The scaling of specific cutting energy is studied when micro-cutting ductile metals. A unified framework for understanding the scaling in specific cutting energy is first presented by viewing the cutting force as a combination of constant, increasing, and decreasing force components, the independent variable being the uncut chip thickness. Then, an attempt is made to isolate the constant force component by performing high rake angle orthogonal cutting experiments on OFHC Copper. The data shows a trend towards a constant cutting force component as the rake angle is increased. In order to understand the source of this constant force component the chip-root is investigated. By quickly stopping the spindle at low cutting speeds, the chip is frozen and the chip-workpiece interface is examined in a scanning electron microscope. Evidence of ductile tearing ahead of the cutting tool is seen at low and high rake angles. At higher cutting speeds a quick-stop device is used to obtain chip-roots. These experiments also clearly indicate evidence of ductile fracture ahead of the cutting tool in both OFHC Copper and Al-2024 T3. To model the cutting process with ductile fracture leading to material separation the finite element method is used. The model is implemented in a commercial finite element software using the explicit formulation. Material separation is modeled via element failure. The model is then validated using the measured cutting and thrust forces and used to study the energy consumed in cutting. As the thickness of layer removed is reduced the energy consumed in material separation becomes important. Simulations also show that the stress state ahead of the tool is favorable for ductile fracture to occur. Ductile fracture in three locations in an interface zone at the chip root is seen while cutting with edge radius tool. A hypothesis is advanced wherein an element gets wrapped around the tool edge and is stretched in two directions leading to fracture. The numerical model is then used to study the difference in stress state and energy consumption between a sharp tool and a tool with a non-zero edge radius.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 99-114).

The Earth's magnetic field is generated in its fluid outer core through dynamo action. In this process, convection and differential rotation of an electrically conducting fluid maintain the magnetic field against its ohmic decay. Using numerical models, we can investigate planetary dynamo processes and the importance of various core properties on the dynamo. In this thesis, I use numerical dynamo models in Earth-like geometry in order to understand the influence of inner core electrical conductivity and the choice of thermal and velocity boundary conditions on the resulting magnetic field. I demonstrate how an electrically conducting inner core can reduce the frequency of reversals and produce axial-dipolar dominated fields in our models. I also demonstrate that a strong planetary magnetic field intensity does not imply that the dynamo operates in the strong field regime as is usually presumed. Through a scaling law analysis, I find that irrespective of the choice of thermal or velocity boundary conditions, the available power determines the magnetic and velocity field characteristics like the field strength, polarity and morphology. Also, whether a dynamo model is in a dipolar, transitional or multipolar regime is dependent on the force balance in the model. I demonstrate that the Lorentz force is balanced by the Coriolis force in the dipolar dynamo regime models resulting in magnetostrophically balanced dynamos whereas the Lorentz force is balanced by the Inertial force (and not the Coriolis force) in the multipolar dynamo regime models resulting in a non-magnetostrophically balanced dynamo. The generation mechanism differs between the regimes and depends on the velocity boundary conditions. The zonal flows of the stress-free models are stronger than in the no-slip models, and bistability is more prominent when stress-free boundary conditions are used. A single scaling law may be feasible for all the models, but there does appear to be some variation for models with different thermal and velocity boundary conditions. The results presented in this thesis are not only applicable to the geodynamo, but will also aid in understanding the dynamos of other planets and exoplanets.

The Earth's magnetic field is generated in its fluid outer core through dynamo action. In this process, convection and differential rotation of an electrically conducting fluid maintain the magnetic field against its ohmic decay. Using numerical models, we can investigate planetary dynamo processes and the importance of various core properties on the dynamo. In this thesis, I use numerical dynamo models in Earth-like geometry in order to understand the influence of inner core electrical conductivity and the choice of thermal and velocity boundary conditions on the resulting magnetic field. I demonstrate how an electrically conducting inner core can reduce the frequency of reversals and produce axial-dipolar dominated fields in our models. I also demonstrate that a strong planetary magnetic field intensity does not imply that the dynamo operates in the strong field regime as is usually presumed. Through a scaling law analysis, I find that irrespective of the choice of thermal or velocity boundary conditions, the available power determines the magnetic and velocity field characteristics like the field strength, polarity and morphology. Also, whether a dynamo model is in a dipolar, transitional or multipolar regime is dependent on the force balance in the model. I demonstrate that the Lorentz force is balanced by the Coriolis force in the dipolar dynamo regime models resulting in magnetostrophically balanced dynamos whereas the Lorentz force is balanced by the Inertial force (and not the Coriolis force) in the multipolar dynamo regime models resulting in a non-magnetostrophically balanced dynamo. The generation mechanism differs between the regimes and depends on the velocity boundary conditions. The zonal flows of the stress-free models are stronger than in the no-slip models, and bistability is more prominent when stress-free boundary conditions are used. A single scaling law may be feasible for all the models, but there does appear to be some variation for models with different thermal and velocity boundary conditions. The results presented in this thesis are not only applicable to the geodynamo, but will also aid in understanding the dynamos of other planets and exoplanets.

At the ballistic limit velocity of a soft armor target pack, the impact response has been shown to be decoupled in the thickness direction, with the initial few plies behaving in an inelastic fashion via off-axis failure modes such as transverse shear or diametral compression. Past the initial few layers, the remaining plies dissipate energy via membrane-like responses, which only involve in-plane tensile failure modes of the constituent fibers. Since these initial plies only contribute to energy absorption via inelastic kinetic energy transfer, previous studies have shown that these plies may be replaced with another material with other desirable properties, such as lower manufacturing costs or stab-resistance.<div>However, the methodology of determining these parameters is still largely empirical. Armor panels are typically impacted and the shot outcomes subsequently evaluated in order to achieve a quantitative ballistic performance for the panel. Additionally, the ballistic performance is usually determined with respect to a particular projectile. Several models have been proposed to provide an efficient method of predicting ballistic limit determination, but results are sometimes difficult to translate across different projectile-target pairs.<br></div><div>The main research direction in the first volume looking at soft armor impact failure modes and design optimization is obviously of immediate relevance to this dissertation. We start off with an examination of the different types of failure modes that impact on fibrous armors may yield. Subsequently, building on these concepts, we take a deeper look into how different impact parameters cause different failure modes,and we end with a discussion of how the armor panel may be designed around these different failure modes. Although some rudimentary analytical and modeling efforts have been put forth, the current work places more emphasis heavily on experimental techniques and observations, as is the nature of the work typically produced by our research group.<br></div><div><br></div>

We present comparative results from simulations of a lattice and an off-lattice model of a homopolymer, in the context of kinetics of the collapse transition. Scaling laws related to the collapse time, cluster coarsening and aging behavior are compared. Although in both models the cluster growth is independent of temperature, the related exponents turn out to be different. Conversely, the aging and associated scaling properties are found to be universal, with the nonequilibrium autocorrelation exponent obeying a recently derived bound.

Halo currents (HCs) in post-disruption plasmas can be large enough to exert significant electromagnetic loads on structures surrounding the plasma. These currents have axisymmetric and non-axisymmetric components, both of which pose threats to the vacuum vessel and other components. However, the non-axisymmetric forces can rotate, amplifying the displacements they cause when the rotation is close to the structures’ resonant frequencies. A new physically motivated scaling law has been developed that describes the rotation frequencies of these HCs and has been validated against measurements on HBT-EP, Alcator C-Mod, and other tokamaks. This scaling law can describe the time-evolution of the asymmetric HC rotation throughout disruptions on HBT-EP as well as the time-averaged rotation on C-Mod. The scaling law can also be modified to include the edge safety factor at the onset of rotation (𝒒_𝑜𝑛𝑠𝑒𝑡), which significantly improves its validity when applied to machines like C-Mod, where 𝒒_𝑜𝑛𝑠𝑒𝑡 changes frequently. The 𝒒_𝑜𝑛𝑠𝑒𝑡 dependence is explained by the relationship between the poloidal structure of the HC asymmetries and the MHD instabilities that drive them, which has been observed experimentally for the first time using a novel set of current sensing limiter tiles installed on HBT-EP. The 1/𝑎² and 𝒒_𝑜𝑛𝑠𝑒𝑡-dependence of the rotation suggest that the HCs predominantly rotate poloidally. This remains consistent with the toroidal rotation observed on HBT-EP and other tokamaks through the “Barber Pole Illusion” and the direction of rotation’s dependence on the direction of 𝐼_𝑝. This scaling law is used to make projections for next generation tokamaks like ITER and SPARC, which predicts that rotation will be resonant on ITER. However, resonant effects can still be avoided if the duration of the disruption is kept short enough to prevent two rotations from being completed.

The ASTM E119 is a large-scale test used to qualify assemblies for fire resistance, including heat transmission and structural integrity. The test requires specialized furnaces and full-scale assemblies that are 3.0 m (10 ft) or more on each side, making it very expensive to perform. In this study, we investigated the feasibility of the scaling methodology for a reduced-scale fire resistance test on different types of wood-based structures, specifically commercially available intumescent coating applied onto wood and bolted lap joints in wood. We build upon a previously developed scaling methodology for wood and gypsum boards, which integrated geometric scaling, Fourier number time scaling, and furnace boundary condition matching. Intumescent coating presents a particular challenge in scaling in that it expands when exposed to fire conditions. To account for this expansion, we identified a relationship between initial dry film thickness and final expanded thickness through cone calorimeter tests and integrated it into a modified scaling methodology. This approach was then validated through fire exposure tests in furnace on wood samples painted with intumescent coating at full, half, and quarter scales. Finally, we demonstrated the scaling laws for joints under combined thermo-structural loading, by subjecting wood-based half-lap joint samples to combined bending and thermal loading at half and quarter scale. The samples were subjected to static three-point bending with the load scaled to achieve structural similitude, while simultaneously being exposed to a scaled fire exposure on the bottom surface. Our study provides insights into the practical application of scaling methodology for testing the fire resistance of joints and fire-resistant coated wood, paving the way for more cost-effective and quicker fire testing for the wood-based composite industry. / Master of Science / The ASTM E119 is a critical test standard that evaluates the fire resistance of various building materials, including wood-based structures. However, the standard tests are quite expensive due to the need for specialized equipment and large-scale samples. In this study, we explored the potential of using a scaled-down fire resistance test on different types of wood-based materials, including commercially available fire-resistant coated wood and joints. We built on existing scaling methods for wood and gypsum boards and adapted it to account for the unique properties of intumescent coating - a fire-resistant material that expands when exposed to high temperatures. By conducting a series of tests, we developed a modified scaling approach to accommodate the expansion of the coating. We then validated this new method by performing fire exposure tests at various scales on wood samples coated with intumescent coating. Finally, we adapted the scaling methods to account for wood based bolted joints. We tested the fire resistance of wood-based half-lap joints under combined heat and structural stress at smaller scales. Our study offers valuable insights into a more cost-effective and efficient method for testing fire resistance in wood-based structures. By providing a reliable scaling approach for fire-resistant coated wood and joints, our work has the potential to make fire testing more accessible for the wood composite industry, ultimately leading to safer and better-performing buildings.

<p dir="ltr">In this dissertation, I use methods of theoretical physics to study principles governing the stochastic dynamics of living timekeepers in a few different contexts. First, focusing on the phenomenon of stochastic growth and division processes in the simplest living organism (the bacterial cell), I present a procedure for analyzing high-throughput, high-precision dynamic datasets to identify emergent simplicities, in particular scaling laws, that provide new insights into a long-standing problem (that of cell size homeostasis). Recasting the question from a stochastic, intergenerational viewpoint (i.e., one that considers the entire life histories of individual cells without recourse to a priori mechanistic assumptions), and taking advantage of identified emergent simplicities to achieve dimensional reduction of the problem, permits a reformulation that captures the inherent stochasticity of individual cells. Identification of discrete modes by which homeostasis is maintained---in particular, via reflexive (elastic) adaptation of cell size and reflective (plastic) adaptation of growth rate---provides important insights into key system constraints that govern living bacterial cells, with additional implications for the design of functional adaptive synthetic homeostats. The observation of non-Markovian dynamics in single-cell growth rates implies the existence of intergenerational memory and plastic adaptation in these simple organisms. I also present my work on the process of early endosomal maturation in human cell lines, multi- fork DNA replication in Escherichia coli cells, and a physics principle and theory predictions for emergent periodicity in a decentralized follow-the-leader dynamic in a collective of randomly signaling agents. This body of work provides mechanistic insights into how temporal organization in outcomes emerges despite the inherently stochastic nature of the constituent dynamics, with each system adopting its own mechanism to achieve this universal goal.</p>

The pressure fluctuations under a high Reynolds Number, rough-wall, turbulent, boundary layer have been studied in the Virginia Tech Stability Wind Tunnel. Rough surfaces of varying element height (1-mm, 3-mm), shape (hemispheres, cylinders) and spacing (5.5-mm, 10.4-mm, 16.5-mm) were investigated in order to ascertain how the turbulent pressure fluctuations change with changes in roughness geometry. Rough surfaces which contain two types of elements are investigated and relationships between the combination surface and the individual surfaces have been uncovered. Measurements of the wall pressure fluctuations were made using pinhole microphones and hotwire measurements were made to obtain the velocity and turbulence field. Among the principal findings is the development of two scaling laws for the low frequency pressure fluctuations. Both of these are based on the idea that the defect between the edge velocity and some local boundary layer velocity sustains the pressure fluctuations in the outer regions of the flow. The first scaling uses the broadband convection velocity as the local velocity of the large scale pressure fluctuations. The second scaling uses the mean boundary layer velocity. Both these scalings appear more robust than the previously proposed scalings for the low frequency region and are able to scale the pressure spectra of all the data to within 3.5-dB. In addition, it was proven that the high frequency shear friction velocity scaling of Meyers et al. (2015) is universal to rough surfaces of different element shape and density. Physical insights into the shear friction velocity, on which this scaling is based, have been revealed. This includes an empirical formula which estimates the element pressure drag coefficient from the roughness density and the Reynolds number. The slopes in the mid-frequency region were found to vary with element density and microphone location such that a useful scaling could not be determined for this region. The possibility of an overlap region is explored and the expectation of a -1 slope is disproved. It is hypothesised that an evanescent decay of the mid-frequency pressure fluctuations occurs between their actual location and the wall where they are measured. A method for accounting for this decay is presented in order to scale the pressure fluctuations in this region. Lastly, a piecewise interpolation function for the pressure spectrum of rough wall turbulent boundary layers was proposed. This analytical function is based on the low frequency scaling on mean velocity and the high frequency scaling of Meyers et al. (2015) The mid-frequency is estimated by a spline interpolation between these two regions. / Ph. D.