Par la mise en œuvre de simulations numériques d'un modèle bidimensionnel de verre de Lennard-Jones, nous étudions l'effet de la température sur les mécanismes élémentaires de la déformation dans les matériaux amorphes. Nous présentons un ensemble très complet de données couvrant plusieurs décades de taux de cisaillement à différentes températures en dessous et jusqu'à la transition vitreuse. Les mesures, qui portent sur la diffusion transverse, la contrainte macroscopique ainsi que sur des champs mésoscopiques (déformation, contrainte) et leurs corrélations spatiales, conduisent à proposer que la dynamique des avalanches identifiée précédemment dans les simulations athermiques continue d'être à l'œuvre - en restant presque inchangée - jusqu'à la transition vitreuse. Nous arguons que dans la gamme de paramètres utilisée l'effet des fluctuations thermiques revient à déplacer les seuils auxquels les événements dissipatifs se produisent, ce qui se traduit par une forte baisse du niveau de contrainte macroscopique aux températures les plus basses / Using numerical simulations of a model two-dimensional Lennard-Jones glass, we study the effect of small temperatures on the elementary mechanisms of deformation in amorphous materials. A very extensive data set covering several decades of shear rate at various temperatures below and up to the glass transition was compiled. Measurements, which include transverse diffusion, macroscopic stress, and coarse-grained fields (strain, stress) and their spatial correlations, lead us to propose that the avalanche dynamics previously identified in athermal simulations continues to be at work -- and nearly unchanged -- up to the glass transition. It is then argued that in this range, thermal fluctuation essentially shift the strains at which dissipative events take place, which results in a sharp drop of the macroscopic stress level at the lowest temperatures

HCP materials are exceedingly being used as alloys and composites in several high strength light weight applications such as aerospace and aeronautical structures, deep sea maritime applications, and as biocompatible materials. To understand the deformation of HCP materials, reliable tools and techniques are required. One such technique is the Elasto-Plastic Self Consistency (EPSC) model. ESPC models use Eshelby’s Inclusion Theory as their basic formulation to model the strain experienced by a grain within a strained material sample. One of the oldest approximations (or models) used to model the grain’s strain within a strained sample is the Taylor’s Assumption (TA). TA assumes that each grain is strained to the same average value. EPSC models are different from the TA model since each grain modelled by the EPSC model would be strained to a different value. This is possible and obtained by solving an infinite domain boundary value problem. This key advantage of the EPSC model can therefore predict localized weak spots within material samples.EPSC models use the concept of eigen strain where the inhomogeneous grain is replaced with an equivalent inclusion. The technique proposed in this research is used to simulate uniaxial tension of rolled textured Magnesium. The number of deformation modes used in this research is seven. Both slipping systems and twinning systems are included in the simulation. The hardening phenomenon is described as a function of self-hardening as well as latent-hardening. As stated in (S. Kweon, 2020), modelling the interactive hardening requires a more robust numerical iterative technique. An improved robust iterative numerical technique is explained in (Daniel Raja, 2021) and (Soondo Kweon D. S., 2021). This research implements the equivalent inclusion theory in combination with the numerical iterative technique developed in the aforementioned papers.The report begins with the need for this research and advocates for the same. Then, the conceptional theories and the imaginary thought experiment performed by John D. Eshelby is presented. The concept of “Eigen Strain” which serves as the base work needed to understand and formulate the Equivalent Inclusion Theory is described in detail. The Equivalent Inclusion is then presented and developed. The concept of Green’s Function is presented and explained. These concepts serve as the building block for the derivation and calculation of the Eshelby Tensor which relates the concepts of eigen strain and constrained strain. The report concludes the theory section with the amalgamation of the ideas of the Green’s Function and Eigen Strain to develop the Eshelby Tensor for an Isotropic material as well as Anisotropic materials. In the following section, the unit cell accompanied with the deformation modes within the unit cell of an HCP material that are used in these simulations are presented. Following unit cell model, the crystal plasticity model which includes plastic deformation, hardening laws, and elastic deformation is elaborated. The results obtained from the simulation are presented and salient features are highlighted that are observed in the results. Lastly, the report concludes by pointing out key “take aways” from this research and identifies possible avenues for future research.Additionally, ten appendices are included towards the end of this report to enhance understanding of complicated derivations and solutions. Lastly, the author’s vita is included at the end of the report.

A mathematical model has been created based on J.D. Eshelby's equivalent inclusion method that can predict the elastic modulus and damping capability in the form of Joule heat for any piezoelectric ceramic-reinforced metal matrix composite system. Specifically, barium titanate (BaTiO₃), lead titanate (PbTiO₃), and zinc oxide (ZnO) piezoelectric ceramics have been modeled as dispersed particles shaped as spheres, prolate spheroids, and discs within a host of common structural metallic matrices including 304 stainless steel, mild steel, aluminum, brass, copper, lead, magnesium, nickel, Ni-20wt%Cr, tin, titanium, Ti-6Al-4V(at%), and tungsten. Composite systems that were predicted to exhibit the greatest level of damping capacity include copper, aluminum, and magnesium matrices reinforced with PbTiO₃, BaTiO₃, and ZnO, in descending order of damping magnitude. In general, higher-conducting, lower-stiffness metallic matrices coupled with more-piezoelectric, higher-stiffness ceramic reinforcement resulted in the greatest level of predicted damping capability and enhanced composite elastic modulus. Additionally, a Ni-20wt%Cr-30v%BaTiO₃ composite has been created using mechanical alloying processing. Specifically, pure constituent powders were combined stoichiometrically in a SPEX milling vial utilizing a charge ratio of 4:1 and subsequently milled for 24 hours. Separate composite powder samples were then annealed in a hydrogen tube furnace at 400°C, 500°C, and 600°C for one and five hours at each temperature. X-ray diffraction was performed on the as-milled and the annealed powders revealing that each was composed of the starting constituents in the appropriate proportions. Representative powders were mounted and polished using common metallographic procedures and microstructures were examined by optical microscopy, scanning electron microscopy, and transmission electron microscopy. All of the powders exhibited a good dispersion of BaTiO₃ particles ranging in diameter from 1μm to about 25nm with no noticeable difference between the as-milled and the annealed powders. / Master of Science

Eshelby-type inclusion problems of an infinite or a finite homogeneous isotropic elastic body containing an arbitrary-shape inclusion prescribed with an eigenstrain and an eigenstrain gradient are analytically solved. The solutions are based on a simplified strain gradient elasticity theory (SSGET) that includes one material length scale parameter in addition to two classical elastic constants. For the infinite-domain inclusion problem, the Eshelby tensor is derived in a general form by using the Green’s function in the SSGET. This Eshelby tensor captures the inclusion size effect and recovers the classical Eshelby tensor when the strain gradient effect is ignored. By applying the general form, the explicit expressions of the Eshelby tensor for the special cases of a spherical inclusion, a cylindrical inclusion of infinite length and an ellipsoidal inclusion are obtained. Also, the volume average of the new Eshelby tensor over the inclusion in each case is analytically derived. It is quantitatively shown that the new Eshelby tensor and its average can explain the inclusion size effect, unlike its counterpart based on classical elasticity. To solve the finite-domain inclusion problem, an extended Betti’s reciprocal theorem and an extended Somigliana’s identity based on the SSGET are proposed and utilized. The solution for the disturbed displacement field incorporates the boundary effect and recovers that for the infinite-domain inclusion problem. The problem of a spherical inclusion embedded concentrically in a finite spherical body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. It is demonstrated through numerical results that the newly obtained Eshelby tensor can capture the inclusion size and boundary effects, unlike existing ones. Finally, a homogenization method is developed to predict the effective elastic properties of a heterogeneous material using the SSGET. An effective elastic stiffness tensor is analytically derived for the heterogeneous material by applying the Mori-Tanaka and Eshelby’s equivalent inclusion methods. This tensor depends on the inhomogeneity size, unlike what is predicted by existing homogenization methods based on classical elasticity. Numerical results for a two-phase composite reveal that the composite becomes stiffer when the inhomogeneities get smaller.

The Eshelby-type problems of an arbitrary-shape polygonal or polyhedral inclusion embedded in an infinite homogeneous isotropic elastic material are analytically solved using a simplified strain gradient elasticity theory (SSGET) that contains a material length scale parameter. The Eshelby tensors for a plane strain inclusion with an arbitrary polygonal cross section and for an arbitrary-shape polyhedral inclusion are analytically derived in general forms in terms of three potential functions. These potential functions, as area integrals over the polygonal cross section and volume integrals over the polyhedral inclusion, are evaluated. For the polygonal inclusion problem, the three area integrals are first transformed to three line integrals using the Green's theorem, which are then evaluated analytically by direct integration. In the polyhedral inclusion case, each of the three volume integrals is first transformed to a surface integral by applying the divergence theorem, which is then transformed to a contour (line) integral based on Stokes' theorem and using an inverse approach. In addition, the Eshelby tensor for an anti-plane strain inclusion with an arbitrary polygonal cross section embedded in an infinite homogeneous isotropic elastic material is analytically solved. Each of the newly derived Eshelby tensors is separated into a classical part and a gradient part. The latter includes the material length scale parameter additionally, thereby enabling the interpretation of the inclusion size effect. For homogenization applications, the area or volume average of each newly derived Eshelby tensor over the polygonal cross section or the polyhedral inclusion domain is also provided in a general form. To illustrate the newly obtained Eshelby tensors and their area or volume averages, different types of polygonal and polyhedral inclusions are quantitatively studied by directly using the general formulas derived. The numerical results show that the components of the each SSGET-based Eshelby tensor for all inclusion shapes considered vary with both the position and the inclusion size. It is also observed that the components of each averaged Eshelby tensor based on the SSGET change with the inclusion size.

Par la mise en œuvre de simulations numériques d'un modèle bidimensionnel de verre de Lennard-Jones, nous étudions l'effet de la température sur les mécanismes élémentaires de la déformation dans les matériaux amorphes. Nous présentons un ensemble très complet de données couvrant plusieurs décades de taux de cisaillement à différentes températures en dessous et jusqu'à la transition vitreuse. Les mesures, qui portent sur la diffusion transverse, la contrainte macroscopique ainsi que sur des champs mésoscopiques (déformation, contrainte) et leurs corrélations spatiales, conduisent à proposer que la dynamique des avalanches identifiée précédemment dans les simulations athermiques continue d'être à l'œuvre - en restant presque inchangée - jusqu'à la transition vitreuse. Nous arguons que dans la gamme de paramètres utilisée l'effet des fluctuations thermiques revient à déplacer les seuils auxquels les événements dissipatifs se produisent, ce qui se traduit par une forte baisse du niveau de contrainte macroscopique aux températures les plus basses

Orientador: Daniel Mário Ugarte / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-17T20:15:26Z (GMT). No. of bitstreams: 1 Tizei_LuizHenriqueGalvao_D.pdf: 12237887 bytes, checksum: e97ac7041ecfd4c30088cf9b43d9849a (MD5) Previous issue date: 2011 / Resumo: O desenvolvimento de novos materias tem grande interesse devido à ocorrência de novos fenômenos e propriedades, as quais podem ser usadas em futuras aplicações tecnológicas. Em particular, nas últimas décadas, esforços imensos foram realizados buscando compreender nanomateriais e os efeitos da redução de tamanho e de dimensão. Entre os diferentes avanços alcançados, podemos citar o desenvolvimento significativo de nanofios semicondutores (estruturas quasi-unidimensionais) com dezenas ou centenas de nanometros de espessura e milhares de nanometros de comprimento. O método mais utilizado para o crescimento de nanofios é o método catalítico chamado VLS (Vapor-Líquido-Sólido), no qual uma nanopartícula metálica serve como sorvedouro preferencial de átomos de um vapor e, também, como posição para a formação de um sólido (nanofio). O VLS foi proposto por Wagner e Ellis nos anos 60. Em nossos trabalhos, nos concentramos no estudo de nanofios de semicondutores III-V crescidos em um reator de Epitaxia de Feixe Químico (CBE) catalisados por nanopartículas de Au. Mais especificamente, estudamos nanofios de InP, InAs, InGaP, InAsP e heteroestruturas InP/InAs/InP. Como a qualidade de interfaces e homogeneidade química do material crescido, influenciam diretamente as propriedades ópticas e elétricas de nanofios, nossa pesquisa nos levou a avaliar os limites da aplicação de diversas técnicas de microscopia eletrônica de transmissão aplicadas: TEM (Microscopia Eletrônica de Transmissão), STEM (Microscopia Eletrônica de Transmissão em Varredura), HRTEM (Microscopia Eletrônica de Transmissão de Alta Resolução), EDS (Espectroscopia de Raios-X Dispersados em Energia) e EELS (Espectroscopia de Perda de Energia de Elétrons). Como consequência, determinamos os limites de detecção de variações químicas e de medidas de larguras de interfaces das diferentes técnicas. Em particular, devido às limitações impostas pelo dano por radiação no material, propusemos o uso de deslocamentos químicos de plasmons (EELS) para a caracterização química de nanoestruturas de semicondutores III-V. Desenvolvemos uma metodologia para a análise de seções transversais de nanofios de InAsP. Os experimentos realizados indicam a diferença entre os semicondutores produzidos por crescimento axial (catalítico) e por radial (bidimensional). Além disso, a análise química detalhada de heteroestruturas InP/InAs/InP levou a detecção de concentrações inesperados de As no segmento final de InP. Interpretamos esta observação como uma indicação de que As difunde através da nanopartícula catalisadora durante o crescimento, demonstrando uma rota de incorporação de elementos do grupo V em nanofios crescidos pelo método VLS. Finalmente, estudamos os efeitos de defeitos estruturais extendidos, como discordâncias na morfologia e distorções estruturais de nanofios. Neste sentido, observamos a torção de Eshelby em nanofios de InP contendo discordâncias em parafuso únicas. Nossos resultados mostram que as taxas de torção medida são muito maiores (até 100%) do que o previsto pela teoria elástica macroscópica. Isto mostra as mudanças significativas nas propriedades mecânicas e estruturais em nanoestruturas e ilustra o papel importante de estudos detalhados de microscopia eletrônica para a análise de deformações em nanoestruturas / Abstract: The development of new materials has great interest due to the possibility of finding new phenomena and properties, which can be used in technological applications. In particular, in the last decades, huge efforts have been made in order to understand nanomaterials and, the effects of size and dimensionality reduction. Among different advances, it is worth noting the significant development of semiconductor nanowires (quasi-one dimensional structures) with tens or hundreds of nanometers in diameter and thousands of nanometers in length. The catalytic method VLS (Vapor-Liquid-Solid) is the most used approach for nanowire preparation, in which a metal nanoparticle serves as a preferential sink for atoms from a vapor and, also, as the position for the solid nucleation; this method was proposed by Wagner and Ellis in the 60s. In our work, we have focused on the study of III-V semiconductor nanowires grown by Chemical Beam Epitaxy (CBE) catalyzed by Au nanoparticles. Specifically, we have studied different III-V nanowires (InP, InAs, InGaP and InAsP), as ell as, some heterostructured wires (InP/InAs/InP). As the quality of interfaces and the chemical homogeneity of materials directly influence the optical and electrical properties of nanowires, our research have led us to assess the limit of applicability of several characterization techniques based on transmission electron microscopy: TEM (Transmission Electron Microscopy), STEM (Scanning Transmission Electron Microscopy), HRTEM (High Resolution Transmission Electron Microscopy), EDS (Energy Dispersed X-Ray Spectroscopy) and EELS (Electron Energy Loss Spectroscopy). As a consequence, we have determined the detection limit for the measurement of chemical composition variations and interface widths. In particular, due to the limitations imposed by radiation damage on III-V nanowires, we have proposed the use of Plasmon chemical shifts (EELS) to the chemical characterization of III-V nanostructures. We have analyzed the cross sections of InAsP nanowires and we have been able to reveal a difference between the semiconductors materials produced by the axial (catalytic) and radial (bidimensional) growth. Through the detailed chemical analysis of InP/InAs/InP heterostructures we have detected an unexpected concentration of As in the last InP segment of the heterostructure. We have interpreted this result as an indication that As diffuses through the catalytic nanoparticle during growth. This demonstrates an incorporation route for group V atoms in nanowires grown by VLS. Finally, we have studied the effects of extended structural defects, like dislocations, in the morphology and structural distortions of nanowires. In this sense, we have observed the Eshelby twist in InP nanowires containing a single screw dislocation. Our results show that measured twist rates are much larger (up to 100%) than the predictions from the elasticity theory. This shows the significant change of mechanical and structural properties in nanoscale and, illustrates the important role of a careful electron microscopy studies to analyze deformations in nanostructures / Doutorado / Física da Matéria Condensada / Doutor em Ciências

Předkládaná dizertační práce se zabývá stanovením hlavních členů Williamsova asymptotického rozvoje popisujícího rovinné elektro-elastické pole v okolí piezoelektrických bi-materiálových vrubů a trhlin na rozhraní za použití rozšířeného Lechnického-Eshelbyho-Strohova formalismu v návaznosti na čistě anizotropní pružnost. Je ukázáno, že rozšířený Lechnického-Eshelbyho-Strohův formalismus představuje spolu s moderními programovacími koncepty v jazyku Python efektivní a také praktický nástroj pro lomovou analýzu piezoelektrických bi-materiálů. Teoretická část práce popisuje aspekty anizotropní pružnosti a její návaznost na piezoelektrické materiály. Základní rovnice zaměřené na speciální typy monoklinických materiálů, které umožňují oddělení rovinného a anti-rovinného problému, jsou vyjádřeny pomocí komplexních potenciálů. V praktické části práce je sestaven problém vlastního hodnot pro bi-materiálový vrub, na jehož základě jsou stanoveny exponenty singularity a pomocí dvoustavového -integrálu také zobecněné faktory intenzity napětí. Veškeré vztahy a numerické procedury jsou následně rozšířeny na problém piezoelektrických bi-materiálových vrubů a podrobně prozkoumány v uvedených příkladech. Zvláštní pozornost je věnována přechodu asymptotického řešení téměř zavřených vrubů a trhlin na rozhraní. Vliv směru polarizace na asymptotické řešení je také zkoumán. Přesnost stanovení zobecněných faktorů intenzity napětí je testována srovnáním asymptotického řešení a řešení získaného pomocí metody konečných prvků s velmi jemnou sítí konečných prvků. Na závěr je formalismus modifikován pro nepiezoelektrické materiály.

<p dir="ltr">This thesis explores the thermodynamics and mechanics of reaction-diffusion interfaces in solid materials, focusing on configurational forces for bulks and surfaces, which are essential in understanding phenomena like electromigration, phase separation, and void evolution. The work is divided into four themes: bulk and surface configurational mechanics, electromigration in solder joints, and solid mixture theory. The thesis develops theories based on continuum mechanics and configurational forces, deriving Eshelby stress tensors and balance laws for interfaces. Experimental work on electromigration in SnBi solder joints is used to validate the theory. The research contributes to advancing the understanding of solid-state diffusion and phase evolution in engineering materials.</p>