Yun-Bo Yi

Mechanical properties of nanotube sheets: Alterations in joint morphology and achievable moduli in manufacturable materials

Nanotube sheets, or “bucky papers,” have been proposed for use in actuating, structural and electrochemical systems, based in part on their potential mechanical properties. Here, we present results of detailed simulations of networks of nanotubes/ropes, with special emphasis on the effect of joint morphology. We perform detailed simulations of three-dimensional joint deformation, and use the results to inform simulations of two-dimensional (2D) networks with intertube connections represented by torsion springs. Upper bounds are established on moduli of nanotube sheets, using the 2D Euler beam-network simulations. Comparisons of experimental and simulated response for HiPco-nanotube and laser-ablated nanotube sheets, indicate that ∼2–30-fold increases in moduli may be achievable in these materials. Increasing the numbers of interrope connections appears to be the best target for improving nanotube sheet stiffnesses in materials containing straight segments.

Eigenvalue solution of thermoelastic instability problems using Fourier reduction

A finite–element method is developed for determining the critical sliding speed for thermoelastic instability of an axisymmetric clutch or brake. Linear perturbations on the constant–speed solution are sought that vary sinusoidally in the circumferential direction and grow exponentially in time. These factors cancel in the governing thermoelastic and heat–conduction equations, leading to a linear eigenvalue problem on the two–dimensional cross–sectional domain for the exponential growth rate for each Fourier wavenumber. The imaginary part of this growth rate corresponds to a migration of the perturbation in the circumferential direction. The algorithm is tested against an analytical solution for a layer sliding between two half–planes and gives excellent agreement, for both the critical speed and the migration speed. Criteria are developed to determine the mesh refinement required to give an adequate discrete description of the thermal boundary layer adjacent to the sliding interface. The method is then used to determine the unstable mode and critical speed in geometries approximating current multi–disc clutch practice.

Analytical approximation of the percolation threshold for overlapping ellipsoids of revolution

Analytic approximations for percolation points in two–dimensional and three–dimensional particulate arrays have been reported for only a very few, simple particle geometries. Here, an analytical approach is presented to determine the percolative properties (i.e. statistical cluster properties) of permeable ellipsoids of revolution. We generalize a series expansion technique, previously used by other authors to study arrays of spheres and cubes. Our analytic solutions are compared with Monte Carlo simulation results, and show good agreement at low particle aspect ratio. At higher aspect ratios, the analytic approximation becomes even more computationally intensive than direct simulation of a number of realizations. Additional simulation results, and simplified, closed–form bounding expressions for percolation thresholds are also presented. Limitations and applications of the asymptotic expressions are discussed in the context of materials design and design of sensor arrays.

Statistical geometry of random fibrous networks, revisited: Waviness, dimensionality, and percolation

Waviness alters both geometric and mechanical properties of stochastic fibrous networks and significantly affects overall mechanical response, but few results are available in the literature on the subject. In this work, we explore the importance of the dimension of constituent fibers (1D vs 2D) in determination of percolation thresholds, and other fundamental statistical properties of fibers having geometric waviness, in adaptation of classical theories on random lattices to practical applications, including analysis of nanotube ropes and collagen bundles. Although the so-called “curl ratio” clearly affects the statistical properties, as evaluated by Kallmes and Corte a few decades ago, we have found some results in this classic work to be inaccurate for systems containing fibers of moderate waviness. Our main findings include the independence of the mean number of crossings with regard to waviness, as well as the nonlinear dependence of probability of intersection on waviness. Our investigation of perco...

Effect of nanorope waviness on the effective moduli of nanotube sheets

Using a micromechanics approach, we recently investigated the theoretical limits on achievable moduli in nanotube mats by stiffening of bonds. However, the waviness intrinsic to many manufacturing processes also clearly plays an important role in stiffness of these materials. To study the effect of waviness on mechanical properties, we modeled fiber segments as sinusoids, generated networks comprised of these fibers, and performed simulations of deformations of the networks. In contradiction of classical work by Kallmes and Corte [Tappi J. 43, 737 (1960)], we found the number of fiber crossings in these networks to be independent of fiber waviness, leading to identification of the number of fiber crossings as a necessary and sufficient parameter to specify network geometry, for either wavy or straight fibers. Our mechanical modeling results suggest that reducing the waviness of nanotube ropes would significantly improve Young’s moduli in these materials. However, reduction of waviness would not produce the improvements achievable with higher bond density; for random sheets, assuring connections among all intersecting ropes appears to be the most direct route toward improving the overall sheet properties. There remains a persistent discrepancy between statistically predicted bond densities and physical bond densities, based on moduli of these materials.

Effect of Geometry on Thermoelastic Instability in Disk Brakes and Clutches

The finite element method is used to reduce the problem of thermoelastic instability (TEI) for a brake disk to an eigenvalue problem for the critical speed. Conditioning of the eigenvalue problem is improved by performing a preliminary Fourier decomposition of the resulting matrices. Results are also obtained for two-dimensional layer and three-dimensional strip geometries, to explore the effects of increasing geometric complexity on the critical speeds and the associated mode shapes. The hot spots are generally focal in shape for the three-dimensional models, though modes with several reversals through the width start to become dominant at small axial wavenumbers n, including a thermal banding mode corresponding to n = 0. The dominant wavelength (hot spot spacing) and critical speed are not greatly affected by the three-dimensional effects, being well predicted by the two-dimensional analysis except for banding modes. Also, the most significant deviation from the two-dimensional analysis can be approximated as a monotonic interpolation between the two-dimensional critical speeds for plane stress and plane strain as the width of the sliding surface is increased. This suggests that adequate algorithms for design against TEI could be developed based on the simpler two-dimensional analysis.

Particle Compression and Conductivity in Li-Ion Anodes with Graphite Additives

We performed coupled theoreticallexperimental studies on Li-ion cells to quantify reductions in anode resistivity and/or contact resistance between the matrix and the current collector with the addition of amorphous carbon coatings and anode compression. We also aimed to identify microstructural changes in constituent particles due to anode compression, using models of permeable-impermeable coatings of graphite particles. We studied three anode materials, SL-20, GDR-6 (6 wt % amorphous carbon coating), and GDR-14 (14 wt % amorphous carbon coating). Four compression conditions (0, 100, 200, and 300 kg/cm 2 ) were examined. Experimental results indicated that electrical resistivities for unpressed materials were reduced with addition of amorphous carbon coating (for unpressed materials: ρ SL-20 > ρ GDR-6 > ρ GDR-14 ). Contact resistances were reduced for SL-20 anodes by the application of pressure. Overall, the two-dimensional (2D) impermeable particle mathematical model provided reasonable agreement with the experiments for SL-20 and GDR-6 materials, indicating that coatings remain intact for these materials even at moderate pressures (100 and 200 kg/cm 2 ). Conductivities of SL-20 and GDR-6 anodes exposed to the highest pressure (300 kg/cm 2 ) fell short of model predictions, suggesting particle breakage. For the GDR-14 graphite, both 2D models underestimated conductivity for all processing conditions. We conclude that the 2D simulation approach is useful in determining the state of coating.

Two-Dimensional vs. Three-Dimensional Clustering and Percolation in Fields of Overlapping Ellipsoids

Maximum depth-to-particle-dimension ratios in which systems can be treated as two-dimensional (2D) rather than three-dimensional (3D) systems in determining percolative properties have not been reported. This problem is of great technological significance. 3D solutions for percolation in even low-density systems pose much more intensive computational problems than their 2D analogs and also result in significantly different predictions for percolation onset. Moreover, many materials and sensing applications require analysis of domains of finite thickness. Adequate loading of particles is required, e.g., in electrodes in advanced batteries and fuel cells to ensure good conductivity. Adequate deployment of sensors into fields of finite thickness such as oblate, neuronal cells is required, e.g., to detect specific ions. A systematic determination of the effect of these arrangements on percolation properties is needed for both applications. Here, we provide comparisons of cluster sizes, densities, and percolation points among monodisperse, 2D and 3D systems of overlapping ellipsoids by systematically increasing the depth of the 3D system relative to particle dimensions. We investigate the effect of several boundary condition assumptions on the resulting particle orientations, emphasizing the probability of formation of large clusters. A method of experimental determination of percolation onset is also suggested, using the maximum change in cluster size.

Eigenvalue Solution of Thermoelastic Damping in Beam Resonators Using a Finite Element Analysis

A finite element formulation is developed for solving the problem related to thermoelastic damping in beam resonator systems. The perturbation analysis on the governing equations of heat conduction, thermoleasticity, and dynamic motion leads to a linear eigenvalue equation for the exponential growth rate of temperature, displacement, and velocity. The numerical solutions for a simply supported beam have been obtained and shown in agreement with the analytical solutions found in the literature. Parametric studies on a variety of geometrical and material properties demonstrate their effects on the frequency and the quality factor of resonance. The finite element formulation presented in this work has advantages over the existing analytical approaches in that the method can be easily extended to general geometries without extensive computations associated with the numerical iterations and the analytical expressions of the solution under various boundary conditions. DOI: 10.1115/1.2748472

Thermoelastic Instabilities in Automotive Disc Brakes — Finite Element Analysis and Experimental Verification

The thermomechanical feedback process due to frictional heating in sliding systems can cause thermoelastic instability (TEI), leading eventually to localization of load and high temperatures at the sliding interface. TEI in caliper/disc brake systems is an intermittent contact problem, since material points on the disc experience periods of contact with the pad alternating with periods of non-contact. The stability problem is here solved numerically by setting up a frame of reference stationary with respect to the pad and seeking a solution for the heat conduction and thermoelastic equations that varies exponentially in time. The upwind scheme is introduced in the finite element formulation to avoid possible numerical difficulties associated with the large convective terms.