Microstructure-based numerical modeling of the mechanical behavior of Mg alloys

Dentro de los materiales estructurales, el magnesio y sus aleaciones están siendo el foco de una de profunda investigación. Esta investigación está dirigida a comprender la relación existente entre la microestructura de las aleaciones de Mg y su comportamiento mecánico. El objetivo es optimizar las aleaciones actuales de magnesio a partir de su microestructura y diseñar nuevas aleaciones. Sin embargo, el efecto de los factores microestructurales (como la forma, el tamaño, la orientación de los precipitados y la morfología de los granos) en el comportamiento mecánico de estas aleaciones está todavía por descubrir. Para conocer mejor de la relación entre la microestructura y el comportamiento mecánico, es necesaria la combinación de técnicas avanzadas de caracterización experimental como de simulación numérica, a diferentes longitudes de escala. En lo que respecta a las técnicas de simulación numérica, la homogeneización policristalina es una herramienta muy útil para predecir la respuesta macroscópica a partir de la microestructura de un policristal (caracterizada por el tamaño, la forma y la distribución de orientaciones de los granos) y el comportamiento del monocristal. La descripción de la microestructura se lleva a cabo mediante modernas técnicas de caracterización (difracción de rayos X, difracción de electrones retrodispersados, así como con microscopia óptica y electrónica). Sin embargo, el comportamiento del cristal sigue siendo difícil de medir, especialmente en aleaciones de Mg, donde es muy complicado conocer el valor de los parámetros que controlan el comportamiento mecánico de los diferentes modos de deslizamiento y maclado. En la presente tesis se ha desarrollado una estrategia de homogeneización computacional para predecir el comportamiento de aleaciones de magnesio. El comportamiento de los policristales ha sido obtenido mediante la simulación por elementos finitos de un volumen representativo (RVE) de la microestructura, considerando la distribución real de formas y orientaciones de los granos. El comportamiento del cristal se ha simulado mediante un modelo de plasticidad cristalina que tiene en cuenta los diferentes mecanismos físicos de deformación, como el deslizamiento y el maclado. Finalmente, la obtención de los parámetros que controlan el comportamiento del cristal (tensiones críticas resueltas (CRSS) así como las tasas de endurecimiento para todos los modos de maclado y deslizamiento) se ha resuelto mediante la implementación de una metodología de optimización inversa, una de las principales aportaciones originales de este trabajo. La metodología inversa pretende, por medio del algoritmo de optimización de Levenberg-Marquardt, obtener el conjunto de parámetros que definen el comportamiento del monocristal y que mejor ajustan a un conjunto de ensayos macroscópicos independientes. Además de la implementación de la técnica, se han estudiado tanto la objetividad del metodología como la unicidad de la solución en función de la información experimental. La estrategia de optimización inversa se usó inicialmente para obtener el comportamiento cristalino de la aleación AZ31 de Mg, obtenida por laminado. Esta aleación tiene una marcada textura basal y una gran anisotropía plástica. El comportamiento de cada grano incluyó cuatro mecanismos de deformación diferentes: deslizamiento en los planos basal, prismático, piramidal hc+ai, junto con el maclado en tracción. La validez de los parámetros resultantes se validó mediante la capacidad del modelo policristalino para predecir ensayos macroscópicos independientes en diferentes direcciones. En segundo lugar se estudió mediante la misma estrategia, la influencia del contenido de Neodimio (Nd) en las propiedades de una aleación de Mg-Mn-Nd, obtenida por extrusión. Se encontró que la adición de Nd produce una progresiva isotropización del comportamiento macroscópico. El modelo mostró que este incremento de la isotropía macroscópica era debido tanto a la aleatoriedad de la textura inicial como al incremento de la isotropía del comportamiento del cristal, con valores similares de las CRSSs de los diferentes modos de deformación. Finalmente, el modelo se empleó para analizar el efecto de la temperatura en el comportamiento del cristal de la aleación de Mg-Mn-Nd. La introducción en el modelo de los efectos non-Schmid sobre el modo de deslizamiento piramidal hc+ai permitió capturar el comportamiento mecánico a temperaturas superiores a 150_C. Esta es la primera vez, de acuerdo con el conocimiento del autor, que los efectos non-Schmid han sido observados en una aleación de Magnesio. The study of Magnesium and its alloys is a hot research topic in structural materials. In particular, special attention is being paid in understanding the relationship between microstructure and mechanical behavior in order to optimize the current alloy microstructures and guide the design of new alloys. However, the particular effect of several microstructural factors (precipitate shape, size and orientation, grain morphology distribution, etc.) in the mechanical performance of a Mg alloy is still under study. The combination of advanced characterization techniques and modeling at several length scales is necessary to improve the understanding of the relation microstructure and mechanical behavior. Respect to the simulation techniques, polycrystalline homogenization is a very useful tool to predict the macroscopic response from polycrystalline microstructure (grain size, shape and orientation distributions) and crystal behavior. The microstructure description is fully covered with modern characterization techniques (X-ray diffraction, EBSD, optical and electronic microscopy). However, the mechanical behaviour of single crystals is not well-known, especially in Mg alloys where the correct parameterization of the mechanical behavior of the different slip/twin modes is a very difficult task. A computational homogenization framework for predicting the behavior of Magnesium alloys has been developed in this thesis. The polycrystalline behavior was obtained by means of the finite element simulation of a representative volume element (RVE) of the microstructure including the actual grain shape and orientation distributions. The crystal behavior for the grains was accounted for a crystal plasticity model which took into account the physical deformation mechanisms, e.g. slip and twinning. Finally, the problem of the parametrization of the crystal behavior (critical resolved shear stresses (CRSS) and strain hardening rates of all the slip and twinning modes) was obtained by the development of an inverse optimization methodology, one of the main original contributions of this thesis. The inverse methodology aims at finding, by means of the Levenberg-Marquardt optimization algorithm, the set of parameters defining crystal behavior that best fit a set of independent macroscopic tests. The objectivity of the method and the uniqueness of solution as function of the input information has been numerically studied. The inverse optimization strategy was first used to obtain the crystal behavior of a rolled polycrystalline AZ31 Mg alloy that showed a marked basal texture and a strong plastic anisotropy. Four different deformation mechanisms: basal, prismatic and pyramidal hc+ai slip, together with tensile twinning were included to characterize the single crystal behavior. The validity of the resulting parameters was proved by the ability of the polycrystalline model to predict independent macroscopic tests on different directions. Secondly, the influence of Neodymium (Nd) content on an extruded polycrystalline Mg-Mn-Nd alloy was studied using the same homogenization and optimization framework. The effect of Nd addition was a progressive isotropization of the macroscopic behavior. The model showed that this increase in the macroscopic isotropy was due to a randomization of the initial texture and also to an increase of the crystal behavior isotropy (similar values of the CRSSs of the different modes). Finally, the model was used to analyze the effect of temperature on the crystal behaviour of a Mg-Mn-Nd alloy. The introduction in the model of non-Schmid effects on the pyramidal hc+ai slip allowed to capture the inverse strength differential that appeared, between the tension and compression, above 150_C. This is the first time, to the author's knowledge, that non-Schmid effects have been reported for Mg alloys.

Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

The R8-BC8 phases and crystal growth in monocrystalline silicon under microindentation with a spherical indenter

The morphology and distribution of high-pressure metastable phases BC8 and R8, formed in monocrystalline silicon under microindentation, were identified and assessed using transmission electron microscopy nanodiffraction analysis. It was discovered that the crystal growth inside the transformation zone was stress-dependent with large crystals in its central region. The crystal size could also be increased using higher maximum indentation loads. The BC8 and R8 phases distributed unevenly across the transformation zone, with BC8 crystals mainly in the center of the zone and smaller R8 fragments in the peripheral regions. Such phase distribution was in agreement with the theoretical residual stress analysis.

Microstructure of Pharyngeal Tooth Enameloid in the Parrotfish Scarus rivulatus (Pisces:Scaridae)

The microstructure of parrotfish pharyngeal teeth was examined using scanning electron microscopy to infer possible mechanical properties of the dentition with respect to their function. Parrotfish tooth enameloid is formed from fluorapatite crystals grouped into bundles. In the upper and lower pharyngeal jaw, the majority of the crystal bundles are orientated either perpendicularly or vertically to the enameloid surface. The only exception is in the trailing apical enameloid in which the majority of bundles are orientated perpendicularly or horizontally to the trailing surface. A distinct transition occurs through the middle of the apex between the leading and trailing enameloid in teeth of the lower pharyngeal jaw. This transition appears less distinct in the teeth of the upper pharyngeal jaw. Enameloid microstructure indicates that shear forces predominate at the apex of the teeth. In the remainder of the enameloid, the microstructure indicates that wear is predominant, and the shear forces are of less importance.

Characterisation of femtosecond laser inscribed long period gratings in photonic crystal fibre

The use of high intensity femtosecond laser sources for inscribing fibre gratings has attained significant interest. The principal advantage of high-energy pulses is their ability for grating inscription in any material type without preprocessing or special core doping - the inscription process is controlled multi-photon absorption, void generation and subsequent local refractive index changes. The formation of grating structures in photonics crystal fibre has proven difficult, as the presence of holes within the fibre that allow wave-guidance impair and scatter the femtosecond inscription beam. Here we report on the consistent manufacture of long period gratings in endlessly single mode microstructure fibre and on their characterisation to external perturbations. Long period gratings are currently the subject of considerable research interest due to their potential applications as filters and as sensing devices, responsive to strain, temperature, bending and refractive index. Compared to the more mature fibre Bragg grating sensors, LPGs have more complex spectra, usually with broader spectral features. On the other hand they are intrinsically sensitive to bending and refractive index. Perhaps more importantly, the fibre design and choice of grating period can have a considerable influence over the sensitivity to the various parameters, for example allowing the creation of a bend sensor with minimal temperature cross-sensitivity. This control is not possible with FBG sensors. Here we compare the effects of symmetric and asymmetric femtosecond laser inscription.

Comparison between femtosecond laser and fusion-arc inscribed long period gratings in photonic crystal fibre

The use of high intensity femtosecond laser sources for inscribing fibre gratings has attained significant interest. The principal advantage of high-energy pulses is their ability for grating inscription in any material type without preprocessing or special core doping. In the field of fibre optical sensing LPGs written in photonic crystal fibre have a distinct advantage of low temperature sensitivity over gratings written in conventional fibre and thus minimal temperature cross-sensitivity. Previous studies have indicated that LPGs written by a point-by-point inscription scheme using a low repetition femtosecond laser exhibit post-fabrication evolution leading to temporal instabilities at room temperatures with respect to spectral location, strength and birefringence of the attenuation bands. These spectral instabilities of LPGs are studied in photonic crystal fibres (endlessly single mode microstructure fibre) to moderately high temperatures 100°C to 200°C and their performance compared to fusion-arc fabricated LPG. Initial results suggest that the fusion-arc fabricated LPG demonstrate less spectral instability for a given constant and moderate temperature, and are similar to the results obtained when inscribed in a standard single mode fibre.

Microstructural degradation of aluminide coatings on single crystal nickel based superalloys during high temperature exposure

An investigation, employing edge-on transmission electron microscopy, of the microstructure of aluminide diffusion coatings on a single crystal y' strengthened nickel base super alloy is reported. An examination has been made of the effect of postcoating exposure at 1100°C on the stability of the coating matrix, a B2 type phase, nominally NiAl. Precipitation in the coating is considered with respect to both decomposition of the B2 matrix to other Ni-Al (plus titanium) phases and the formation of chromium bearing precipitates. A comparison is drawn with behaviour at lower temperatures (850-950°C). © 1995 The Institute of Materials.

Deformation microstructure under nanoindentations in Cu using 3D x-ray structural microscopy

We have used a recently developed x-ray structural microscopy technique to make nondestructive, submicron-resolution measurements of the deformation microstructure below a 100mN maximum load Berkovich nanoindent in single crystal Cu. Direct observations of plastic deformation under the indent were obtained using a ~0.5 µm polychromatic microbeam and diffracted beam depth profiling to make micron-resolution spatially-resolved x-ray Laue diffraction measurements. The local lattice rotations underneath the nanoindent were found to be heterogeneous in nature as revealed by geometrically necessary dislocation (GND) densities determined for positions along lines beneath a flat indent face and under the sharp Berkovich indent blade edges. Measurements of the local rotation-axes and misorientation-angles along these lines are discussed in terms of crystallographic slip systems.

Effect of microstructure upon elastic behaviour of human tooth enamel

Tooth enamel is the stiffest tissue in the human body with a well-organized microstructure. Developmental diseases, such as enamel hypomineralisation, have been reported to cause marked reduction in the elastic modulus of enamel and consequently impair dental function. We produce evidence, using site-specific transmission electron microscopy (TEM), of difference in microstructure between sound and hypomineralised enamel. Built upon that, we develop a mechanical model to explore the relationship of the elastic modulus of the mineral-protein composite structure of enamel with the thickness of protein layers and the direction of mechanical loading. We conclude that when subject to complex mechanical loading conditions, sound enamel exhibits consistently high stiffness, which is essential for dental function. A marked decrease in stiffness of hypomineralised enamel is caused primarily by an increase in the thickness of protein layers between apatite crystals and to a lesser extent by an increase in the effective crystal orientation angle. © 2009 Elsevier Ltd. All rights reserved.

Femtosecond and UV inscribed grating characterization in photonic crystal fibres:optimization for sensing applications

Photonic crystal fibres (PCF) and more commonly microstructure fibres, remain interesting and novel fibre types and when suitably designed can prove to be "ideal" for sensing applications, as the different geometrical arrangement of the air holes alters their optical wave-guiding properties, whilst also providing tailored dispersion characteristics. This impacts the performance of grating structures, which offer wavelength encoded sensing information. We undertake a study on different air hole geometries and proceed with characterization of fibre Bragg and long period gratings, FBG and LPG, respectively that have been inscribed (using either a femtosecond or ultraviolet laser system) within different designs of microstructured fibre that are of interest for sensing applications. © 2012 SPIE.

Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

On the microstructure, growth pattern and original porosity of belemnite rostra: insights from calcitic Jurassic belemnites

Calcitic belemnite rostra are usually employed to perform paleoenvironmental studies based on geochemical data. However, several questions, such as their original porosity and microstructure, remain open, despite they are essential to make accurate interpretations based on geochemical analyses.This paper revisits and enlightens some of these questions. Petrographic data demonstrate that calcite crystals of the rostrum solidum of belemnites grow from spherulites that successively develop along the apical line, resulting in a “regular spherulithic prismatic” microstructure. Radially arranged calcite crystals emerge and diverge from the spherulites: towards the apex, crystals grow until a new spherulite is formed; towards the external walls of the rostrum, the crystals become progressively bigger and prismatic. Adjacent crystals slightly vary in their c-axis orientation, resulting in undulose extinction. Concentric growth layering develops at different scales and is superimposed and traversed by a radial pattern, which results in the micro-fibrous texture that is observed in the calcite crystals in the rostra.Petrographic data demonstrate that single calcite crystals in the rostra have a composite nature, which strongly suggests that the belemnite rostra were originally porous. Single crystals consistently comprise two distinct zones or sectors in optical continuity: 1) the inner zone is fluorescent, has relatively low optical relief under transmitted light (TL) microscopy, a dark-grey color under backscatter electron microscopy (BSEM), a commonly triangular shape, a “patchy” appearance and relatively high Mg and Na contents; 2) the outer sector is non-fluorescent, has relatively high optical relief under TL, a light-grey color under BSEM and low Mg and Na contents. The inner and fluorescent sectors are interpreted to have formed first as a product of biologically controlled mineralization during belemnite skeletal growth and the non-fluorescent outer sectors as overgrowths of the former, filling the intra- and inter-crystalline porosity. This question has important implications for making paleoenvironmental and/or paleoclimatic interpretations based on geochemical analyses of belemnite rostra.Finally, the petrographic features of composite calcite crystals in the rostra also suggest the non-classical crystallization of belemnite rostra, as previously suggested by other authors.

The Crystal-t Algorithm: A New Approach To Calculate The Sle Of Lipidic Mixtures Presenting Solid Solutions.

Lipidic mixtures present a particular phase change profile highly affected by their unique crystalline structure. However, classical solid-liquid equilibrium (SLE) thermodynamic modeling approaches, which assume the solid phase to be a pure component, sometimes fail in the correct description of the phase behavior. In addition, their inability increases with the complexity of the system. To overcome some of these problems, this study describes a new procedure to depict the SLE of fatty binary mixtures presenting solid solutions, namely the Crystal-T algorithm. Considering the non-ideality of both liquid and solid phases, this algorithm is aimed at the determination of the temperature in which the first and last crystal of the mixture melts. The evaluation is focused on experimental data measured and reported in this work for systems composed of triacylglycerols and fatty alcohols. The liquidus and solidus lines of the SLE phase diagrams were described by using excess Gibbs energy based equations, and the group contribution UNIFAC model for the calculation of the activity coefficients of both liquid and solid phases. Very low deviations of theoretical and experimental data evidenced the strength of the algorithm, contributing to the enlargement of the scope of the SLE modeling.

Crystal Structure Of (3e)-3-[(4-nitro-phen-oxy)-meth-yl]-4-phenyl-but-3-en-2-one.

In the title compound, C17H15NO4, the conformation about the C=C double bond [1.348 (2) Å] is E with the ketone group almost co-planar [C-C-C-C torsion angle = 7.2 (2)°] but the phenyl group twisted away [C-C-C-C = 160.93 (17)°]. The terminal aromatic rings are almost perpendicular to each other [dihedral angle = 81.61 (9)°] giving the mol-ecule an overall U-shape. The crystal packing feature benzene-C-H⋯O(ketone) contacts that lead to supra-molecular helical chains along the b axis. These are connected by π-π inter-actions between benzene and phenyl rings [inter-centroid distance = 3.6648 (14) Å], resulting in the formation of a supra-molecular layer in the bc plane.

Crystal Structure Of (3e)-3-(2,4-di-nitro-phen-oxy-meth-yl)-4-phenyl-but-3-en-2-one.

In the title compound, C17H14N2O6, the conformation about the C=C double bond [1.345 (2) Å] is E, with the ketone moiety almost coplanar [C-C-C-C torsion angle = 9.5 (2)°] along with the phenyl ring [C-C-C-C = 5.9 (2)°]. The aromatic rings are almost perpendicular to each other [dihedral angle = 86.66 (7)°]. The 4-nitro moiety is approximately coplanar with the benzene ring to which it is attached [O-N-C-C = 4.2 (2)°], whereas the one in the ortho position is twisted [O-N-C-C = 138.28 (13)°]. The mol-ecules associate via C-H⋯O inter-actions, involving both O atoms from the 2-nitro group, to form a helical supra-molecular chain along [010]. Nitro-nitro N⋯O inter-actions [2.8461 (19) Å] connect the chains into layers that stack along [001].