∆). The strain, 0, is due to elastic deformation of austenite, while

Tis the transformation strain. These parameters are useful in the analysis and

discussion of pseudoelastic response of Co38Ni33Al29 and Co49Ni21Ga30 alloys as

a funciton of crystallographic orientation and thermomechanical treatments as

follows.

Figure 3.10: A typical pseudoelastic response showing the loading-unloading

curves used to define the PE parameters.

Figures 3.11 and 3.12 lay out the orientation and cooling rate dependencies of

the pseudoelastic behavior of the Co38Ni33Al29 single crystals studied. It should

be noted that the general trend in stress-strain behavior of the [110] and [123]

orientations resembles that of CoNiAl polycrystals Karaca et al. (2003). It was

proposed by Karaca et al. (2003) that the second stress drop at the end of the

plateau region in CoNiAl polycrystals indicates a two-stage martensitic transfor-

mation. A similar response is observed for the [110] oriented crystals investigated

in this study (Fig. 3.11).

The alteration of the critical stress in the [110] orientation with increasing

deformation (Fig. 3.11) is linked to the role of irreversible mechanisms, such

Figure 3.11: Pseudoelastic response of [110]-oriented WQ Co38Ni33Al29 single

crystals at 60 ◦C. Canadinc et al. (2007).

as dislocation generation and formation of residual martensite, which assist the

forward transformation in subsequent cycles Efstathiou et al. (2004); Hamilton

et al. (2006); Karaca et al. (2004). Interestingly, the critical stresses are quite

stable for increasing strain levels in the [123] orientation (Fig. 3.12), where the

irreversible mechanisms play a less pronounced role. Furthermore, stress hys-

teresis increases slightly with increased strain levels in all orientations (Figs. 3.11

and 3.12), which can be attributed to defect generation coupled with frictional

dissipation. For instance, compression tests on the [001]-oriented single crystals

revealed large stress hysteresis despite the lack of significant dislocation activity.

Earlier studies confirmed that compression along the [001] orientation activates

a relatively higher number of variants Hamilton et al. (2004). In such a case, the

stress hysteresis is governed by multi-variant interaction, i.e. by variants that

are preferentially oriented along the applied stress direction (SIM) and variants

oriented in accordance with the internal stress fields, and interaction of moving

phase fronts with the γ-phase. Another contribution to the large stress hysteresis

in the [001]-oriented crystals comes from the high resistance against dislocation

Figure 3.12: The pseudoelastic response of [001] (at 170 ◦C for WQ and at 60 ◦C

for AC) and [123] (at 107 ◦C for WQ and at 33 ◦C for AC) oriented Co38Ni33Al29

single crystals. The curves are plotted with identical scales to allow for compar-

ison of the actual stress-strain response. The negative slope at the start of the

unloading part of the AC [001] curve stems from an extensometer effect due to a

short instability upon quick release of the load. Canadinc et al. (2007).

slip in the matrix, which suppresses twin boundary motion and detwinning. This

in turn increases variant-variant interaction, leading to a high stress hysteresis.

Such interaction reflects as an ascending flow curve in the stress-strain response,

rather than a plateau typically observed in conventional SMAs. Consequently,

the propagation stress change per unit strain in stress-strain response is higher

in the case of the [001] orientation in comparison to the [110] and [123] orienta-

tions. Nevertheless, the slip activity and local stress fields in the [110] orientation

create nucleation sites for favorable CVPs and promote the growth of a SCV,

altering the variant-variant interactions. Hence in the [110] and [123]-oriented

samples, low stress hysteresis is primarily due to local plasticity, instead of the

variant-variant interactions.

One more remark regarding the pseudoelastic response of the [001]-oriented

samples is that this orientation attains large PE strains even in the absence of

pronounced dislocation activity and detwinning strains. This observation is asso-

ciated with the high RSSF and easy reorientation of variants in the direction of

the external stress. Moreover, the similarity between PE strains and transforma-

tion strains indicate the similarity between CVPs in SIM and thermally-induced

martensite CVPs.

As stated earlier, compression along the [123] direction in B2 crystals acti-

vates only one CVP, altering the interaction among the variants. In this case, the

availability of favorable variants to the local stress fields is minimized, reducing

transformation strains or detwinning strains, as evidenced by the experimen-

tal results on [123] oriented single crystals (Table 3.1). The ascending stress-

strain curve displayed by [123] oriented AC samples is linked to the interaction of

twin boundary or moving phase fronts with γ0precipitates or γ-phase boundaries

(Fig. 3.12). By contrast, the lack of variant-variant interaction, low volume frac-

tion of γ-phase and absence of γ0precipitates in WQ [123] oriented crystal brings

about very low resistance to mobile twin boundary or phase front, resulting in a

descending stress-strain curve (Fig. 3.12).

In B2-structured alloys, the low critical transformation stress, high slip resis-

tance and B2 atomic ordering allow for excellent transformation recoverability

when loaded in the [001] direction as seen in the case of Co38Ni33Al29 alloys dis-

cussed above and NiTi alloys by Sehitoglu et al. (2000). Thus, it became a com-

mon approach to characterize the [001]-oriented crystals first and then evaluate

the effect of crystallographic orientation on the transformation and deformation

behaviors in order to develop a strong textured material.

Figure 3.13 shows the pseudoelastic response of Co49Ni21Ga30 [001]-oriented

crystal at different temperatures. The crystal exhibited the PE strains of about

4.3 % at low temperatures (≤120 ◦C) and altered strains of about 3 % at

higher temperatures. The latter can be attributed to the formation of self-

accommodating martensite at higher temperatures as the prevailing high stress

levels have the tendency to induce a higher number of martensite variants. This

increases the variant-variant interaction, which in turn will result in an ascending

loading plateau at elevated temperatures as seen in Fig. 3.13. This will be dis-

cussed in detail later in Chapter 4with in-situ observations at high temperatures.

Figure 3.13: Pseudoelasticity and its dependency on temperature in an as-grown

[001]-oriented Co49Ni21Ga30 single crystal.

Figure 3.14 shows the stress-strain curves of [235]-oriented Co49Ni21Ga30 crys-

tal where the test temperatures were raised progressively up to 200 ◦C. It is clear

from the figure that L¨uder’s type deformation prevails in this orientation. This

type of behavior generally takes place in SMAs when the resistance to the trans-

formation interface propagation is lower than that to the nucleation of martensite

Canadinc et al. (2007). L¨uder’s type behavior is also observed during the reverse

transformation, i.e. upon unloading the reverse transformation of SIM begins

with a lower stress (the point where the unloading curve changes its slope) and

is followed by an increase of the stress to a higher plateau level. The SIM trans-

formation starts as soon as the stress-strain curve deviates from linearity and a

first transformation band appears. The upper limit of the L¨uder’s type deforma-

tion marks the moment when this band has spread over the entire cross section

Figure 3.14: Pseudoelastic response of [235]-oriented Co49Ni21Ga30 single crystal

as a function of temperature. Dadda et al. (2009).

of the specimen Liu et al. (1995). As the band reaches the free surface of the

sample a portion of the elastic energy stored during its growth is released, result-

ing in a decrease in the resistance to the propagation of the band interface Liu

et al. (1995). This decreases the plateau stress to lower levels causing the typical

L¨uder’s type deformation. Moreover, the in-situ and DIC studies in the next

Chapter 4will reveal that the each stress rise (other than the first upper limit)

in the plateau region corresponds to the formation of a new transformation inter-

face (band) every time. Similarly, the lower stress limit for the reversion of the

martensite during unloading indicates the point when the propagating austenite

band reaches the free surface of the specimen, instead of being associated with

the nucleation of austenite Liu et al. (1995). Finally, the irrecoverable strains

at elevated temperature (≥180 ◦C) that limit the sample to exhibit any further

perfect pseudoelasticity in Fig. 3.14 are linked to the martensite stabilization cou-

pled with the plastic accommodation in the material due to the high prevailing

stresses.

Figure 3.15 shows the σF or

crit values (see the definition in Fig. 3.10 on page

Figure 3.15: The representation of PE temperature ranges in terms of Clausius-

Clapeyron ( CC) curves for Co49Ni21Ga30 and Co38Ni33Al29 alloys. All the

Co38Ni33Al29 alloys in the figure are solutionized and the curves are represented

by dashed curves, while solid curves refer to the Co49Ni21Ga30 alloys.

39) obtained for both the alloys as a function of test temperature. The linear

curves follow the CC-relationship (Eq. 1.3 on page 11) and some of the curves

deviate from the linearity, for instances, in the case of [235] and [123]-oriented

Co49Ni21Ga30 alloys. This deviation was attributed to the plasticity by dislocation

slip in the material that occur prior to SIM transformation Dadda et al. (2006b).

It should be noted here that all the CC-curves of as-grown Co49Ni21Ga30 crystals

converge almost to the same point when they are extrapolated to the zero stress

level on the abscissa, which is considered as the Mstemperature (-20 ◦C) under

stress free conditions. This is in good agreement with that evaluated using DSC

measurements in Fig. 3.7. The temperature ranging from Msto the point where

the curves depart from linearity is considered as the PE range in Fig. 3.15 (cf.

Fig. 1.6). The different values of Mstemperatures for Co38Ni33Al29 single crystals

in Fig. 3.15, 20 and -60 ◦C for WQ and AC, respectively, is associated with the

variation in chemical composition of the matrix, which is in turn because of the

differences in the amount of precipitation (Fig. 3.1).

Fig. 3.15 also demonstrates that the CC-slope of [001]-oriented crystals is al-

ways lower than for the other orientations. In other words, the [001] orientation

tends to undergo SIM transformation in a much easier fashion than the [123]

and [235] orientations for a given temperature. This difference purely stems from

the crystallography and depends on Schmid’s law where the initiation of SIM

begins when the shear stress acting on the habit plane resolved in the direction

of transformation reaches a certain critical value. To gain further insight into

this behavior, resolved shear stress factors (RSSFs) and theoretical total (CVP

formation plus detwinning) transformation strains calculated in the framework

of energy minimization theory Dadda et al. (2008); Sehitoglu et al. (2001a) have

been displayed as a function of crystallographic orientation in a unit stereographic

triangle shown in Figures 3.16(a) and 3.16(b), respectively, for Co49Ni21Ga30 al-

loys. The negative values represent the compression stress state.

The RSSF value is an indicator of the critical stresses needed for SIM, the

level of transformation strains and the recoverability upon loading along differ-

ent orientations. The high RSSF value implies that the critical transformation

stresses would be low, i.e. low CC-slopes, the transformation strains would be

larger and the recoverability would be high. Table 3.2 lists the RSSFs for vari-

ous single crystal of both Co38Ni33Al29 and Co49Ni21Ga30 alloys along with their

Schmid’s factor for slip in the austenite, theoretical transformation strains that

include both CVP formation (CV P ) and detwinning (det) strains, experimentally

obtained maximum transformation strains, CC-slopes and PE temperature win-

dow. It is clear from the table that the aforementioned RSS criterion is valid in

both alloy systems as the [001] orientation with largest RSSF value (0.56) exhibits

the lower CC-slopes, larger transformation strains with complete recoverability

than that observed in the other orientations with lower RSSF values of 0.35 and

0.33 for [123] and [235] orientations, respectively.

Moreover, based on the results shown Table 3.2, a criterion has been estab-

lished to develop HTPMs that can demonstrate pseudoelasticity at high temper-

atures. The crystals with high RSSF, i.e. favorable orientation for the marten-

(a)

(b)

Figure 3.16: Co49Ni21Ga30 (a) RSSF and (b) CVP formation (CV P ) and de-

twinning (det) strains as a function of crystallographic orientation. Dadda et al.

(2008).

sitic transformation with respect to the applied stress, and low values of Schmid

factors, i.e. unfavorable orientation for the slip system in the austenite, demon-

strate a large pseudoelastic temperature window. For example, the [001]-oriented

Co49Ni21Ga30 crystal with largest RSSF and zero Schmid factor demonstrates

remarkably high-temperature pseudoelasticity at temperatures as high as 325

◦C (Fig. 3.13) with large PE window of 300 ◦C (Table 3.2). This extends the

utility of these alloys over a wider temperature range in comparison to NiM-

nGa Chernenko et al. (2003), CuAlNi Otsuka & Wayman (1999), CoNiAl Karaca

et al. (2003), and NiTi Sehitoglu et al. (2000) alloys, which exhibit pseudoe-

lastic temperature ranges of about 80, 125, 160 and 200 ◦C, respectively. This

makes as-grown Co49Ni21Ga30 an alternative to Cu-based, NiTi-based and NiM-

nGa HTSMAs. However, a detailed study on the stability of SIM transformation

behavior at high temperatures is required for their successful utility as presented

in the next chapters. Moreover, the upperbound for PE temperature range in the

Co38Ni33Al29 system is still open (>250 ◦C) and one would expect large temper-

ature range due its low CC-slope of 1 MPa/◦C (Table 3.2). Thus, future research

should be focused on the development of high temperature Co-Ni-Al systems.

3.3 Chapter Summary

The basic shape memory characteristics of Co38Ni33Al29 and Co49Ni21Ga30 single

crystals were analyzed and presented utilizing isostress thermal cycles and isother-

mal loading-unloading cycles at different temperatures in this chapter. The key

findings of this study are given as follows:

1. The [001]-oriented Co38Ni33Al29 single crystals subjected to high cooling

rates following a high temperature heat treatment exhibit large phase trans-

formation strains of about 4.1 % under compressive stress levels as low as 50

MPa. The maximum transformation strain observed is in agreement with

the theoretical corresponding variant pair (CVP) transformation strain.

2. Similar to the [001] orientation, the [110]-oriented single crystals with high

cooling rates exhibit large transformation strains of 4 % under compres-

sive stresses as low as 50 MPa. Nevertheless, this strain value exceeds

the theoretical CVP transformation strain, indicating a significant contri-

bution of detwinning strains to the overall phase transformation strain.

Therefore, the results emphasize the need for texturing polycrystalline ag-

gregates of the current material near the <001>and <110>poles with an

optimum γ-phase volume fraction to achieve high transformation strains in

Co38Ni33Al29.

3. Near-perfect pseudoelasticity above the Aftemperature was obtained in

compression tests with a maximum pseudoelastic strain of about 4.3 %.

The Co38Ni33Al29 samples investigated in this work demonstrate a large

pseudoelastic window (>250 ◦C). Thus, Co38Ni33Al29 alloys with optimum

ductile γ-phase content are suitable for conventional pseudoelastic applica-

tions at elevated temperatures.

4. The Co38Ni33Al29 single crystals studied demonstrate good cyclic stability

and trainability with a maximum two-way shape memory effect (TWSME)

strain of 2.7%. The TWSME strain obtained for the [001]-oriented air

cooled samples constitutes an evidence of the substantial role of the ductile

γ-phase for trainability in the absence of pronounced dislocation activity.

5. Owing to the most favorable orientation for the transformation and least

favorable for dislocation slip, the [001]-oriented Co49Ni21Ga30 single crystals

exhibit about 4.4% transformation strains at compressive stress levels as low

as 4 MPa, and a fully recoverable 4.3 % pseudoelastic strain. Perfect pseu-

doelasticity was observed in the temperature range from room-temperature

to 325 ◦C indicating their excellent high temperature capability.

6. The pseudoelastic temperature range is limited by the occurrence of slip,

which sets in the range of 650-750 MPa at least for [123] and [235]-oriented

Co49Ni21Ga30 samples. Further thermomechanical treatments are expected

to increase the matrix strength that will raise the flow resistance of austenite

so that the alloys can undergo stress-induced martensitic transformation

even at higher temperatures. The results open the possibility to tailor

textured polycrystalline material with a strong <100>component along

the loading axis for its outstanding high-temperature pseudoelasticity.

Table 3.2: Maximum resolved shear stress factors (RSSFs), Schmids factors (SF) for the slip system {110}<001>

in the austenite, theoretical transformation strains (CV P +det), maximum experimentally obtained pseudoelastic

strains, Clausius-Clapeyron slopes and pseudoelastic temperature window for Co49Ni21Ga30 (CNG) and Co38Ni33Al29

(CNA) single crystals under compressive loading conditions.

Theoretical Estimations Experimental Values

CV P +det Max Exp CC-slope PE-Window

Specimen RSSF SF (%) T(%) (MPa/◦C) (◦C)

CNG [001] 0.56 0.0 4.4 4.3 2.3 >300

CNG [123] 0.35 0.4 3.6 3.4 2.6 220

CNG [235] 0.33 0.42 3.0 3.0 3.9 200

CNA [001]-WQ 0.54 0.0 4.4 4.3 1.0 >200

CNA [123]-AC 0.35 0.4 3.3 3.6 2.25 >250

Chapter 4

Co49Ni21Ga30-alloys as a

High-temperature Pseudoelastic

Material

4.1 Introduction

This chapter deals with the analysis of high-temperature in-situ microstructural

observations in correlation with the stress-strain response during SIM transfor-

mations in Co49Ni21Ga30 alloys. Especially, as-grown Co49Ni21Ga30 [001]-oriented

crystals under compressive loading conditions were used as they exhibit a large

PE window as shown in Figs. 3.13 and 3.15 on pages 43 and 45 in the last chapter.

The effect of training on the PE behavior and its temperature range has also been

established and it is found that trained crystals exhibit PE response at tempera-

tures as high as 425 ◦C. Moreover, the PE behavior in terms of stress hysteresis

and critical transformation stress levels and their variation with test temperatures

are analyzed and discussed in this chapter. In-situ OM and DIC were carried

out at various stages during the PE experiments to follow the evolution of the

stress-induced phase transformation at elevated temperatures and to track the

propagation of phase boundaries. This information is essential for the modeling

of inhomogeneous deformation regimes in SMAs Abeyaratne & Knowles (1993).

In-situ microscopy revealed the martensite stabilization due to pinning of moving

interfaces in Co49Ni21Ga30 alloys especially at elevated temperatures (>120 ◦C),

which is macroscopically reflected by the shift of the unloading curve to lower

stress levels. Along with microscopy observations, the spatial visualization of

strain localization obtained by using DIC revealed heterogeneous transformation

characteristics at temperatures below 120 ◦C, above which the nucleation and

growth characteristics of SIM transformation are quasi-homogeneous resulting in

a multi-variant configuration, which was later inherited by the trained crystal.

An insight into the evolution of microstructure and stress-strain behavior in terms

of stress hysteresis with test temperatures is provided, and the possible operant

mechanisms are presented.

4.2 Microstructure-pseudoelastic property rela-

tionships

4.2.1 Mechanical property variation with temperature

Figure 4.1 demonstrates the variation in the PE parameters such as stress hys-

teresis, ∆σ, and the critical transformation stress levels for both forward, (σF or

crit ),

and reverse, (σRev

crit ), transformations obtained from the curves shown in Fig. 3.13

on page 43 in Chapter 3. The definitions for the aforementioned parameters are

given in Fig. 3.10 on page 39. Fig. 4.1 demonstrates that σF or

cr follows a linear

relationship with a CC-slope of of 2.2 MPa/◦C, and also shows a significant varia-

tion of stress hysteresis with test temperature, accordingly the plot is divided into

two regions. An almost constant stress hysteresis of about 20 MPa is observed

in Region I, i.e., until the test temperature reaches about 120 ◦C. An increase

in temperature above 120 ◦C brings about a continuous rise in stress hysteresis

reaching the highest level of 350 MPa at 320 ◦C (Regions II), which is an 18 fold

increase from the value obtained in region I. The deviation of the σRev

cr values

from linearity in the temperature regions II in the figure explains the increase

in the stress hysteresis. This trend in σRev

cr suggests the difficulty in nucleation

of habit planes necessary for the onset of the reverse transformation Chernenko

et al. (2004). This is known as mechanical stabilization of martensite Liu & Favier

(2000); Picornell et al. (2001) due to inelastic deformations such as martensite

Figure 4.1: The evolution of stress hysteresis and critical transformation stress

levels with test temperatures in as-grown Co49Ni21Ga30 [001]-oriented crystal.

reorientation (MR) and/or detwinning that prevail(s) during the forward trans-

formation. The degree of difficulty depends on the amount of detwinning as it

removes the back stress that was stored in the twinned martensite, which would

have aided the back transformation upon unloading Dadda et al. (2006b,2008);

Gall et al. (1999). Moreover, the transformation strain, T(cf. Fig. 3.10 for

definition), decreases gradually with temperature beginning at 4.3 % strain and

saturates at around 3 % strain above 100 ◦C. The observed variation in, ∆σ

and Tcan be understood as a change in the martensite morphology during SIM

transformation and its dependency on the temperature is clarified with the help

of in-situ observations in the following section.

4.2.2 Evolution of microstructure with temperature dur-

ing SIM transformations

4.2.2.1 Region I - Constant low stress hysteresis

Figure 4.2: Microstructural changes during pseudoelasticity of as-grown

Co49Ni21Ga30 [001]-oriented single crystal at 40 ◦C. The direction of loading

is represented by σ. The arrow in the micrograph gpoints out the formation of

new phase fronts, whose normals are perpendicular to the original ones.

Systematic in-situ high-spatial resolution optical microscopy has been con-

ducted at critical temperatures in the different regions as defined in Fig. 4.1.

Figure 4.2 shows the micrographs that were recorded at different stages on the

PE curve during loading and unloading paths obtained at 40 ◦C. Figure 4.2a

shows the reference microstructure of the specimen taken at point aon the curve

in the inset. It is clear from Figure 4.2b that the departure of the PE curve

from its initial linearity is characterized by the formation of a single interface

or martensite plate with well defined habit planes indicating the onset of SIM.

Straining of the sample to points cand don the curve results in concurrent

growth of the martensite region via propagation of the phase-front as marked by

arrows in Figs. 4.2c and d. At point eon the curve a new phase front propagates

in the opposite direction as indicated by arrow in Fig. 4.2e further increasing the

volume fraction of martensite. This event, in fact, is reflected in the macroscopic

response as a raise in stress level to 95 MPa on the stress-strain curve at point

e, which is equal to the stress value at point b. A further loading to point f(4.3

%) has resulted in an apparent strain hardening and the corresponding image

shows that the sample almost fully transformed. The resultant total strain of 4.3

% from the formation of a nearly single crystalline martensite from a single crys-

talline austenite is in good agreement with the expected theoretical value shown

in Fig. 3.16(b).

As the martensite becomes unstable upon unloading, the reversion to austenite

takes place by forming numerous additional interfaces, whose habit planes are

perpendicular to the original ones as marked by an arrow in Fig. 4.2g. These new

phase fronts are consumed by the original dominant ones as seen in in Fig. 4.2h

probably by a reorientation mechanism. Unlike the formation and propagation

of a single interface during the forward transformation, reverse transformation

is characterized by the nucleation of multiple emanating phase fronts. The SIM

transformation is always accompanied by the formation of mis-match dislocations

due to the difference in the crystal structures of austenite (parent) and martensite

Otsuka & Wayman (1999), and these will be left behind as the moving interface

sweeps through fresh austenite areas. Upon unloading, these dislocated regions

will act like nucleation sites forming new interfaces for the growth of austenite.

As seen in Fig. 4.2i, further unloading lead to the coalescence of austenite variants

and thickening of austenite regions reducing the total number of visible interfaces.

The reverse transformation further proceeds upon unloading to 1.8 % and 0.8 %,

points j(Figs. 4.2j) and k(Figs. 4.2k) on the PE curves, respectively. Finally,

the sample reverts back to austenite phase recovering its initial microstructure

and orientation at minimum applied stress levels.

Figure 4.3: Local strain distribution during stress-induced martensite transfor-

mation in Co49Ni21Ga30 [001]-oriented single crystal at 40 ◦C. The elastic strain,

0, of -0.5 % (defined in Fig. 3.10 on page 39) was subtracted as the focus was

only on the transformation strains. See main text for detail.

Figure 4.3 presents the PE response of a companion as-grown Co49Ni21Ga30

[001]-oriented sample at 40 ◦C and the evolution of the localized component of the

strain in the loading direction (yy) and its distribution at the mesoscopic scale

obtained by DIC at different stages of loading and unloading. The inflection

point where the curve deviates from linearity is characterized by the appearance

of a band with a localized transformation strain of about -1.4 % within the band

and its morphology is similar to that captured by the optical microscope seen in

Fig. 4.2b. If only optical imaging is available, this would be typically interpreted

as a completely transformed martensite plate with well defined habit planes.

By contrast, DIC revealed that the strain inside the band does not show the

saturation value of the transformation strain (Sat

T rans), which is -4.3 % in the

current alloy Dadda et al. (2008) under compressive loading conditions as marked

on the scale bar in the figure. This demonstrates that the transformation is only

partially complete when the bands form and proceeds with further loading as one

can see from Figure 4.3c. In addition, similar reports on NiTi sheets elsewhere

Daly et al. (2007) using DIC seem to indicate that this is true for the other

existing SMAs as well.

Further straining leads to growth of the martensite as can be seen in Figs. 4.3d

and e. Fig. 4.3f demonstrates that new bands appear (green bands on top-left

corner) when the moving phase front stops, concomitant with the raise in local

stress at point f, which is similar to the observation made at point ein Fig. 4.2e.

This suggests that the nucleation of bands always starts at a little higher stresses

than that required for their propagation. This can also be inferred from the stress

drops at points bmarked on either curves shown in Figs. 4.2 and 4.3. In addition,

frequent occurrence of such events has led to the periodic stress drops and raises

along the loading path, for example points fand gin Fig. 4.3. The serrated

features of the stress-strain response are attributed to the stick-slip motion of the

phase boundaries Vainchtein (2002) and can only appear when the experiments

are performed at sufficiently slow loading rates as experimentally observed and

simulated elsewhere Dadda et al. (2008); Vainchtein (2002).

Loading of the sample to point hon the curve has resulted in the increase in

martensite volume fraction and also the onset of an apparent strain hardening.

The latter can be attributed to the elastic deformation of martensite as one can

see purple islands in completely transformed blue region (Figs. 4.3h and i). How-

ever, both DIC (Fig. 4.3) and microscopy (Fig. 4.2) observations unequivocally

verified that the end of the loading plateau does not imply the completeness of

the transformation in SMAs. This can be seen as green and yellow bands (par-

tially transformed regions) in Fig. 4.3i. Upon unloading, the reverse transforma-

tion begins with the formation of multiple variants within the fully transformed

martensitic regions as seen before in Fig. 4.2, thus, deserves the same explana-

tion. The transforming localized bands and their growth characteristics during

SIM suggest that the transformation is heterogeneous on the macroscopic scale

in Co49Ni21Ga30 alloys at low temperatures. Moreover, the spatial variation of

strains within the individual bands points out the transformation heterogeneity

in the specimen at the microscopic level as well (Fig. 4.3).

4.2.2.2 Region II - Increasing stress hysteresis

Figure 4.4: Pseudoelastic response and variation in the microstructure during

forward and reverse transformation in Co49Ni21Ga30 [001]-oriented crystal at 120

◦C. Differently oriented arrows indicate the coexistence of two different types of

habit-plane variants. The interfaces marked by the downward pointing arrows

in Figs. 4.4b and d were consumed during the growth of the other dominant

martensite plate.

In order to gain insight into the change in stress hysteresis at 120 ◦C (end

of region I, Fig. 4.1), in-situ observations were made and representative micro-

graphs are shown in Figure 4.4 along with the PE response at 120 ◦C. The forward

transformation is initially characterized by the formation of many variants (phase

boundaries) with the progression of loading as indicated by arrows, but further

growth of martensite is achieved by the propagation of a single interface (pointed

out by the arrow in Fig. 4.4c) consuming the others as indicated in Figs. 4.4b-e.

In addition, each wave pattern in the stress-strain curve corresponds to the ap-

pearance and coalescence of new interfaces with the moving phase front. Further

loading results in the growth of martensite by transforming remaining pockets

of austenite regions (Fig. 4.4f) and also in a considerable strain hardening. The

reverse transformation is accompanied by the activation of numerous interfaces

as it was discussed earlier for Figs. 4.2 and 4.3 and finally the sample retained

its original structure at the minimum stress level (Figs. 4.4g-k). The increase

in stress hysteresis at 120 ◦C (Fig. 4.1) can be associated with the energy dissi-

pated in the form of frictional work that is spent overcoming the resistance to

the motion of the dominant interface. One would expect a high resistance to the

propagating inter-phase boundary in this case because of the increased amount

of interacting events with the other interfaces as seen in Fig. 4.4.

Unlike in Fig. 4.4, the images in Figure 4.5 show that the nucleation and

growth of SIM in the sample at 200 ◦C is characterized by the simultaneous

formation and growth of multiple variants, which is an indicative of a quasi-

homogeneous transformation behavior in SMAs Abeyaratne & Knowles (1993);

Shaw & Kyriakides (1995). Because of the significant increase in test temper-

ature (200 ◦C) and raise in interacting events emanating from simultaneously

propagating variants (Figs. 4.5b-d), continuation of the transformation requires

an increase in the applied stress. This brings about an ascending as well as

a wavy nature of stress-strain curve as seen from the figure. Further loading

resulted in a change in the material contrast due to significant change in the

topography (Figs. 4.5e-f), which indicates the progression of transformation and

growth of martensite regions. Upon unloading, the images in Figs. 4.5h-i demon-

strate hardly any changes in the martensite morphology until point jis reached

on the curve suggesting difficulty for the reverse transformation. The latter also

Figure 4.5: Evolution of microstructure with the forward and backward stress-

induced phase transformations in Co49Ni21Ga30 [001]-oriented single crystal at

200 ◦C.

implies the occurrence of detwinning of twinned martensite variants, thus, a large

stress hysteresis is recorded for this test temperature. Since the transformation

is nearly homogeneous, it is hard to notice any events at the microscopic level

that are taking place at the intermediate strain levels between the marked points

on the curve. Further unloading led to the material to retrieve its original mi-

crostructure in the austenite state (Fig. 4.5j-k).

4.3 Effect of Training on the Pseudoelasticity

As the SME and PE phenomena are often repeated in several applications that

utilize SMA devices, it is necessary to understand the trainability, reproducibil-

ity and stability of these properties, and which can be done by adopting several

training methods. Most training procedures are based on the repetition of trans-

formation cycles from the parent to preferentially oriented martensite. Some of

the examples are: repetition of one-way memory effect, temperature cycles at a

constant strain or stress, and pseudoelastic cycling. This is generally observed

that the training will result in complete recoverability and/or improved shape

memory properties and/or TWSME. This is achieved by the formation of com-

plex dislocation arrays which have the lowest energy in the repeatedly induced

’trained’ martensite variants. In addition, the increased dislocation density will

suppress further slip deformation by raising the strength of the matrix. This in

turn generates martensite at lower stress levels due to the favorable stress fields

around these defects leading to TWSME phenomenon or complete recoverability.

The schematic in Figure 4.6 shows the two sequences of experiments namely

Block 1and 2that were carried out on two different companion Co49Ni21Ga30

specimens. The isostress thermal cycles and a single loading-unloading cycle at

each temperature step at Level 1are referred as Type I and II training proce-

dures, respectively. In the figure, Type II training experiments at Level 2will

provide an insight into the pre-transformation history effects in terms of repro-

ducibility, recoverability and stability of pseudoelastic behavior in Co49Ni21Ga30

alloys. Moreover, the instances of Type I and II training experiments can be seen

in Figs. 3.8 and 3.13 on page 37 and 43 in Chapter 3, respectively.

Figure 4.7 shows a strong temperature dependence of stress-strain response

of a Type I trained Co49Ni21Ga30 [001]-oriented crystal. The stress-strain loading

path after the initial linear elastic deformation exhibits a typical plateau type re-

sponse at low temperatures, (<120 ◦C), while higher temperatures bring about

an ascending stress-strain curve with a pronounced strain hardening. This be-

havior is similar to that observed in as-grown crystals in Figs. 3.13,4.2 and 4.5,

thus, a multi-variant martensite morphology is schematically depicted in Fig. 4.7

at elevated temperatures (200 ◦C). The multi-variant morphology offers higher

resistance to the propagating interface because of increased variant-variant in-

teractions (Fig. 4.5) during the progression of SIM transformation giving rise to

an ascending type stress-strain response. Similarly, based on the in-situ observa-

tions made on an as-grown alloy (see Figs. 4.2 and 4.3), a schematic illustrating

Figure 4.6: Schematic illustration of Type I and II training procedures that were

adopted for this study. The first appearance of residual strains in a PE curve

determined the maximum test temperature Tmax.

fewer preferred variants is indicated in Fig. 4.7 for low temperature regimes as

large transformation strains and a plateau type loading characteristics are more

pronounced.

Figure 4.8 shows the pseudoelastic response of a Type II trained Co49Ni21Ga30

[001]-oriented crystal as well as that of an as-grown crystal for comparison. It is

clear from the figure that training had a significant influence on the mechanical

behavior especially the reduced transformation strains at low test temperatures.

This is explained by recording the microstructures at various stages of loading-

unloading path of the curve at 40 ◦C obtained for Type II trained crystal as

shown in Figure 4.9.

The curve in Fig. 4.9 shows that loading of the specimen resulted in a near

plateau region of A-C and is followed by a pronounced strain hardening in the C-

D portion. The microstructure evolution in A-D region is similar to the one that

was observed during training at high temperatures (200 ◦C, Fig. 4.5). Except

that deformation to points Cand Dled to the transformation of the encircled

Figure 4.7: Pseudoelastic response of Type I trained Co49Ni21Ga30 single crystal

as a function of temperature. The schematics illustrate the expected martensitic

morphology and potential internal twinning of variants is not shown Dadda et al.

(2006b).

area of the sample, which was not observed in earlier results shown in Figs. 4.2

and 4.5. Further loading beyond point Dchanges the progression (slope) of

the stress-strain curve resulting in a second plateau (D-E). This is pertaining to

inelastic deformations such as MR and/or detwinning of martensite, which hinder

the reverse transformation resulting in residual strains as seen in the figure. This

is deformation induced martensite stabilization and can be realized from the

microstructures recorded during unloading that hardly evolve in the specimen

from point Eto G. When the stress reaches its minimum value, the sample

recovers only 1 % strain and the rest was recovered completely after heating the

sample to 100 ◦C demonstrating the typical SME phenomenon. The latter is

expected when the stabilized martensite undergoes MR or detwinning processes.

The in-situ microscopy results at high temperatures on Type II trained crystals

are not reported here as the microstructure is stabilized and no significant changes

in martensite morphology were noticed. The differences in the PE behavior of

Figure 4.8: Pseudoelastic response of Type II trained Co49Ni21Ga30 [001]-oriented

single crystal as a function of temperature in comparison with those obtained from

as-grown crystal.

Type I and II trained crystals (Fig. 4.7 and 4.8, respectively) can obviously

be linked to the type of training and a possible small variation in the chemical

composition of the samples that were used. The presence of low stress levels of

only 200 MPa (Fig. 3.8) and higher stresses levels above 600 MPa (Fig. 3.13) in

Type I and II training, will evolve dislocation structure and their distribution

in the material differently as shown in TEM images in Figures 4.10 and 4.11,

respectively. The relatively high density of dislocated regions in Type II trained

crystal (Fig. 4.11) offer more number of nucleation sites for the onset of numerous

variants resulting in a multi-variant morphology and whose simultaneous growth

will lead to homogeneous type transformation as seen in Fig. 4.9. This also

altered the transformation strains in Type II trained crystal in the whole range

of operating temperatures.

Figure 4.12 shows the evolution of stress hysteresis with temperature and its

dependency on the type of training. Interestingly, the same trend prevails in the

stress hysteresis regardless of the condition of the sample. However, in the case of

Figure 4.9: Microstructural evolution during stress-induced phase transformation

in the Type II trained Co49Ni21Ga30 [001]-oriented crystal at 40 ◦C.

Figure 4.10: Bright field image showing the microstructure of Type I trained

Co49Ni21Ga30 [001]-oriented single crystals.

Figure 4.11: TEM image showing the dislocations in Type II trained Co49Ni21Ga30

[001]-oriented single crystals.

Figure 4.12: Effect of the training on the evolution of stress hysteresis with test

temperature in as-grown Co49Ni21Ga30 [001]-oriented single crystals.

trained crystals; the region IIT rained starts at slightly higher temperatures of about

180 ◦C and a new region IIIT rained is defined as the stress hysteresis decreases.

The former suggests that the detwinning seems to be delayed in trained samples,

which is in good agreement with earlier TEM studies Dadda et al. (2008) where

the detwinning was partially suppressed in a pre-fatigued Co49Ni21Ga30 [123]-

oriented crystal due to the increased amount of dislocations during the cycling.

Figure 4.13: Evolution of critical stress levels for both forward (solid lines, full

symbols) and reverse (dashed lines, open symbols) transformations with the train-

ing in [001]-oriented Co49Ni21Ga30 single crystals.

Moreover, the decreasing trend of stress hysteresis values observed for region

IIIT rained in Fig. 4.12 can be related to the decreasing and increasing values of

σF or

cr and σRev

cr , respectively above 325 ◦C as shown in Fig. 4.13. The deviation

of σF or

cr from its linear CC-curve, can be attributed to plastic yielding of the

austenite, which now occurs prior to the SIM Dadda et al. (2006b); Sehitoglu

et al. (2000). This fits to the occurrence of similar deviations observed for [123]

and [235]-oriented crystals in the range of 650-800 MPa in Fig. 3.15 on Page 45

clearly supporting the onset of yield in Co49Ni21Ga30 alloys via slip deformation.

The increase in σRev

cr (Fig. 4.13) is linked to the incomplete phase transforma-

tion, thereby, untransformed regions of austenite help the onset of the reverse

transformation.

The increase in stress hysteresis in region II is connected to the dominant

detwinning and associated martensite stabilization, which is in fact seen as the

shift of the unloading curve to lower stress levels, i.e. the decrease in σRev

cr in

Fig. 4.13. The occurrence of this mechanism at elevated temperatures can be

linked to the easier mobility of martensite twin boundaries due to high thermal

activation in Co49Ni21Ga30 alloys.

In addition, martensite stabilization due to symmetry conforming-short range

ordering (SC-SRO), especially in B2 ordered alloys that undergo thermoelastic

martensite transformations should not be ruled out in the present case. Owing to

the diffusionless nature of martensitic transformation, the resultant martensite

inherits the high temperature B2 crystal symmetry, which is now thermody-

namically unstable as this is different from the L10symmetry of martensite in

Co49Ni21Ga30 alloys. The restoration of the L10symmetry or ordering can be

achieved via atomic rearrangement within the sublattice of the imperfectly or-

dered martensite, i.e. SC-SRO, which is similar to the atomic diffusion process

in ordered usual intermetallics. This is the only way that a martensite can lower

its free energy without altering the average martensite structure (equilibrium

phase) Ren & Otsuka (1997). This inhibits the reverse transformation initially,

i.e. stabilizes the martensite, resulting in an increase in the critical transforma-

tion temperature (As) for the martensite to austenite (Figure 4.14). Moreover, a

raise in Astemperatures is thermodynamically equivalent to a decrease in σRev

cr .

This behavior, in fact, can be observed from the PE curves at 120 ◦C shown in

Fig. 4.8 before and after training.

Furthermore, the current TEM investigations also provide quintessential ev-

idence of SC-SRO in Co49Ni21Ga30 alloys. The martensite band-like contrast

marked with a white arrow in Fig. 4.15 in the B2-matrix, whose selected area

electron diffraction pattern confirms the B2 structure, indicates the existence of

a ’faulted’ (ghost like martensite) SRO symmetry in the cubic phase and was

termed as microstructure memory by Otsuka et al. Otsuka & Ren (2001). This

Figure 4.14: Thermograms of Co49Ni21Ga30 alloy under as-grown (dashed) and

Type II trained (solid) condition. The method of intersecting slope lines has

been adopted to determine transformation temperatures. The dashed arrows

represent the shift of transformation temperatures to higher temperatures as a

result of training while the solid ones show the direction of cooling and heating

paths.

phenomenon has been reported for off-stoichiometric Au-Cd alloys as a manifes-

tation of SC-SRO Otsuka & Ren (2001).

Note that the SC-SRO is associated with the diffusion of atoms at the sub-

lattice level that may involve mobile point defects such as vacancies, anti-site de-

fects or both (triple defects, TDs). And the deviation from stoichiometry brings

about a high density of point defects in any ordered system Ren & Otsuka (1997).

One would expect the same in the present Co-21Ni-30Ga (at. %) system as it

deviates from stoichiometry and also possesses ordered B2-austenite and L10-

martensite structures. Although there is no direct experimental evidence of these

point defects, the resultant stabilization effects can easily be realized from the

macroscopic and microscopic observations made in the present study. For ex-

ample, the shift of the unloading curve to lower stress levels (Fig. 4.13), which

Figure 4.15: Bright field TEM image of a trained Co49Ni21Ga30 [001]-oriented

crystal showing the stabilized martensite needles pinned at the secondary phase

γparticles as marked out by a black arrow. The white arrow indicates a ghost

like martensitic structure. The inset displays the corresponding selected area

diffraction pattern (SADP) confirming the B2 crystal structure of the matrix.

means martensite stabilization, is observed only at elevated temperatures (region

II in Fig. 4.13). This implies that the mobilization of vacancies due to thermal

activity is increased speeding up the diffusion process, thereby the stabilization

phenomenon. This will also increases the number interaction events with linear

(dislocations) and planar (interphase or intervariant boundaries) defects bringing

about Cottrell-type pinning atmospheres around these defects, strongly affect-

ing the mobility of propagating interfaces. This enhances further diffusion (on a

rather large distance) of point defects migrating to interfaces because of energet-

ically more favorable positions in the vicinity of interfaces Kustov et al. (2004b).

This can lead to a drop in the local free energy of martensite interfaces stabiliz-

ing the martensite plates, which is called kinetic pinning-induced stabilization by

Kustov et al. in their recent work Kustov et al. (2004a). Presence of such pinned

interfaces require a higher chemical driving force for the reverse transformation

to proceed, thus, decreased σRev

cr values have been recorded in the current study.

Moreover, during the forward transformation, as soon as the pinning occurs

and the local thermoelastic balance is shifted to higher stress levels due to the

raise of the friction stress acting on the boundary, another martensite plate can

be easily nucleated as is evident from microscopy (point e, Fig. 4.2) and DIC

(points f-g, Fig. 4.3) results. This mechanism seems to be more pronounced at

high temperatures due to the aforementioned diffusion mechanisms that involve

point defects, which immobilizes propagating interfaces. This rationalizes the

formation of a high number of interphase boundaries in Co49Ni21Ga30 alloys at

elevated temperatures in region II (Figs. 4.4 and 4.5). In order to verify the tem-

perature dependent microstructural changes, a companion sample was tested for

one thousand pseudoelastic cycles repeatedly invoking a single phase-front and its

growth during SIM at 40 ◦C. When the sample temperature was increased to 200

◦C in the subsequent PE test, the specimen exhibited new interphase boundaries

and their growth. This experiment suggests that the pinning of moving phase

fronts is inherent to Co49Ni21Ga30 alloys at elevated temperatures, which will lead

to the formation of multiple variants.

As the coherent inter-phase boundaries are accompanied by the generation

of defects such as dislocations during SIM transformation Otsuka & Wayman

(1999), this increases the dislocation density and their distribution changing the

microstructure of the original material. The defected regions and corresponding

stress fields in the matrix nucleate the same oriented variants in subsequent phase

transformations. Thus, the stable microstructure and favorable internal stresses

acquired by the trained crystals improved the recoverability allowing the sam-

ple to exhibit pseudoelasticity in the temperature window of 400 ◦C (Figs. 4.7

and 4.8). Moreover, as the self-accommodating martensite is useful in applica-

tions that require energy absorption and vibration mitigation, the current results

suggest that Co49Ni21Ga30 alloys have the potential for such applications involv-

ing elevated temperatures and higher stresses. As many SMA applications often

involve a large number of loading and unloading cycles, it is imperative to under-

stand the cyclic deformation behavior of Co49Ni21Ga30 alloys for their successful

usage. Thus, the next chapter will deal with cyclic stability of these alloys at

high temperatures.

4.4 Chapter Summary

In this chapter, the effects of repeated stress-induced phase transformation on the

PE behavior of as-grown Co49Ni21Ga30 [001]-oriented crystals were analyzed as a

function of temperature under compression. The results revealed that dislocation

activity, detwinning, point defects, SC-SRO and the associated martensite stabi-

lization are the determining factors in the evolution of microstructure as well as

the PE characteristics in Co49Ni21Ga30 alloys. The main findings of this chapter

can be summarized as follows:

1. The samples irrespective of their initial condition exhibit the same trends in

the stress hysteresis evolution, yet, a strong dependency on test temperature

prevails. A temperature region with a constant stress hysteresis is recorded

below 120 and 180 ◦C for as-grown and trained crystals, respectively. Above

these temperatures stress hysteresis increases monotonically in both cases,

which is attributed to the ease of detwinning at elevated temperatures due to

the high mobility of twin boundaries and the resultant shift of the unloading

curve to lower stress levels.

2. During the training, the kinetic pinning-induced martensite stabilization

is more pronounced at elevated temperatures due to high thermal-activity,

which provides room for diffusion of point defects facilitating the pinning

of propagating interfaces. This has resulted in the formation of multiple

variants during the training process beginning from 120 ◦C giving way to the

formation of self-accommodating martensite, thus the alloy exhibits lower

transformation strains and serrated plus ascending stress-strain response.

3. The in-situ observations revealed that the nucleation and growth charac-

teristics of SIM transformation on the microscopic as well as macroscopic

scale are heterogeneous as the martensite growth proceeds via single prop-

agating interface in room-temperature - 120 ◦C range and becomes quasi-

homogeneous at elevated temperatures (>120 ◦C), which remained con-

stant even after training in the Co49Ni21Ga30 [001]-oriented crystal at all

test-temperatures.

4. In the trained [001]-oriented single crystals, the stress required for the on-

set of yield of austenite is as high as 800 MPa at room-temperature, which

is 20 folds higher than the critical stress needed for SIM. This is a nec-

essary condition for obtaining large transformation strains by restricting

the slip activity. This has in fact facilitated the samples to exhibit perfect

pseudoelasticity at temperatures as high as 425 ◦C bringing about a large

pseudoelastic window of more than 400 ◦C. This is remarkably larger than

in NiTi-based, Cu-based and NiMnGa alloys marking Co49Ni21Ga30 alloys

as promising candidate material for numerous applications involving high

stresses and elevated temperature.

Chapter 5

Cyclic Stability of Co49Ni21Ga30

Single Crystals

5.1 Introduction

In this chapter, experimental results about the cyclic deformation behavior of

single crystalline Co49Ni21Ga30 SMAs are presented for compressive loading con-

ditions at elevated temperatures. In Chapter 4, Co49Ni21Ga30 alloys have been

identified as the promising HTPM that can undergo a stress-induced phase trans-

formation at temperatures as high as 425 ◦C with a complete shape recovery of at

least 3 % strain. However, their success depends on the complete understanding of

their cyclic stability, especially at high-temperatures. The results demonstrated

a poor cyclic stability of as-grown crystals above 200 ◦C. Thus, appropriate

heat-treatments were conducted to minimize the functional degradation, espe-

cially at elevated temperatures (>200 ◦C) as dislocation slip characteristics in

these alloys can be modified by incorporating the disordered γ-phase (A1) and/or

ordered γ0-phase (L12) in the ordered β-matrix (austenite, B2). In addition, the

high strength, relatively low density and good corrosion resistance facilitate the

utility of Co49Ni21Ga30 alloys in various applications.

Moreover, these alloys are also considered as MSMA candidates owing to their

natural ferromagnetism Craciunescu et al. (2002); Oikawa et al. (2001); Sato et al.

(2003) that can demonstrate MSME as mentioned in Section 1.8 of Chapter 1.

This phenomenon can occur at frequencies of the order of 1 kHz Marioni et al.

(2003), and thus stable cyclic behavior is paramount for the envisaged applica-

tions of MSMAs. Upon cyclic loading of conventional SMAs, stress-induced dis-

location motion results in degradation of the PE properties. Similarly, magneto-

plasticity could be a limiting factor for MSMAs since the MSME involves the

motion of twinning dislocations, hence magnetic-field induced transformations

may experience the same cyclic degradation as in the case of stress-induced phase

transformations M¨ullner et al. (2003).

Cyclic deformation at ambient temperatures resulted in rapid accumulation of

irrecoverable strains in the [123]-oriented crystals. However, after a few cycles the

samples demonstrated cyclic stability with fully recoverable transformation. By

contrast, the [001]-oriented crystals displayed excellent cyclic stability with hardly

any change in stress-strain characteristics. The use of single crystals promotes

a systematic bias of operant deformation mechanisms (martensite variant reori-

entation, detwinning, and dislocation slip) and their association with the cyclic

stress-strain response (CSSR). The present results demonstrate that slip defor-

mation accompanying the phase transformation and martensite stabilization play

a major role in determining the cyclic transformation behavior. Macroscopically,

dislocation slip and the resultant stabilized martensite result in the accumulation

of residual strain with cycling and the corresponding internal stress fields alters

the critical transformation stress levels softening the CSSR.

5.2 Cyclic Stress-Strain Response at Ambient

Temperatures

Figures 5.1 and 5.2 present the cyclic PE response of the [001] and [123]-oriented

samples, respectively. It is obvious from the data that the cyclic stress-strain re-

sponses are significantly different from each other. The compression behavior of

the [001]-oriented crystal in Figure 5.1 remains relatively unchanged with cycling,

i.e. it displays a constant transformation stress and stress hysteresis typically ob-

served upon activation of a single martensite variant. By contrast, cyclic loading

along the [123] orientation decreased the transformation stress by about 20 %

while increasing the stress-strain slope as shown in Figure 5.2. As the critical

Figure 5.1: Cyclic stress-strain response at a constant maximum strain of 2.5

% in Co49Ni21Ga30 [001]-oriented crystal at ambient temperature Dadda et al.

(2008).

stress for the reverse transformation remained unchanged, the decrease in trans-

formation stress for the forward transformation alters the stress hysteresis from

cycle to cycle until it reaches saturation (Fig. 5.2). The instability in the cyclic

behavior of the [123]-oriented crystal is attributed to the dislocations and their

associated internal stress fields that help the transformation to occur at lower

stress levels in subsequent cycles.

A quantitative measure of cyclic degradation resistance of a particular orien-

tation is the permanent strain at a given cycle number. Therefore, permanent

strains (P S) as defined in Fig. 5.2 are plotted as a function of number of cycles in

Figure 5.3. Fig. 5.3 demonstrates that the magnitude of P S in case of the [001]

orientation increases slightly and reaches a value of only 0.1 % after 1000 cycles.

By contrast, P S in the [123] orientation is accumulated rapidly in the early stages

of cycling (1-50 cycles) and saturates after about 50 cycles at 0.9 %. Fig. 5.3 also

shows the variation of stress hysteresis (∆σ) with the number of cycles, the mag-

nitude of which decreases rapidly from 60 to 35 MPa in the [123] orientation, a 40

Figure 5.2: Cyclic stress-strain response at a constant maximum strain of 2.5 %

in Co49Ni21Ga30 [123]-oriented crystals at ambient temperature. The dashed lines

in the first cycle indicate the approach adopted to calculate the critical stress for

the forward transformation Dadda et al. (2008).

% reduction reaching saturation in about 50 cycles. Thus, the damping capacity

of the [123]-oriented crystal is reduced initially but quickly reaches a steady state.

The results demonstrate that prior training is an effective means to stabilize the

PE characteristics in Co49Ni21Ga30 alloys. The small change in ∆σfrom 15 to

13 MPa with cycling in the [001]-oriented sample is an indication that only few

dislocations are generated upon cyclic loading. Thus, interaction of dislocations

with moving phase fronts and stabilization of martensite is less pronounced in

this case.

The [001]-oriented crystal demonstrates a high resistance to cyclic degradation

(Fig. 5.1), as dislocation slip is curtailed in this orientation due to zero Schmid

factor(cf. Table 3.2). By contrast, the stress-strain characteristics of the [123]-

oriented crystal evolves with cycling (Fig. 5.2). In the first phase of cycling (cycles

1 to 50), a dual phase austenite-martensite microstructure develops (Fig. 5.4) at

the end of loading as the strain amplitude chosen is less than the expected maxi-

Figure 5.3: Accumulation of permanent strains, P S, and evolution of stress hys-

teresis, ∆σ, with the number of cycles in [001] and [123] oriented Co49Ni21Ga30

single crystals at ambient temperatures Dadda et al. (2008).

mum transformation strain values for the [123] orientation (see Table 3.2). Upon

unloading, the specimen will revert back to the austenite with a small fraction of

stabilized residual martensite due to the ease of dislocation slip in the [123] orien-

tation because of the non-zero Schmid factor (Table 3.2). As a result, permanent

strains accumulate in each cycle and a stable dual phase microstructure is devel-

oped during cycling as recorded by TEM in Fig. 5.4. The strong internal stress

fields associated with the microstructure promote and control the transformation.

In other words, these residual or stabilized martensite regions (Fig. 5.4) act as

pre-existing local nucleation sites for the transformation, lower the critical stress

levels for the transformation in subsequent cycles, and thus, govern the evolution

of the PE characteristics. As a result, the overall flow stress of the loading curve

is altered in subsequent cycles causing a considerable amount of cyclic soften-

ing until the material behavior reaches a saturation point as seen in Fig. 5.2.

Cyclic saturation will be reached when the generation of additional defects be-

comes negligible, and thus, the volume fraction of retained martensite remains

Figure 5.4: TEM images showing residual martensite after cyclic loading in

Co49Ni21Ga30 single crystals with [123] orientation. The pinned martensite in

both cases appears to have strong stress fields as indicated by the contrast change

at the martensite-austenite interface and substantial dislocation activity is also

evident Dadda et al. (2008).

constant. When such a stable microstructure is induced due to repeated cycling,

the material begins to exhibit a fully recoverable transformation (Fig. 5.2).

In addition, the long-range stress fields associated with the increase in dislo-

cation density during cycling promote multiplicity of martensite CVPs. Conse-

quently, the growth of martensite will become more difficult increasing the trans-

formation stress-strain slope during cycling as seen in Fig. 5.2. Moreover, the

increased dislocation density seems to suppress detwinning as a twinned marten-

site morphology is observed in the cyclically deformed sample in Figure 5.4. This

will increase recoverability due to the substantial back stresses accommodated by

the internally twinned martensite, which assist the reverse transformation. Thus,

despite the initial changes in the PE behavior, the resistance to cyclic degradation

is improved after some initial training cycles.

Based on the experimental results presented herein and theoretical values of

RSSFs and Schmid factors for slip deformation shown in Table 3.2 on page 50 in

Chapter 3, it can be concluded that single crystals with low RSSF, i.e. unfavor-

able orientation of the martensite variants with respect to the applied stress state,

and large Schmid factor, i.e. a favorable orientation of the slip system, demon-

strate a large stress hysteresis, cf. the [123] orientation. In turn, the large stress

hysteresis results in rapid evolution of cyclic stress-strain response, but reaches a

steady state in terms of PE behavior after few initial cycles. On the other hand,

the [001] orientation with large RSSF and zero Schmid factor exhibits constant

PE characteristics through out cyclic loading. Therefore, a thorough study to un-

derstand the CSSR in this orientation at elevated temperatures has been carried

out and presented in the following sections.

5.3 Cyclic deformation behavior at elevated tem-

peratures

Figure 5.5 show the CSSR of Co49Ni21Ga30 as-grown and untrained [001]-oriented

crystal at different temperatures with a constant strain range(∆). The ∆was

chosen until an apparent elastic deformation of SIM sets in the curve (Fig. 3.10).

It is clear from the figure the crystal exhibit stable CSSR without undergoing

any cyclic degradation at temperatures below 100 ◦C, which is similar to that

observed for [001]-oriented crystals with a strain range of 2.5 % strains in Fig. 5.1.

However, the material exhibits a slight decrease in transformation stress levels

during cycling at 100 ◦C, which can be connected to the favorable internal stress

fields around the transformation defects. On the other hand, the CSSR at 200

◦C degrades rapidly in terms of accumulation of residual strain (res) of about

1 %, and the large drop in ∆σand σF or

crit values resulted in a small stress-strain

hysteresis loop at the 1000th cycle as shown in Fig. 5.5 for 200 ◦C.

Since Type II training has resulted in a stable microstructure (Fig. 4.9), one

would expect a stable CSSR in Type II trained crystals. Figure 5.6 shows the

CSSR of Type II trained crystal at 200 and 300 ◦C. As anticipated, Fig. 5.6 shows

a stable CSSR that is achieved within the first 50 cycles, during this period

a relatively lower degree of degradation took place compared to that recorded

Figure 5.5: Cyclic stress-strain response of untrained as-grown Co49Ni21Ga30

[001]-oriented crystal at different temperatures.

Figure 5.6: Cyclic stress-strain response of Type II trained as-grown Co49Ni21Ga30

[001]-oriented crystal at different temperatures.

Figure 5.7: Normalized residual strains (res/T) with the number of cycles in

as-grown Co49Ni21Ga30 [001]-oriented crystals at different temperatures.

for the untrained crystal at 200 ◦C in Fig. 5.5. Finally, the material degraded

completely without undergoing any SIM transformation at 300 ◦C resulting in

linear stress-strain hysteresis loops after 500 cycles as seen in Fig. 5.6. This is

further clarified in Figure 5.7 by plotting the normalized residual strains, res/T

a dimensionless quantity, with the number of cycles. Fig. 5.7 demonstrates that

the res/Tvalues accumulates rapidly and reaches a saturation within the first

few cycles for all the crystals shown here and the magnitude of which is a clear

measure of the degree of cyclic degradation in Co49Ni21Ga30 alloys. The material

is completely degraded in terms of its functional properties when res/Treaches

unity, as it happened for the case of as-grown crystal at 200 ◦C and the trained

crystal at 300 ◦C, which means a complete suppression of SIM transformation is

taking place in the material upon cycling.

However, the residual strains accumulated in the as-grown crystal shown in

Fig. 5.7 were recovered upon heating the sample to 400 ◦C but some of them

were retained in the specimen, when it was cooled down to room-temperature.

This was not the case with the trained as-grown crystal, which was cycled at

Figure 5.8: A bright field TEM image of Type II trained Co49Ni21Ga30 [001]-

oriented crystal after 1000 cycles at 300 ◦C shown in Fig. 5.6.

300 ◦C, thus, subsequent TEM investigations were made on this specimen to

understand the deformation mechanisms and evolution of the microstructure.

Figure 5.8 shows the TEM image of the fatigued sample at 300 ◦C and reveals

the formation of fine precipitates (γ-phase) in the matrix. From the particle

analysis of the dark field image shown in Fig. 5.9, the volume fraction of γphase

was 35-40 %. Moreover, Figure 5.10 shows a microstructure of a sample heat-

treated for 36 hours at 300 ◦C demonstrating a high density of γprecipitates in

the βmatrix. Note that the fatigue test at 300 ◦C shown in Fig. 5.6 took 36

hours for the completion. These studies point out that the β-matrix of as-grown

Co49Ni21Ga30 crystals is unstable at elevated temperatures and decomposes into

non-transformable γ-phase.

The cyclic behavior at elevated temperatures (Figs. 5.5,5.6 and 5.7) suggest

that the wider the stress hysteresis the faster the cyclic degradation, which is sim-

ilar to that observed for [123]-oriented crystals discussed earlier. Therefore, the

crystals operating in region II (Fig. 4.12 on page 66 in Chapter 4) degrades rapidly

under cyclic loading conditions. This is consistent with the aforementioned crite-

Figure 5.9: The corresponding dark fields image shown in Fig. 5.8. The contrast

has been reversed to better display the γparticles in the matrix.

Figure 5.10: A general microstructural morphology of Co49Ni21Ga30 sample heat-

treated for 36 hours at 300 ◦C and air cooled.

rion for the occurrence of cyclic degradation based on stress hysteresis and the ori-

entation. The large hysteresis in region II was associated with the high dislocation

density, which is needed to dissipate the elastic stored energy through the relax-

ation of coherency stresses at the inter-phase boundaries, detwinning, diffusion of

point-defects to interfaces pinning their propagation and the incoming marten-

site stabilization. Under these circumstances, any SMA material subjected to

repeated transformations, especially to cyclic loading-unloading conditions, will

cease to exhibit any functional properties. Furthermore, the decomposition of the

material into other non-transformable phases such as γat elevated temperatures

added to the effect, suppressing the transformation completely as seen in Fig. 5.6

at 300 ◦C. This has offered a motivation to carry out several aging treatments

based on the information provided elsewhere by Schlagel et al. (2004), and the

results that demonstrate improved cyclic stability are discussed as follows.

Figure 5.11 shows micrographs of heat treated samples, revealing the distribu-

tion of γparticles in the matrix. As expected the samples aged for longer period,

i.e. 900 ◦C for 24 hours, possess higher volume fraction of γof about 17 vol. %

(Fig. 5.11b), while the other sample contains 5 vol. % secondary phase (γ) in the

matrix (Fig. 5.11a).

Figure 5.11: Micrographs of solutionized Co49Ni21Ga30 single crystal samples

heat-treated for (a) 4 hours at 1100 ◦C and water quenched and (b) 24 hours

at 900 ◦C and water quenched. Solutionization was conducted at 1200 ◦C for 4

hours followed by water quenching.

The pseudoelastic behavior of Type II trained Co49Ni21Ga30 aged samples and

its dependency on the heat-treatments are emphasized with the aid of CC-curves

shown in Figure 5.12. Type II training has been employed in order to stabilize the

pseudoelastic cyclic behavior as seen before in the case of as-grown crystals. In-

terestingly, the deviation from linearity in the stress range of 650-750 MPa clearly

indicates the onset of plasticity in the material, which in fact limits pseudoelas-

ticity and its temperature range in Co49Ni21Ga30 alloys. Thus, the suppression of

slip deformation via austenite strengthening is a necessary condition to obtain a

large PE window in these alloys. Moreover, the dependency of Mstemperatures

at zero stress levels, PE window and CC-slopes can be attributed to the change

in chemical composition of austenite due to the precipitation process, and the

results are summarized in Table 5.1.

Figure 5.12: Clausius-Clapeyron curves for different heat-treated Co49Ni21Ga30

[001]-oriented samples after Type II training.

Table 5.1 shows that the higher the volume fraction of γ-phase the higher the

CC-slope, which is linked to strengthening of austenite. This will also change the

chemical composition of the matrix as the precipiation requires Co-depletion to

form the Co-rich γphase, which rationalizes the decrease in Mstemperatures to

-75 ◦C in the case of material with the high amount of γfrom -5 ◦C in the case

of as-grown or solutionized case (Table 5.1).

Table 5.1: Clausius-Clapeyron slopes, volume fraction of γphase, Mstemper-

atures and pseudoelastic temperature window for Type II trained Co49Ni21Ga30

[001]-oriented single crystals with different initial heat-treated conditions.

Type II Trained

Co49Ni21Ga30

Init Cond.

CC-slope

(MPa/◦C)

Vol Frac

γ-phase (%)

Ms(◦C) PE-window

(◦C)

As-grown 2 5 -5 400

1200 ◦C 4hrs 2 0 -5 >300

1100 ◦C 4hrs 2.3 7 -25 325

900 ◦C 24hrs 2.7 17 -75 325

Figure 5.13: Cyclic stress-strain response of heat-treated Co49Ni21Ga30 [001]-

oriented single crystals at 300 ◦C after Type II training.

Figure 5.13 shows the pseudoelastic cycling results of heat-treated and Type II

trained samples at 300 ◦C. The figure clearly demonstrates that the sample heat

treated at 900 ◦C for 24 hours reaches a stable cyclic behavior after some degree

of degradation within the first few cycles. The stable behavior is attributed to the

increase in matrix strength due to the high amount of secondary phase particles

Figure 5.14: Normalized residual strains at the 1000th cycle indicating the limits

of cyclic stability in Co49Ni21Ga30 [001]-oriented single crystalline shape memory

alloys.

in the material, which might have curtailed the dislocation activity during the

cycling.

The analysis about the cyclic stability of Co49Ni21Ga30 [001]-oriented sin-

gle crystals under different thermomechanical conditions is summarized in Fig-

ure 5.14. This was done by plotting the normalized residual strain at the 1000th

cycle, 1000

res /T, as a function of temperature. This figure provides the information

about the temperature ranges in which the Co49Ni21Ga30 alloys can be applied

safely with minimum cyclic degradation (since 1000

res /Tis <0.2), after some prior

thermomechanical treatments.

In addition, the material with high CC-slopes reaches the yield levels of about

700 MPa very quickly (Fig. 5.12), thus, depressing the PE temperature range.

The opposite is true in the case of those Co49Ni21Ga30 alloys with low CC-slopes.

This underlines that the strengthening of matrix in an attempt to curtail the dislo-

cation activity is pivotal to increase the PE temperature window in Co49Ni21Ga30

alloys. This can be achieved through incorporating fine coherent γ0(Ni3Ga) pre-

cipitates in the matrix by adopting appropriate heat-treatments. Recently, a two-

fold increase in transformation stress levels Co35Ni35Al30 alloy system with fine

subnanometer coherent γ0:Ni3Al precipitates has been found by our group. There-

fore, this research can be extended further by optimizing the thermo-mechanical

treatments to improve the high-temperature capability of Co49Ni21Ga30 alloys.

5.4 Chapter Summary

In this chapter, cyclic deformation behavior of Co49Ni21Ga30 single crystals at

ambient as well as at elevated temperatures has been examined and the important

findings can be summarized as follows:

1. In the [001] orientation, dislocation motion is curtailed inhibiting slip due to

the unfavorable {110}<001>slip systems. Hence, [001]-oriented crystals

demonstrate near perfect pseudoelastic stress-strain behavior with excellent

cyclic stability, i.e. small frictional dissipation and negligible influence of

strain history on the cyclic behavior. The narrow hysteresis of only 15

MPa, the lack of dislocation slip and suppression of detwinning observed,

all suggest that polycrystalline aggregates with a prominent [001] texture

component are highly attractive for applications.

2. In the case of the sample with [123] orientation, dislocation activity during

the phase transformation accounts for the rapid evolution of the stress-strain

response during the early stage of cycling loading and the accumulation of

permanent strains. The stress fields of the dislocations promote the for-

ward transformation and induce cyclic softening. Dislocations impede the

reverse transformation, interact with the detwinning process and stabilize

the stress-induced martensite upon unloading.

3. After only 50 cycles, the [123]-oriented Co49Ni21Ga30 single crystal exhibited

stable cyclic behavior with fully recoverable transformation. In addition,

ease of dislocation generation, formation of multiple CVPs, detwinning and

martensite stabilization are the rationale behind the large stress hysteresis

of 70 MPa in the [123]-oriented Co49Ni21Ga30 single crystals. The resultant

high damping capacity of a polycrystalline material with a strong [123]

texture component would make the material attractive for applications in-

volving energy absorption and vibration mitigation.

4. In Co49Ni21Ga30 [001]-oriented crystal, a stable cyclic stress-strain response

is observed below 200 ◦C regardless of the initial condition of the sam-

ple. After initial thermomechanical training, the samples tested at 200 ◦C

exhibit a decrease in transformation stresses and accumulation of residual

strains initially but reach a stable response within the first few hundred

cycles. However, the as-grown samples are unstable at higher temperatures

(300 ◦C) as the β-matrix tends to decompose into the Co-rich γphase com-

pletely suppressing the SIM transformation. Consequently, a rapid cyclic

degradation occurred at elevated temperature due to the complete suppres-

sion of SIM transformation at 300 ◦C.

5. The cyclic response of Co49Ni21Ga30 [001]-oriented crystals at 300 ◦C is

improved by heat-treating the samples at 900 ◦C for 24 hours after initial

solutionization treatment at 1200 ◦C for 4 hours, which was in fact achieved

through strengthening of the matrix by incorporating fine γprecipitates.

6. The cyclic stress-strain response in the Co49Ni21Ga30 single crystals that ex-

hibit wide stress hysteresis, which is either inherent to the crystallographic

orientation or due to the operating temperature, will degrade rapidly and

reaches a saturation, while in those samples with narrow hysteresis is sta-

ble without undergoing any cyclic degradation in terms of accumulation of

residual strains and drop in observed stress hysteresis.

Chapter 6

Summary & Future Research

In the present study, the research regarding different aspects concerning newly

developed Co-base SMAs with reference to their high-temperature capability was

carried out. A thorough experimental study about mechanical and functional

properties of a Co49Ni21Ga30 and Co38Ni33Al29 (in at.%) single crystalline al-

loys was executed understanding the effects due to crystallographic orientation

and thermomechanical treatments. In particular, the deformation mechanisms

involved in the material’s stress-strain behavior during thermomechanical train-

ing was investigated; the resultant high-temperature pseudoelasticity was studied

together with the variation in its characteristic hysteresis as a function of tem-

perature. Furthermore, the effects of training on the pseudoelastic behavior were

evaluated in terms of its temperature range in correlation with the microstructural

evolution. The latter was achieved by using systematic in-situ microscopy obser-

vations at high-temperatures. This information is necessary to model the hetero-

geneous/homogeneous transformation behavior of Co49Ni21Ga30 and Co38Ni33Al29

alloys. Many of the experimental investigations summarized above, were executed

on both as-grown and thermomechanically treated material and the results are

compared in order to evaluate their mechanical and functional performance in

order to develop new Co49Ni21Ga30 and Co38Ni33Al29 high-temperature pseudoe-

lastic materials.

The [001] and [110] oriented Co38Ni33Al29 single crystals subjected to high

cooling rates following a solutionization treatment at 1350 ◦C for 24 hours ex-

hibit large phase transformation strains of about 4.1 % under compressive stress

levels as low as 50 MPa. In the case of [110] oriented single crystals this strain

value exceeds the theoretical CVP transformation strain, indicating a significant

contribution of detwinning strains to the overall phase transformation strain.

Moreover, near-perfect pseudoelasticity above the Aftemperature was obtained

in compression tests with a maximum pseudoelastic strain of about 4.3 %. The

Co38Ni33Al29 single crystals investigated in this work demonstrate a large pseu-

doelastic window of more than 250 ◦C, good cyclic stability and trainability with

a maximum TWSME strain of 2.7%.

The TWSME strain obtained for the [001]-oriented air cooled Co38Ni33Al29

samples constitutes an evidence of the substantial role of the ductile γ-phase for

trainability in the absence of pronounced dislocation activity. Otherwise, during

thermal cycling, due to the development of plasticity in orientations that are

more favorable for the dislocation activity, an internal stress field was created;

this stress field interact with the phase transformation allowing the formation of

a preferentially oriented martensitic structures during cooling. This benefits the

formation of the TWSME in the material remembering a low temperature shape.

Therefore, the results emphasize the need for texturing polycrystalline aggregates

of the current material with an optimum γ-phase volume fraction to achieve high

performance in Co38Ni33Al29 alloys according to the application demand.

In as-grown Co49Ni21Ga30 specimens, the low critical transformation stress

due to high RSSF value, i.e. low CC-slope, high slip resistance in the austenite

due to zero Schmid factor and B2 atomic ordering allow for excellent transfor-

mation recoverability with a large PE temperature range of about 325 ◦C when

loaded in the [001] direction. Moreover, the [001]-oriented Co49Ni21Ga30 single

crystals exhibit 4.4 % transformation strains at compressive stress levels as low

as 4 MPa, and a fully recoverable 4.3 % pseudoelastic strain at low temperatures.

The thermomechanical training resulted in a stable microstructure improving the

transformation recoverability, which in turn resulted in a large PE window of 400

◦C with recoverable strain of 3 % strains in the temperature range of 40-425 ◦C.

In addition, the pseudoelasticity, especially the hysteretic behavior of the

material as a function of temperature was analyzed with the help of in-situ mi-

croscopy as this information is required to control the necessary parameters in

designing Co49Ni21Ga30 actuators that utilize the pseudoelastic phenomenon. The

Co49Ni21Ga30 [001]-oriented samples irrespective of their initial condition exhibit

the same trends in the stress hysteresis evolution, yet, a strong dependency of

hysteresis on test temperatures has also prevailed. A temperature region with

a constant stress hysteresis is recorded below 120 and 180 ◦C for as-grown and

trained crystals, respectively. Above these temperatures, the stress hysteresis

increases monotonically to a maximum of 350 MPa in both cases, which is at-

tributed to the ease of detwinning due to high mobility of twin boundaries (be-

cause of high thermal activity) and the resultant shift of the unloading curve

to lower stress levels. Moreover, the in-situ observations revealed that the nu-

cleation and growth characteristics of SIM transformation on the microscopic as

well as macroscopic scale are heterogeneous as the martensite growth proceeds

via a single propagating interface in the room-temperature to 120 ◦C range and

becomes quasi-homogeneous at elevated temperatures (>120 ◦C), which remained

constant even after training at all test temperatures (40-425 ◦C).

During the training, the kinetic pinning induced martensite stabilization is

more pronounced at elevated temperatures due to high thermal-activity, which

provides room for diffusion of point defects facilitating the pinning of propagating

interfaces. This has resulted in the formation of multiple variants beginning from

120 ◦C giving way to the formation of self-accommodating martensite. Thus the

alloy exhibits lower transformation strains and ascending stress-strain response

with serrated features at elevated temperatures. Moreover, due to the training,

the martensite structure was stabilized by the residual stress field around the

defects that were generated during the repeated transformation. As consequences,

an increase in the phase transformation temperatures (Ms) and in the slope of

the stress plateau together with a reduction in the stress for the onset of SIM

are observed. A Co49Ni21Ga30 actuator could also be useful for the production of

composite materials for shape and vibration control opening a new perspective in

many industrial applications owing to its ability to exhibit large stress hysteresis

of about 350 MPa.

In addition, the training methods that involve isothermal loading-unloading

cycles at different temperatures brought about a stable cyclic stress-strain re-

sponse (CSSR) in Co49Ni21Ga30 alloys at temperatures as high as 200 ◦C. How-

ever, at 300 ◦C the material degraded rapidly due to the precipitation of un-

transformable γ-phase and the consequently suppressing the SIM transformation

in these alloys. This phenomenon was curtailed in the heat-treated samples at

900 ◦C for 24 hours followed by water-quenching and finally a stable CSSR was

achieved at 300 ◦C. Moreover, a correlation between the size of stress hysteresis

and CSSR has been established in Co49Ni21Ga30 alloys: the samples with wide

stress hysteresis, which is either inherent to the crystallographic orientation or

due to the operating temperature, exhibit rapid degradation during the first phase

of cycling (within the first few hundred cycles) and reach a saturation, while in

those specimens that demonstrate a narrow hysteresis (<50 MPa) a stable CSSR

is observed without any cyclic degradation in terms of accumulation of residual

strains and decrease in transformation stress levels and stress hysteresis values.

Future studies could be oriented to understand the cyclic stability, fatigue

behavior and transformation reproducibility and recoverability with reference to

pseudoelastic behavior of Co38Ni33Al29 alloys at elevated temperatures, as these

issues have not been addressed so far. Further studies can be focused on the op-

timization of thermomechanical treatments of Co49Ni21Ga30 alloys in order to in-

crease the matrix strength and ductility, thereby, improve their high-temperature

capability above 400 ◦C. The experimental data acquired in this study can be

used to develop a constitutive model which is capable of simulating the shape

memory and pseudoelastic behavior of Co38Ni33Al29 and Co49Ni21Ga30 alloys.

Future work should be carried out to analyze the abilities of the proposed ap-

proach in predicting the hysteretic behavior of the material under more complex

loading conditions, such as simultaneous variation of both stress and tempera-

ture, through specific experimental tests. Furthermore, to increase the practical

usefulness of the proposed method in controlling Co38Ni33Al29 and Co49Ni21Ga30

actuators, which are usually driven by an electric current, further studies should

be carried out to improve the model with the relationship current versus temper-

ature.

One can draw SMA wires out of these alloys with sufficient amount of soft γ

phase in the material, then bring back the material to the desired microstructure

by using appropriate heat-treatments. Thus, future work should also focus on

the robust thermomechanical characterization of these alloys under tensile load-

ing conditions. Currently, some investigations that include analysis of tension-

compression asymmetry are underway. It is also found that tension brought

about the lowest CC-slope of about 0.8 MPa/◦C in [001]-oriented solutionized

Co49Ni21Ga30 samples, which can be exploited to achieve a large PE-temperature

window in these alloys.

Acknowledgements

First of all, many thanks to my adviser Prof. Hans J. Maier, whose academic

and financial support over the years made this research possible. His enthusiasm

and collaborative spirit helped to create a great environment, and his amazingly

broad knowledge and experience gave my research both direction and inspiration.

I would also like to thank Prof. Ibrahim Karaman, Department of Mechanical

Engineering, Texas A&M University, Texas, USA. He provided me many valuable

suggestions, ideas and useful discussions that improved the quality of this research

study.

I would also like to thank Prof. Yuri V. Chumlyakov, Siberian Physical Tech-

nical Institute, Tomsk, Russia, for providing the single crystals, who also shared

his ideas and provided me with constructive advice.

I gratefully acknowledge the support of Deutsche Forschungsgemeinschaft

(DFG), US Army Research Office (DAAD 19-02-1-0261, W911NF-06-1-0319) US

National Science Foundation - Division of Materials Research (0244126, 0805293),

and the US Civilian Research and Development Foundation (RE1-2525-TO-03,

RUE1-2690-TO-05).

It is a pleasure to acknowledge the experimental assistance that I received from

Kristina Duschik, Barbara Fl¨oing-Herring and Sabrina Spr¨unken, which has been

very helpful in learning new techniques and approaches.

Very thanks to my girlfriend Neeraja that has accepted faithfully and gladly

the challenges and uncertainties associated with the life of a doctoral student;

her love and patience are for me essential.

References

Abeyaratne, R. & Knowles, J.K. (1993). A continuum model of a themoe-

lastic solid capable of undergoing phase transitions. J Mech Phys Solids,41-3,

541–571. 51,59

Brown, P.J., Ishida, K., Kainuma, R., Kanomata, T., Neumann, K.U.,

Oikawa, K., Ouladdiaf, B. & Ziebeck, K.R.A. (2005). Crystals struc-

tures and phase transitions in ferromagnetic shape memory alloy based on Co-

Ni-Al and Co-Ni-Ga. Journal of Physics: Condensed Matter,17, 1301–1310.

Canadinc, D., Dadda, J., Maier, H.J., Karaman, I., Karaca, H.E. &

Chumlyakov, Y.I. (2007). On the role of the cooling rate and crystallographic

orientation on the shape memory properties of CoNiAl single crystals under

compression. Smart Materials and Structures,16, 1006–1015. 2,14,18,26,27,

29,32,34,40,41,43

Chernenko, V.A., L’vov, V., Pons, J. & Cesari, E. (2003). Superelasticity

in high-temperature NiMnGa alloys. Journal of Applied of Physics,93, 2394.

Chernenko, V.A., Pons, J., Cesari, E. & Zasimchuk, I.K. (2004). Trans-

formation behaviour and martensite stabilization in the ferromagnetic Co-Ni-

Ga heusler alloy. Scripta Materialia,50, 225–229. 14,18,52

Chernenko, V.A., Besseghini, S., Villa, E., Gambardella, A. & Prez-

Landazabal, J.I. (2007). Elastic and superelastic properties of Co49Ni22Ga29

single crystal. Applied Physics Letters,90, 201914. 18

Chu, T.C., Ranson, W.F., Sutton, M.A. & Peters, W.H. (1985). Appli-

cations of Digital-Image-Correlation Techniques to Experimental Mechanics.

Experimental Mechanics,25, 232–244. 21,23

Craciunescu, C.M., Kishi, Y., Graef, M.D., Lograsso, T.A. & Wut-

tig, M. (2002). Cobalt-base ferromagnetic shape memory alloys. Smart Struc-

tures and Materials, SPIE,4669, 235–244. 14,74

Dadda, J., Canadinc, D., Maier, H.J., Karaman, I., Karaca, H.E.

& Chumlyakov, Y.I. (2006a). Stress-strain-temperature behaviour of [001]

single crystals of Co49Ni21Ga30 ferromagnetic shape memory alloys under com-

pression. Philosophical Magazine A,87-16, 2313–2322. 2,14,18,36,37

Dadda, J., Maier, H.J., Karaman, I., Karaca, H.E. & Chumlyakov,

Y.I. (2006b). Pseudoelasticity at elevated temperatures in [001] oriented

Co49Ni21Ga30 single crystals under compression. Scripta Materialia,55, 663–

666. 2,14,18,38,45,53,63,67

Dadda, J., Maier, H.J., Niklasch, D., Karaman, I., Karaca, H.E.

& Chumlyakov, Y.I. (2008). Pseudoelasticity and cyclic stability in

Co49Ni21Ga30 shape memory alloy single crystals at ambient temperature. Met-

allurgical and Materials Transactions A,39A, 2026–2039. 2,18,37,46,47,53,

57,67,76,77,78,79

Dadda, J., Maier, H.J. & Karaman, I. (2009). High-temperature pseu-

doelasticity of co-ni-ga shape memory alloy single crystals under compression.

SMST2007 Tsukuba, Japan, Conference Proceedings, 659–666. 2,18,44

Daly, S., Ravichandran, G. & Bhattacharya, K. (2007). Stress-induced

martensitic phase transformation in thin sheets of nitinol. Acta Materialia,55,

3593–3600. 57

Duerig, T.W., Melton, K.N., St¨

ockel, D. & Wayman, C.M. (1990).

Egineering aspects of Shape Memory Alloys. Butterworth-Heinemann. 3,4,12,

Efstathiou, C., Sehitoglu, H., Johnson, A.J.W., Hamilton, R.F.,

Maier, H. & Chumlyakov, Y. (2004). Large reduction in critical stress

in CoNiAl upon repeated transformation. Scripta Materialia,51, 979–985. 14,

18,27,40

Eggeler, G., Hornbogen, E., Yawny, A., Heckmann, A. & Wagner,

M. (2004). Structural and functional fatigue of NiTi shape memory alloys.

Materials Science and Engineering A,378, 24–33. 13

Firstov, G.S., Humbeeck, J.V. & Koval, Y.N. (2004a). Comparison of

high temperature shape memory behaviour for ZrCu-based, TiNiZr and TiNiHf

alloys. Scripta Materialia,50, 243–248. 15

Firstov, G.S., Humbeeck, J.V. & Koval, Y.N. (2004b). High-temperature

shape memory alloys some recent developments. Materials Science and Engi-

neering A,378, 2–10. 14

Gall, K. & Maier, H.J. (2002). Cyclic deformation mechanisms in precipi-

tated NiTi shape memory alloys. Acta Materialia,50, 4643–4657. 13

Gall, K., Sehitoglu, H., Chumlyakov, Y.I. & Kireeva, I.V. (1999).

Pseudoelastic cyclic stress-strain response of over-aged single crystal Ti-

50.8at%Ni. Scripta Materialia,40, 7–12. 13,53

Hamilton, R.F., Sehitoglu, H., Chumlyakov, Y. & Maier, H.J. (2004).

Stress dependence of the hysteresis in single crystal NiTi alloys. Acta Materi-

alia,52, 3383–3402. 14,30,32,33,40

Hamilton, R.F., Sehitoglu, H., Efstathiou, C., Maier, H.J.,

Chumlyakov, Y. & Zhang, X.Y. (2005). Transformation of CoNiAl sin-

gle crystals in tension. Scripta Materialia,53, 131136. 14,18

Hamilton, R.F., Sehitoglu, H., Efstathiou, C., Maier, H.J. &

Chumlyakov, Y. (2006). Pseudoelasticity in CoNiAl single and polycrystals.

Acta Materialia,54, 587–599. 18,40

Ishida, K., Kainuma, R., Ueno, N. & Nishizawa, T. (1991). Ductility

enhancement in NiAl (B2)-base alloys by microstuctural control. Metallurgical

Transactions A,22A, 441–446. 26

Kainuma, R., Ise, M., Jia, C.C., Ohatani, H. & Ishida, K. (1996). Phase

equilibria and microstuctural control in the NiCoAl system. Intermetallics,4,

S151–S158. 15,16

Karaca, H.E., Karaman, I., Lagoudas, D.C., Maier, H.J. &

Chumlyakov, Y.I. (2003). Recoverable stress-induced martensitic transfor-

mation in a ferromagnetic Co-Ni-Al alloy. Scripta Materialia,49, 831–836. 15,

18,29,39,48

Karaca, H.E., Karaman, I., Chumlyakov, Y.I., Lagoudas, D.C. &

Zhang, X. (2004). Compressive response of a single crystalline CoNiAl shape

memory alloy. Scripta Materialia,51, 261–266. 18,29,40

Karaman, I., Karaca, H.E., Basaran, B., Lagoudas, D.C.,

Chumlyakovc, Y. & Maier, H. (2006). Stress-assisted reversible magnetic

field-induced phase transformation in Ni2MnGa magnetic shape memory alloys.

Scripta Materialia,55, 403–406. 14

Kato, H., Ozu, T., Hashimoto, S. & Miura, S. (1999). Cyclic stress-strain

response of superelastic Cu-Al-Mn alloy single crystals. Materials Science and

Engineering A,264, 245–253. 13

Kimura, Y., Miura, S., Suzuki, T. & Mishima, Y. (1994). Microstructure

and mechanical properties of two-phase alloys based on the b2 -type inter-

metallic compound coal in the co-ni-al ternary system. Materials Transactions

(JIM),35-11, 800–807. 15,26

Kustov, S., Pons, J., Cesari, E. & Humbeeck, J.V. (2004a). Pinning-

induced stabilization of martensite part I. stabilization due to static pinning of

interfaces. Acta Materialia,52, 3075–3081. 70

100

Kustov, S., Pons, J., Cesari, E. & Humbeeck, J.V. (2004b). Pinning-

induced stabilization of martensite part II. kinetic stabilization in Cu-Zn-Al

alloy due to pinning of moving interfaces. Acta Materialia,52, 3083–3096. 70

Li, Y.X., Liu, H.Y., Meng, F.B., Yan, L.Q., Liu, G.D., Dai, X.F.,

Zhang, M., Liu, Z.H., Chen, J.L. & Wua, G.H. (2004). Magnetic field-

controlled two-way shape memory in CoNiGa single crystals. Applied Physics

Letters,84, 3495–3496. 14

Liu, J., Zheng, H., Huang, Y., Xia, M. & Li, J. (2005). Microstructure

and magnetic field induced strain of directionally solified ferromagnetic shape

memory CoNiAl alloys. Scripta Materialia,53, 29–33. 18,26

Liu, J., Xie, H., Huo, Y., Zheng, H. & Li, J. (2006). Microstructure evolu-

tion in CoNiGa shape memory alloys. Journal of Alloys and Compounds,420,

145–157. 16,17,18,34

Liu, Y. & Favier, D. (2000). Stabilization of of martensite due to shear defor-

mation via variant reorientation on polycrystalline NiTi. Acta Materialia,48,

3489–3499. 52

Liu, Y., Favier, D. & Orgeas, L. (1995). Influence of elastic energy on the

unloading behaviour of NiTi shape memory alloys. Journal de Physique IV ,

5-C8, 593–598. 44

Liu, Y., Xie, Z. & Humbeeck, J.V. (1999). Cyclic deformation of NiTi shape

memory alloys. Materials Science and Engineering A,273-275, 673–678. 13

Ma, Y., Jiang, C., Li, Y., Wang, C. & Liu, X. (2007). Heusler type CoNiGa

alloys with high martensitic transformation temperature. Materials Science

Forum,546-549, 2241–2244. 18

Marioni, M.A., OHandley, R.C. & Allen, S.M. (2003). Pulsed magnetic

field-induced actuation of NiMnGa single crystals. Applied Physics Letters,83,

3966–3968. 74

101

Meyer, D., Maier, H.J., Dadda, J., Karaman, I. & Karaca, I. (2006).

Thermally and stress-induced martensitic transformation in CoNiAl ferromag-

netic shape memory alloy single crystals. Materials Science and Engineering

A,438-440, 875–878. 2,18,30

Miyazaki, S., Imai, T., Igo, Y. & Otsuka, K. (1986). Effect of cyclic

deformation on the pseudoelasticity characteristics of Ti-Ni alloys. Metallurgical

Transactions A,17, 115–120. 13

Mosley, M.J. & Mavroidis, C. (2001). Experimental nonlinear dynamics

of a shape memory alloy wire bundle actuator. Journal of Dynamic Systems,

Measurement, and Control,123, 103–112. 33

M¨

ullner, P., Chernenko, V.A. & Kostorz, G. (2003). A microscopic

approach to the magnetic-field-induced deformation of martensite (magneto-

plasticity). Journal of Magnetism and Magnetic Materials,267, 325–334. 75

Nemat-Nasser, S. & Guo, W.G. (2006). Superelastic and cyclic response of

NiTi sma at various strain rates and temperatures. Mechanics of Materials,

38, 463–474. 13

Niklasch, D., Dadda, J., Maier, H.J. & Karaman, I. (2008).

Magneto-microstructural coupling during stress-induced phase transformation

in Co49Ni21Ga30 ferromagnetic shape memory alloy single crystals single crys-

tals. Journal of Materials Science,43, 6890–6901. 2,14

O’Handley, R.C. (1998). Model for strain and magnetization in magnetic

shape-memory alloys. Journal of Applied Physics,83-6, 3263–3270. 14

Oikawa, K., Ota, T., Gejima, F., Ohmori, T., Kainuma, R. & Ishida,

K. (2001). Phase equilibria and phase transformations in new B2-type ferro-

magnetic shape memory alloys of Co-Ni-Ga and Co-Ni-Al systems. Materials

Transactions (JIM),42, 2472–2475. 14,15,17,18,24,74

Oikawa, K., Ota, T., Imano, Y., Omori, T., Kainuma, R. & Ishida, K.

(2006). Phase equilibria and phase transformation of Co-Ni-Ga ferromagnetic

102

shape memory alloy system. Journal of Phase Equilibria and Diffusion,27,

75–82. 14,17

Otsuka, K. & Ren, X. (1999). Recent devlopments in the research of shape

memory alloys. Intermetallics,7, 511. 14,15

Otsuka, K. & Ren, X. (2001). Mechanisms of martensite aging effects and

new aspects. Materials Science and Engineering A,312, 207–218. 68,69

Otsuka, K. & Wayman, C.M. (1999). Shape Memory Materials. Cambridge

University Press. 3,4,7,12,14,15,48,55,71

Panchenko, E.Y., Chumlyakov, Y.I., Kireeva, I.V., Ovsyannikov,

A.C., Sehitoglu, H., Karaman, I. & Maier, H.J. (2008). Effect of dis-

perse Ti3Ni4particles on the martensitic transformations in titanium nickelide

single crystals. The Physics of Metals and Metallography,106-6, 577–589. 7,

Patoor, E., Lagoudas, D.C., Entchev, P.B., Brinson, L.C. & Gao,

X. (2006). Shape memory alloys, Part I: General properties and modeling of

single crystals. Mechanics of Materials,38, 391–429. 7

Picornell, C., Pons, J. & Cesari, E. (2001). Stabilization of martensite by

applying compressive stress in Cu-Al-Ni single crystals. Acta Materialia,49,

4221–4230. 38,52

Ren, X. & Otsuka, K. (1997). Origin of rubber-like behaviour in metal alloys.

Nature,389, 579–582. 68,69

R¨

osner, H., Schlossmacher, P., Shelyakov, A.V. & Glezer, A.M.

(2001). The influence of coherent TiCu plate-like precipitates on the thermoe-

latic martensitic transformation in melt-spun Ti50Ni25Cu25 shape memory al-

loys. Acta Materialia,49, 1541–1548. 7,8

Sato, M., Okazaki, T., Furuya, Y. & Wuttig, M. (2003). Magnetostric-

tive and shape memory properties of heusler type Co2-Ni-Ga alloys. Materials

Transactions (JIM),44-3, 372–376. 14,74

103

Schlagel, D.L., Lograsso, T.A. & Pecharsky, O. (2004). Phase stability

of single crystalline Co-Ni-Ga shape memory alloy. Materials Research Society

Symposium Proceedings,785, 219–224. 18,85

Segui, C., Cesari, E., Font, J., Muntasell, J. & Chernenko, V.A.

(2005). Martensite stabilization in a high temperature NiMnGa alloy. Scripta

Materialia,53, 315–318. 14

Sehitoglu, H., Karaman, I., Anderson, R., Zhang, X., Gall, K.,

Maier, H.J. & Chumlyakov, Y. (2000). Compressive response of NiTi sin-

gle crystals. Acta Materialia,48, 3311–3326. 30,33,42,48,67

Sehitoglu, H., Anderson, R., Karaman, I., Gall, K. & Chumlyakov,

Y. (2001a). Cyclic deformation behaviour of single crystal NiTi. Materials Sci-

ence and Engineering A,314, 67–74. 13,46

Sehitoglu, H., Karaman, I., Zhang, X., Chumlyakov, A.V.Y. &

Maier, H.J. (2001b). Straintemperature behavior of NiTiCu shape memory

single crystals. Acta Materialia,49, 3621–3634. 30,33

Sehitoglu, H., Hamilton, R., Canadinc, D., Zhang, X.Y., Gall, K.,

Karaman, I., Chumlyakov, Y. & Maier, H.J. (2003). Detwinning in NiTi

alloys. Metallurgical and Materials Transactions A,34, 5–13. 30,33

Shaw, J.A. & Kyriakides, S. (1995). Thermomechanical aspects of NiTi. J

Mech Phys Solids,43, 1243–1281. 59

Sozinov, A., Likhachev, A.A., Lanska, N. & Ullakko, K. (2002). Gi-

ant magnetic-field-induced strain in NiMnGa seven-layered martensitic phase.

Applied Physics Letters,80, 1746–1748. 14

Strnadel, B., Ohashi, S., Ohtsuka, H., Ishihara, T. & Miyazaki, S.

(1995). Cyclic stress-strain characteristics of Ti-Ni and Ti-Ni-Cu shape memory

alloys. Materials Science and Engineering A,202, 148–156. 13

Tian, W.H., Hibino, M. & Nemoto, M. (1998). Crystal structure and mor-

phology of Co precipitates in B2-ordered (Ni,Co)Al. Intermetallics,6, 121–129.

104

Ullakko, K., Huang, J.K., Kanter, C., O’Handley, R.C. & Kokorin,

V. (1996). Large magnetic-field-induced strains in Ni2MnGa single crystals.

Applied Physics Letters,69, 1966–1968. 14,24

Vainchtein, A. (2002). Dynamics of non-isothermal martensitic phase transi-

tions and hysteresis. International Journal of Solids and Structures,39, 3387–

3408. 57

Yawny, A., Sade, M. & Eggeler, G. (2005). Pseudoelastic cycling of ultra-

fine-grained NiTi shape-memory wires. International Journal of Materials Re-

search and Advanced Techniques,96, 608–618. 13

Zhang, M., Br¨

uck, E., de Boer, F.R. & Wu, G. (2005). Magnetic, marten-

sitic transformation magnetostriction and shape memory effect in Co50Ni20Ga30

melt-spun ribbons. Journal of Physics D: Applied Physics,38, 1361–1364. 14

105