Modeling of shape memory alloys with plasticity

Shape memory alloys are a special class of metals that can undergo large deformation yet still be able to recover their original shape through the mechanism of phase transformations. However, when they experience plastic slip, their ability to recover their original shape is reduced. This is due to the presence of dislocations generated by plastic flow that interfere with shape recovery through the shape memory effect and the superelastic effect. A one-dimensional model that captures the coupling between shape memory effect, the superelastic effect and plastic deformation is introduced. The shape memory alloy is assumed to have only 3 phases: austenite, positive variant martensite and negative variant martensite. If the SMA flows plastically, each phase will exhibit a dislocation field that permanently prevents a portion of it from being transformed back to other phases. Hence, less of the phase is available for subsequent phase transformations. A constitutive model was developed to depict this phenomena and simulate the effect of plasticity on both the shape memory effect and the superelastic effect in shape memory alloys. In addition, experimental tests were conducted to characterize the phenomenon in shape memory wire and superelastic wire. ^ The constitutive model was then implemented in within a finite element context as UMAT (User MATerial Subroutine) for the commercial finite element package ABAQUS. The model is phenomenological in nature and is based on the construction of stress-temperature phase diagram. ^ The model has been shown to be capable of capturing the qualitative and quantitative aspects of the coupling between plasticity and the shape memory effect and plasticity and the super elastic effect within acceptable limits. As a verification case a simple truss structure was built and tested and then simulated using the FEA constitutive model. The results where found to be close the experimental data. ^

Ionized cluster beam deposition: Modeling, cluster size measurement and applications

Clusters are aggregations of atoms or molecules, generally intermediate in size between individual atoms and aggregates that are large enough to be called bulk matter. Clusters can also be called nanoparticles, because their size is on the order of nanometers or tens of nanometers. A new field has begun to take shape called nanostructured materials which takes advantage of these atom clusters. The ultra-small size of building blocks leads to dramatically different properties and it is anticipated that such atomically engineered materials will be able to be tailored to perform as no previous material could.^ The idea of ionized cluster beam (ICB) thin film deposition technique was first proposed by Takagi in 1972. It was based upon using a supersonic jet source to produce, ionize and accelerate beams of atomic clusters onto substrates in a vacuum environment. Conditions for formation of cluster beams suitable for thin film deposition have only recently been established following twenty years of effort. Zinc clusters over 1,000 atoms in average size have been synthesized both in our lab and that of Gspann. More recently, other methods of synthesizing clusters and nanoparticles, using different types of cluster sources, have come under development.^ In this work, we studied different aspects of nanoparticle beams. The work includes refinement of a model of the cluster formation mechanism, development of a new real-time, in situ cluster size measurement method, and study of the use of ICB in the fabrication of semiconductor devices.^ The formation process of the vaporized-metal cluster beam was simulated and investigated using classical nucleation theory and one dimensional gas flow equations. Zinc cluster sizes predicted at the nozzle exit are in good quantitative agreement with experimental results in our laboratory.^ A novel in situ real-time mass, energy and velocity measurement apparatus has been designed, built and tested. This small size time-of-flight mass spectrometer is suitable to be used in our cluster deposition systems and does not suffer from problems related to other methods of cluster size measurement like: requirement for specialized ionizing lasers, inductive electrical or electromagnetic coupling, dependency on the assumption of homogeneous nucleation, limits on the size measurement and non real-time capability. Measured ion energies using the electrostatic energy analyzer are in good accordance with values obtained from computer simulation. The velocity (v) is measured by pulsing the cluster beam and measuring the time of delay between the pulse and analyzer output current. The mass of a particle is calculated from m = (2E/v$\sp2).$ The error in the measured value of background gas mass is on the order of 28% of the mass of one N$\sb2$ molecule which is negligible for the measurement of large size clusters. This resolution in cluster size measurement is very acceptable for our purposes.^ Selective area deposition onto conducting patterns overlying insulating substrates was demonstrated using intense, fully-ionized cluster beams. Parameters influencing the selectivity are ion energy, repelling voltage, the ratio of the conductor to insulator dimension, and substrate thickness. ^

Structure-based modeling of head -related transfer functions towards interactive customization of binaural sound systems

One of the most popular techniques for creating spatialized virtual sounds is based on the use of Head-Related Transfer Functions (HRTFs). HRTFs are signal processing models that represent the modifications undergone by the acoustic signal as it travels from a sound source to each of the listener's eardrums. These modifications are due to the interaction of the acoustic waves with the listener's torso, shoulders, head and pinnae, or outer ears. As such, HRTFs are somewhat different for each listener. For a listener to perceive synthesized 3-D sound cues correctly, the synthesized cues must be similar to the listener's own HRTFs. ^ One can measure individual HRTFs using specialized recording systems, however, these systems are prohibitively expensive and restrict the portability of the 3-D sound system. HRTF-based systems also face several computational challenges. This dissertation presents an alternative method for the synthesis of binaural spatialized sounds. The sound entering the pinna undergoes several reflective, diffractive and resonant phenomena, which determine the HRTF. Using signal processing tools, such as Prony's signal modeling method, an appropriate set of time delays and a resonant frequency were used to approximate the measured Head-Related Impulse Responses (HRIRs). Statistical analysis was used to find out empirical equations describing how the reflections and resonances are determined by the shape and size of the pinna features obtained from 3D images of 15 experimental subjects modeled in the project. These equations were used to yield “Model HRTFs” that can create elevation effects. ^ Listening tests conducted on 10 subjects show that these model HRTFs are 5% more effective than generic HRTFs when it comes to localizing sounds in the frontal plane. The number of reversals (perception of sound source above the horizontal plane when actually it is below the plane and vice versa) was also reduced by 5.7%, showing the perceptual effectiveness of this approach. The model is simple, yet versatile because it relies on easy to measure parameters to create an individualized HRTF. This low-order parameterized model also reduces the computational and storage demands, while maintaining a sufficient number of perceptually relevant spectral cues. ^

Lattice boltzmann modeling of fluid flow to determine the permeability of a karst specimen

A limestone sample was scanned using computed tomography (CT) and the hydraulic conductivity of the 3D reconstructed sample was determined using Lattice- Boltzmann methods (LBM) at varying scales. Due to the shape and size of the original sample, it was challenging to obtain a consistent rectilinear test sample. Through visual inspection however, 91 mm and 76 mm samples were digitally cut from the original. The samples had porosities of 58% and 64% and produced hydraulic conductivity values of K= 13.5 m/s and K=34.5 m/s, respectively. Both of these samples were re-sampled to 1/8 and 1/64 of their original size to produce new virtual samples at lower resolutions of 0.542 mm/lu and 1.084 mm/lu, while still representing the same physical dimensions. The hydraulic conductivity tended to increase slightly as the resolution became coarser. In order to determine an REV, the 91 mm sample was also sub-sampled into blocks that were 1/8 and 1/64 the size of the original. The results were consistent with analytical expectations such as those produced by the Kozeny-Carman equation. A definitive REV size was not reached, however, indicating the need for a larger sample. The methods described here demonstrate the ability of LBM to test rock structures and sizes not normally attainable.