Interplay of martensitic phase transformation and plastic slip in polycrystals

Inspired by key experimental and analytical results regarding Shape Memory Alloys (SMAs), we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip. The framework is novel in the way it treats plasticity on par with transformation.

We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.

We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the $\alpha$--$\gamma$ and $\alpha$--$\varepsilon$ transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the $\alpha$--$\varepsilon$ model.

Effects of particle size ratio on single particle motion in colloidal dispersions

The motion of a single Brownian particle of arbitrary size through a dilute colloidal dispersion of neutrally buoyant bath spheres of another characteristic size in a Newtonian solvent is examined in two contexts. First, the particle in question, the probe particle, is subject to a constant applied external force drawing it through the suspension as a simple model for active and nonlinear microrheology. The strength of the applied external force, normalized by the restoring forces of Brownian motion, is the Péclet number, Pe. This dimensionless quantity describes how strongly the probe is upsetting the equilibrium distribution of the bath particles. The mean motion and fluctuations in the probe position are related to interpreted quantities of an effective viscosity of the suspension. These interpreted quantities are calculated to first order in the volume fraction of bath particles and are intimately tied to the spatial distribution, or microstructure, of bath particles relative to the probe. For weak Pe, the disturbance to the equilibrium microstructure is dipolar in nature, with accumulation and depletion regions on the front and rear faces of the probe, respectively. With increasing applied force, the accumulation region compresses to form a thin boundary layer whose thickness scales with the inverse of Pe. The depletion region lengthens to form a trailing wake. The magnitude of the microstructural disturbance is found to grow with increasing bath particle size -- small bath particles in the solvent resemble a continuum with effective microviscosity given by Einstein's viscosity correction for a dilute dispersion of spheres. Large bath particles readily advect toward the minimum approach distance possible between the probe and bath particle, and the probe and bath particle pair rotating as a doublet is the primary mechanism by which the probe particle is able to move past; this is a process that slows the motion of the probe by a factor of the size ratio. The intrinsic microviscosity is found to force thin at low Péclet number due to decreasing contributions from Brownian motion, and force thicken at high Péclet number due to the increasing influence of the configuration-averaged reduction in the probe's hydrodynamic self mobility. Nonmonotonicity at finite sizes is evident in the limiting high-Pe intrinsic microviscosity plateau as a function of bath-to-probe particle size ratio. The intrinsic microviscosity is found to grow with the size ratio for very small probes even at large-but-finite Péclet numbers. However, even a small repulsive interparticle potential, that excludes lubrication interactions, can reduce this intrinsic microviscosity back to an order one quantity. The results of this active microrheology study are compared to previous theoretical studies of falling-ball and towed-ball rheometry and sedimentation and diffusion in polydisperse suspensions, and the singular limit of full hydrodynamic interactions is noted.

Second, the probe particle in question is no longer subject to a constant applied external force. Rather, the particle is considered to be a catalytically-active motor, consuming the bath reactant particles on its reactive face while passively colliding with reactant particles on its inert face. By creating an asymmetric distribution of reactant about its surface, the motor is able to diffusiophoretically propel itself with some mean velocity. The effects of finite size of the solute are examined on the leading order diffusive microstructure of reactant about the motor. Brownian and interparticle contributions to the motor velocity are computed for several interparticle interaction potential lengths and finite reactant-to-motor particle size ratios, with the dimensionless motor velocity increasing with decreasing motor size. A discussion on Brownian rotation frames the context in which these results could be applicable, and future directions are proposed which properly incorporate reactant advection at high motor velocities.

Self-assembly of brush polymers

The unique structure and properties of brush polymers have led to increased interest in them within the scientific community. This thesis describes studies on the self-assembly of these brush polymers.

Chapter 2 describes a study on the rapid self-assembly of brush block copolymers into nanostructures with photonic bandgaps spanning the entire visible spectrum, from ultraviolet to near infrared. Linear relationships are observed between the peak wavelengths of reflection and polymer molecular weights. This work enables "bottom-up" fabrication of photonic crystals with application-tailored bandgaps, through synthetic control of the polymer molecular weight and the method of self-assembly.

Chapter 3 details the analysis of the self-assembly of symmetrical brush block copolymers in bulk and thin films. Highly ordered lamellae with domain spacing ranging from 20 to 240 nm are obtained by varying molecular weight of the backbone. The relationship between degree of polymerization and the domain spacing is reported, and evidence is provided for how rapidly the brush block copolymers self-assemble and achieve thermodynamic equilibrium.

Chapter 4 describes investigations into where morphology transitions take place as the volume fraction of each block is varied in asymmetrical brush block copolymers. Imaging techniques are used to observe a transition from lamellar to a cylindrical morphology as the volume fraction of one of the blocks exceeds 70%. It is also shown that the asymmetric brush block copolymers can be kinetically trapped into undulating lamellar structures by drop casting the samples.

Chapter 5 explores the capability of macromolecules to interdigitate into densely grafted molecular brush copolymers using stereocomplex formation as a driving force. The stereocomplex formation between complementary linear polymers and brush copolymers is demonstrated, while the stereocomplex formation between complementary brush copolymers is shown to be restricted.

Hall coefficient and resistivity of an amorphous palladium-silicon alloy

The Hall coefficient and resistance in several specimens of an amorphous metallic alloy containing 80 at.% palladium and 20 at.% silicon have been investigated at temperatures between 4.2°K and room temperature. An ideal limiting behavior of these transport coefficients was analyzed on the basis of the nearly free electron model to yield a carrier density of 9 x 10²² cm.^-3, or about 1.7 electrons per palladium atom, and a mean free path of about 9Å which is almost constant with temperature. The deviations of the individual specimens from this ideal behavior, which were small but noticeable in the relative resistivity and much greater in the Hall coefficient, can be explained by invoking disk-shaped crystalline regions with low resistivity and a positive Hall coefficient. A detailed calculation shows how a volume fraction of such crystalline material too small to be noticed in X-ray diffraction could have a significant effect on the resistivity and a much greater effect on the Hall coefficient.

溶胶-凝胶光波导环形谐振腔的挥发性有机化合物传感特性

采用溶胶-凝胶法制作波导环形谐振腔, 讨论了环形谐振腔器件的传输特性。测量了在不同物质、不同体积分数的挥发性有机化合物(VOC)蒸气气氛下器件的传输光谱的敏感性。结果表明, 谐振波长随甲醇、乙醇、丙醇等醇类化合物, 以及丙酮、甲醛等蒸气体积分数的上升而向长波方向移动, 具有高的灵敏度, 且两者基本呈线性关系。其中, 对丙醇最敏感, 灵敏度达到1.403 pm/10-6。对甲烷和二甲苯也有微弱反应, 但是其灵敏度很低。也测量了水蒸气对传输谱特性的影响。观察到传输谱衬比度对不同挥发性有机化合物物质蒸气的不同敏

溶胶-凝胶条波导Sagnac环的乙醇蒸气传感特性

采用有机/无机混合溶胶-凝胶法制作条形光波导,并将条波导接入光纤Sagnac 环中,测量了输出光功率随环境气氛中乙醇蒸气体积分数变化的特性,表明在实验研究的范围内,输出信号与乙醇蒸气体积分数呈正弦变化。根据Sagnac环结构输出特性的基本关系,反映了溶胶-凝胶条波导在乙醇蒸气气氛下产生了双折射效应。观察到双折射相移与乙醇体积分数的亚线性关系。对实验数据拟合,计算了偏振相移的线性项和二次项系数,得到所制备的条波导的双折射对乙醇体积分数的响应为Δn≈4.4×10-2。测量了信号变化的时间演变特性,典型的上升和

Experimental study on inertial effects in liquid-solid flows

This thesis presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Reynolds (defined by the shear rate and particle diameter) and Stokes numbers, ranging from 3 ≤ Re ≤ 1.6 × 10³ and 0.4 ≤ St ≤ 195. The experiments use a specifically designed Couette cylindrical rheometer that allows for probing the transition from transporting a pure liquid to transporting a dense suspension of particles. Measurements of the shear stress are presented for a wide range of particle concentration (10 to 60% in volume) and for particle to fluid density ratio between 1 and 1.05. The effective relative viscosity exhibits a strong dependence on the solid fraction for all density ratios tested. For density ratio of 1 the effective viscosity increases with Stokes number (St) for volume fractions (φ) lower than 40% and becomes constant for higher φ. When the particles are denser than the liquid, the effective viscosity shows a stronger dependance on St. An analysis of the particle resuspension for the case with a density ratio of 1.05 is presented and used to predict the local volume fraction where the shear stress measurements take place. When the local volume fraction is considered, the effective viscosity for settling and no settling particles is consistent, indicating that the effective viscosity is independent of differences in density between the solid and liquid phase. Shear stress measurements of pure fluids (no particles) were performed using the same rheometer, and a deviation from laminar behavior is observed for gap Reynolds numbers above 4× 10³, indicating the presence of hydrodynamic instabilities associated with the rotation of the outer cylinder. The increase on the effective viscosity with Stokes numbers observed for mixtures with φ ≤ 30% appears to be affected by such hydrodynamic instabilities. The effective viscosity for the current experiments is considerably higher than the one reported in non-inertial suspensions.

Topology optimization of silicon anode structures for lithium-ion battery applications

This thesis presents a topology optimization methodology for the systematic design of optimal multifunctional silicon anode structures in lithium-ion batteries. In order to develop next generation high performance lithium-ion batteries, key design challenges relating to the silicon anode structure must be addressed, namely the lithiation-induced mechanical degradation and the low intrinsic electrical conductivity of silicon. As such, this work considers two design objectives of minimum compliance under design dependent volume expansion, and maximum electrical conduction through the structure, both of which are subject to a constraint on material volume. Density-based topology optimization methods are employed in conjunction with regularization techniques, a continuation scheme, and mathematical programming methods. The objectives are first considered individually, during which the iteration history, mesh independence, and influence of prescribed volume fraction and minimum length scale are investigated. The methodology is subsequently extended to a bi-objective formulation to simultaneously address both the compliance and conduction design criteria. A weighting method is used to derive the Pareto fronts, which demonstrate a clear trade-off between the competing design objectives. Furthermore, a systematic parameter study is undertaken to determine the influence of the prescribed volume fraction and minimum length scale on the optimal combined topologies. The developments presented in this work provide a foundation for the informed design and development of silicon anode structures for high performance lithium-ion batteries.

The tunable negative refractive index in granular composite

The effective refractive index of a kind of granular composite, which consists of granular metallic and magnetic inclusions with different radius embedded in a host medium, is theoretically investigated. Results show that for certain volume fractions of these two inclusions, the negative permittivity peak shifts to low frequency and the peak value increases with increasing radius ratio of the radius of magnetic granulae to that of metallic granulae. Simultaneously, peak value of permeability decreases with the radius ratio, and value peak shifts to high frequency with increasing volume fraction of magnetic inclusion. Therefore, the radius ratio can affect the effective refractive index considerably, and it is found that by adjusting the radius ratio, the refractive index may change between negative and positive values for certain volume fractions of the two inclusions. (c) 2005 Elsevier B.V. All rights reserved.

Investigação da microarquitetura óssea através de microtomografia 3D

A microtomografia computadorizada (uCT) é uma técnica de ensaio não destrutivo, frequentemente utilizada no estudo da estrutura interna de ossos, com uma resolução espacial da ordem de mícrons. Neste trabalho, seis pares de amostras ósseas (fêmur de rato) foram estudados através da uCT. Os ensaios foram conduzidos na presença ou não de filtros de alumínio (espessura de 0,25; 0,50 e 0,75 mm), utilizando-se três níveis de resolução (33,3; 15,0 e 9,5 um). Os parâmetros de arquitetura óssea BS (área óssea da amostra), BV (volume ósseo da amostra), TS (área superficial da amostra), TV (volume da amostra), BV/TV (razão entre o volume ósseo e o volume da amostra), BS/BV (razão entre a área óssea da amostra e o volume ósseo da amostra), Tb.N (densidade trabecular), Tb.Th (espaçamento entre as trabéculas), Tb.Sp (separação trabecular), conectividade e anisotropia foram determinados através das análises em duas (2D) e/ou três (3D) dimensões. A comparação entre os valores dos parâmetros obtidos através dessas análises foi realizada através do teste t pareado e da correlação de Pearson. Com base nos resultados, foi possível determinar a influência da resolução da imagem na qualidade dos parâmetros da arquitetura óssea obtidos através das análises 2D e/ou 3D. Os dados mostram que a presença de filtro de alumínio também afeta a qualidade desses parâmetros. Assim, os melhores resultados são obtidos com resolução máxima e filtro de alumínio com espessura de 0,25 ou 0,50 mm.

The toughness of adipose tissue: measurements and physical basis.

The measured toughness J(C) of adipose and dermal porcine tissues are 4.1 and 17 kJ m(-2), respectively, via a trouser tear test. An assessment is made of the contribution to overall toughness from the microstructural elements. The analysis suggests that the toughness of adipose tissue is determined by the collagen network that surrounds the adipocytes. The volume fraction of the interlobular septa is sufficiently low for it to make a negligible contribution to the macroscopic toughness.

Wear of hardfacing white cast irons by solid particle erosion

The response of three commercial weld-hardfacing alloys to erosive wear has been studied. These were high chromium white cast irons, deposited by an open-arc welding process, widely used in the mineral processing and steelmaking industries for wear protection. Erosion tests were carried out with quartz sand, silicon carbide grit and blast furnace sinter of two different sizes, at a velocity of 40 m s-1 and at impact angles in the range 20° to 90°. A monolithic white cast iron and mild steel were also tested for comparison. Little differences were found in the wear rates when silica sand or silicon carbide grit was used as the erodent. Significant differences were found, however, in the rankings of the materials. Susceptibility to fracture of the carbide particles in the white cast irons played an important role in the behaviour of the white cast irons. Sinter particles were unable to cause gross fracture of the carbides and so those materials with a high volume fraction of carbides showed the greatest resistance to erosive wear. Silica and silicon carbide were capable of causing fracture of the primary carbides. Concentration of plastic strain in the matrix then led to a high wear rate for the matrix. At normal impact with silica or silicon carbide erodents mild steel showed a greater resistance to erosive wear than these alloys. © 1995.

Crystal growth of melt-textured Nd-123 under 1% oxygen partial pressure atmosphere

Crystal growth of melt-textured Nd-123 pseudo-crystals was investigated via an isothermal solidification with top-seeding technique under a 1%O2 in N2 atmosphere. Non-steady state solidification was observed at low undercooling, in contrast to an almost linear growth at higher undercooling. Similar to processing in air, the substitution of Nd/Ba was found to decrease from the seed position to the edge of the crystal. In addition, the volume fraction of Nd-422 particles decreased in the solid as solidification proceeded. As a result of these microstructural inhomogeneities, the critical temperature and the critical current density varied within the crystal even for samples processed isothermally, despite the narrow solid solution range of the Nd-123 phase under a reduced pO2 atmosphere.

Mineralization and nanomechanical properties in Articular Calcified Cartilage (ACC)

The contribution of the relative volumes of mineral and collagen to the nanomechanical behavior of articular calcified cartilage is explored using nanoindentation, quantitative backscattered electron imaging, and finite element analysis. Elastic modulus generally increases with mineral volume fraction. In highly mineralized tissues, the mineral occupation of water space significantly increases modulus with addition of little mineral. Mineral and organic phases were modeled using Hashin-Shtrikman composite bounds, calculated as a function of mineral volume fraction. Modulus values fall between the Hashin-Shtrikman bounds, indicating some intermediate degree of mineral phase connectivity. Such connectivity in ACC is greater than that achieved in bone and results from uniform collagen orientation and large volume of water space available for mineral occupation.

Development of a universal stress sensor for graphene and carbon fibres

Carbon fibres are a significant volume fraction of modern structural airframes. Embedded into polymer matrices, they provide significant strength and stiffness gains by unit weight compared with competing structural materials. Here we use the Raman G peak to assess the response of carbon fibres to the application of strain, with reference to the response of graphene itself. Our data highlight the predominance of the in-plane graphene properties in all graphitic structures examined. A universal master plot relating the G peak strain sensitivity to tensile modulus of all types of carbon fibres, as well as graphene, is presented. We derive a universal value of - average - phonon shift rate with axial stress of around -5ω0 -1 (cm -1 Mpa-1), where ω0 is the G peak position at zero stress for both graphene and carbon fibre with annular morphology. The use of this for stress measurements in a variety of applications is discussed. © 2011 Macmillan Publishers Limited. All rights reserved.