Titanium Based Alloys

CHAPTER 1

Crystallography and mechanisms of constituent phase transformations in Titanium-based alloys

1.1 General remarks concerning Titanium-based alloys

At the present moment Titanium and Titanium-based alloys represents a class of important metallic materials used, with outstanding results, in modern applications starting from automotive industry to biomedical field. This large field of applications makes, at the moment, these materials to be one of the most studied, large efforts being dedicated to further understanding their behaviour and to improving their performances. It was showed that the specific properties exhibited by these alloys are greatly influenced by the internal micro-structure, which in its turn is greatly influenced by nature of constitutive parent phases and by the applied thermo-mechanical processing route [1].

In the case of pure Titanium it was proved that both temperature and applied pressure can influence its allotropic transformations (figure 1.1), from α-Ti (hexagonal close packed – HCP) phase at ambient temperature to β-Ti (body centred cubic – BCC) phase at high temperature, with a transition temperature of about 882°C. Applying pressure, the ω-Ti (hexagonal/trigonal) phase can be induced, it was showed that the minimum applied pressure in order to induce ω-Ti phase is around 2GPa [2]. The triple point in which all three phases meet was determined to be around 667°C and 9GPa [2]. Analysing the temperature-applied pressure phase diagram can be noticed that only α-Ti ⇔ β-Ti, α-Ti ⇔ ω-Ti and β-Ti ⇔ ω-Ti transitions are possible, at various temperatures and applied pressures.

Fig. 1.1. Temperature-pressure phase diagram for Titanium [2]

The exhibited properties of Titanium-based alloys are greatly influenced by the specific phase structure (containing α-Ti, β-Ti and ω-Ti phases) and also by the volume fraction of these phases, opening the way of “engineering” the properties by an adequate thermo-mechanical processing route.

A way to stir the phase structure consist in adding alloying elements with the aim to promote stability of a certain phase or to form intermetallic compounds which may improve the envisaged properties. For example, if adding Tantalum the stability temperature of the β-Ti phase is decreased and for a certain volume fraction of Tantalum the β-Ti phase become stable even at ambient temperature; with a direct effect on exhibited elastic modulus, towards a lower value in comparison with the elastic modulus of α-Ti phase (due to the specific mechanical properties of β-Ti phase).

1.2 Titanium-based alloys classification

The most common classification of Titanium-based alloys is based on its allotropic transformations and on its stable phases at ambient temperature and applied pressure. The volume fraction of the constituent phases at ambient temperature and applied pressure is influenced by the nature and by the volume fraction of the alloying elements. Usually, the alloying elements can be divided in two categories, function on promoted stable phase, in α-stabilizing elements and β-stabilizing elements [3].

Un-alloyed Titanium and its alloys, with one or more α-stabilizing elements, leads to a fully α-Ti phase, at ambient temperature and applied pressure, and are known as α-Ti alloys. It was showed that the α-Ti alloys exhibit good mechanical properties, corrosion resistance and weldability [4]. However, the α-Ti alloys are not amenable to heat treatment strengthening.

If at ambient temperature and applied pressure, the structure consists in a mixture of α-Ti and β-Ti phase, than the alloys are named (α+β)-Ti alloys. These alloys contain both α-stabilizing and β-stabilizing alloying elements. Generally, the (α+β)-Ti alloys possess high mechanical properties at ambient temperatures and good mechanical properties at high temperature [5]. The exhibited properties can be manipulated by varying the volume fractions of both α-Ti and β-Ti phases, using various thermo-mechanical processing routes. In the (α+β)-Ti alloys class, two sub-classes can be mentioned, these being “near α-Ti” and “near β-Ti” alloys, referring to alloys whose compositions place them near the α/(α+β) or the β/(α+β) phase boundaries, respectively [6].

In the case of β-Ti alloys, the β-Ti phase is stabilized at ambient temperature and applied pressure by the addition of an adequate amount of β-stabilizing elements. The strength of β-Ti alloys is generally greater than that of α-Ti alloys. Due to the specific higher density of BCC crystallographic structure in comparison with HCP crystallographic structure, the β-Ti alloys are prone to ductile–brittle transition at low temperatures [7]

According to the α-stabilizing and/or β-stabilizing character the alloying elements; these can be divided into the following categories [7]:

(α+β) isomorphous alloying elements; the alloying element X is completely soluble in the β-Ti phase and α-Ti phase (Zr; Hf);

β isomorphous alloying elements; the alloying element X is completely soluble in the β-Ti phase and partially in α-Ti phase (Nb; Ta; V; Mo);

β eutectoid alloying elements; the alloying element X has a limited solubility in the β-Ti phase, at cooling the β-Ti phase decomposes eutectoidally into the α-Ti phase and an appropriate intermetallic phase TixXy (Fe; Cu; Ni; Cr; Mn; Ph; Ag; Au; Be; Si; Sn; Bi);

β peritectoid alloying elements; the alloying element X has a limited solubility in the α-Ti phase, at cooling the β-Ti phase decomposes peritectically into the α-Ti phase and an appropriate intermetallic phase TixXy (B; Al; Sc; Ga; La; Ca; Gd; Nd; Ge; C);

simple peritectic; the alloying element X is completely soluble in the α-Ti phase even in liquid phase (O; N).

The archetypical α-stabilizing and β-stabilizing alloying elements used as addition to Titanium-based alloys are represented by the Al and Mo. Usually, is useful to describe the Titanium-based alloy composition by terms of “equivalent” Al and Mo contents. The computation relation for Al equivalent quantity is [7]:

The computation relation for Mo equivalent quantity is [7]:

where: [X] indicates the concentration of the element X in wt.%.

During the last decade many Titanium alloys were commercial available, the most common being the following [1]:

α-Ti alloys; Ti-5Al-2.5Sn;

near α-Ti alloys; Ti-8Al-1Mo-1V, Ti-6Al-2Sn-4Zr-2Mo;

(α+β)-Ti alloys; Ti-6Al-4V, Ti-6Al-2Sn-6V, Ti-3Al-2.5V ();

near β-Ti alloys; Ti-6Al-2Sn-4Zr-6Mo, Ti-5Al-2Sn-2Zr-4Cr-4Mo, Ti-3Al-10V-2Fe;

β-Ti alloys; Ti-13V-11Cr-3Al, Ti-15V-3Cr-3Al-3Sn, Ti-4Mo-8V-6Cr-4Zr-3Al, Ti-11.5Mo-6Zr-4.5Sn.

1.3 Crystallography of constituent phases in Titanium-based alloys

The low temperature equilibrium phase of Titanium consists of α-Ti phase. The α-Ti phase has a HCP crystalline cell, belonging to the space group P63/mmc, with the main crystalline cell parameters a and c. The α-Ti phase spatial view is presented in figure 1.2. The high temperature equilibrium phase consists of β-Ti phase. The β-Ti phase has a BCC crystalline cell, belonging to the space group Im-3m, with the main crystalline cell parameter a. The β-Ti phase spatial view being presented in figure 1.3.

Phases such as the α-Ti and β-Ti are equilibrium phases and the corresponding phase fields are delimitate in equilibrium phase diagrams, according to Titanium-based alloys composition.

Equilibrium phase diagrams are usually developed by deducing the initial states of alloys which have been quenched from different temperatures to room temperature, however, the quenching process may lead to the formation also of non-equilibrium phases. The most important non-equilibrium phases in Titanium-based alloys are represented by the α’-Ti hexagonal martensite, the α’’-Ti orthorhombic martensite and the athermal ω-Ti phases. All these phases can be formed during cooling by athermal displacive transformations [1].

In the case of displacive transformations, the atomic movement can be initiated by a homogenous distortion, through shuffling of lattice planes mechanisms, displacement waves mechanisms or by a combination of these mechanisms, resulting a movement of a large number of atoms in a diffusionless transformation process. In the case of displacive transformation, the atomic movement do not require thermal activation and therefore cannot be suppressed by the quenching [1,8].

Assuming the case of a Titanium-based alloy heated in the β field, on rapid quenching the martensite is obtained. If the Titanium-based alloy is a α-Ti alloy, then at cooling the obtained martensite is α’-Ti HCP martensite. If the Titanium-based alloy is a β-Ti alloy, then at cooling the obtained martensite can be either α’-Ti HCP martensite or α’’-Ti orthorhombic martensite (figure 1.4), depending on solute content of β-stabilizing elements.

Fig. 5.4. Crystallographic spatial view of α’’-Ti orthorhombic phase.

In the special case of a narrow range of composition, another athermal process can occur at cooling, namely the formation of ω-Ti phase from the parent β-Ti phase [1].

The modern theories concerning martensitic transformation assume that the interface between transformed martensite and the parent phase is macroscopically invariant. The driving force of martensitic transformation is assumed to be shear, which consists of three components [1]:

the lattice shear (Bain strain), which determine the change in lattice during transformation;

the lattice invariant shear, which provides an un-distorted habit plane for transformation;

the rigid body rotation, to ensure that the un-distorted habit plane is un-rotated.

There are a number of choices for relating the lattices of the parent β-Ti phase and transformed α’-Ti and α’’-Ti phases. The correct choice of lattice correspondence is generally made by selecting the one which involves the minimum distortion and rotation of the lattice vectors.

The crystallographic accommodation during α-Ti α’’-Ti phase transition is schematically presented in figure 1.5.

The lattice parameters, aα’’, bα’’and cα’’ of the α’’-Ti phase and aα’’and cα’’ of the α-Ti phase, are related as follows:

Fig. 1.5. Crystallographic accommodation during α-Ti α’’-Ti phase transition.

In the case of β-Ti alloys, the martensitic transformation can be either hexagonal α’-Ti martensite or α’’-Ti orthorhombic martensite. The crystallographic accommodation during β-Ti α’-Ti phase transition is schematically presented in figure 1.6, while in the case of β-Ti α’’-Ti phase transition is schematically presented in figure 1.7. In fact, the α’’-Ti martensite is a distorted hexagonal structure, with same atoms positions like in hexagonal structure but with distorted lattice parameters, with values between these of BCC and HCP structures [1].

It was showed that the β-Ti α’-Ti involves the activation of the shear systems and [9-11]. The orientation relationship between the β-Ti and α’-Ti phase has been observed to be approximately: and [9-11].

In the case of β-Ti and α’’-Ti phases the orientation relationship has been observed to be approximately: and inclined to approximately 2° from and ; and [1,12].

The lattice parameters, aα’and cα’’ of the α’-Ti phase and aβ of the β-Ti phase, are related as follows:

The relationship between lattice parameters, aα’’, bα’’ and cα’’ of the α’’-Ti phase and aβ of the β-Ti phase, is as follows:

There are two ways to obtain martensite structure in Titanium-based alloys: by quenching from β-Ti phase field (athermal martensite) and by applying an external stress (stress-induced martensite). The α’’-Ti orthorhombic martensite can be formed by stress-induced transformation or athermally. The α’-Ti hexagonal martensite can be formed only athermally. There are Titanium-based alloys, in which both martensite types can be formed [1].

It was reported that in the case of some quenched β-Ti alloys, at stress levels below 150 MPa in the β-Ti phase the α’’-Ti orthorhombic martensite appear. The α’’-Ti orthorhombic martensite accommodates the applied load by a lattice strain distortion. It was showed that the formation of α’’-Ti orthorhombic martensite is accompanied by mechanical twinning [13].

Another metastable phase which can be formed in Titanium-based alloys is represented by the ω-Ti phase, which can be formed in the following situations [1]:

during application of hydrostatic pressure to the α-Ti phase – either by a static pressure or by a shock pressure;

during quenching from the β-Ti phase field;

during aging the metastable β-Ti phase.

The structure of the ω-Ti phase has been determined to be either hexagonal, belonging to the space group P6/mmm [14], or trigonal, belonging to the space group P-3m1 [1], depending on the solute concentration.

The orientation relationship between the β-Ti and ω-Ti phases has been observed to be approximately: and [11].

The lattice parameters, aω and cω of the structure and aβ of the β-Ti phase structure, are related as follows:

A comparison of the lattice parameters of the ω-Ti phase computed from the aβ value of the corresponding β-Ti phase and those experimentally observed shows that the divergence between the two is negligibly small for the athermal β-Ti ω-Ti phase transition [1], the recorded difference being associated with a linear contraction of about 5% (volume contraction ∼15%) [1].

Two orientation relationships between the α-Ti and ω-Ti phases were observed, firstly: -, and secondly: -[1]. Based on observed crystallographic relations two α-Ti ω-Ti transition mechanisms were proposed, firstly, the α-Ti ω-Ti transition is direct one, and secondly, the α-Ti ω-Ti is a two steps transition, following the sequence: α β ω, with an intermediary β metastabil phase [1].

An advanced investigation tool used to investigate the specific features of crystallographic transformations, at crystalline scale level, occurred during thermo-mechanical processing of metallic materials, is represented by the X-ray diffraction investigations techniques, presented in the next section.

CHAPTER 2

Features of transformations at crystalline scale level analysed by XRD

2.1 Overview of the XRD line profile analysis; Theoretical base

The X-ray diffraction investigation technique is a common investigation method used to investigate the crystalline structure of metallic materials by determining crystalline cell parameters, lattice distortions, micro-strains at lattice level, average coherent crystalline size, etc. [15-17]. At the present moment, the X-ray diffraction is intensively used in investigations concerning bulk materials (nano-crystalline and micro-crystalline materials), powder materials and thin solid films.

The incident beam of X-ray radiation, generated by a X-ray source, interacts with the atoms of a crystalline material polarizing its atoms, resulting atomic forces in opposite directions due to the negatively charged electrons and positively charged nucleus, resulting an oscillation in charge distribution of the electronic dipoles with same frequency ν as the incidence beam (electromagnetic wave). The oscillating dipoles in turn radiate electromagnetic waves, with same ν frequency, and the waves propagate in all direction (the diffracted X-ray radiation is scattered in all directions). The scattered X-ray radiation from one atom interacts destructively with X-ray radiation scattered from other atoms except in certain preferred directions, as showed in figure 2.1.

Fig. 2.1. X-ray diffraction from successive planes of atoms.

As observed in figure 2.1, constructive interference occurs if the pathway difference between 2 incidence waves is proportional with an integer number of wavelengths [15-17].

Because:

where: n – represents the order of the intensity maximum; – represents the wavelength of used X-ray radiation; – represents the scattering angle (the angle of incidence X-ray radiation); d – represents the interplanar spacing.

The relation 2.2 is named the Bragg’s law and gives a simple relation between X-ray wavelength, interplanar spacing and angle of the diffracted beam.

The interplanat spacing d can be computed, in the case of cubic crystalline system, by the following relation [15-17]:

where: a – represents the cubic crystalline cell parameter; k, k, l – represents the Miller indices corresponding to (hkl) crystallographic plane.

The interplanar spacing d, in the case of other crystalline cells can be computed using the following relations [15-17]:

tetragonal system:

hexagonal system:

orthorhombic system:

rhombohedral system:

monoclinic system:

One of the most used X-ray diffraction investigation set-up consist in – 2 scans. The position of X-ray source is a fix one; only sample and detector are moving, the sample is rotating with a certain angle while the detector rotates with a 2 angle, as presented in figure 2.2. In this way the detector is following the strongest signal coming from the first order diffraction. In this set-up the obtained results concerning materials constituent crystalline phases and orientations can be determine, due to the fact that only out of plane crystalline orientations are investigated. If considering that the structure of metallic materials contains grains with random orientations and in order to investigate the random oriented grains, during measurement the sample must rotate also around its vertical axe with the ω speed. In this way a larger volume fraction of grains are investigated during X-ray diffraction measurement.

Fig. 2.2. X-ray diffraction set-up in -2 scans.

If during X-ray diffraction measurements the scattering vector s is always perpendicular to the sample surface that the set-up geometry is named Bragg-Brentano [15-17].

The X-ray diffraction measurements enable the identification of materials constituent phases by measuring the exact angular position of diffraction lines corresponding to various interplanar spacing of the constituent phase crystalline structure.

The main characterization parameters of a diffraction line are the following:

diffraction line position;

diffraction line intensity;

diffraction line shape.

As showed above, the position of a diffraction line is determined by the Bragg’s law, and is influenced by the wavelength of the X-ray radiation and by the crystalline cell system geometry.

The intensity of a diffracted line depends on several parameters, such as:

volume fraction of constituent phases;

scattering factor F;

temperature factor;

set-up geometry;

used X-ray wavelength.

The general expression corresponding to a diffraction line given by [18], is as follows:

where: – represents the multiplicity of the scattering plane (hkl); – represents the combined Lorentz-polarisation factor; – represents the structure factor (accounts for the scattering power of all constituent atoms); – represents an absorption term depending on the scattering (set-up) geometry.

In the case of Bragg-Brentano geometric set-up the Lorentz-polarisation factor is:

where: – representsangular position of the diffraction line; – represents the fraction of vertically polarised radiation in the diffraction plane.

The relationship between type and position of atoms forming the crystalline unit cell and the magnitude of their contribution to each (hkl) diffraction line is expressed by the structure factor . The general mathematical expression quantifying the influence of structure factor , is as follows:

where: – represents the atoms of the crystalline unit cell; – represents the scattering power of the atom n, and is influenced by the number and configuration of electrons in the atom and also by the scattering angle ; – represents the factor which describes the thermal motion of the atom in terms of mean-square atomic displacements away from the equilibrium atomic position in an ideal static structure (Debye-Waller factor).

In the case of isotropic thermal motion, the Debye-Waller factor may be written as:

where: – represents the temperature factor B(T), which varies with the atomic mass and with the strength of interatomic forces acting on the reference atom. The main effect of the temperature factor is represented by the reduction of scattering power at higher scattering angles, due to the smearing of the electron density around the atom.

The shape of a diffraction line depends on several influence factors, such as [15-17]:

characteristics of X-ray source and X-ray detector;

sample absorbance;

sample microstructural characteristics: coherent crystalline size distribution; micro-structural disorder; crystalline microstrain at lattice level.

The most important influence factor in respect to the shape of a diffraction line is represented by the X-ray diffractometer geometric setup (instrument broadening) and the sample microstructural characteristics (sample broadening). The instrument broadening includes effects arising from non-ideal X-ray optics, wavelength dispersion, sample transparency, axial divergence, flat-sample effect, detector resolution, etc. [19].

In the case of sample microstructural characteristics, the following influence factors can be mentioned [20]:

coherent crystallite size: if considering that a perfect crystalline structure extends in all directions to infinity, in the case of real crystalline structures these show a deviation from perfect crystalline structures due to their finite size. The coherent crystalline size is a measure for the size of a coherently scattering domain and may not be identical to the grain (particle) size of a polycrystalline material, due to extended defects existence. The extended defects disrupt the periodic atomic arrangement of crystalline structure, typically along a 2D plane which also represents an interface between two neighbouring ordered domains, such as: stacking faults, small-angle domain boundaries, dislocation walls, etc;

strain broadening: due to existing of non-uniform crystalline lattice distortion, faulting, antiphase domain boundaries, grain surface relaxation, etc., at crystalline lattice level microstrain appear, which is influence the line diffraction broadening.

In the case of X-ray diffraction data analysis, one must process the experimental recorded XRD spectra in order to decompose it and to determine for any diffraction line its corresponding position, amplitude (intensity) and width. The first step in processing the XRD recorded data is to deconvolute the profile and determine the specific profile of each component diffraction line (one must remember that the recorded profiles represents a convolution of all present individual diffraction lines). After obtaining the deconvoluted profiles for every present diffraction lines the computations concerning position, amplitude and width can be performed.

In order to deconvolute experimental recorded XRD spectra’s on must carefully choose the profile (shape) type of constituent diffracted line. Usually, the following diffraction lines profiles are used [15-17,21-23]:

Lorentz (Cauchy) profiles: used in the case of ordered coherent crystalline size;

Gauss profiles: used in the case of distorted crystalline size;

Voight profiles: used in the case of mixed crystalline size.

If considering an experimental recorded diffraction line, presented in figure 2.3, can be observed that the fitted profile corresponds to three overlapping diffraction lines, after fitting and deconvoluting process for each diffraction line is determined its position, amplitude (intensity) and width.

Fig. 2.3. Processed XRD spectra’s, showing the presence of recorded experimental data, fitted data and deconvoluted constituent diffraction lines .

Commonly, the width of a diffraction line is expressed as FWHM (Full Width at Half Maximum) parameter, due to the easy way to compute its value. In complex analysis the integral breadth is used, and represents the total area under a diffraction line divided by the diffraction line intensity, representing the width of a rectangle having the same area and the same intensity with the diffraction line.

The recorded width of a diffraction lines contains, beside sample contribution, the instrument contribution, which must be determined in order to have valid results concerning sample width.

The instrument contribution (instrument broadening) can be determined using measured etalon samples, such as NIST 660a LaB6; NIST 640c Si; NIST 674b CeO2 standards, and expressing the instrument broadening using Cagliotti function [24,25]:

where: U, V, W – represents the correction parameters, which are experimental determined for each diffractometer geometric set-up based on etalon samples measurements.

In order to determine sample contribution on recorded diffraction line FWHM, one can subtract its contribution using the following relations [24,25]:

in the case of Lorentzian profiles:

in the case of Gaussian profiles:

Same mathematic formalism can be applied if the integral breadth approach is used.

If considering the case of ordered coherent crystalline size, its value can be computed using Scherrer equation [15-17]:

where: – represents the wavelength of used X-ray radiation, – represents the position corresponding to diffraction line which is used in computation, D – represents the value of coherent crystalline size, k – represents a constant of proportionality (Scherrer constant). The value of k constant is k = 0.94 in the case of spherical crystallite with cubic symmetry, usually, in computations k = 1.

Few considerations must be made in the case of coherent crystalline size when using Scherrer equation:

above a certain size, there is no line diffraction broadening;

in practice, the maximum observed size for a standard laboratory diffractometer is between (80 – 120) nm;

in practice, the minimum observed size is typically between 3 to 10 nm, depending on the investigated material;

If considering the case of distorted crystalline size, one must consider also the influence of microstrain. The easiest way to analyse such profiles is represented by the Williamson-Hall approach [15-17]:

where: ε – represents the average microstrain.

If ones plot the as a function of for each diffraction line recorded in the XRD spectra corresponding to a specific crystalline phase, a graphic similar with the one presented in figure 2.4 can be obtained (Williamson-Hall plot). If a linear fit procedure is performed, the obtained intercept and slope are representing the coherent crystalline size and the average microstrain.

Fig. 2.4. Williamson-Hall plot.

2.2 Advanced analysis of crystallographic texture

Crystallographic texture developed inside materials structures during thermal and mechanical processing can be determined using various methods [26-28]. Many developed methods only allow a quantitative analysis of the texture, while others allow only qualitative results. The most important quantitative texture investigation techniques are represented by the X-ray diffraction, using dedicated texture goniometers [26-28], and the EBSD (electron backscatter diffraction) technique in Scanning Electron Microscopes (SEM).

In a typical laboratory, the texture measurements are performed using X-ray diffraction instruments equipped with special designed goniometers (figure 2.5) which allows multiple rotation axes for measured specimens [26-28]. Mainly, the specimens must rotate, during X-ray texture measurement, around their OZ and OX axes. In the case of OZ axis the performed rotation angle during X-ray measurement is φ = 0° – 360°. The rotation around OX axis, typically, is = 0° – 90°. In order to measure a specific (hkl) pole figure, taking into consideration the specific wavelength of used X-ray radiation the diffractometer geometric setup must satisfy the Bragg’s law:

where: – represents the wavelength of used X-ray radiation; – represents the interplanar spacing of (hkl) crystallographic plane; – represents the corresponding scattering angle of (hkl) diffraction line; n – represents a multiple integer.

The interplanar spacing, in the case of cubic crystalline systems, can be determined using the following equations [29]:

where: a, b, c – represents the crystalline cell parameters; h, k, l – represents the Miller indices of the (hkl) crystallographic plane.

Knowing the necessary scattering angle for a certain (hkl) diffraction line and its corresponding (hkl) pole figure, the diffractometer geometric setup is easily obtained by rotating the specimen around OY axis, the X-ray source (2) and the X-ray detector (3) in order to assure the 2 necessary scattering angle.

Fig. 2.5. Schematic representation of X-ray diffraction measurement setup; 1 – measured sample; 2 – X-ray radiation source; 3 – X-ray radiation detector.

The measurement techniques of a (hkl) pole figure assume the following steps: first, the diffractometer geometric setup is performed in order to realize the 2 necessary scattering angle; second, the X-ray radiation is started and measurement begin; third, the angle is set to = 0° while the φ angle will change from φ = 0° to φ = 360° during measurement, the change in φ angle is performed with an imposed step, function of desired measurement resolution (lower the step the higher obtained measurement resolution) obtaining the variation of (hkl) diffraction line intensity on a circle trajectory in the measured (hkl) pole figure (figure 2.6); fourth, after a complete φ rotation, the angle is increased with a certain step (lower the step the higher obtained measurement resolution) and the φ angle will perform, again, a complete rotation, obtaining a second variation of (hkl) diffraction line intensity on a different circle trajectory in the measured (hkl) pole figure (figure x.6), in same way the measurements are performed until = 90°. In this way, each measurement point of (hkl) pole figure is defined by a ( – φ) pair.

Fig. 2.6. Schematic representation of X-ray diffraction measurement results;

each measurement point being defined by a ( – ) pair.

As observed, the (hkl) pole figure presents the variation of (hkl) diffraction line intensity in respect to specimen reference directions (XYZ).

Fig. 2.7. Schematic representation of sample reference system; 1 – rolled sample; 2 – rolling cylinders; RD – rolling direction; TD – transverse direction; ND – normal direction.

As observed in figure 2.7-a, if assuming as deformation process the forming by rolling processing, the rolled specimen 1 is deformed and elongated mainly along the OX axis of the sample reference system. Taking into consideration the main processing directions: rolling direction – RD, transverse direction – TD and normal direction – ND and the sample reference system axes, an identifying process considering main directions can be applied, resulting as main sample reference axes the processing directions (figure 2.7-b):

The graphical representation of a (hkl) pole figures actually represents the map in projection of (hkl) diffraction line intensity, resulting a “geographic” map of a hemisphere (North pole in the center), commonly named stereographic projection, and giving a map of [hkl] crystal direction in respect to sample reference system [26,28,30].

Fig. 2.8. Schematic representation of stereographic projection for a random cubic single crystal in the case of <100> family directions; a – cubic crystalline cell with <100> directions; b – stereographic projection of a cubic single crystal and <100> directions; c – equatorial projection of <100> directions (100) pole figure.

If assuming a cubic crystal and the <100> directions family, the stereographic projection of <100> family is obtained as follows: if assuming an arbitrary spatial orientation of cubic crystal and placing the sample reference system (RD-TD-ND) in the center of the cube and both in the centre of a sphere, the equatorial sphere plane (including the RD-TD axes) divide the cube in two parts, only [100], [010] and [001] crystalline directions (figure 2.8-a) being above equatorial plane. If considering the P1, P2 and P3 the points from the sphere surface in which the [100], [010] and [001] crystalline directions intercepts the sphere surface (North hemisphere) and connecting these points with the South pole, the intersection points between P1-S, P2-S and P3-S connection lines and equatorial plane give P1’, P2’ and P3’ points, representing the equatorial projection of <100> crystalline directions (figure 2.8-b). The equatorial projection of <100> crystalline directions gives the information contained in (100) pole figure (figure 2.8-c).

If assuming a cubic crystal and the <111> directions family, the stereographic projection of <111> family is obtained as follows: if assuming an arbitrary spatial orientation of cubic crystal and placing the sample reference system (RD-TD-ND) in the center of the cube and both in the centre of a sphere, the equatorial sphere plane (including the RD-TD axes) divide the cube in two parts, only [], [], [] and [] crystalline directions (figure 2.9-a) being above equatorial plane. If considering the P1, P2, P3 and P4 the points from the sphere surface in which the [], [], [] and [] crystalline directions intercepts the sphere surface (North hemisphere) and connecting these points with the South pole, the intersection points between P1-S, P2-S, P3-S and P4-S connection lines and equatorial plane give P1’, P2’, P3’ and P4’ points, representing the equatorial projection of <111> crystalline directions (figure 2.9-b). The equatorial projection of <100> crystalline directions gives the information contained in (100) pole figure (111) pole figure (figure 2.9-c).

Fig. 2.9. Schematic representation of stereographic projection for a random cubic single crystal in the case of <111> family directions; a – cubic crystalline cell with <111> directions; b – stereographic projection of a cubic single crystal and <100> directions; c – equatorial projection of <111> directions (111) pole figure.

Fig. 2.10. Schematic representation of (110) pole figures; a – representation of a cubic crystalline cell with (110) plane and [110] direction; b – (110) pole figure with no-texture (random orientation distribution); c – (110) pole figure with texture.

In the case of polycrystalline materials the pole figures comprise many possible spatial orientations for a certain [hkl] crystalline direction, due to the large number of crystalline grains contained inside materials, each grain having a specific spatial crystalline orientation. Considering the [110] crystalline direction (figure 2.10-a), if the obtained (110) pole figure shows a random distribution of [110] crystal direction in respect to the sample reference system (figure 2.10-b) can be assumed that the polycrystalline material structure show no-texture; if a certain distribution around specific points can be detected then can be assumed that polycrystalline material shows texture – a preferred spatial orientation in respect to sample reference system (figure 2.10-c).

In order to describe the spatial position of a crystalline cell in respect to sample reference system many methods were developed [26,28]. The most common method to describe the spatial position assume the use of three rotations around specific axes, the Bunge system assumes rotations of the Sz-Cy-Cz axes (Sx-Sy-Sz – representing the sample reference system; Cx-Cy-Cz – representing the crystalline cell reference system) [26,28,31,32].

The rotation angles around axes being as follows: 1 angle – rotation around Sz axis (figure 2.11-a); angle – rotation around Cy axis (figure 2.11-b); 2 angle – rotation around Cz axis (figure 2.11-c) (1–2 being named Euler angles). Must be noticed that, using Bunge system, any spatial position of a crystalline cell in respect to sample reference system, can be accurately described by using Euler 1–2 angles (figure 2.11-d).

Fig. 2.11. Schematic representation of crystalline system rotations (Cx-Cy-Cz) in respect to sample reference system (Sx-Sy-Sz); Euler angles (1–2).

The most common and simple method used to describe developed textures in a rolled sheet metallic material consist of a two-component designation. Miller indices are implemented in order to describe spatial position of planes and directions. The dominant (hkl) plane aligned parallel to the rolling plane and the dominant [uvw] crystallographic direction aligned with the rolling direction are specified. Therefore, rolling textures are indicated by the pair (hkl)[uvw] or by families of planes and directions {hkl}<uvw>.

In the case of cubic crystalline systems the relationship between an orientation, in Bunge system (1–2), and the associate texture component {hkl}<uvw>, using Miller indices, can be expressed using the following equation [28]:

In the case of hexagonal crystalline systems the correlation equations between an orientation, in Bunge system (1–2), and associate texture component {hkil}<uvtw>, using Miller-Bravais indices, and also considering the specifics of hexagonal crystalline cell, can be expressed using the following equation [33]:

A complex way to describe the distribution of crystal orientations is assure by Orientation Distribution Function (ODF), which describes the normalized probability distribution of orientations as a function of three variables [29,34]. As variables, usually Euler angles are used (1–2). The spatial distribution of variables depends on sample reference system symmetry and also on crystalline system symmetry. In the case of orthorhombic sample reference system symmetry and cubic crystalline symmetry, the spatial distribution of Euler variables is:

In the case of orthorhombic sample reference system symmetry and hexagonal crystalline symmetry, the spatial distribution of Euler variables is:

In the case of triclinic sample reference system symmetry and cubic crystalline symmetry, the spatial distribution of Euler variables is:

In the case of triclinic sample reference system symmetry and hexagonal crystalline symmetry, the spatial distribution of Euler variables is:

The Orientation Distribution (OD) is a central concept in texture analysis of materials and also in the study of properties anisotropy (due to crystallographic directional dependent response during testing) [28,34-38]. In the case of texture analysis the OD assumes the occurrence frequency of a specified texture component in a given space. The value of the OD function is represented by the probability density of existence for a specified texture component.

The OD can be mathematically defined using any appropriate space, usually using Euler angles (). In Euler space, a spatial orientation can be defined by three rotations around specific axes. In this way each point in the OD represents a single specific orientation or a texture component.

Due their specific properties, the OD can be used in order to compute the presence, or the absence, of a specific texture component, to compute the volume fraction of a given texture component or to analyse the properties anisotropy in poly-crystalline materials [28,32,34].

The OD always can be described by a mathematical function named Orientation Distribution Function (ODF). This notion, firstly, was introduced by Bunge, in order to mathematically describe the fitting coefficients of generalized spherical harmonics in the case of pole figure data [26,28,39].

The projection of a 3D orientation distribution on to a 2D pole figure causes a loss in information which leads to no possibility to determine the orientation density of crystallites in respect to sample reference frame. Thus, for quantitative analysis of developed texture a 3D description of the ODF is required. The ODF cannot be directly measured using X-ray diffraction, being needed to calculate the ODF starting from experimental measured pole figures [27,28,30,34,35].

The general mathematical relation of OD is given by the equation:

where: g – represents an orientation; V – represents the volume of a body; dV(g) – represents the volume with g orientation; dg – represents the g orientation variation (also called misorientation); – represents the entire orientation space; and Δ- represents the region around the g orientation.

Another equation describing the OD considers the discretization of space and is given by the following relation:

where: g – represents an orientation; dg – represents the g orientation variation (misorientation); N – represents the number of cells discretizing the volume V; and dN(g)- represents the cells number with g orientation.

The macro-texture Pole Figure (PF) measurements are used as input in ODF computation. In the case of pole figure, the mathematical equation describing its behaviour is defined by the following relation:

where: dV/V – represents the volume fraction of crystals having their crystal direction h parallel to the sample direction y – typically given by two pole figure angles ( – φ);

The PF’s are commonly expressed using reflecting lattice plane normal, using Miller or Miller-Bravais indices, in which the (hkl) or (hkil) indices correspond to coordinates of the crystal direction h in the reciprocal lattice.

For ODF compotation the pole figure must be normalized and the results must be in MRD (Multiples of a Random Density), the normalization process is performed using the following equation:

The PF is defined by the direction y in a 2D pole figure Ph(y), and corresponds to a region in the 3D ODF f(g) space, that contains all possible rotations with angle in the y direction. The mathematical relation describing this relation is as follows:

where:

The relation (2.35) represents the fundamental equation for ODF computation, which must to be solved in order to calculate the ODF [26,28]. Using only one pole figure as input to solve the ODF results in incomplete data, for this reason in order to determine the ODF one must use more PF’s.

At the moment, mathematical formalisms were developed in order to determine the Pole Figures (PF) to Orientation Distribution Function (ODF) transformation, by the use of various kernel functions. The most used kernel functions are the following [40,41]:

von Mises Fisher;

de la Vallee Poussin;

Abel Poisson;

Square Singularity;

Gauss Weierstrass;

Dirichlet;

etc.

At the moment, one of the best mathematical approaches in respect to PF to ODF transformation is based on modified least-squares estimator method [41,42] using the following equation:

where: – represents the number of pole figure used in f(g) estimation; – represents the number of specimen directions; – represents the normalized vector of f(g); – represents Radon transform; – represents the superposed lattice planes; – represents the specimen direction; – represents the diffraction counts.

Based on ODF, computations concerning the volume fraction with a certain orientation can be performed, starting from the following equation:

where: Vf(g)- represents the volume fraction with a certain g orientation.

Considering the particularities of Euler space, the volume fraction of a specific orientation (), can be determined using the following equations:

If considering:

and the volume of the space defined by the Euler angles (; ; ) equal to:

if the texture is random then the OD is defined such that it has the same value of unity everywhere, than can be written:

Usually, in computation the OD space is discretized using 5x5x5° cells size; in this case the volume fraction of a specific orientation is determined by the equation:

and the relation between a specific orientation and its volume fraction is given by the equation:

In texture analysis the most used parameter to quantify the texture strength, i.e. the extent of a preferred orientation, is represented by the texture index – F [26,28,43]. The mathematical equation describing the texture index being the following:

The texture index helps in results comparison between developed texture components in series of samples, if same types of texture components are present in the polycrystalline materials.

The ODF can be graphical presented by a spatial cylindrical plot in Euler space () (figure 2.12-a). In this representation for each () orientation a single point is obtained [28]. As observed, the cylindrical plot considers the periodicity of Euler angles in the rage of = 0° – 360°; = 0° – 90°; = 0° – 90°. In the cylindrical space the sample reference system (RD, TD, ND) consist of linear segments parallel to cylinder axes (figure 2.12-b). Using cylindrical space representation the ODF is typical represented in 2 = const. sections.

Fig. 2.12. Schematic representation of Orientation Distribution Function (ODF) in respect to Euler angles (1–2) using cylindrical space; a – ODF (1–2) cylindrical space; b – main planes representation in Euler (1–2) cylindrical space.

The ODF typical graphical representation is represented by a spatial Cartesian plot (orthogonal axes) in Euler space () (figure 2.13-a) [28]. For each constitutive cell is assigned an intensity equal to the volume fraction in that cell, ∆V, divided by the volume of orientation space associated with that cell, ∆Ω and multiplied by the total volume of orientation space.

Usually, the ODF’s are presented in 2 = const. sections, in the case of cubic crystalline symmetry the most important sections are represented by the 2 = 0° and 2 = 45° sections. In the case of hexagonal crystalline symmetry the most important sections are represented by the 2 = 0° and 2 = 30° sections. In these sections, usually most important developed fibers are presented, for example, in the case of cubic crystals (both BCC – body centred cubic and FCC – face centred cubic) the most important texture fibers are resented in figure x.13, being τ-fiber, -fiber and ϴ-fiber in 2 = 45° section (figure 2.13-c) and α-fiber in 2 = 0° section (figure 2.13-b) [28,34,37].

Fig. x.13. Schematic representation of Orientation Distribution Function (ODF) in respect to Euler angles (1–2) and representation of most common developed fibers; a –ODF (1–2) space; b – 2 = 0° ODF section; c – 2 = 45° ODF section.

If considering a material with cubic crystalline system, in this case, the α-textural fiber is spreading from 1–2 = 0°-45°-0° (figure 2.14-a) to 1–2 = 30°-45°-0° (figure 2.14-b) to 1–2 = 60°-45°-0° (figure 2.14-c) to 1–2 = 90°-45°-0° (figure 2.14-d). Computing the associate {hkl}<uvw>texture components can be obtained:

Must be noticed that in the case of α-textural fiber the (011) plane aligns perpendicular to ND direction and parallel to normal plane (RD-TD).

Fig. 2.14. Schematic representation of crystalline system (Cx-Cy-Cz) in respect to sample reference system (Sx-Sy-Sz) in the case of α-textural fibre; a – Euler 1–2 rotations = 0°-45°-0°; b – Euler 1–2 rotations = 30°-45°-0°; c – Euler 1–2 rotations = 60°-45°-0°; d – Euler 1–2 rotations = 0°-45°-0°.

The -textural fiber is spreading from 1–2 = 0°-55°-45° (figure 2.15-a) to 1–2 =30°-55°-45° (figure 2.15-b) to 1–2 = 60°-55°-45° (figure 2.15-c) to 1–2 = 90°-55°-45° (figure 2.15-d). Computing the associate {hkl}<uvw>texture components can be obtained:

Also, the (111) plane in the case of textural fiber aligns perpendicular to ND direction and parallel to normal plane (RD-TD).

Fig. 2.15. Schematic representation of crystalline system (Cx-Cy-Cz) in respect to sample reference system (Sx-Sy-Sz) in the case of -textural fibre; a – Euler 1–2 rotations = 0°-55°-45°; b – Euler 1–2 rotations = 30°-55°-45°; c – Euler 1–2 rotations = 60°-55°-45°; d – Euler 1–2 rotations = 0°-55°-45°.

Fig. 2.16. Schematic representation of crystalline system (Cx-Cy-Cz) in respect to sample reference system (Sx-Sy-Sz) in the case of τ-textural fibre; a – Euler 1–2 rotations = 0°-0°-45°; b – Euler 1–2 rotations = 30°-0°-45°; c – Euler 1–2 rotations = 45°-0°-45°.

The τ-textural fiber is spreading from 1–2 = 0°-0°-45° (figure 2.16-a) to 1–2 = 30°-0°-45° (figure 2.16-b) to 1–2 = 45°-0°-45° (figure 2.16-c). Computing the associate {hkl}<uvw>texture components can be obtained:

Also, must be noticed that in the case of τ-textural fiber the (001) plane aligns perpendicular to ND direction and parallel to normal plane (RD-TD).

The ϴ-textural fiber is spreading from 1–2 = 90°-0°-45° (figure 2.17-a) to 1–2 = 90°-30°-45° (figure 2.17-b) to 1–2 = 90°-60°-45° (figure 2.17-c) to 1–2 = 90°-90°-45° (figure 2.17-d). Computing the associate {hkl}<uvw>texture components can be obtained:

The () plane of the ϴ-textural fiber aligns perpendicular to RD direction and parallel to rolling plane (TD-ND).

Fig. 2.17. Schematic representation of crystalline system (Cx-Cy-Cz) in respect to sample reference system (Sx-Sy-Sz) in the case of ϴ-textural fibre; a – Euler 1–2 rotations = 90°-0°-45°; b – Euler 1–2 rotations = 90°-30°-45°; c – Euler 1–2 rotations = 90°-60°-45°; d – Euler 1–2 rotations = 90°-90°-45°.

Besides texture fibers also other specific individual texture components can be developed during thermo-mechanical processing of metallic materials, such as:

Cube texture component – 1–2 = 0°-0°-0° (figure 2.18-a)

Goss texture component – 1–2 = 0°-45°-0° (figure 2.18-b)

Brass texture component – 1–2 = 35°-45°-0° (figure 2.18-c)

Copper texture component – 1–2 = 90°-45°-45° (figure 2.18-d)

Computing the associate {hkl}<uvw>texture components in the case of individual texture components can be obtained:

Fig. 2.18. Schematic representation of spatial orientation some texture components; a – Cube texture component 1–2 = 0°-0°-0°; b – Goss texture component 1–2 = 0°-45°-0°; c – Brass texture component 1–2 = 35°-45°-0°; d – Copper texture component 1–2 = 90°-45°-45°.

CHAPTER 3

Thermo-mechanical processing and characterization procedure of investigated Titanium-based alloys

3.1 General considerations concerning investigated alloys

In order to analyse the influence of applied thermo-mechanical processing route on developed structural features (existing phases, lattice parameters, developed texture components and fibers) in the case of advanced Titanium-based alloys, two Titanium alloy classes were selected to be advanced investigated, namely, α-Titanium and β-Titanium classes.

As compositional elements only 3d, 4d and 5d transition metals (β-isomorphous stabilizing elements) were selected, as presented in table 3.1, in order to supress intermetallic compound formation during alloying and to obtain “only” α-Ti (hexagonal) and β-Ti (cubic) phases. Also, metastable phases can be induced in the structure by means of thermal and/or mechanical processing. As metastable possible phases can be mentioned the following phases: α’-Ti phase (hexagonal martensite); α’’-Ti phase (orthorhombic martensite) and ω-Ti phase (hexagonal/trigonal omega).

Table 3.1. Selected d-transition metals.

Fig. 3.1. Classification of α, α+β and β Titanium-based alloys [45].

Using Yukawa and Morinaga approaches [44, 45], as compositional range for the alloying elements the following compositions were computed:

β-Titanium alloy: Ti-25Nb-25Ta (wt%): ; ;

β-Titanium alloy: Ti-29Nb-9Ta-10Zr (wt%): ; ;

α-Titanium alloy: Ti-10Zr-5Nb-5Ta (wt%): ; ;

where: – represents the energy level of “d” orbitals; – represents the bond order.

The mathematical relations used to determine the and values are the following:

where: – represents the atomic mass fraction corresponding to alloying element “i”; – represents the energy level of “d” orbitals of alloying element “i”; – represents the bond order of alloying element “i”.

In figure 3.1 the classification of α, α+β and β Titanium-based alloys [45] according and parameters is presented. Can be observed that in the case of both Ti-25Nb-25Ta (wt%) and Ti-29Nb-9Ta-10Zr (wt%) alloys, according to their and parameters, they are placed in the class of β-Titanium alloys, while the Ti-10Zr-5Nb-5Ta (wt%) alloy is placed in the class of α-Titanium alloys.

As synthesis technique the melting in cold crucible induction in levitation was used (figure 3.2). The synthesis equipment was FiveCeles MP25, with a melting capacity of 30 cm3. Due to the large difference in melting temperatures of alloying elements (Ti: 1660°C; Nb: 2468°C; Ta: 2996°C; Zr: 1855°C), for each investigated alloy, two re-melts were performed in order to assure the alloy’s chemical homogeneity.

Fig. 3.2. Images of synthesis equipment and the melt “levitating” inside furnace inductor.

The main advantage of using such synthesis technique resides from the ultra-low/non-existing contamination of the melt during synthesis and, also, from the possibility to use in alloying process elements with large differences in melting temperatures.

It was proved [46-52] that using this synthesis technique is possible to obtain alloys used even in medical applications and/or aeronautical industry.

3.2 Thermo-mechanical processing of investigated Titanium-based alloys

In the following section the thermo-mechanical processing routes, applied to investigate alloys, will be presented. Must be specified that in all cases all heat treatments (homogenization, recrystallization, aging) were performed using a GERO SR 100×500 heat treatment oven, and all mechanical processing’s were performed using a Mario di Maio LQR120AS rolling-mill, at 3 m/min rolling speed.

3.2.1 Ti-29Nb-9Ta-10Zr alloy

The Ti-29Nb-9Ta-10Zr alloy thermo-mechanical processing route, used in order to investigate alloy’s behaviour during Multi Pass Rolling (MPR), is presented in figure 3.3. As observed, after alloy synthesis, in order to increase the alloy homogeneity, a homogenisation treatment was performed at 950°C for 6 hours, in high vacuum. In order to obtain a refined microstructure, a first cold-rolling was applied using a thickness reduction of 60%, followed by a recrystallization treatment, to remove the strain-hardening resulted during cold deformation. The recrystallization treatment was performed at 780°C for 30 min, in high vacuum. Recrystallized samples were water quenched in order to obtain a bi-modal structure consisting of parent β-Ti phase and temperature-induced α”-Ti phase.

After recrystallization, the cold-rolling processing by MPR was initiated, in order to realize a thickness reduction of 20% (structural state 1), 40% (structural state 2) and 60% (structural state 3). All these structural states are investigated in 4.1 and 5.1.1 sections.

Fig. 3.3. Thermo-mechanical processing route applied to Ti-29Nb-9Ta-10Zr (wt%),

in order to investigate alloy’s behaviour during MPR processing.

In order to investigate the effects of recrystallization treatment performed on heavily deformed specimens, the following processing route was applied (figure 3.4); after homogenization treatment, the alloy was heavily deformed by MPR at ambient temperature, until a thickness reduction of 90% was obtained. Upon deformed alloy a recrystallization treatment was applied, using the following heating temperatures: 780°C (structural state 1), 830°C (structural state 2) and 880°C (structural state 3). All these structural states are investigated in 4.1 and 5.3.1 sections.

For all recrystallization treatments the treatment duration was set to 30 min and high vacuum as treatment environment. All recrystallized samples were water quenched in order to obtain a bi-modal structure consisting of parent β-Ti phase and temperature-induced α”-Ti phase.

Fig. 3.4. Thermo-mechanical processing route applied to Ti-29Nb-9Ta-10Zr (wt%),

in order to investigate alloy’s behaviour after recrystallization.

Fig. 3.5. Thermo-mechanical processing route applied to Ti-29Nb-9Ta-10Zr (wt%),

in order to investigate alloy’s behaviour after recrystallization followed by aging.

The influence of aging treatment was investigated also. The thermo-mechanical processing route applied, in order to investigate the specific effects of aging treatment (figure 3.5), was similar with the one applied in the case of recrystallization, with the difference that after recrystallization the aging was applied. The aging parameters were identical for all recrystallized states: aging temperature 400°C, aging duration: 30 min, high vacuum as treatment environment, with the cooling performed inside furnace. The resulted structural states consisted of the following states: structural state 1 – corresponding to sample recrystallized at 780°C and aged at 400°C; structural state 2 – corresponding to sample recrystallized at 830°C and aged at 400°C; structural state 3 – corresponding to sample recrystallized at 880°C and aged at 400°C; All these structural states are investigated in 4.1 and 5.3.2 sections.

3.2.2 Ti-25Nb-25Ta alloy

The Ti-25Ta-25Nb (wt%) alloy was thermo-mechanical processed with a double aim, firstly to obtain ultra-thin strips, with an approx. thickness of 30 μm, by Severe Plastic Deformation (SPD) processing using MPR technique, and secondly to obtain stacks of layers by SPD – Accumulative Roll Bonding (ARB) processing.

If total accumulate plastic strain during deformation is exceeding the threshold of 2, than can be said the deformation process is a SPD one.

Fig. 3.6. Thermo-mechanical processing route applied to Ti-24Nb-25Ta (wt%),

in order to produce SPD processed ultra-thin strips by MPR processing.

In order to obtain the SPD processed ultra-thin strips the applied processing route (figure 3.6) consists in a first cold-rolling step with a thickness reduction of about 85.83% (equivalent plastic strain, ε = 1.95), followed by a recrystallization treatment in argon protective atmosphere, at 850°C for 30 minutes, with a cooling in water in order to stabilize the β-Ti phase at ambient temperature and also to promote a bi-modal structures consisting of β-Ti and α’’-Ti phases. The recrystallization treatment was performed in order to remove the strain-hardening effects resulted during the first cold-rolling. After recrystallization, a second cold-rolling was performed, with a thickness reduction of about 91.17% (equivalent strain, ε = 2.42), in order to achieve final strips thickness ~ 30 μm (investigated structural state 1). This structural state was investigated in 4.2 and 5.2.1 sections.

The second aim of thermo-mechanical processing of Ti-25Nb-25Ta alloy was to obtain stacks of layers by SPD – Accumulative Roll Bonding (ARB) (figure 3.7). The applied processing route consists of the following steps: after synthesis, the alloy was homogenized for 6 hours at 950°C under high vacuum; the processing was continued by a first cold-rolling with a total accumulate strain of 1.85 and a recrystallization treatment at 850°C for 30 minutes and water cooling. The processing route was continued by a second cold-rolling; with a total accumulate plastic strain of 1.25, in order to obtain the “precursor” layer for ARB processing initiation. The ARB processing was conducted in order to obtain stacks of layers (sheets), resulting after the second ARB pass a stack containing 4 layers (structural state 1) and after fourth ARB pass a stack containing 16 layers (structural state 2). All these structural states are investigated in 4.2 and 5.2.2 sections.

Fig. 3.7. Thermo-mechanical processing route applied to Ti-24Nb-25Ta (wt%),

in order to produce SPD-ARB stacks.

3.2.3 Ti-10Zr-5Nb-5Ta alloy

The thermo-mechanical processing route applied to Ti-10Zr-5Nb-5Ta (wt%) alloy in order to investigate alloy’s behaviour during Multi Pass Rolling (MPR), is presented in figure 3.8. As observed, after alloy synthesis, in order to increase the alloy homogeneity, a homogenisation treatment was performed at 950°C for 6 hours, in high vacuum. The processing route was continued by a first cold-rolling; with a total accumulate plastic strain of 1.84, in order to refine the grain structure. The cold-rolling was followed by a recrystallization treatment performed at 850°C for 30 minutes in high vacuum and air cooling; with the aim to remove the strain-hardening resulted during cold deformation.

After recrystallization, the cold plastic deformation processing was continued by a second cold-rolling with a total accumulate plastic strain of 1.34, resulting the investigated structural state 1. This structural state was investigated in 4.3 and 5.1.2 sections.

Fig. 3.8. Thermo-mechanical processing route applied to Ti-10Zr-5Nb-5Ta (wt%),

in order to produce MPR processed strips.

Fig. 3.9. Thermo-mechanical processing route applied to Ti-10Zr-5Nb-5Ta (wt%),

in order to produce SPD-ARB stacks.

The second thermo-mechanical processing route applied to Ti-10Zr-5Nb-5Ta alloy, was to obtain stacks of layers by SPD – Accumulative Roll Bonding (ARB) (figure 3.9). The applied processing route consists of the following steps: after synthesis, the alloy was homogenized for 6 hours at 950°C under high vacuum; the processing was continued by a first cold-rolling with a total accumulate strain of 1.84 and a recrystallization treatment at 850°C for 30 minutes and air cooling. The processing route was continued by a second cold-rolling; with a total accumulate plastic strain of 1.34, in order to obtain the “precursor” layer for ARB processing initiation. The ARB processing was conducted in order to obtain stacks of layers (sheets), resulting after the first ARB pass a stack containing 2 layers (structural state 1), after the second ARB pass a stack containing 4 layers (structural state 2) and after third ARB pass a stack containing 8 layers (structural state 3). All these structural states are investigated in 4.3 and 5.2.3 sections.

3.3 XRD measurements on investigated Titanium-based alloys

All XRD measurements were performed using a Philips PW 3710 diffractometer, with wavelength of Cu k-alpha (λ = 1.5406 Å) and a Panalytical X’Pert PRO MRD diffractometer with a wavelength of Cu k-alpha (λ = 1.5418 Å), in order to determine the phase structure and phase characteristics for all investigated alloys.

The recorded XRD spectra’s were simulated and fitted. The XRD spectra simulation was performed using MAUD v2.33 software package. In order to determine for each peak the position, intensity and peak broadening – FWHM (Full Width at Half Maximum) the XRD spectra’s were fitted. The fitting procedure was performed using PeakFit v4.12 software package, using a pseudo-Voigt or a Lorentz diffraction line profile in fitting procedure.

Before XRD measurements the alloys samples were prepared by the following procedure:

samples mounting: hot mounting using phenolic powder (mounting temperatures: 180°C);

samples grinding and polishing: used procedure is presented in table 3.2.

Table 3.2. Applied grinding and polishing procedure.

The above preparation procedure was used in order to obtain samples with flat, oxide-free investigation surfaces.

3.4 Textural measurements on investigated Titanium-based alloys

After performing the XRD investigations, same samples were used in advanced textural investigations.

The texture characterization was performed using a Philips PW 3710 diffractometer, with Cu k-alpha (λ = 1.5406 Å) wavelength. In the case of β-Titanium alloys the (110), (200) and (211) Pole Figures (PF’s) were measured, while in the case of α-Titanium alloys the (002), (100), (101) and (101) Pole Figures (PF’s) were measured.

All PF’s were collected in 5° increments: 0°-χ-85°, 0°–355°. The texture analysis was performed using MTEX v3.5.0 software package. The PF’s raw data was analysed, using Gaussian distribution, Ghost correction and intensities normalization. Inverse Pole Figures (IPF’s) and Orientation Distribution Functions (ODF’s) were computed.

Taking into consideration the low intensity of α”-Ti phase diffraction lines in comparison with β-Ti and α-Ti diffraction lines, and also the α”-Ti diffraction lines positions, closely to β-Ti and α-Ti diffraction lines, makes the recording of α”-Ti phase PF’s very difficult, for this reason only the texture of β-Ti and α-Ti phases is analysed and presented in the section 5.

CHAPTER 4

Advanced XRD characterization of thermo-mechanical processed Titanium-based alloys

The main objective of XRD investigations performed on thermo-mechanical processed Ti-29Nb-9Ta-10Zr, Ti-25Nb-25Ta and Ti-10Zr-5Nb-5Ta alloys was to determine the influence of applied processing routes on lattice parameters of α-Ti, β-Ti and α’’-Ti phases. In order to fully assess the developed crystallographic texture of a certain phase during thermo-mechanical processing one must compute the ODF. In ODF computation the crystallographic features, such as lattice parameters and crystalline system, being influential factors.

4.1 XRD characterization of thermo-mechanical processed Ti-29Nb-9Ta-10Zr alloy

The first applied thermo-mechanical processing route on Ti-29Nb-9Ta-10Zr (wt%) alloy targeted the investigations of specific phenomena occurred during MPR processing, assuming the following thicknesses reduction: 20% (structural state 1), 40% (structural state 2) and 60% (structural state 3) – as presented in section 3.2.1. The recorded XRD spectra of 20% thickness reduction state, presented in figure 4.1-a, shows the presence of (110), (200) and (211) diffraction lines corresponding to β-Ti phase and the (020), (002), (200), (220), (202) and (222) diffraction lines corresponding to α’’-Ti phase. In order to compute the recorded XRD spectra the β-Ti phase was indexed in BCC system – Im-3m, while the α”-Ti phase was indexed in orthorhombic system – Cmcm [53]. In the XRD spectra fitting procedure a pseudo-Voight diffraction line profile was used, due to the introduced effects of mechanical processing upon materials micro-structure.

Fig. 4.1. XRD recorded spectra in the case of 20% cold-rolled Ti-29Nb-9Ta-10Zr (wt%) alloy (a); detailed XRD spectra corresponding to 2θ = (36° – 41°) (b); and 2θ = (67° – 74°) (c).

The recorded XRD spectra was fitted and deconvoluted in individual diffraction lines for all observed phases. In figure 4.1-b a detailed zoom corresponding to 2θ = (36° – 41°) is presented, can be observed that the convolution of α’’-Ti (020), β-Ti (110) and α’’-Ti (002) diffraction lines accurately describe the recorded XRD spectra. Another detailed zoom corresponding to 2θ = (67° – 74°) is presented in figure 4.1-c, where can be observed that the convolution of β-Ti (211), α’’-Ti (220) and α’’-Ti (202) diffraction lines, also, accurately describe the recorded XRD spectra. For each constitutive diffraction line its position, intensity and FWHM parameters were computed during XRD spectra fitting procedure.

Based on diffraction lines positions (2θ) and assumed crystalline systems, the lattice parameters corresponding to β-Ti and α’’-Ti phases were computed, it was obtained that in the case of β-Ti phase the lattice parameter was: a = 3.30Å, while in the case of α’’-Ti phase the lattice parameters were as follows: a = 3.23Å, b = 4.72Å and c = 4.62Å [54].

The recorded XRD spectra of 40% thickness reduction state, presented in figure 4.2-a, shows the presence of (110), (200) and (211) diffraction lines corresponding to β-Ti phase and the (020), (002), (200), (220), (202) and (222) diffraction lines corresponding to α’’-Ti phase. Same assumptions were made in the case of 40% cold-rolling state with the ones in the case of 20% cold rolled state, in respect to crystalline systems of constituent phases and diffraction lines profile used during XRD spectra fitting and deconvoluting process. Figure 4.2-b shows a detailed zoom corresponding to 2θ = (36° – 41°), can be observed that the convolution of α’’-Ti (020), β-Ti (110) and α’’-Ti (002) diffraction lines accurately describe the recorded XRD spectra. Another detailed zoom corresponding to 2θ = (66° – 74°) is presented in figure 4.1-c, where can be observed that the convolution of β-Ti (211), α’’-Ti (220) and α’’-Ti (202) diffraction lines, also, accurately describe the recorded XRD spectra.

The computed lattice parameters for both β-Ti and α’’-Ti phases showed identical lattice parameters with the ones obtained after 20% cold-rolled state (changes are identified only in the third digit).

Fig. 4.2. XRD recorded spectra in the case of 40% cold-rolled Ti-29Nb-9Ta-10Zr (wt%) alloy (a); detailed XRD spectra corresponding to 2θ = (36° – 41°) (b); and 2θ = (66° – 74°) (c).

The recorded XRD spectra of 60% thickness reduction state, presented in figure 4.3-a, shows the presence of same diffraction lines in respect to both β-Ti and α’’-Ti phases. Also, in the case of detailed zooms around (110) β-Ti diffraction line (figure 4.3-b) and (211) β-Ti diffraction line (figure 4.3-c) can be observed that the convolution of constituent diffraction lines accurately describe the recorded XRD spectra.

The computed lattice parameters for both β-Ti and α’’-Ti phases showed an identical lattice parameter a = 3.30Å in the case of β-Ti phase, while in the case α’’-Ti phase a change is detected, the parameters were as follows: a = 3.21Å, b = 4.70Å and c = 4.60Å [54].

Fig. 4.3. XRD recorded spectra in the case of 60% cold-rolled Ti-29Nb-9Ta-10Zr (wt%) alloy (a); detailed XRD spectra corresponding to 2θ = (36° – 41°) (b); and 2θ = (66° – 74°) (c).

Comparing the intensity of α”-Ti phase diffraction lines corresponding to 20%, 40% and 60% cold-rolling states, can be observed an increase in α”-Ti phase diffraction lines intensity, due to the fact that the stress-induced martensitic transformation progresses with increasing of cold deformation (increasing the volume fraction of α”-Ti phase). At 60% cold-rolling reduction the stress-induced martensitic transformation is still not suppressed by this large deformation, this suggest that the volume fraction of α”-Ti phase can still be increased by further cold-rolling deformation [54].

The diffraction lines broadening (FWHM parameter) in the case of both β-Ti and α’’-Ti phases increases with the increase of cold deformation, suggesting a continuous decrease in grain-size of both β-Ti and α’’-Ti phases, due to a combination of increasing grain refinement and internal stress caused by the cold deformation [55-59].

The second applied thermo-mechanical processing route on Ti-29Nb-9Ta-10Zr (wt%) alloy targeted the investigations of specific phenomena occurred during recrystallization thermal treatment, using as initial state a 90% cold-rolled state. The investigated recrystallization temperatures were as follows: 780°C (structural state 1), 830°C (structural state 2) and 880°C (structural state 3) – as presented in section 3.2.1.

The recorded XRD spectra corresponding to a recrystallization at 780°C, presented in figure 4.4-a, shows the presence of (110), (200) and (211) diffraction lines corresponding to β-Ti phase and the (020), (111), (002), (022), (200), (130), (131), (220), (202) and (113) diffraction lines corresponding to α’’-Ti phase. In order to compute the recorded XRD spectra the β-Ti phase was indexed in BCC system – Im-3m, while the α”-Ti phase was indexed in orthorhombic system – Cmcm. In the XRD spectra fitting procedure a Lorentz diffraction line profile was used, due to the introduced effects of recrystallization upon materials micro-structure.

Fig. 4.4. XRD recorded spectra in the case of 90% cold-rolled and recrystallized at 780°C Ti-29Nb-9Ta-10Zr (wt%) alloy (a); detailed XRD spectra corresponding to 2θ = (67° – 72°) (b).

Figure 4.4-b shows a detailed zoom corresponding to 2θ = (67° – 72°), can be observed that the convolution of α’’-Ti (131), α’’-Ti (220), β-Ti (211), α’’-Ti (202) and α’’-Ti (113) diffraction lines accurately describe the recorded XRD spectra. For each constitutive diffraction line its position, intensity and FWHM parameters were computed during XRD spectra fitting procedure.

Based on diffraction lines positions (2θ) and assumed crystalline systems, the lattice parameters corresponding to β-Ti and α’’-Ti phases were computed, it was obtained that in the case of β-Ti phase the lattice parameter was: a = 3.31Å, while in the case of α’’-Ti phase the lattice parameters were as follows: a = 3.31Å, b = 4.76Å and c = 4.66Å [60].

Fig. 4.5. XRD recorded spectra in the case of 90% cold-rolled and recrystallized at 830°C Ti-29Nb-9Ta-10Zr (wt%) alloy (a); detailed XRD spectra corresponding to 2θ = (68° – 72°) (b).

The recorded XRD spectra corresponding to a recrystallization at 830°C, presented in figure 4.5-a, shows the presence of same diffraction lines for both β-Ti and α’’-Ti phases. Same assumptions were made in the case of recrystallization at 830°C with the ones in the case of recrystallization at 780°C, in respect to crystalline systems constituent phases and diffraction lines profile used during XRD spectra fitting and deconvoluting process.

Figure 4.5-b shows a detailed zoom corresponding to 2θ = (68° – 72°), can be observed that the convolution of α’’-Ti (131), α’’-Ti (220), β-Ti (211), α’’-Ti (202) and α’’-Ti (113) diffraction lines accurately describe the recorded XRD spectra. For each constitutive diffraction line its position, intensity and FWHM parameters were computed.

The computed lattice parameters corresponding to β-Ti phase showed a lattice parameter: a = 3.30Å, while in the case of α’’-Ti phase the computed lattice parameters were as follows: a = 3.29Å, b = 4.75Å and c = 4.63Å.

Same observed diffraction lines in respect to both β-Ti and α’’-Ti phases were detected in the case of the recrystallization performed at 880°C (figure 4.6-a). The detailed zoom corresponding to 2θ = (69° – 71°) (figure 4.6-b) shows that the constituent diffraction lines accurately describe the recorded XRD spectra. The computed lattice parameters corresponding to β-Ti phase showed a lattice parameter: a = 3.285Å, while in the case of α’’-Ti phase the computed lattice parameters were as follows: a = 3.28Å, b = 4.73Å and c = 4.63Å [60].

Fig. 4.6. XRD recorded spectra in the case of 90% cold-rolled and recrystallized at 880°C Ti-29Nb-9Ta-10Zr (wt%) alloy (a); detailed XRD spectra corresponding to 2θ = (69° – 71°) (b).

Comparing the lattice parameters of α”-Ti phase obtained in the case of mechanical processing with the ones obtained in the case of thermal processing, a large difference can be detected in respect to lattice parameter a parameter (a = (3.31 – 3.28) Å – mechanical processing; a = (3.23 – 3.21) Å – thermal processing), this large change corroborate with the specifics of processing method, suggesting that two formation mechanisms are involved in α”-Ti phase formation, in the case of mechanical processing the α”-Ti phase is formed due to a stress induce transformation, while in case of thermal processing the α”-Ti phase is formed due to a thermal induce transformation.

Another important observation can be made in respect to intensity of β”-Ti phase diffraction lines, can be observed a transition from the most intense diffraction line (110) to (211), indicating a preferred orientation development in recrystallized β-Ti grains, as a result of thermal treatment.

Analysing the diffraction lines broadening (FWHM parameter) in the case of both β-Ti and α’’-Ti phases, can be observed a decreases with the increase of recrystallization temperature, suggesting a continuous increase in grain-size of both β-Ti and α’’-Ti phases, due to the growth of recrystallized β-Ti grains and athermal growth of α’’-Ti grains as a result of water quenching [61].

The third applied thermo-mechanical processing route on Ti-29Nb-9Ta-10Zr (wt%) alloy targeted the investigations of specific phenomena occurred during aging thermal treatment, performed on recrystallized states. The following structural states were investigated: recrystallized at 780°C followed by aging at 400°C (structural state 1), recrystallized at 830°C followed by aging at 400°C (structural state 2) and recrystallized at 880°C followed by aging at 400°C (structural state 3) – as presented in section 3.2.1.

The recorded XRD spectra corresponding to recrystallization at 780°C followed by aging at 400°C, presented in figure 4.7-a, shows the presence of (110), (200) and (211) diffraction lines corresponding to β-Ti phase and the (020), (111), (002), (022), (200), (130), (131), (220), (202) and (113) diffraction lines corresponding to α’’-Ti phase. In order to compute the recorded XRD spectra the β-Ti phase was indexed in BCC system – Im-3m, while the α”-Ti phase was indexed in orthorhombic system – Cmcm. In the XRD spectra fitting procedure a Lorentz diffraction line profile was used, due to the introduced effects of aging upon materials micro-structure. Figure 4.7-b shows a detailed zoom corresponding to 2θ = (69° – 70.5°), one can observe that the constituent diffraction lines accurately describe the recorded XRD spectra.

Based on diffraction lines positions (2θ) and assumed crystalline systems, the lattice parameters corresponding to β-Ti and α’’-Ti phases were computed, it was obtained that in the case of β-Ti phase the lattice parameter was: a = 3.31Å, while in the case of α’’-Ti phase the lattice parameters were as follows: a = 3.30Å, b = 4.73Å and c = 4.63Å.

Fig. 4.7. XRD recorded spectra in the case of recrystallized at 780°C followed by aging at 400°C Ti-29Nb-9Ta-10Zr (wt%) alloy (a); detailed XRD spectra corresponding to 2θ = (69° – 70.5°) (b).

The recorded XRD spectra corresponding to recrystallization at 830°C followed by aging at 400°C, presented in figure 4.8-a, shows the presence of β-Ti and α’’-Ti phases diffraction lines. Figure 4.8-b shows a detailed zoom corresponding to 2θ = (69° – 70.5°), where can observe that the constituent diffraction lines accurately describe the recorded XRD spectra. Computed lattice parameters corresponding to β-Ti and α’’-Ti phases showed the following: a = 3.31Å in the case of β-Ti phase, and a = 3.30Å, b = 4.73Å and c = 4.63Å in the case of α’’-Ti phase, values that are similar with the ones computed in the case of recrystallization at 780°C followed by aging at 400°C.

Fig. 4.8. XRD XRD recorded spectra in the case of recrystallized at 830°C followed by aging at 400°C Ti-29Nb-9Ta-10Zr (wt%) alloy (a); detailed XRD spectra corresponding to 2θ = (69° – 70.5°) (b).

Similar observations concerning presented phases can be made, also, in the case of performed recrystallization at 880°C followed by aging at 400°C (figure 4.9-a and figure 4.9-b). Very small differences are obtained in the case of computed lattice parameters of both β-Ti and α’’-Ti phases, showing the following values: a = 3.305Å in the case of β-Ti phase, and a = 3.295Å, b = 4.725Å and c = 4.625Å in the case of α’’-Ti phase.

Fig. 4.9. XRD recorded spectra in the case of recrystallized at 880°C followed by aging at 400°C Ti-29Nb-9Ta-10Zr (wt%) alloy (a); detailed XRD spectra corresponding to 2θ = (69° – 70.5°) (b).

4.2 XRD characterization of thermo-mechanical processed Ti-25Nb-25Ta alloy

The first applied thermo-mechanical processing route on Ti-25Nb-25Ta (wt%) alloy targeted the investigations of specific phenomena occurred during SPD-MPR processing with a large plastic strain of about 2.42, resulting investigated structural state 1 – as presented in section 3.2.2.

Figure 4.10-a shows the recorded XRD spectra in the case of SPD-MPR processed alloy, were can be detected the presence of (110), (200) and (211) diffraction lines corresponding to β-Ti phase, and the presence of (020), (022), (200), (131), (220) and (202) diffraction lines corresponding to α’’-Ti phase. In order to compute the recorded XRD spectra the β-Ti phase was indexed in BCC system – Im-3m, while the α”-Ti phase was indexed in orthorhombic system – Cmcm. In the XRD spectra fitting procedure a pseudo-Voight diffraction line profile was used, due to the introduced effects of mechanical processing upon materials micro-structure.

In the case of and detailed 2θ = (66° – 74°) XRD spectra (figure 4.10-b) the presence of (131), (220) and (202) α”-Ti phase and (211) β-Ti phase diffraction lines can be observed. Must be noticed that the fitted data accurately describe experimental recorded XRD spectra.

For each constitutive diffraction line its position, intensity and FWHM parameters were computed during XRD spectra fitting procedure. Computed lattice parameter corresponding to β-Ti phase showed a value close to a = 3.28 Å, while lattice parameters of α”-Ti phase were computed to: a = 3.21 Å; b = 4.73 Å and c = 4.63 Å [62]. Similar observations were reported in the case of thermo-mechanically processed Ti-22Nb-6Ta alloy [63], were the parent β-Ti phase showed a lattice parameter close to a = 3.289 Å while lattice parameters of α”-Ti phase close to: a = 3.221 Å; b = 4.766 Å and c = 4.631 Å.

Fig. 4.10. XRD recorded spectra in the case of SPD-MPR processed Ti-25Nb-25Ta (wt%) alloy (a) detailed XRD spectra corresponding to 2θ = (66° – 74°) (b).

The second applied thermo-mechanical processing route on Ti-25Nb-25Ta (wt%) alloy targeted the investigations of specific phenomena occurred during SPD-ARB processing of stacks of multiple layers. As investigated structural states the following were considered: investigated structural state 1; consisting in stack containing 4 SPD-ARB layers and structural state 2 – consisting in a stack containing 16 SPD-ARB layers – as presented in section 3.2.2.

Figures 4.11 and 4.12 show the recorded XRD spectra in the case of SPD-ARB 4 layers state (figure 4.11) and in the case of SPD-ARB 16 layers state (figure 4.12), were can be detected the presence of (110), (200) and (211) diffraction lines corresponding to β-Ti phase, and the presence of (020), (002), (111), (022), (200), (131), (220) and (202) diffraction lines corresponding to α’’-Ti phase. In order to compute the recorded XRD spectra the β-Ti phase was indexed in BCC system – Im-3m, while the α”-Ti phase was indexed in orthorhombic system – Cmcm. In the XRD spectra fitting procedure a pseudo-Voight diffraction line profile was used.

For each constitutive diffraction line its position, intensity and FWHM parameters were computed during XRD spectra fitting procedure. In both SPD-ARB 4 layers state case and SPD-ARB 16 layers state case, the computed lattice parameter corresponding to β-Ti phase showed a value close to a = 3.28 Å, while lattice parameters of α”-Ti phase were computed to: a = 3.21 Å; b = 4.73 Å and c = 4.63 Å [64].

Fig. 4.11. XRD recorded spectra in the case of SPD-ARB 4 layers processed Ti-25Nb-25Ta (wt%) alloy.

Fig. 4.12. XRD recorded spectra in the case of SPD-ARB 16 layers processed Ti-25Nb-25Ta (wt%) alloy.

4.3 XRD characterization of thermo-mechanical processed Ti-10Zr-5Nb-5Ta alloy

The applied thermo-mechanical processing route on Ti-10Zr-5Nb-5Ta (wt%) alloy targeted the investigations of specific phenomena occurred during both MPR and SPD-ARB processing of stacks of multiple layers. As investigated structural states the following were considered: investigated structural state 1, resulted after MPR processing with an accumulate plastic strain of ε = 1.34 and used as ARB “precursor”; structural state 2, consisting in a stack containing 2 SPD-ARB layers; structural state 3, consisting in a stack containing 4 SPD-ARB layers; structural state 4, consisting in a stack containing 8 SPD-ARB layers – as presented in section 3.2.3.

Figure 4.13-a shows the recorded XRD spectra in the case of MPR processed alloy, were can be detected the presence of (100), (002), (101), (102), (110), (103) and (112) diffraction lines corresponding to α-Ti phase, and the presence of (002), (111), (022) and (200) diffraction lines corresponding to α’’-Ti phase. In order to compute the recorded XRD spectra the α-Ti phase was indexed in HCP system – P63/mmc, while the α”-Ti phase was indexed in orthorhombic system – Cmcm [65]. In the XRD spectra fitting procedure a pseudo-Voight diffraction line profile was used, due to the introduced effects of mechanical processing upon materials micro-structure. For each constitutive diffraction line its position, intensity and FWHM parameters were computed during XRD spectra fitting procedure. Computed lattice parameter corresponding to α-Ti phase were as follows: a = 2.98 Å and c = 4.78 Å (a/c = 1.605), while lattice parameters of α”-Ti phase were computed to: a = 3.25 Å; b = 4.74 Å and c = 4.85 Å [65].

Fig. 4.13. XRD spectra in the case of Ti-10Zr-5Nb-5Ta (wt%) alloy; MPR processed (a); SPD-ARB 2 layers processed (b); SPD-ARB 4 layers processed (c); SPD-ARB 8 layers processed (d);

In the case of all SPD-ARB processed states (figures 4.13-b – 4.13-d) can be observed that position of both α-Ti and α”-Ti diffraction lines show almost no-variation. The computed lattice parameters of both α-Ti and α”-Ti phases were almost identical (differences were obtained in the third digit) with the ones computed in the “precursor” case. Only differences in diffraction lines intensity and broadening (FWHM) can be observed, suggesting that the SPD-ARB processing is influencing the developed crystallographic preferred orientation and the grain size.

CHAPTER 5

Advanced crystallographic texture analysis of thermo-mechanical processed Titanium-based alloys

In order to investigate the influence of applied thermo-mechanical processing route on specific developed texture features in Titanium-based alloys, two cases were considered, firstly, the case of crystallographic texture developed during mechanical processing, and secondly, the case of crystallographic texture developed during thermal processing. As investigated Titanium-based alloys the following compositions were investigated: Ti-29Nb-9Ta-10Zr (wt%) and Ti-25Nb-25Ta (wt%) as β-Ti alloys and Ti-10Zr-5Nb-5Ta (wt%) as α-Ti alloy.

The influence of mechanical processing route was investigated in the following conditions:

for an applied plastic strain below Severe Plastic Deformation – SPD limit; by Multi Pass Rolling – MPR processing; maximum applied plastic strain during MPR processing ε = 1.34;

for an applied plastic strain above Severe Plastic Deformation – SPD limit; by Multi Pass Rolling – MPR processing; maximum applied plastic strain during MPR processing ε = 2.42;

for an applied plastic strain above Severe Plastic Deformation – SPD limit; by Accumulative Roll Bonding – ARB processing; maximum applied plastic strain during ARB processing: ε = 3.2.

The influence of thermal processing route was investigated on 90% thickness reduction (total applied plastic strain ε = 2.31) cold-rolled Ti-29Nb-9Ta-10Zr (wt%) alloy samples, in the following conditions:

recrystallization treatment performed at a temperature between 780°C and 880°C;

aging treatment performed, on recrystallized samples, at 400°C.

5.1 Crystallographic texture developed during MPR processing

During mechanical processing of metallic materials a spatial preferred crystalline orientation can be developed, due to involved deformation mechanisms consisting in terms of active slip/twinning systems. The preferred crystalline orientation obtained as a result of mechanical processing is called deformation texture.

During mechanical processing mainly two fibering processes are developed, first refers to crystallographic fibering produced by crystallographic re-orientation of crystalline grains during deformation and second, refers to mechanical fibering produced by alignment of inclusions, cavities, etc. in the main direction of the deformation process, both being important factors in stirring the properties of mechanical processed materials. From textural point of view only crystallographic fibering is important.

In the case of Titanium-based alloys the developed fibers and specific individual texture components, as a consequence of mechanical processing, plays an important role in “engineering” materials properties in order to maximize the materials performance for specific application domains.

5.1.1 β-Titanium alloys

Considering the case of β-Titanium alloys it was showed that during mechanical processing by cold-rolling, starting from homogenized structures till 90% thickness-reduction, the main developed texture consist of α-fiber, -fiber and also some specific individual texture components [63].

The most easiest way to realize high plastic strains on deformed metallic materials consist of Multi Pass Rolling – MPR processing, which assumes the realization of the total imposed plastic strain by successive rolling passes with an imposed strain (see 3.2.1 section). As a representative β-Titanium alloy the Ti-29Nb-9Ta-10Zr (wt%) alloy is considered and analysed. The thermo-mechanical processing route applied to Ti-29Nb-9Ta-10Zr alloy in order to investigate the influence of MPR processing is presented in 3.2.1 section.

In order to calculate the ODFs, few assumptions must be made, first, sample crystalline symmetry indexed in cubic Im-3m system, and second, sample geometric symmetry indexed in orthorhombic mmm system. The ODF’s were computed using experimental measured (110), (200) and (211) pole figures of the β-Ti phase, and processed using de la Vallée Poussin kernel function, Gaussian distribution, Ghost correction and intensities normalization. During ODF’s computation the misorientation was set to 3°.

Using computed ODF’s the analyse of developed texture by terms of Inverse Pole Figure (IPF), the IPF’s showing how a selected direction in the sample reference system is distributed in the crystal reference system, corresponding to a 20% thickness reduction by cold-rolling (figure 5.1), 40% thickness reduction by cold-rolling (figure 5.2) and 60% thickness reduction by cold-rolling (figure 5.3), was performed.

Fig. 5.1. Representation of IPF’s corresponding to 20% cold-rolled Ti-29Nb-9Ta-10Zr alloy.

Fig. 5.2. Representation of IPF’s corresponding to 40% cold-rolled Ti-29Nb-9Ta-10Zr alloy.

Fig. 5.3. Representation of IPF’s corresponding to 60% cold-rolled Ti-29Nb-9Ta-10Zr alloy.

Analysing the IPF’s one can was observed that: in the case of 20% cold-rolled state [111] crystallographic direction is most likely parallel to sample normal direction (ND), the [111]//ND pair reaching an intensity close to 2.5 MRD (MRD – Multiple of a Random Density). In the case of RD and TD directions most intense observed pairs are [101]//RD and [101]//TD, with an intensity of 0.7 MRD and respectively 1.0 MRD. Same observation can be made in the case of 40% cold-rolled state and 60% cold-rolled, with the difference that the observed pairs intensity is increasing.

The maximum intensity is obtained in the case of [111]//ND pair, reaching an intensity close to 4.2 MRD in the case of 60% cold-rolling state. This increase in observed pairs intensity can be attributed to the increased number of grains resulted during cold-rolling grain refining process and also to the grain rotations resulted during deformation.

The most relevant and important texture fibers developed during thermo-mechanical processing of cubic metallic materials are [66-68]:

α-fiber (crystallographic fibre axis <110> parallel to the rolling direction, including major components: {001}<110>; {112}<110>;{111}<110>);

-fiber (crystallographic fibre axis <111> parallel to the normal direction, including major components: {110}<110>; {111}<112>);

η-fiber (crystallographic fibre axis <001> parallel to the rolling direction, including major components: {001}<100>; {011}<100>);

ζ-fiber (crystallographic fibre axis <011> parallel to the normal direction, including major components: {011}<100>; {011}<211>; {011}<111>); {011}<011>);

ε-fiber (crystallographic fibre axis <011> parallel to the transversal direction, including major components: {001}<011>; {112}<111>; {111}<112>); {011}<100>);

θ-fiber (crystallographic fibre axis <001> parallel to the normal direction, including major components: {001}<100>; {001}<110>).

Figure 5.4 shows the ODF’s sections corresponding to 2 = 0°, 2 = 15°, 2 = 30° and 2 = 45° of the 20% cold-rolled state, in the case of Ti-29Nb-9Ta-10Zr alloy.

The highest orientation densities are obtained in the case of 2 = 45° section, with a maximum of orientation density close to 3.1 MRD corresponding to ()[] and ()[] texture components, both being invariants of {111}<110> system and belonging to -fibre, while an orientation density between 2.4 MRD to 2.6 MRD is observed in the case of ()[] and ()[] texture components, both being invariants of {111}<112> system and belonging also to -fibre. Smaller orientation density, between 1.8 MRD to 2.0 MRD, are observed in the case of ()[], ()[] and ()[] texture components.

In the case of α-fibre, 2 = 0° section, which spreads from ()[] to ()[] to ()[] to ()[], can be observed a weak orientation density with the maximum close to 1.9 MRD in the case of ()[] texture component.

Comparing the 40% cold-rolled state (figure 5.5) with 20% cold-rolled state (figure 5.4) can be observed an important increase in orientation density of ()[] texture component from 1.8 MRD to respectively 4.1 MRD, becoming a major texture component (figure 5.5-a). A smaller increase in observed in the case of ()[] and ()[] texture components, from 3.1 MRD to respectively 4.1 MRD. Must be noticed that the orientation density of ()[] and ()[] texture components, both being invariants of {001}<100> system, show dramatically increase to almost 3.4 MRD (figure 5.5-a). The α-fibre components show increase in orientation density, with the maximum close to 2.9 MRD in the case of ()[] texture component.

In the case of 60% cold-rolled state (figure 5.6) can be observed that the orientation density of ()[] and ()[] texture components increases to a maximum value of about 4.3 MRD, becoming a major texture component (figure 5.6-a). The orientation density of -fibre texture components, expressed by ()[], ()[], ()[] and ()[] texture components, increase to 4.2 MRD in the case of {111}<110> invariants and respectively to 4.1 MRD in the case of {111}<112> invariants (figure 5.6-a). Also, the orientation density of ()[] texture component increase to 4.1 MRD, becoming a major texture component.

The {001}<110> texture component, with ()[] and ()[] invariants, is commonly observed in BCC titanium alloys after cold-rolling [63,66,69,70]. It was reported in the case of Ti-35Nb-7Zr-5Ta [56] and Ti-25Nb-10Ta-1Zr-0.2Fe [59] that the -fibre expressed by {111}<110> and by {111}<112> texture components, is the most important developed texture component after cold-rolling with 70% thickness reduction.

Fig. 5.4. Representation of ODF’s corresponding to 20% cold-rolled Ti-29Nb-9Ta-10Zr alloy;

a – ODF section: 2 = 0°; b – ODF section: 2 = 15°; c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

Fig. 5.5. Representation of ODF’s corresponding to 40% cold-rolled Ti-29Nb-9Ta-10Zr alloy;

a – ODF section: 2 = 0°; b – ODF section: 2 = 15°; c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

Fig. 5.6. Representation of ODF’s corresponding to 60% cold-rolled Ti-29Nb-9Ta-10Zr alloy;

a – ODF section: 2 = 0°; b – ODF section: 2 = 15°; c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

This type of variation in developed texture components can be explained by the differences in activation mechanism of each texture component [54]. During plastic deformation, as a consequence of the shear on specific favourable oriented crystal planes and directions the grains deform due to slip and/or twinning. The number of active slip/twinning systems is affected by the applied strain and constraints between neighbouring grains. Slip/twinning activation and their variation within and between grains determine the deformation microstructure and the change of grains orientation. During cold-rolling, the slip/twinning planes rotate due to dislocation glide, the rotation being towards the tensile axis, as a consequence of constraint of the axis. Slip/twinning planes rotation make possible the activation of different {hkl}<uvw> texture components [71].

A way to explain how a texture component can be activated during deformation can be made using the Schmid factor (SF) analysis. If considered a (hkl) slip plane and an orthogonal slip direction [uvw] to the slip plane and assuming a simple shear in a specific direction then computation of the SF associated to (hkl)[uvw] slip system is possible. Same computation can be made in the case of (hkl)[uvw] twinning systems [71,72]. The Schmid factor (SF) can be defined as:

where – represents the angle between the simple shear direction and normal to the slip/twinning plane; ϕ – represents the angle between the simple shear direction slip/twinning direction. The λ and ϕ angles can take values between 0° and 180°.

Computed values of SF associated to major observed texture components are presented in table 5.1. As observed, firstly activated deformation mechanisms consist in slip deformation followed by twinning. Associating data concerning SF’s values of activated slip/twinning systems with intensity of deformation, expressed by thickness reduction, leads to assumption that in early stages of deformation, up to 20% thickness reduction, only slip systems are activated, mainly ()[] and ()[] systems. Increasing the intensity of deformation, up to 40% thickness reduction, the ()[] slip system becomes active. Besides slip deformation, twinning deformation appears, the ()[] twinning system being activated. Further increasing the intensity of deformation, up to 60% thickness reduction, the ()[], ()[] and ()[] slip systems remain active but the ()[] twinning system is replaced by the ()[] and ()[] systems [54].

Table 5.1. Obtained SF’s for observed slip/twinning systems.

In order to compute the volume fraction of a certain orientation – texture component (1–2), and the texture index (F), it was assumed a misorientation of 15°.

In tables 5.2, 5.3 and 5.4 computed data concerning volume fraction of specified texture components and the texture index are presented. Analysing the texture index F, one can observe that increasing applied plastic deformation (thickness reduction) the texture index is increasing, from 1.27 in the case of 20% thickness reduction, to 1.46 in the case of 40% thickness reduction and finally to 1.53 in the case of 60% thickness reduction. As observed, the slop of the increase is higher for thickness reductions up to 40% and lower in the case of a thickness reduction between 40% and 60%.

This behaviour can be explained by the specific of deformation mechanisms involved in plastic deformation, in the first stages of deformation the grains of a polycrystalline materials are deforming by slip followed by twinning, both on low Miller indexes planes, until a saturation process is reached. In order to further accommodate an increased plastic strain the grains suffer a rotation and fragmentation (a grain refining process) together with activated slip and twinning on high Miller indexes planes. The resulted smaller grains with random orientations decreasing the texture strength (texture index). The texture index is influenced by the competitive balance between grains rotation and grains fragmentation during plastic deformation. For a higher plastic deformation intensity the grains rotation process is surpassed by the grain fragmentation (grain refining) process.

Table 5.2. Texture characteristics (texture components, volume fraction and texture index) developed

in case of 20% thickness reduction by MPR processing of Ti-29Nb-9Ta-10Zr alloy.

Analysing data concerning volume fraction of investigated texture components can be observed that the -fiber texture components show the higher volume fraction. Applying 20% thickness reduction leads to a volume fraction of about (0.0538 – 0.0531) is recorded in the case of and (0.0501 – 0.0497) is recorded in the case of . One must remember that these values correspond to individual texture components and in the case of entire -fiber volume fractions these values must be added for all texture components.

Can be observed that the volume fraction of -fiber texture components reaches a “plateau” to 40% thickness reduction, when a volume fraction of about (0.0837 – 0.0831) is recorded in the case of and (0.0761 – 0.0751) is recorded in the case of . Further increase in accommodate plastic strain up to 60% thickness reduction, has a small influence in volume fraction of -fiber texture components, when a volume fraction of about (0.0814 – 0.0815) is recorded in the case of and (0.0784 – 0.0775) is recorded in the case of . This can be explained also by the specifics of plastic deformation at higher plastic strains, the competitive process between grains rotation and grains fragmentation (grains refining) balancing the volume fraction of a specific texture component. At higher plastic strains, in order to accommodate the increased strain, the grains are likely to fragment, resulting grains with random orientation, than to rotate towards preferred spatial orientations [54].

Table 5.3. Texture characteristics (texture components, volume fraction and texture index) developed

in case of 40% thickness reduction by MPR processing of Ti-29Nb-9Ta-10Zr alloy.

Table 5.4. Texture characteristics (texture components, volume fraction and texture index) developed

in case of 60% thickness reduction by MPR processing of Ti-29Nb-9Ta-10Zr alloy.

5.1.2 α-Titanium alloy

As a representative α-Titanium alloy the Ti-10Zr-5Nb-5Ta (wt%) alloy is considered and analysed. The applied thermo-mechanical processing route on Ti-10Zr-5Nb-5Ta alloy, in order to investigate the influence of MPR processing, is presented in 3.2.3 section.

The following assumptions were made in order to calculate the ODF: the specimen symmetry was indexed in orthorhombic mmm system while the crystalline symmetry was indexed in hexagonal P63/mmc system [65]. The ODF was computed using experimental measured (002), (100), (101) and (102) pole figures of the α-Ti phase, and processed using de la Vallée Poussin kernel function, Gaussian distribution, Ghost correction and intensities normalization. During ODF’s computation the misorientation was set to 3°.

Fig. 5.7. Representation of IPF’s corresponding to 75% cold-rolled Ti-10Zr-5Nb-5Ta alloy.

Fig. 5.8. Representation of ODF’s corresponding to 75% cold-rolled Ti-10Zr-5Nb-5Ta; a – ODF section: 1 = 0°; b – ODF section: 1 = 15°; c – ODF section: 1 = 30°; d – ODF section: 1 = 45°.

Figure 5.7 shows the representation of Inverse Pole Figures for a 75% thickness reduction in the case of MPR processed Ti-10Zr-5Nb-5Ta alloy, in respect to RD, TD and ND sample reference system. One can observe that, if we consider the RD direction, the IPF shows which crystallographic directions in the polycrystalline material are parallel to the sample rolling direction [65]; in this case can be observed that the []//RD pair reaches an intensity close to 3.7 MRD and the []//RD pair reaches an intensity close to 3. In the case of TD direction, can be observed that no pairs parallel to TD are formed. Analysing the ND direction one can observe that low intensity []//ND, []//ND, []//ND and []//ND pairs are formed and all showing intensities close to 2.5 MRD. The highest intensity recorded, close to 3.0 MRD, is detected in the case of []//ND pair.

The most relevant and important texture fibers and individual texture components developed during thermo-mechanical processing of HCP – hexagonal close-packet materials are [73]:

{} basal fibre: including major components ()[] and ()[];

{} fibre: including major components ()[] and ()[];

{} fibre: including major components ()[] and ()[];

texture component ()[];

texture component ()[];

texture component ()[];

texture component ()[].

In the case of HCP materials the ODF’s are represented, also, in the Bunge system (1–2) (φ1 = 0° – 90°; Φ = 0° – 90°; φ2 = 0° – 60°) using φ1 sections. The most important ODF sections corresponds to φ1 = 0° and φ1 = 45°.

In the case of φ1 = 0° section (figure 5.8-a), the most important observed texture components are: high intensity texture components: ()[] and ()[], showing an orientation density close to 7.7 MRD; ()[] and ()[], showing an orientation density close to 6.9 MRD; basal fibre {0001}, including major components ()[] and ()[], with an orientation density close to 5.9 MRD; {} fibre, including major components ()[] and ()[], with an orientation density close to 5.1 MRD;

Analysing the φ1 = 45° section (figure 5.8-d), one can observe that fewer texture components are present, the most intense being the basal fibre {0001} with the major component ()[], with and orientation density close to 6.9 MRD; and the individual texture components ()[] and ()[], both showing a low orientation density close to 4.1 MRD.

In order to compute the volume fraction of a certain orientation – texture component (1–2), and the texture index (F), it was assumed a misorientation of 15°.

In table 5.5 computed data concerning volume fraction of specified texture components and texture index are presented. One can observe that the higher volume fraction is obtained in the case of -fiber (spreading from to texture components) and -fiber (spreading from to texture components) with a component volume fraction of about 0.0870 and respectively 0.0695. Also, other texture components are presented showing a volume fraction between 0.0093 and 0.0829.

Analysing the texture index (texture strength), can be observed that is situated close to 1.86. This value being useful as comparison element for further processed states studied from textural point of view.

Table 5.5. Texture characteristics (texture components, volume fraction and texture index) developed in case of 75% thickness reduction by MPR processing of Ti-10Zr-5Nb-5Ta alloy.

5.2 Crystallographic texture developed during SPD processing

5.2.1 β-Titanium alloys processed by MPR

As a representative β-Titanium alloys the Ti-25Nb-25Ta (wt%) alloy is considered and analysed. The Severe Plastic Deformation – SPD processing route applied to Ti-25Nb-25Ta alloy, in order to investigate the influence of SPD processing, is presented in 3.2.2 section.

The SPD term is used in the case of mechanical processing of a metallic material if the total applied plastic strain (ε), during mechanical processing, is grater then 2.

In the case of SPD by MPR processing of Ti-25Nb-25Ta alloy, with a thickness reductions above 91% (ε > 2.42) and obtaining ultra-thin specimens with a final thickness close to 30 μm, ultra-strength phenomena was identified [62]. The recorded strain-stress diagram (figure 5.9) shows the presence of ultimate tensile strength (UTS) in the range of 2400 – 2500 MPa, while for the same alloy in as-cast condition the UTS limit is situated close to 680 MPa.

Similar high values for various SPD processed β-type titanium alloys were reported also [74] TIMETAL-LCB – UTS = 1640 MPa; Ti-15-3 – UTS = 1840 MPa; β-21S – UTS = 1620 MPa; VT-22 – UTS = 1755 MPa.

Due to the large applied strain the initial grains are heavily deformed and fragmented, result a micro/nano-scale crystalline structure with a highly preferred spatial orientation. Knowing that the materials properties are direction dependent, the increase in ultimate tensile strength exhibited by the cold-rolled Ti-25Nb-25Ta alloy must be, beside strain-hardening, the result of grains rotations and re-arrangements towards preferred orientations which gives the maximum strength to applied stress [62].

Fig. 5.9. Strain-stress diagram of as-cast and SPD processed Ti-25Nb-25Ta alloy.

In order to calculate the ODF, few assumptions must be made, first, sample crystalline symmetry indexed in cubic Im-3m system, and second, sample geometric symmetry indexed in orthorhombic mmm system. The ODF was computed using experimental measured (110), (200) and (211) pole figures of the β-Ti phase, and processed using de la Vallée Poussin kernel function, Gaussian distribution, Ghost correction and intensities normalization. During ODF computation the misorientation was set to 3°.

Analysing the IPF’s of the β-Ti phase (figure 5.10), can be noticed that the [001] crystallographic direction is most likely parallel to sample normal direction (ND), the [001]//ND pair reaching an intensity close to 11.6 MRD. In the case of [111] crystallographic direction can be observed that the intensity of [111]//ND pair exhibits an intensity close to 7.8 MRD. The third intense pair consist of [101]//TD pair, with an intensity close to 5.1 MRD.

Comparing the results obtained in the case of 60% cold-rolling reduction (Ti-29Nb-9Ta-10Zr) and 92% cold-rolling reduction (Ti-25Nb-25Ta) in respect to more intense developed pair, can be observed that increasing the applied strain affects the developed pair, changing the preferred orientation from [111]//ND to [001]//ND.

The computed ODF sections (figure 5.11) show the presence of a weaker -fibre, spreading from {111}<110> to {111}<112> texture components, with an orientation density close to 11.3 MRD (figure x.22-b). The most intense observed texture components are: ()[] and ()[] with an orientation density close to 21.4 (figure 5.11-a) and ()[] and ()[] with an orientation density close to 22.3 (figure 5.11-b).

Comparing the results obtained in the case of 60% cold-rolling reduction (Ti-29Nb-9Ta-10Zr) and 91% cold-rolling reduction (Ti-25Nb-25Ta) in respect to more intense developed texture components, can be observed that increasing the applied strain affects the developed texture components, decreasing the orientation density of the -fiber and increasing the orientation density of the {001}<110> texture components.

Fig. 5.10. Representation of IPF’s corresponding to 92% cold-rolled Ti-25Nb-25Ta alloy.

Fig. 5.11. Representation of ODF’s corresponding to 92% cold-rolled Ti-25Nb-25Ta;

a – ODF section: 2 = 0°; b – ODF section: 2 = 45°.

In order to compute the volume fraction of a certain orientation – texture component (1–2), and the texture index (F), it was assumed a misorientation of 15°.

In table 5.6 computed data concerning volume fraction of specified texture components and texture index are presented. One can observe that the higher volume fraction is obtained in the case of , and texture components, all belonging to texture family. In all cases the volume fraction being situated close to 0.13.

A smaller volume fraction is obtained in the case of -fiber texture components, when a volume fraction of about (0.1159 – 0.1181) is recorded in the case of texture components, and respectively (0.1121 – 0.1110) in the case of texture components.

Taking into consideration the specific of ODF in Euler space, in order to compute the entire -fiber volume fraction, one must consider all -fiber texture components:

family: ; ; ; ; ; ;

family: ; ; ; ; ; .

In this case the entire -fiber volume fraction containing both and families is determined using the average volume fraction of each family, using the following relation:

Same formalism can be applied in the case of texture family, considering the following texture components: ; ; ; ; ; ; ; , by using the following relation:

Table 5.6. Texture characteristics (texture components, volume fraction and texture index) developed in case of 91% thickness reduction by MPR processing of Ti-25Nb-25Ta alloy.

Comparing the texture index for 91% thickness reduction (Ti-25Nb-25Ta) with the texture index for 60% thickness reduction (Ti-29Nb-9Ta-10Zr) and ignoring the fact that are two distinct β-Titanium alloys, can be observed that in the first case the texture index is situated close to 3.43 while in the second case is situated close to 1.53. This means that at ultra-high intense plastic deformation when a nano-structure is reached (due to intense grain refining) the nano-grains tend to favour the rotation process in competition with fragmentation process. In the case to nano-grains deformation the necessary stress to deform the structure is drastically increased due to an inverse Hall-Petch relation, forcing the nano-grains more prone to rotation [75-78].

5.2.2 β-Titanium alloys processed by SPD-ARB

As a representative β-Titanium alloy the Ti-25Nb-25Ta (wt%) alloy is considered and analysed here. The SPD by Accumulative Roll Bonding – ARB processing route applied to Ti-25Nb-25Ta alloy is presented in 3.2.2 section.

In order to calculate the ODF’s, few assumptions must be made, first, sample crystalline symmetry indexed in cubic Im-3m system, and second, sample geometric symmetry indexed in orthorhombic mmm system [64]. The ODF’s were computed using experimental measured (110), (200) and (211) pole figures of the β-Ti phase, and processed using de la Vallée Poussin kernel function, Gaussian distribution, Ghost correction and intensities normalization. During ODF computation the misorientation was set to 3°.

As showed in 3.2.2 section, the SPD processing was performed using ARB technique, resulting “sacks” of layers, with a double number of layers after each ARB pass. Under investigation were stacks of layers containing 4 (after second ARB pass) and 16 layers (after fourth ARB pass).

The total equivalent plastic strain accumulated during ARB processing can be computed using the following equation [79,80]:

where: n – represents the ARB cycle number.

Computing the evolution of equivalent accumulated strain, results that the plastic strain is increased (multiplied) by a factor of 0.8 after each ARB cycle. In this way, after second ARB pass the plastic strain is 1.6 and after fourth ARB pass the plastic strain is 3.6. If considering the plastic strain accumulated during obtaining of ARB “precursor” sample, in excess of 1.25, can be assumed that even after second ARB pass the total plastic strain exceeds the 2 value limit. In this way all investigated structural states being SPD produced.

Analysing the IPF’s corresponding to 4 layers ARB state (figure 5.12), can be noticed that the [001] crystallographic direction is most likely parallel to sample normal direction (ND), the [001]//ND pair reaching an intensity close to 5.7 MRD. The second most intense pairs are represented by the [111]//ND and [11]//ND pairs, with and intensity close to 3.6 MRD. Same approximately intensity is recorded also for in the case of [101]//RD pair.

Fig. 5.12. Representation of IPF’s corresponding to SPD 4 layers ARB processed Ti-25Nb-25Ta alloy.

Fig. 5.13. Representation of IPF’s corresponding to SPD 16 layers ARB processed Ti-25Nb-25Ta alloy.

The IPF’s corresponding to 16 layers ARB state (figure 5.13) show a similar behaviour with the one recorded in the case of 4 layers ARB state, with the difference only in active pairs intensity. In the 16 layers ARB state the maximum intensity of 2.6 MRD is obtained in the case of [001]//ND pair. As observed, the intensity is less than half in comparison with 4 layers ARB state.

The computed ODF’s sections corresponding to 4 layers ARB state (figure 5.14). In the ODF 2 = 0° section (figure 5.14-a) can be observed that the only active texture component is represented by the {001}<110> family, spreading from ()[] to ()[], with and orientation density close to 10.9 MRD. The ODF 2 = 45° section (figure 5.14-d) shows the presence of a weaker -fibre, spreading from {111}<110> to {111}<112> texture components, with a maximum orientation density close to 4.5 MRD (figure 5.14-d). The most intense observed texture components are represented by the: ()[] and ()[] with an orientation density close to 10.9 (figure 5.14-d). The second intensity is obtained in the case of ()[] texture component, with an orientation density close to 8.5 MRD (figure 5.14-d).

If comparing the ODF 16 layers ARB case with the ODF 4 layers ARB case, similar behaviour with the one recorded in the IPF’s case can observed, the maximum orientation density is reduced at half, to approximately 5.4 MRD (figure 5.15), in comparison with 10.9 MRD recorded in the case of 4 layers ARB state (figure 5.14). Also in this case maximum orientation density is recorded in the case of {001}<110> family, spreading from ()[] to ()[], with and orientation density close to 5.4 MRD.

In order to compute the volume fraction of a certain orientation – texture component (1–2), and the texture index (F), it was assumed a misorientation of 15°.

Fig. 5.14. Representation of ODF’s corresponding to SPD 4 layers ARB processed Ti-25Nb-25Ta alloy;

a – ODF section: 2 = 0°; b – ODF section: 2 = 15°; c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

In tables 5.7 and 5.8 computed data concerning volume fraction of specified texture components and texture index are presented. Analysing the texture index F, one can observe that increasing applied plastic deformation the texture index is decreasing, from 2.44 in the case of 4 layers ARB state, to 1.52 in the case of 16 layers ARB state.

Fig. 5.15. Representation of ODF’s corresponding to SPD 16 layers ARB processed Ti-25Nb-25Ta alloy;

a – ODF section: 2 = 0°; b – ODF section: 2 = 15°; c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

Analysing data concerning volume fraction of investigated texture components can be observed that the -fiber texture components show the higher volume fraction. In the case of 4 layers ARB processed state (table 5.7) the computed volume fraction of -fiber texture components is closely situated to (0.11 – 0.12) corresponding to , and respectively (0.17 – 0.11) corresponding to . The second high volume fraction is recorded in the case of α-fiber texture components, which spreads from , showing a volume fraction of about 0.075, to , with a volume fraction of about 0.14 – almost double in comparison.

Same variation is recorded also in the case of 16 layers ARB state (table 5.8), when smaller values corresponding to computed volume fractions are obtained in both -fiber and α-fiber texture components cases.

This drastically decrease in IPF’s intensity, ODF’s orientation density and volume fraction of different texture components, must be due to, firstly, the increased number of grains resulted during SPD processing, and secondly, due to reduced grain size of the SPD processed β-Ti phase. Also, the grains rotation/fragmentation competitive process during large plastic strains must be considered in explaining the observed evolution in terms of intensities, orientation densities and computed volume fractions [64].

Table 5.7. Texture characteristics (texture components, volume fraction and texture index) developed in case of SPD 4 layers ARB processed Ti-25Nb-25Ta alloy.

Table 5.8. Texture characteristics (texture components, volume fraction and texture index) developed in case of SPD 16 layers ARB processed Ti-25Nb-25Ta alloy.

5.2.3 α-Titanium alloys processed by ARB

As a representative α-Titanium alloy the Ti-10Zr-5Nb-5Ta (wt%) alloy is considered and analysed here. The applied thermo-mechanical processing route is presented in 3.2.3 section.

The following assumptions were made in order to calculate the ODF’s: the specimen symmetry was indexed in orthorhombic mmm system while the crystalline symmetry was indexed in hexagonal P63/mmc system. The ODF’s were computed using experimental measured (002), (100), (101) and (102) pole figures of the α-Ti phase, and processed using de la Vallée Poussin kernel function, Gaussian distribution, Ghost correction and intensities normalization. During ODF’s computation the misorientation was set to 3°.

As showed in 3.2.3 section, the SPD processing was performed using ARB technique, resulting “sacks” of layers, with a double number of layers after each ARB pass. Under investigation were obtained stacks containing 2 layers (after first ARB pass), 4 layers (after second ARB pass) and 8 layers (after third ARB pass).

Computing the evolution of equivalent accumulated strain, results that the strain is increased (multiplied) by a factor of 0.8 after each ARB cycle. In this way, after 1 ARB pass the strain is 0.8, after second ARB pass the strain is 1.6 and after third ARB pass the strain is 2.4. Considering that the ARB procedure is started using a cold-rolled precursor, with a plastic strain of about 1.36, and “superimposing” the total strain supported by the material after first ARB pass (0.8) results that the total accumulated strain exceeds the threshold limit value of 2, in this way we can say that in our particular case we have a SPD processing even after first ARB cycle [65].

Figures 5.16, 5.17 and 5.18 show the representation of IPF’s corresponding to first, second and third ARB pass, in respect to RD, TD and ND sample reference system. Comparing the developed pairs in the case of 75% cold-rolled alloy (section 3.2.3) which consisted as “precursor” for the ARB processing, with the ARB processed states, one can observe that, if we consider the RD direction, the []//RD pair is no-longer the most intense one, the most intense being []//TD, showing an intensity close to 3.4 MRD (2 layers ARB), 3.8 MRD (2 layers ARB) and 4.2 MRD (2 layers ARB). Another important observation can refer to []//ND, []//ND, []//ND developed pair in the case of precursor material, as observed for all ARB passes a translation of []//ND []//ND and []//ND []//ND can be noticed.

Fig. 5.16. Representation of IPF’s corresponding to 2 layers ARB processed Ti-10Zr-5Nb-5Ta alloy.

Fig. 5.17. Representation of IPF’s corresponding to 4 layers ARB processed Ti-10Zr-5Nb-5Ta alloy.

Fig. 5.18. Representation of IPF’s corresponding to 8 layers ARB processed Ti-10Zr-5Nb-5Ta alloy.

Fig. 5.19. Representation of ODF’s corresponding to 2 layers ARB processed Ti-10Zr-5Nb-5Ta alloy; a – ODF section: 1 = 0°; b – ODF section: 1 = 15°; c – ODF section: 1 = 30°; d – ODF section: 1 = 45°.

Fig. 5.20. Representation of ODF’s corresponding to 4 layers ARB processed Ti-10Zr-5Nb-5Ta alloy; a – ODF section: 1 = 0°; b – ODF section: 1 = 15°; c – ODF section: 1 = 30°; d – ODF section: 1 = 45°.

Computed ODF’s corresponding to 2 layers ARB state, 4 layers ARB state and 8 layers ARB state are presented in figures 5.19, 5.20 and 5.21, using φ1 = 0°, φ1 = 15°, φ1 = 30° and φ1 = 45° sections. In the case of φ1 = 0° ODF section, comparing the developed texture components in the case of precursor state with the ARB processed states, can be observed a transition of the highest orientation density from ()[] and ()[] system to ()[] and ()[] system, from 7.9 MRD to 4.64 MRD in the case of 2 layers ARB – figure 5.19-a, 4.26 MRD, in the case of 4 layers ARB – figure 5.20-a, 4.81 MRD in the case of 8 layers ARB – figure 5.21-a. Another important observation refer to transition from ()[] and ()[] system to ()[] and ()[] system, as the second in orientation density developed during ARB processing, which is reaching an orientation density close to 4.20 MRD, in the case of 2 layers ARB – figure 5.19-a, 3.82 MRD in the case of 4 layers ARB – figure 5.20-a, 3.51 MRD in the case of 8 layers ARB – figure 5.21-a.

Must be noticed that a new texture component is developed exclusively by the ARB processing, namely the ()[] texture component, which is increasing in orientation density with progress of ARB processing, from 2.8 MRD, in the case of 2 layers ARB – figure 5.19-a, to 4.4 MRD, in the case of 8 layers ARB – figure 5.21-a.

Fig. 5.21. Representation of ODF’s corresponding to 8 layers ARB processed Ti-10Zr-5Nb-5Ta alloy; a – ODF section: 1 = 0°; b – ODF section: 1 = 15°; c – ODF section: 1 = 30°; d – ODF section: 1 = 45°.

In the case of φ1 = 45° ODF section, comparing the developed texture components in the case of precursor state with the ARB processed states, can be observed a transition form ()[] and ()[] components to ()[], ()[] and ()[] texture components, with and decreasing orientation density, from 2.84 MRD (figure 5.19-d) to 2.31 MRD (figure 5.21-d). Also, must be noticed that the orientation density of )[] and )[] texture components is increasing with progress of ARB processing, from 2.43 MRD (figure 5.19-d) to 3.13 MRD (figure 5.21-d).

In order to compute the volume fraction of a certain orientation – texture component (1–2), and the texture index (F), it was assumed a misorientation of 15°.

In tables 5.9, 5.10 and 5.10 computed data concerning volume fraction of specified texture components and texture index are presented.

Analysing the texture index F, one can observe that as a result of the increased applied plastic deformation during ARB processing the texture index is slowly increasing, from 1.38 (in the case of 2 layers ARB processed state), to 1.39 (in the case of 4 layers ARB processed state), and finally to 1.53 (in the case of 8 layers ARB processed state). As observed, the texture index is almost equal for both 2 layers and 4 layers ARB states, suggesting that the first ARB steps have a negligible influence upon texture index.

The computed volume fractions corresponding to major texture components show approximately identical volume fractions in all cases, suggesting that the ARB processing has a negligible influence upon volume fraction.

If comparing computed volume fractions in the case of MPR processed state, section 5.1.2 – table 5.5, with the SPD-ARB states, for example in the case of major texture components and , can be observed that the volume fractions is decreasing from 0.087 to a half value of about 0.041, showing a decrease in “strength” due to SPD-ARB processing.

This behaviour suggest that in order to accumulate the increased plastic strain, the structure is heavily refined, due to a combination of intense fragmentation with limited grain rotation.

If taking into consideration the specifics of slip/twinning deformation in HCP structures and considering the specifics SPD processing, results that due to the limited slip/twinning deformation of HCP structures at higher plastic strains, the rotation/fragmentation competitive process represents the main influential process [65].

Table 5.9. Texture characteristics (texture components, volume fraction and texture index) developed

in case of ARB 2 layers processing of Ti-10Zr-5Nb-5Ta alloy.

Table 5.10. Texture characteristics (texture components, volume fraction and texture index) developed

in case of ARB 4 layers processing of Ti-10Zr-5Nb-5Ta alloy.

Table 5.11. Texture characteristics (texture components, volume fraction and texture index) developed

in case of ARB 8 layers processing of Ti-10Zr-5Nb-5Ta alloy.

5.3 Crystallographic texture developed during thermal processing

As showed, the mechanical processing of a Titanium-based alloy, both for non-SPD and SPD deformation produces a preferred crystalline orientation. This preferred crystalline orientation depends on crystalline symmetry of the deformed material, and also on the intensity (accommodate plastic strain) of the mechanical processing.

If after mechanical processing a thermal processing stage is applied, the result of such thermal treatment is appearance of a crystalline preferred orientation, generally different from the crystalline preferred orientation resulted after mechanical processing, with a higher orientation density (increased texture strength). Usually, after cold-mechanical processing an annealing or recrystallization treatment is applied, for this reason the resulted preferred orientation is called annealing or recrystallization texture.

As influence factors of annealing/recrystallization texture must be mentioned the influence of preferred orientation of the nuclei of recrystallized/annealed grains and also on the growth process of the recrystallized/annealed grains. If considering the specifics of the recrystallized nuclei formation in relation with the parent deformed phase, results that the recrystallized texture is influenced by the preferred orientation developed during mechanical processing.

Other influence factors upon obtained annealing/recrystallization texture are represented by the following: annealing/recrystallization temperature; thermal treatment duration; obtained grain sized and grains orientation during mechanical processing. One must remember that the factors that determine formation of a fine recrystallization structure favours the formation of a structure with random oriented grains, for this reason special attention must be paid to thermal-processing parameters settling. If a highly oriented structure is desired as a result of thermal treatment, then longer treatment durations must be applied, in order to promote formation of recrystallized grains with large dimensions.

5.3.1 Crystallographic texture developed as a result of recrystallization

As a representative β-Titanium alloy the Ti-29Nb-9Ta-10Zr (wt%) alloy is considered and analysed. The applied thermo-mechanical processing route is presented in 3.2.1 section. Must be mentioned that the starting material consist of a 90% cold-rolled state (total accumulate plastic strain ε = 2.31) obtained by MPR processing.

In order to calculate the ODFs, few assumptions must be made, first, sample crystalline symmetry indexed in cubic Im-3m system, and second, sample geometric symmetry indexed in orthorhombic mmm system. The ODF’s were computed using experimental measured (110), (200) and (211) pole figures of the β-Ti phase, and processed using de la Vallée Poussin kernel function, Gaussian distribution, Ghost correction and intensities normalization. During ODF’s computation the misorientation was set to 3°.

Figures 5.22, 5.23 and 5.24 show the representation of IPF’s corresponding to a recrystallization temperature of 780°C, 830°C and 880°C, in respect to RD, TD and ND sample reference system. One can observe that in all cases the [111]//ND pair is reaching the highest intensity, close to 11.2 MRD in the case of 780°C, close to 13.48 MRD in the case of 830°C and 17.1 MRD in the case of 880°C. Other formed crystallographic pairs are: [101]//RD, [101]//TD with transition to []//TD and []//ND. All other formed crystallographic pairs show negligible intensities in comparison with [111]//ND pair. If comparing the [111]//ND pair intensity with the one observed in the case of 60% cold-rolled state (section 5.1.1) situated close to 4.01 MRD, can be observed that the obtained intensity in the case of 780°C, as recrystallization temperature, is approximately three times bigger and is further increasing with increasing recrystallization temperature, to more than four times in the case of 880°C, as recrystallization temperature.

This behaviour suggesting that the resulted recrystallization texture is much more “stronger” in comparison with initial deformation texture.

Fig. 5.22. Representation of IPF’s corresponding to 90% cold-rolled followed

by recrystallization at 780°C Ti-29Nb-9Ta-10Zr alloy.

Fig. 5.23. Representation of IPF’s corresponding to 90% cold-rolled followed

by recrystallization at 830°C Ti-29Nb-9Ta-10Zr alloy.

Fig. 5.24. Representation of IPF’s corresponding to 90% cold-rolled followed

by recrystallization at 880°C Ti-29Nb-9Ta-10Zr alloy.

Figures 5.25, 5.26 and 5.27 show the representation of computed ODF’s in the case of recrystallization treatment performed at 780°C, 830°C and 880°C. One can observe that in all cases the maximum orientation density is obtained in the case of -fibre components ()[] and ()[]. In all cases the highest orientation density is recorded in the case of ()[] texture component, close to 21.6 MRD in the case of 780°C (figure 5.25), close to 24.2 MRD in the case of 830°C (figure 5.26) and close to 31.1 MRD in the case of 880°C (figure 5.27). Other major texture components can be observed, with a similar behaviour with the one recorded in the case of ()[] texture components, but with smaller orientation density, such as: ()[], , , , texture components.

Fig. 5.25. Representation of ODF’s corresponding to 90% cold-rolled

followed by recrystallization at 780°C Ti-29Nb-9Ta-10Zr alloy; a – ODF section: 2 = 0°;

b – ODF section: 2 = 15°; c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

Fig. 5.26. Representation of ODF’s corresponding to 90% cold-rolled

followed by recrystallization at 830°C Ti-29Nb-9Ta-10Zr alloy; a – ODF section: 2 = 0°;

b – ODF section: 2 = 15°; c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

Fig. 5.27. Representation of ODF’s corresponding to 90% cold-rolled

followed by recrystallization at 880°C Ti-29Nb-9Ta-10Zr alloy; a – ODF section: 2 = 0°;

b – ODF section: 2 = 15°; c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

If comparing the obtained ()[] orientation density in the case of recrystallization treatment with the orientation density obtained in case of 60% cold-rolled state (section 5.1.1) situated close to 4.2 MRD, can be observed that the orientation density is five times bigger in the case of 780°C as recrystallization temperature and increasing to more than seven times bigger in the case of 880°C. This behaviour suggests, again, that the resulted recrystallization texture is much more “stronger” in comparison with initial deformation texture.

In order to compute the volume fraction of a certain orientation – texture component (1–2), and the texture index (F), it was assumed a misorientation of 15°.

Table 5.12. Texture characteristics (texture components, volume fraction and texture index) developed

in case of 90% cold-rolled followed by recrystallization at 780°C Ti-10Zr-5Nb-5Ta alloy.

Table 5.13. Texture characteristics (texture components, volume fraction and texture index) developed

in case of 90% cold-rolled followed by recrystallization at 830°C Ti-10Zr-5Nb-5Ta alloy.

Table 5.14. Texture characteristics (texture components, volume fraction and texture index) developed

in case of 90% cold-rolled followed by recrystallization at 880°C Ti-10Zr-5Nb-5Ta alloy.

In tables 5.12, 5.13 and 5.14 computed data concerning volume fraction of specified texture components and texture index are presented. Analysing the texture index F, one can observe that increasing the recrystallization temperature the texture index is increasing too, from 5.86 in the case of 780°C as recrystallization temperature (table 5.12), to 6.40 in the case of 830°C as recrystallization temperature (table 5.13) and finally to 6.83 in the case of 880°C as recrystallization temperature (table 5.14). Again, if comparing the texture index obtained in the case of 60% cold rolled state (section 5.1.1) showing a value of 1.53, with the ones obtained in the case of recrystallization state, from 5.86 to 6.83, supports the increased texture “strength” developed during thermal processing in comparison with mechanical processing.

If analysing the volume fraction of the most intense orientation density, namely the -fiber texture components and taking into consideration the specific of ODF in Euler space, in order to compute the entire -fiber volume fraction, one must consider all -fiber texture components:

family: ; ; ; ; ; ;

family: ; ; ; ; ; .

The entire -fiber volume fraction containing both and families in the case of 780°C as recrystallization temperature can be computed as follows:

In the case of 830°C as recrystallization temperature, the computed -fiber volume fraction can be computed as follows:

In the case of 880°C as recrystallization temperature, the computed -fiber volume fraction can be computed as follows:

As observed, the volume fraction of the entire -fiber is increasing with increasing the recrystallization temperature, if considering as base the 780°C temperature then applying a temperature of 830°C leads to a 16% increasing in volume fraction, while applying a temperature of 880°C leads to a 46% increasing in volume fraction. This showing that with increasing the recrystallization temperature the obtained texture “strength” is increasing as well.

Another way to increase the texture “strength”, beside temperature increasing, can be represented by the treatment duration increasing [81,82]. Must be mentioned that, in performed investigations a 30 minutes treatment duration was used, duration which can be considered a “short” recrystallization duration used to obtain a refined (not a coarse-grained) recrystallized structure.

5.3.2 Crystallographic texture developed as a result of aging

As a representative β-Titanium alloy the Ti-29Nb-9Ta-10Zr (wt%) alloy is considered and analysed. The applied thermo-mechanical processing route is presented in 3.2.1 section. Must be mentioned that the starting material consist of a 90% cold-rolled state (total accumulate plastic strain ε = 2.31) obtained by MPR processing, on which different recrystallization treatments were performed, using temperatures between 780°C to 880°C. After recrystallization treatment, a second thermal treatment was applied, namely aging treatment, performed at 400°C with 90 minutes duration, upon all recrystallized structural states.

In order to calculate the ODFs, few assumptions must be made, first, sample crystalline symmetry indexed in cubic Im-3m system, and second, sample geometric symmetry indexed in orthorhombic mmm system. The ODF’s were computed using experimental measured (110), (200) and (211) pole figures of the β-Ti phase, and processed using de la Vallée Poussin kernel function, Gaussian distribution, Ghost correction and intensities normalization. During ODF’s computation the misorientation was set to 3°.

Figures 5.28, 5.29 and 5.30 show the representation of IPF’s corresponding to a recrystallization temperature of 780°C, 830°C and 880°C followed by aging at 400°C, in respect to RD, TD and ND sample reference system. One can observe that in all cases the [111]//ND pair is reaching the highest intensity in all cases, close to 9.9 MRD in the case of 780°C followed by aging at 400°C (figure 5.28), close to 19.9 MRD in the case of 830°C (figure 5.29) followed by aging at 400°C and 15.1 MRD in the case of 880°C followed by aging at 400°C (figure 5.30).

Other intense formed crystallographic pairs are: [101]//TD and [001]//ND in the case of 780°C followed by aging at 400°C (figure 5.28) and 830°C followed by aging at 400°C (figure 5.29), while in the case of 880°C followed by aging at 400°C (figure 5.30) a different pair is detected, namely [001]//RD.

The recorded behaviour suggests that during aging different phenomena occurs in recrystallized structures, promoting consolidation of grains with different crystallographic orientations in comparison with ones obtained after recrystallization, especially in the case of recrystallization treatment performed at 780°C and 830°C.

Fig. 5.28. Representation of IPF’s corresponding to recrystallized at 780°C followed

by aging at 400°C Ti-29Nb-9Ta-10Zr alloy.

Fig. 5.29. Representation of IPF’s corresponding to recrystallized at 830°C followed

by aging at 400°C Ti-29Nb-9Ta-10Zr alloy.

Fig. 5.30. Representation of IPF’s corresponding to recrystallized at 880°C followed

by aging at 400°C Ti-29Nb-9Ta-10Zr alloy.

Figures 5.31, 5.32 and 5.33 show the representation of computed ODF’s in the case of recrystallization treatment performed at 780°C, 830°C and 880°C followed by aging at 400°C. One can observe that in the case of recrystallization treatment performed at 780°C, and 830°C followed by aging at 400°C the maximum orientation density is obtained in the case of -fibre components and . In both cases the highest orientation density is recorded in the case of texture component, close to 14.2 MRD in the case of 780°C followed by aging at 400°C (figure 5.31) and close to 26.2 MRD in the case of 830°C followed by aging at 400°C (figure 5.32). Must be noticed this -fibre texture transition from family to family. Another effect of aging is represented by the increase in orientation density of texture family, spreading from to to texture components, to 7.5 MRD in the case of 780°C followed by aging at 400°C (figure 5.31) and to 12.1 MRD in the case of 830°C followed by aging at 400°C (figure 5.32).

Fig. 5.31. Representation of ODF’s corresponding to recrystallized at 780°C followed by aging at 400°C

Ti-29Nb-9Ta-10Zr alloy; a – ODF section: 2 = 0°; b – ODF section: 2 = 15°;

c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

In the case of recrystallization treatment performed at 880°C followed by aging at 400°C the highest orientation density is recorded in the case of -fibre components ()[] and ()[], with the recorded maximum close to 32 MRD in the case of ()[] texture component (figure 5.33). No transition from to family is recorded. All other texture components show a negligible orientation density in comparison with ()[] texture component. Practically, the aging treatment consolidate the -fibre components ()[] and ()[].

In order to compute the volume fraction of a certain orientation – texture component (1–2), and the texture index (F), it was assumed a misorientation of 15°.

Fig. 5.32. Representation of ODF’s corresponding to recrystallized at 830°C followed by aging at 400°C

Ti-29Nb-9Ta-10Zr alloy; a – ODF section: 2 = 0°; b – ODF section: 2 = 15°;

c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

Fig. 5.33. Representation of ODF’s corresponding to recrystallized at 880°C followed by aging at 400°C

Ti-29Nb-9Ta-10Zr alloy; a – ODF section: 2 = 0°; b – ODF section: 2 = 15°;

c – ODF section: 2 = 30°; d – ODF section: 2 = 45°.

In tables 5.15, 5.16 and 5.17 computed data concerning volume fraction of specified texture components and texture index are presented. Analysing the texture index F, one can observe that in the case of recrystallization at 780°C (table 5.12) followed by aging at 400°C (table 5.15) the effect of aging is represented by a decrease in texture index from 5.86 to 3.87; in the case of recrystallization at 830°C (table 5.13) followed by aging at 400°C (table 5.16) the effect of aging is negligible; and in the case of recrystallization at 880°C (table 5.14) followed by aging at 400°C (table 5.17) the effect of aging is represented by an increase in texture index from 6.83 to 8.26.

Table 5.15. Texture characteristics (texture components, volume fraction and texture index) developed

in case of recrystallization at 780°C followed by aging at 400°C Ti-10Zr-5Nb-5Ta alloy.

Table 5.16. Texture characteristics (texture components, volume fraction and texture index) developed

in case of recrystallization at 830°C followed by aging at 400°C Ti-10Zr-5Nb-5Ta alloy.

Table 5.17. Texture characteristics (texture components, volume fraction and texture index) developed

in case of recrystallization at 880°C followed by aging at 400°C Ti-10Zr-5Nb-5Ta alloy.

If analysing the volume fraction of the most intense orientation density, namely the -fiber texture components and taking into consideration the specific of ODF in Euler space, in order to compute the entire -fiber volume fraction, one must consider all -fiber texture components:

family: ; ; ; ; ; ;

family: ; ; ; ; ; .

The entire -fiber volume fraction containing both and families in the case of 780°C as recrystallization temperature can be computed as follows:

In the case of 830°C as recrystallization temperature, the computed -fiber volume fraction can be computed as follows:

In the case of 880°C as recrystallization temperature, the computed -fiber volume fraction can be computed as follows:

Comparing the volume fraction of the -fiber before and after the aging treatment can be observed the following:

in the case of 780°C as recrystallization temperature, the volume fraction before aging treatment was situated close to 2.6829% and after the aging treatment 2.3460%, which represents a decrease of about 14 %;

in the case of 880°C as recrystallization temperature, the volume fraction before aging treatment was situated close to 3.1269% and after the aging treatment 3.8631%, which represents an increase of about 19 %;

in the case of 780°C as recrystallization temperature, the volume fraction before aging treatment was situated close to 3.9354% and after the aging treatment 3.4176%, which represents a decrease of about 15 %;

Besides the -fiber volume fraction one must account also the increased volume fraction of the α-fiber volume fraction, which is promoted by the aging treatment, at least in the case of 780°C and 830°C recrystallization temperatures, and the and texture components.

A final conclusion is rising from analysing the obtained results; one must consider the recrystallization temperature together with aging thermal treatment in order to promote a certain texture component formation and consolidation. Also, the treatment duration can be of importance when desired texture strength is targeted [81,82].

5.4 Concluding remarks

Considering the case of α-Ti and β-Ti alloys, the results of mechanical processing in terms of developed textural components show that the texture “strength” is increasing with increasing the applied plastic strain, if the deformation process is represented by MPR; if after the MPR processing the mechanical processing is continued with a SPD-ARB processing the texture “strength” is decreasing or, at best, remains constant.

Considering the case of β-Ti alloys, the results of thermal processing in terms of developed textural components show that texture “strength” is increasing with recrystallization temperature increasing, the increase is several times in magnitude in comparison with mechanical processing. In the case of complex thermal processing routes, comprising of more than one thermal treatment, special attention must be paid to treatments temperatures and durations in order to control the resulted textural features (texture components, volume fractions, texture index).

REFERENCES

S. Banerjee, P. Muchopadhyay: Phase Transformations: Examples from Titanium and Zirconium Alloys; Pergamon Elsevier, 2007

D.A. Young: Phase Diagrams of the Elements; University of California Press, Berkeley, 1991

E.K. Molchanova: Phase Diagrams of Titanium Alloys; Israel Program for Scientific Translations, Jerusalem, 1965

E.W. Collings: The Physical Metallurgy of Titanium Alloys: American Society for Metals, Metals Park, OH, 1984

F.H. Froes, T.L. Yau, H.G. Weidinger: Materials Science and Technology; Vol. 8 (eds R.W. Cahn, P. Haasen, E.J. Kramer) VCH Publishers, New York, 1996

R.A. Wood: Titanium Alloys Handbook; Metals and Ceramics Information Centre, Battelle, Columbus, OH, 1972

E.W. Collings: Materials Properties Handbook: Titanium Alloys; (eds R. Boyer, G. Welsch and E.W. Collings) ASM International, Materials Park, OH, 1994

I. Polmear: Light alloys; From Traditional Alloys to Nanocrystalls; Fourth edition, Butterworth-Heinemann, Burlington,

H.M. Otte: The Science Technology and Application of Titanium; (eds R.I. Jaffee and N.E. Promisel) Pergamon Press, Oxford, 1970

C. Hammond, P.M. Kelly: The Science Technology and Application of Titanium; (eds R.I. Jaffee and N.E. Promisel) Pergamon Press, Oxford, 1970

J.C. Williams: Titanium Science and Technology; (eds K.C. Russell and H.I. Aaronson) The Metallurgical Society of AIME, Warrendale, PA, 1973

B.A. Hatt, V.G. Rivlin: Phase transformations in superconducting Ti-Nb alloys; Journal of Physics D: Applied Physics, 1, 1145-1150, 1968

S. Banerjee, R.W. Cahn: Solid-Solid Phase Transformations, (eds H.I. Aaronson et al.) TMS, Warrendale, 1982

J.M. Silcock: An X-ray examination of the to phase in TiV, TiMo and TiCr alloys; Acta Metallurgica, 6, 481-493, 1958

H.P. Klug, L.E. Alexander: X-ray Diffraction Procedures, John Wiley and Sons, New York, 1974

R. Jenkins, R.L. Snyder: Introduction to X-ray Powder Diffractometry, John Wiley and Sons, New York, 1996

B.E. Warren, X-ray Diffraction, Courier Dover Publications, Mineola, 1969

I. Langford, D. Louer: Powder Diffraction; Reports on Progress in Physics, 59, 131-234, 1996

H.W. King, E.A. Payzant: An experimental examination of error functions for Bragg-Brentano powder diffractometry; Advances in X-ray Analysis, 36, 663-670, 1993

H.H. Tian, M. Atzmon: Comparison of X-ray analysis methods used to determine the grain size and strain in nanocrystalline materials; Philosophical Magazine, 79, 1769-1786, 1999

C.E. Krill, R. Birringer: Estimating grain-size distributions in nanocrystalline materials from X-ray diffraction profile analysis; Philosophical Magazine, A 77, 621-640, 1998

Th.H. de Keijser, J.I. Langford, E.J. Mittemeijer, A.B.P. Vogels: Use of the Voigt function in a single-line method for the analysis of X-ray diffraction line broadening; Journal of Applied Crystallography, 15, 308-314, 1982

D. Louër: Applications of profile analysis for micro-crystalline properties from total pattern fitting; Advances in X-ray Analysis, 37, 27-35, 1994

G. Caglioti, A. Paoletti, F.P. Ricci: Choice of collimators for a crystal spectrometer for neutron diffraction, Nuclear Instruments, 3, 223-228, 1958

J.I. Langford, The variance as a measure of line broadening: corrections for truncation, curvature and instrumental effects; Journal of Applied Crystallography, 15, 315-322, 1982

H.J. Bunge: Mathematische methoden der texturanalyse; Berlin: Akademie Verlag, 1969

M. Hatherly, W. B. Hutchinson: An introduction to textures in metals; Institution of Metallurgists, 1979

H.J. Bunge: Texture analysis in materials science, Mathematical methods; Butterworths, London, 1982

C. Hammond: The basics of crystallography and diffraction; Oxford University Press, 1997

V. Randle, O. Engler: Texture analysis: macrotexture, microtexture, and orientation mapping; Gordon and Breach Science, New York, 2000

A. Morawiec: Orientations and rotations; Springer-Verlag, 2004

R.J. Roe: Description of crystallite orientation in polycrystal materials III. General solution to pole figure inversion; Journal of Applied Physics, 36, 2024-2031, 1965

N.I. Wang, J.C. Huang: Texture analysis in hexagonal materials; Materials Chemistry and Physics, 81, 11-26, 2003

H.R. Wenk: Preferred orientation in deformed metals and rocks: An introduction to modern texture analysis; New York: Academic Press, 1985

U.F. Kocks, C.N. Tome, H.R. Wenk, H. Mecking: Texture and anisotropy; Cambridge University Press, 1998

J.F. Nye: Physical properties of crystals: Their representation by tensors and matrices; 2nd Edition, Oxford University Press, 1985.

U.F. Kocks, C.N. Tome, H.R. Wenk: Texture and anisotropy: Preferred orientations in polycrystals and their effect on materials properties, Cambridge University Press, 2000

W. Freeden, M.Z. Nashed, T. Sonar (Eds.): Handbook of Geomathematics, Springer-Verlag Berlin Heidelberg, 2010

S. Matthies, G. Vinel, K. Helmig: Standard distributions in texture analysis; Vol 1, Akademie-Verlag Berlin, 1987

F. Bachmann, R. Hielscher, H. Schaeben: Texture analysis with MTEX – Free and open source software toolbox; Solid State Phenomena, 160, 63-68, 2010

R. Hielschera, H. Schaeben: A novel pole figure inversion method: specification of the MTEX algorithm; Journal of Applied Crystallography, 41, 1024-1037, 2008

H. Schaeben, R. Hielscher, J.J. Fundenberger, D. Pottsc,J. Prestind: Orientation density function-controlled pole probability density function measurements: automated adaptive control of texture goniometers; Journal of Applied Crystallography, 40, 570-579, 2007

R. Hielscher, H. Schaebena, D. Chateigner: On the entropy to texture index relationship in quantitative texture analysis; Journal of Applied Crystallography, 40, 371-375, 2007

M. Morinaga, Y. Murata, H. Yukawa: Molecular orbital approach to alloy design; Applied Computational Materials Modeling – Theory, Simulation and Experiment (eds G. Bozzolo, R.D. Noebe, P.B. Abel), Springer, 2007

N. Yukawa, M. Morinaga: Alloy phase stability index diagram, USPATO Patent no. 4.824.637, 1989

V.D. Cojocaru, D. Raducanu, C. Vasilescu, I. Cinca, P. Drob, E. Vasilescu, S.I. Drob: Improvement of the corrosion resistance and structural and mechanical properties of a titanium base alloy by thermo-mechanical processing, Materials and Corrosion-Werkstoffe und Korrosion, 64, 500-508, 2013

I. Cinca, D. Raducanu, A. Nocivin, V.D. Cojocaru: Formation of nano-sized grains in Ti-10Zr-5Nb-5Ta biomedical alloy processed by accumulative roll bonding (ARB), Kovove Materialy-Metallic Materials, 51, 165-172, 2013

V.D. Cojocaru, D. Raducanu, T. Gloriant, E. Bertrand, I. Cinca: Structural observations of twinning deformation mechanism in a Ti-Ta-Nb alloy, Solid State Phenomena, 188, 46-51, 2012

D. Raducanu, V.D. Cojocaru, I. Cinca, I. Dan. Thermo-mechanical processing of a biocompatible Ti-Ta-Nb alloy, Solid State Phenomena, 188, 59-64, 2012

V.D. Cojocaru, T. Gloriant, D.M. Gordin, E. Bertrand, D. Raducanu, I. Cinca, I. Dan: Evaluation of mechanical properties for a Ti-Ta-Nb biocompatible alloy, Journal of Optoelectronics and Advanced Materials, 13, 912 – 916, 2011

D. Raducanu, E. Vasilescu, V.D. Cojocaru, I. Cinca, P. Drob, C. Vasilescu, S.I. Drob: Mechanical and corrosion resistance of a new nanostructured Ti–Zr–Ta–Nb alloy, Journal of the Mechanical Behavior of Biomedical Materials, 4, 1421-1430, 2011

E. Vasilescu, P. Drob, D. Raducanu, V.D. Cojocaru, I. Cinca, D. Iordachescu, R. Ion, M. Popa: In vitro biocompatibility and corrosion resistance of a new implant titanium base alloy, Journal of Materials Science – Materials in Medicine, 21, 1959-1968, 2010

V.D. Cojocaru, I. Thibon, D. Raducanu, I. Cinca, T. Gloriant, D.M. Gordin, I. Cinca: Evaluation of developed texture during cold-rolling deformation of Ti-Nb-Ta-Zr biocompatible alloy, Key Engineering Materials, 592-593, 366-369, 2014

V.D. Cojocaru, D. Raducanu, T. Gloriant, D.M. Gordin, I. Cinca: Effects of cold-rolling deformation on texture evolution and mechanical properties of Ti-29Nb-9Ta-10Zr alloy, Materials Science and Engineering A, 586, 1-10, 2013

L. Wang, W. Lu, J. Qin, F. Zhang, D. Zhang: Influence of cold deformation on martensite transformation and mechanical properties of Ti-Nb-Ta-Zr alloy; Journal of Alloys and Compounds, 469, 512-518, 2009

J.I. Qazi, B. Marquardt, L.F. Allard, H.J. Rack: Phase transformations in Ti-35Nb-7Zr-5Ta-(0.06-0.68)O alloys, Materials Science and Engineering C, 25, 389-397, 2005

M. Niinomi, T. Akahori, S. Katsura, K. Yamauchi, M. Ogawa: Mechanical characteristics and microstructure of drawn wire of Ti-29Nb-13Ta-4.6Zr for biomedical applications, Materials Science and Engineering C, 27, 154-161, 2007

Y.L. Hao, S.J. Li, S.Y. Sun, C.Y. Zheng, R. Yang: Elastic deformation behaviour of Ti-24Nb-4Zr-7.9Sn for biomedical applications, Acta Biomaterialia, 3, 277-286, 2007

Y.F. Xu, D.Q. Yi, H.Q. Liu, X.Y. Wu, B. Wang, F.L. Yang: Effects of cold deformation on microstructure, texture evolution and mechanical properties of Ti-Nb-Ta-Zr-Fe alloy for biomedical applications, Materials Science and Engineering A, 547, 64-71, 2012

C.M. Tabirca, T. Gloriant, D.M. Gordin, I. Thibon, Raducanu, I. Cinca, C.I. Nae, A. Caprarescu, V.D. Cojocaru: Recrystallization temperature influence upon structural changes of 90% cold rolled Ti-29Nb-9Ta-10Zr biocompatible alloy, Key Engineering Materials, 592-593, 370-373, 2014

C. Tabirca, D. Raducanu, T. Gloriant, D.M. Gordin, V.D. Cojocaru, I. Cinca, I. Dan, A. Caprarescu: Structural investigation of thermo-mechanically processed Ti-29Nb-9Ta-10Zr alloy using X-ray diffraction, Journal of Optoelectronics and Advanced Materials, 15, 739-743, 2013

V.D. Cojocaru, D. Raducanu, D.M. Gordin, I. Cinca: Texture in ultra-strength Ti-25Ta-25Nb alloy strips, Journal of Alloys and Compounds, 576, 170-176, 2013

H.Y. Kim, T. Sasaki, K. Okutsu, J.I. Kim, T. Inamura, H. Hosada, S. Myazaki: Texture and shape memory behavior of Ti-22Nb-6Ta alloy, Acta Matererialia, 54, 423-433, 2006

V.D. Cojocaru, D. Raducanu, T. Gloriant, I. Cinca: Texture evolution in a Ti-Ta-Nb alloy processed by severe plastic deformation, JOM-US, 64, 572-581, 2012

V.D. Cojocaru, D. Raducanu, D.M. Gordin, I. Cinca: Texture evolution during ARB (Accumulative Roll Bonding) processing of Ti-10Zr-5Nb-5Ta alloy, Journal of Alloys and Compounds, 546, 260-269, 2013

M. Holscher, D. Raabe, K. Lucke: Relationship between rolling textures and shear textures in f.c.c. and b.c.c. metals, Acta Metallurgica and Materialia, 42, 879-886, 1994

D. Raabe, K. Lucke: Textures of ferritic stainless steels, Materials Science and Technology, 9, 302-312, 1993

B. Sander, D. Raabe: Texture inhomogeneity in a Ti-Nb-based β-titanium alloy after warm rolling and recrystallization, Materials Science and Engineering A, 479, 236-247, 2008

T. Inamura, Y. Kinoshita, J.I. Kim, H.Y. Kim, H. Hosoda, K. Wakashima, S. Miyazaki: Effect of {001}<110> texture on superelastic strain of Ti-Nb-Al biomedical shape memory alloys, Materials Science and Engineering A, 438-440, 865-869, 2006

C. Chen, M.P. Wang, S. Wang, Y.L. Jia, R.S. Lei, F.X. Zia, B. Huo, H.C. Yu: The evolution of cold-rolled deformation microstructure of {001}<110> grains in Ta-7.5 wt% W alloy foils, Journal of Alloys and Compounds, 513, 208-212, 2012

E. Bertrand, P. Castany, I. Peron, T. Gloriant: Twinning system selection in a metastable β-titanium alloy by Schmid factor analysis, Scripta Materialia, 64, 1110-1113, 2011

Z.Y. Fan: On the young's moduli of Ti-6Al-4V alloys, Scripta Metallurgica and Materialia, 29, 1427-1432, 1993

Y.N. Wang, J.C. Huang: Texture analysis in hexagonal materials, Materials Chemistry and Physics, 81, 11-26, 2003

O.M. Ivasishin, P.E. Markovsky, Yu.V. Matviychuk, S.L. Semiatin, C.H. Ward,S. Fox: A comparative study of the mechanical properties of high-strength β-titanium alloys, Journal of Alloys and Compounds, 457, 296-209, 2008

Y. Mishin, D. Farkas, M. J. Mehl, D.A. Papaconstantopoulos: Interatomic potentials for monoatomic metals from experimental data and ab initio calculations, Physical Review B, 59, 3393-3407, 1999

H.P. Van Swygenhoven, M. Derlet, A.G. Froseth: Stacking fault energies and slip in nanocrystalline metals, Nature Materials, 3, 399-403, 2004

F. A. Mohamed: Interpretation of nanoscale softening in terms of dislocation-accommodated boundary sliding, Metallurgical and Materials Transactions A, 38, 340-347, 2007

C.E. Carlton, P.J. Ferreira: What is behind the inverse Hall-Petch effect in nanocrystalline materials ?, Acta Materialia, 55, 3749-3756, 2007

Y. Saito, N. Tsuji, H. Utsunomiya, T. Sakai, R.G. Hong: Ultra-fine grained bulk aluminum produced by accumulative roll-bonding (ARB) process, Scripta Materialia, 39, 221-1227, 1998

N. Tsuji, Y. Ito, Y. Saito, Y. Minamino: Strength and ductility of ultrafine grained aluminum and iron produced by ARB and annealing, Scripta Materialia, 47, 893-899, 2002

J. Málek, F. Hnilica, J. Vesely, B. Smola, S. Bartáková, J. Vanek: The influence of chemical composition and thermo-mechanical treatment on Ti–Nb–Ta–Zr alloys, Materials and Design, 35, 731-740, 2012

Y.F. Xu, D.Q. Yi, H.Q. Liu, B. Wang, F.L. Yang: Age-hardening behavior, microstructural evolution and grain growth kinetics of isothermal ω phase of Ti–Nb–Ta–Zr–Fe alloy for biomedical applications, Materials Science and Engineering A, 529, 326-334, 2011

L I S T O F R E L E V A N T P U B L I C A T I O N S

http://www.researcherid.com/rid/F-8959-2010

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REFERENCES

S. Banerjee, P. Muchopadhyay: Phase Transformations: Examples from Titanium and Zirconium Alloys; Pergamon Elsevier, 2007

D.A. Young: Phase Diagrams of the Elements; University of California Press, Berkeley, 1991

E.K. Molchanova: Phase Diagrams of Titanium Alloys; Israel Program for Scientific Translations, Jerusalem, 1965

E.W. Collings: The Physical Metallurgy of Titanium Alloys: American Society for Metals, Metals Park, OH, 1984

F.H. Froes, T.L. Yau, H.G. Weidinger: Materials Science and Technology; Vol. 8 (eds R.W. Cahn, P. Haasen, E.J. Kramer) VCH Publishers, New York, 1996

R.A. Wood: Titanium Alloys Handbook; Metals and Ceramics Information Centre, Battelle, Columbus, OH, 1972

E.W. Collings: Materials Properties Handbook: Titanium Alloys; (eds R. Boyer, G. Welsch and E.W. Collings) ASM International, Materials Park, OH, 1994

I. Polmear: Light alloys; From Traditional Alloys to Nanocrystalls; Fourth edition, Butterworth-Heinemann, Burlington,

H.M. Otte: The Science Technology and Application of Titanium; (eds R.I. Jaffee and N.E. Promisel) Pergamon Press, Oxford, 1970

C. Hammond, P.M. Kelly: The Science Technology and Application of Titanium; (eds R.I. Jaffee and N.E. Promisel) Pergamon Press, Oxford, 1970

J.C. Williams: Titanium Science and Technology; (eds K.C. Russell and H.I. Aaronson) The Metallurgical Society of AIME, Warrendale, PA, 1973

B.A. Hatt, V.G. Rivlin: Phase transformations in superconducting Ti-Nb alloys; Journal of Physics D: Applied Physics, 1, 1145-1150, 1968

S. Banerjee, R.W. Cahn: Solid-Solid Phase Transformations, (eds H.I. Aaronson et al.) TMS, Warrendale, 1982

J.M. Silcock: An X-ray examination of the to phase in TiV, TiMo and TiCr alloys; Acta Metallurgica, 6, 481-493, 1958

H.P. Klug, L.E. Alexander: X-ray Diffraction Procedures, John Wiley and Sons, New York, 1974

R. Jenkins, R.L. Snyder: Introduction to X-ray Powder Diffractometry, John Wiley and Sons, New York, 1996

B.E. Warren, X-ray Diffraction, Courier Dover Publications, Mineola, 1969

I. Langford, D. Louer: Powder Diffraction; Reports on Progress in Physics, 59, 131-234, 1996

H.W. King, E.A. Payzant: An experimental examination of error functions for Bragg-Brentano powder diffractometry; Advances in X-ray Analysis, 36, 663-670, 1993

H.H. Tian, M. Atzmon: Comparison of X-ray analysis methods used to determine the grain size and strain in nanocrystalline materials; Philosophical Magazine, 79, 1769-1786, 1999

C.E. Krill, R. Birringer: Estimating grain-size distributions in nanocrystalline materials from X-ray diffraction profile analysis; Philosophical Magazine, A 77, 621-640, 1998

Th.H. de Keijser, J.I. Langford, E.J. Mittemeijer, A.B.P. Vogels: Use of the Voigt function in a single-line method for the analysis of X-ray diffraction line broadening; Journal of Applied Crystallography, 15, 308-314, 1982

D. Louër: Applications of profile analysis for micro-crystalline properties from total pattern fitting; Advances in X-ray Analysis, 37, 27-35, 1994

G. Caglioti, A. Paoletti, F.P. Ricci: Choice of collimators for a crystal spectrometer for neutron diffraction, Nuclear Instruments, 3, 223-228, 1958

J.I. Langford, The variance as a measure of line broadening: corrections for truncation, curvature and instrumental effects; Journal of Applied Crystallography, 15, 315-322, 1982

H.J. Bunge: Mathematische methoden der texturanalyse; Berlin: Akademie Verlag, 1969

M. Hatherly, W. B. Hutchinson: An introduction to textures in metals; Institution of Metallurgists, 1979

H.J. Bunge: Texture analysis in materials science, Mathematical methods; Butterworths, London, 1982

C. Hammond: The basics of crystallography and diffraction; Oxford University Press, 1997

V. Randle, O. Engler: Texture analysis: macrotexture, microtexture, and orientation mapping; Gordon and Breach Science, New York, 2000

A. Morawiec: Orientations and rotations; Springer-Verlag, 2004

R.J. Roe: Description of crystallite orientation in polycrystal materials III. General solution to pole figure inversion; Journal of Applied Physics, 36, 2024-2031, 1965

N.I. Wang, J.C. Huang: Texture analysis in hexagonal materials; Materials Chemistry and Physics, 81, 11-26, 2003

H.R. Wenk: Preferred orientation in deformed metals and rocks: An introduction to modern texture analysis; New York: Academic Press, 1985

U.F. Kocks, C.N. Tome, H.R. Wenk, H. Mecking: Texture and anisotropy; Cambridge University Press, 1998

J.F. Nye: Physical properties of crystals: Their representation by tensors and matrices; 2nd Edition, Oxford University Press, 1985.

U.F. Kocks, C.N. Tome, H.R. Wenk: Texture and anisotropy: Preferred orientations in polycrystals and their effect on materials properties, Cambridge University Press, 2000

W. Freeden, M.Z. Nashed, T. Sonar (Eds.): Handbook of Geomathematics, Springer-Verlag Berlin Heidelberg, 2010

S. Matthies, G. Vinel, K. Helmig: Standard distributions in texture analysis; Vol 1, Akademie-Verlag Berlin, 1987

F. Bachmann, R. Hielscher, H. Schaeben: Texture analysis with MTEX – Free and open source software toolbox; Solid State Phenomena, 160, 63-68, 2010

R. Hielschera, H. Schaeben: A novel pole figure inversion method: specification of the MTEX algorithm; Journal of Applied Crystallography, 41, 1024-1037, 2008

H. Schaeben, R. Hielscher, J.J. Fundenberger, D. Pottsc,J. Prestind: Orientation density function-controlled pole probability density function measurements: automated adaptive control of texture goniometers; Journal of Applied Crystallography, 40, 570-579, 2007

R. Hielscher, H. Schaebena, D. Chateigner: On the entropy to texture index relationship in quantitative texture analysis; Journal of Applied Crystallography, 40, 371-375, 2007

M. Morinaga, Y. Murata, H. Yukawa: Molecular orbital approach to alloy design; Applied Computational Materials Modeling – Theory, Simulation and Experiment (eds G. Bozzolo, R.D. Noebe, P.B. Abel), Springer, 2007

N. Yukawa, M. Morinaga: Alloy phase stability index diagram, USPATO Patent no. 4.824.637, 1989

V.D. Cojocaru, D. Raducanu, C. Vasilescu, I. Cinca, P. Drob, E. Vasilescu, S.I. Drob: Improvement of the corrosion resistance and structural and mechanical properties of a titanium base alloy by thermo-mechanical processing, Materials and Corrosion-Werkstoffe und Korrosion, 64, 500-508, 2013

I. Cinca, D. Raducanu, A. Nocivin, V.D. Cojocaru: Formation of nano-sized grains in Ti-10Zr-5Nb-5Ta biomedical alloy processed by accumulative roll bonding (ARB), Kovove Materialy-Metallic Materials, 51, 165-172, 2013

V.D. Cojocaru, D. Raducanu, T. Gloriant, E. Bertrand, I. Cinca: Structural observations of twinning deformation mechanism in a Ti-Ta-Nb alloy, Solid State Phenomena, 188, 46-51, 2012

D. Raducanu, V.D. Cojocaru, I. Cinca, I. Dan. Thermo-mechanical processing of a biocompatible Ti-Ta-Nb alloy, Solid State Phenomena, 188, 59-64, 2012

V.D. Cojocaru, T. Gloriant, D.M. Gordin, E. Bertrand, D. Raducanu, I. Cinca, I. Dan: Evaluation of mechanical properties for a Ti-Ta-Nb biocompatible alloy, Journal of Optoelectronics and Advanced Materials, 13, 912 – 916, 2011

D. Raducanu, E. Vasilescu, V.D. Cojocaru, I. Cinca, P. Drob, C. Vasilescu, S.I. Drob: Mechanical and corrosion resistance of a new nanostructured Ti–Zr–Ta–Nb alloy, Journal of the Mechanical Behavior of Biomedical Materials, 4, 1421-1430, 2011

E. Vasilescu, P. Drob, D. Raducanu, V.D. Cojocaru, I. Cinca, D. Iordachescu, R. Ion, M. Popa: In vitro biocompatibility and corrosion resistance of a new implant titanium base alloy, Journal of Materials Science – Materials in Medicine, 21, 1959-1968, 2010

V.D. Cojocaru, I. Thibon, D. Raducanu, I. Cinca, T. Gloriant, D.M. Gordin, I. Cinca: Evaluation of developed texture during cold-rolling deformation of Ti-Nb-Ta-Zr biocompatible alloy, Key Engineering Materials, 592-593, 366-369, 2014

V.D. Cojocaru, D. Raducanu, T. Gloriant, D.M. Gordin, I. Cinca: Effects of cold-rolling deformation on texture evolution and mechanical properties of Ti-29Nb-9Ta-10Zr alloy, Materials Science and Engineering A, 586, 1-10, 2013

L. Wang, W. Lu, J. Qin, F. Zhang, D. Zhang: Influence of cold deformation on martensite transformation and mechanical properties of Ti-Nb-Ta-Zr alloy; Journal of Alloys and Compounds, 469, 512-518, 2009

J.I. Qazi, B. Marquardt, L.F. Allard, H.J. Rack: Phase transformations in Ti-35Nb-7Zr-5Ta-(0.06-0.68)O alloys, Materials Science and Engineering C, 25, 389-397, 2005

M. Niinomi, T. Akahori, S. Katsura, K. Yamauchi, M. Ogawa: Mechanical characteristics and microstructure of drawn wire of Ti-29Nb-13Ta-4.6Zr for biomedical applications, Materials Science and Engineering C, 27, 154-161, 2007

Y.L. Hao, S.J. Li, S.Y. Sun, C.Y. Zheng, R. Yang: Elastic deformation behaviour of Ti-24Nb-4Zr-7.9Sn for biomedical applications, Acta Biomaterialia, 3, 277-286, 2007

Y.F. Xu, D.Q. Yi, H.Q. Liu, X.Y. Wu, B. Wang, F.L. Yang: Effects of cold deformation on microstructure, texture evolution and mechanical properties of Ti-Nb-Ta-Zr-Fe alloy for biomedical applications, Materials Science and Engineering A, 547, 64-71, 2012

C.M. Tabirca, T. Gloriant, D.M. Gordin, I. Thibon, Raducanu, I. Cinca, C.I. Nae, A. Caprarescu, V.D. Cojocaru: Recrystallization temperature influence upon structural changes of 90% cold rolled Ti-29Nb-9Ta-10Zr biocompatible alloy, Key Engineering Materials, 592-593, 370-373, 2014

C. Tabirca, D. Raducanu, T. Gloriant, D.M. Gordin, V.D. Cojocaru, I. Cinca, I. Dan, A. Caprarescu: Structural investigation of thermo-mechanically processed Ti-29Nb-9Ta-10Zr alloy using X-ray diffraction, Journal of Optoelectronics and Advanced Materials, 15, 739-743, 2013

V.D. Cojocaru, D. Raducanu, D.M. Gordin, I. Cinca: Texture in ultra-strength Ti-25Ta-25Nb alloy strips, Journal of Alloys and Compounds, 576, 170-176, 2013

H.Y. Kim, T. Sasaki, K. Okutsu, J.I. Kim, T. Inamura, H. Hosada, S. Myazaki: Texture and shape memory behavior of Ti-22Nb-6Ta alloy, Acta Matererialia, 54, 423-433, 2006

V.D. Cojocaru, D. Raducanu, T. Gloriant, I. Cinca: Texture evolution in a Ti-Ta-Nb alloy processed by severe plastic deformation, JOM-US, 64, 572-581, 2012

V.D. Cojocaru, D. Raducanu, D.M. Gordin, I. Cinca: Texture evolution during ARB (Accumulative Roll Bonding) processing of Ti-10Zr-5Nb-5Ta alloy, Journal of Alloys and Compounds, 546, 260-269, 2013

M. Holscher, D. Raabe, K. Lucke: Relationship between rolling textures and shear textures in f.c.c. and b.c.c. metals, Acta Metallurgica and Materialia, 42, 879-886, 1994

D. Raabe, K. Lucke: Textures of ferritic stainless steels, Materials Science and Technology, 9, 302-312, 1993

B. Sander, D. Raabe: Texture inhomogeneity in a Ti-Nb-based β-titanium alloy after warm rolling and recrystallization, Materials Science and Engineering A, 479, 236-247, 2008

T. Inamura, Y. Kinoshita, J.I. Kim, H.Y. Kim, H. Hosoda, K. Wakashima, S. Miyazaki: Effect of {001}<110> texture on superelastic strain of Ti-Nb-Al biomedical shape memory alloys, Materials Science and Engineering A, 438-440, 865-869, 2006

C. Chen, M.P. Wang, S. Wang, Y.L. Jia, R.S. Lei, F.X. Zia, B. Huo, H.C. Yu: The evolution of cold-rolled deformation microstructure of {001}<110> grains in Ta-7.5 wt% W alloy foils, Journal of Alloys and Compounds, 513, 208-212, 2012

E. Bertrand, P. Castany, I. Peron, T. Gloriant: Twinning system selection in a metastable β-titanium alloy by Schmid factor analysis, Scripta Materialia, 64, 1110-1113, 2011

Z.Y. Fan: On the young's moduli of Ti-6Al-4V alloys, Scripta Metallurgica and Materialia, 29, 1427-1432, 1993

Y.N. Wang, J.C. Huang: Texture analysis in hexagonal materials, Materials Chemistry and Physics, 81, 11-26, 2003

O.M. Ivasishin, P.E. Markovsky, Yu.V. Matviychuk, S.L. Semiatin, C.H. Ward,S. Fox: A comparative study of the mechanical properties of high-strength β-titanium alloys, Journal of Alloys and Compounds, 457, 296-209, 2008

Y. Mishin, D. Farkas, M. J. Mehl, D.A. Papaconstantopoulos: Interatomic potentials for monoatomic metals from experimental data and ab initio calculations, Physical Review B, 59, 3393-3407, 1999

H.P. Van Swygenhoven, M. Derlet, A.G. Froseth: Stacking fault energies and slip in nanocrystalline metals, Nature Materials, 3, 399-403, 2004

F. A. Mohamed: Interpretation of nanoscale softening in terms of dislocation-accommodated boundary sliding, Metallurgical and Materials Transactions A, 38, 340-347, 2007

C.E. Carlton, P.J. Ferreira: What is behind the inverse Hall-Petch effect in nanocrystalline materials ?, Acta Materialia, 55, 3749-3756, 2007

Y. Saito, N. Tsuji, H. Utsunomiya, T. Sakai, R.G. Hong: Ultra-fine grained bulk aluminum produced by accumulative roll-bonding (ARB) process, Scripta Materialia, 39, 221-1227, 1998

N. Tsuji, Y. Ito, Y. Saito, Y. Minamino: Strength and ductility of ultrafine grained aluminum and iron produced by ARB and annealing, Scripta Materialia, 47, 893-899, 2002

J. Málek, F. Hnilica, J. Vesely, B. Smola, S. Bartáková, J. Vanek: The influence of chemical composition and thermo-mechanical treatment on Ti–Nb–Ta–Zr alloys, Materials and Design, 35, 731-740, 2012

Y.F. Xu, D.Q. Yi, H.Q. Liu, B. Wang, F.L. Yang: Age-hardening behavior, microstructural evolution and grain growth kinetics of isothermal ω phase of Ti–Nb–Ta–Zr–Fe alloy for biomedical applications, Materials Science and Engineering A, 529, 326-334, 2011

L I S T O F R E L E V A N T P U B L I C A T I O N S

http://www.researcherid.com/rid/F-8959-2010

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