Fatigue Assessment of NiTi Wires through the Self- Heating Method 

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NiTi or B2 phase

NiTi or B2 phase (Figure 2-3a) has a Cs-Cl-type B2 ordered structure with a lattice constant a0=0.3015nm at room temperature. The B2 structure can be viewed as an ordered BCC lattice formed by two interpenetrated primitive cubic lattices of Ni and Ti atoms. This crystallographic phase is considered as the parent phase when describing phase transformation processes in NiTi, also denoted as austenite.

Ti3Ni4

Ti3Ni4 are coherent precipitates that form lenticular-shaped domains as observed in the electron micrograph in Figure 2-3d. Its lattice microstructure is rhombohedral with parameters a=0.670nm and +=113.8°. The structure of Ti3Ni4 consist of planes ABCDEF shown in Figure 2-3d, stacked in the direction of axis {111}B2 of B2. Ti3Ni4 precipitates introduce distortion inside the B2 matrix, therefore, they induce internal stress and increase the elastic energy stored in the matrix. This increase of elastic energy may lead to a phase transformation from B2 phase into R-phase, as detailed in later sections.

Martensitic Phase Transformations in NiTi Alloys

Depending on the applied thermomechanical heat treatment, the B2 phase can transform in a single step into B19’ phase upon cooling or follow a two-step phase transformation passing first through the R-phase. A single step phase transformation is observed in the solution treated NiTi, where precipitation reactions are avoided, while two-step phase Figure 2-2 Transformation-Time-Temperature (TTT) diagram of a 52 at. %Ni alloy by Nishida et al. [17]. transformation is observed whenever precipitates or dislocations are introduced into the B2 matrix. The intermediate phase transformation, from B2 to R-phase, is also a martensitic transformation, which shows superelastic and shape memory properties. However, the resulting amount of reversible deformation after B2 to R is much lower than the B2 to B19’ transformation, making it less attractive for applications. The crystallographic calculations of B2→B19’, B2→R and R→B19’ have been tackled by several authors in the literature using the different phenomenological theory of martensitic transformations. In this respect, we highlight the works of Matsumoto et al. [28] and Knowles et al. [29], who used the Wechsler et al. theory to calculate the twin variants upon the B2→B19’ transformation and compared them to experimental diffraction information obtained in NiTi single crystals. We should also mention the work of Hane and Shield who performed an equivalent work using the Ball and James phenomenological theory [18], as well as the work of Zhang et al. who used the Ball and James theory to calculate twin variants upon B2→R→B19’ transformation [19]. We present the main outcome of these studies in the following subsections.

Thermodynamic aspects of phase transformations in NiTi

The martensitic phase transformations in NiTi are considered as thermoelastic first-order phase transformations. From a thermodynamic viewpoint, the driving force that governs the nucleation and propagation of product phases is, as for the forward transformation, a decrease of temperature or an increase of the applied stress. The thermoelastic denomination refers to the reversible nature of phase transformation with temperature. Since phase transformations in SMA’s involve structural distortion, reversibility is fulfilled only if no structural damage occurs during the transformation process. This implies that the interface between parent and product phases must be coherent and that the volume change after the transformation are negligible. In this regard, B2/R→B19’ martensitic transformations in NiTi, although exhibiting one of the best functional properties among SMA’s, presents one Figure 2-5 Schematic representation of self-accommodated wedge of B19’ twinned variants. Structural Fatigue of Superelastic NiTi Wires of the less coherent austenite/martensite interfaces and relatively large volume changes [32].
These interface incoherencies turn out on dissipation of energy and thermal hysteresis. In order to describe the characteristic thermal hysteresis of NiTi alloys, we refer to the phenomenological thermodynamic framework of phase transformations. This framework is based on the evaluation of the Gibbs free energy potential, which consist of as chemical and mechanical energy terms.

Gibbs free energy potential

Diffusionless crystallographic phase transformation results in an atomic rearrangement leading to lattice distortion. Consequently, temperature-induced martensitic transformations in NiTi can be considered as a mechanical-chemical process. This statement allows to establish the following form of the change of mass-specific Gibbs free-energy potential of a transforming system [33]: D = D – D + D + D el ir G H T S E E ,

Heat release/absorption

In first-order phase transformations, the state functions of a transforming thermodynamic system, like specific entropy or specific volume, are not continuous at the transformation phase boundary. In NiTi sudden entropy changes turn out into latent heat release/absorption, which explains the endothermic and exothermic peaks observed in differential scanning calorimetry (DSC) experiments. From the DSC experimental results shown in Figure 2-9, we can observe that B2↔R, B2↔B19’ and R↔B19’ transformations, all release heat when the material experience a high entropy to low entropy change, and absorb heat when the inverted entropy change occurs. To examine the heat absorption/release of a transforming system, let us describe the specific free energy balance over an infinitesimal step during the transformation as: ( ) ( dG = dH -TdS + dEel fm + dEir fm).

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Mechanical Properties of NiTi alloys

The mechanical response of NiTi combines stress-induced phase transformations with other deformation mechanisms such as B2, B19’ and R-phase elasticity, B19’ and R-phase detwinning, and B2 plasticity through dislocation slip. All these mechanisms are stress and temperature dependent, making complex their characterization and modeling. In this section, we show the impact of these mechanisms on the mechanical response of NiTi and describe some of their most relevant characteristics.

Detwinning of B19’ and R-phase

Detwinning occurs mainly when self-accommodated arranges of habit plane variants (HPV) of R or B19’ phases are subjected to stress at temperatures below Mf and Rf respectively. The applied stress causes twin boundary motion and reorientation of HPV’s in such a way that the sum of individual crystal distortions, instead of being canceled, contribute to deform the NiTi sample. Consequently, upon removal of the stress, residual B2 «R B2 «B19′ stress-temperature domains of B2, R and B19’ phases.
deformation remains on the sample (see Figure 2-11). Only by heating the sample above Af then cooling it down, the self-accommodated structures are recreated and the deformation reversed. This phenomenon allows the shape memory effect. Detwinning is characterized by two stages. In the first stage, we observe a stress plateau, which allows deformations up to ~3% in the case of B2→B19’ transformation (Figure 2-11a) and ~0.3% in the case of B2→R transformations (Figure 2-11b). In the second stage, the material exhibits a more pronounced strain hardening response, as observed clearer in the B2→R transformation curves shown in Figure 2-11b. Twins boundaries in R-phase are more mobile than those in B19’ martensite, hence it is substantially easier to move twins in R than in B19’. The yield stresses (plateau stresses) for R-phase are about 5–25 MPa while in B19’ are between 50-250MPa. Both yield stresses decrease by increasing the temperature as illustrated in Figure 2-11.

Table of contents :

List of Figures
List of Tables
Chapter 1. Introduction 
1.1. Introduction
1.2. Generalities of Shape Memory Alloys
1.3. Historical Background and Overview
1.4. Statement of the Problem
1.5. Purpose of the study
1.6. Procedures
1.7. Organization of the dissertation
Chapter 2. State of the Art 
2.1. Physical Metallurgy of NiTi Alloys
2.1.1. Binary Phase Diagram
2.1.2. Martensitic Phase Transformations in NiTi Alloys
2.2. Thermodynamic aspects of phase transformations in NiTi
2.2.1. Thermal hysteresis
2.2.2. Heat release/absorption
2.2.3. Effects of externally applied stresses – Clausius-Clapeyron relation
2.3. Mechanical Properties of NiTi alloys
2.3.1. Detwinning of B19’ and R-phase
2.3.2. Elasticity
2.3.3. Stress-induced phase transformations & superelasticity
2.3.4. Plastic deformation through dislocation slip
2.4. Applications of NiTi
2.4.1. Constrained-recovery
2.4.2. Actuation
2.4.3. Superelastic
2.5. Fatigue of NiTi Alloys
2.5.1. Functional fatigue
2.5.2. Structural fatigue
2.6. Summary
Chapter 3. Tensile Behavior of Hourglass-Shaped NiTi Samples 
3.1. The hourglass shape
3.1.1. Linear-Elastic Response
3.1.2. Non-linear material behavior
3.2. Material of the study
3.2.1. Cold-drawn NiTi wires
3.2.2. Preparation of hourglass-shaped samples
3.2.3. Effects of annealing temperatures
3.3. Thermomechanical behavior of 500°C-annealed NiTi
3.3.1. Stress-strain response
3.3.2. Microstructure evolution resolved via X-ray diffraction
3.3.3. Simulation of the tensile response using 3D finite element analysis
3.4. Summary
Chapter 4. Fatigue of NiTi hourglass-shaped samples 
4.1. Experimental protocol
4.2. S-N curves
4.2.1. Effects of the mean stress
4.2.2. Hints for superelastic NiTi fatigue modeling
4.3. Stress-Strain-N representation
4.4. Fatigue crack characterization
4.4.1. Fracture surfaces
4.4.2. Characterization of the crack’s size
4.4.3. Tensile response evolution
4.5. Microstructure evolution evaluated via high resolution x-ray diffraction
4.6. Summary
Chapter 5. Fatigue Assessment of NiTi Wires through the Self- Heating Method 
5.1. Description of the self-heating method
5.1.1. Background
5.1.2. Thermodynamic framework
5.2. Experimental protocol
5.2.1. Experimental setup
5.2.2. Post-processing of temperature data
5.3. Experimental results
Structural Fatigue of superelastic NiTi wires
5.3.1. Self-heating curves
5.3.2. Effects of the loading frequency
5.3.3. Evolution of the temperature harmonics
5.3.4. Influence of the shape of the sample
5.3.5. Temperature evolution during monotonic tensile tests
5.4. Modeling of the thermomechanical behavior of NiTi
5.4.1. 1D diffusion problem in hourglass-shaped samples
5.4.2. Identification of the heat exchange coefficients
5.4.3. Cyclic thermoelastic effect
5.4.4. Cyclic phase transformation latent heat
5.4.5. Interaction between the thermoelastic effect and the transformation latent heats
5.5. Summary
Conclusions
References

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