Extracting material response from simple mechanical tests on hardening-softening-hardening viscoplastic solids

Compliant foams are usually characterized by a wide range of desirable mechanical properties. These properties include viscoelasticity at different temperatures, energy absorption, recoverability under cyclic loading, impact resistance, and thermal, electrical, acoustic and radiation-resistance. Some foams contain nano-sized features and are used in small-scale devices. This implies that the characteristic dimensions of foams span multiple length scales, rendering modeling their mechanical properties difficult. Continuum mechanics-based models capture some salient experimental features like the linear elastic regime, followed by non-linear plateau stress regime. However, they lack mesostructural physical details. This makes them incapable of accurately predicting local peaks in stress and strain distributions, which significantly affect the deformation paths. Atomistic methods are capable of capturing the physical origins of deformation at smaller scales, but suffer from impractical computational intensity. Capturing deformation at the so-called meso-scale, which is capable of describing the phenomenon at a continuum level, but with some physical insights, requires developing new theoretical approaches.

A fundamental question that motivates the modeling of foams is ‘how to extract the intrinsic material response from simple mechanical test data, such as stress vs. strain response?’ A 3D model was developed to simulate the mechanical response of foam-type materials. The novelty of this model includes unique features such as the hardening-softening-hardening material response, strain rate-dependence, and plastically compressible solids with plastic non-normality. Suggestive links from atomistic simulations of foams were borrowed to formulate a physically informed hardening material input function. Motivated by a model that qualitatively captured the response of foam-type vertically aligned carbon nanotube (VACNT) pillars under uniaxial compression [2011,“Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes,” J. Mech.Phys. Solids, 59, pp. 2227–2237, Erratum 60, 1753–1756 (2012)], the property space exploration was advanced to three types of simple mechanical tests: 1) uniaxial compression, 2) uniaxial tension, and 3) nanoindentation with a conical and a flat-punch tip. The simulations attempt to explain some of the salient features in experimental data, like
1) The initial linear elastic response.
2) One or more nonlinear instabilities, yielding, and hardening.

The model-inherent relationships between the material properties and the overall stress-strain behavior were validated against the available experimental data. The material properties include the gradient in stiffness along the height, plastic and elastic compressibility, and hardening. Each of these tests was evaluated in terms of their efficiency in extracting material properties. The uniaxial simulation results proved to be a combination of structural and material influences. Out of all deformation paths, flat-punch indentation proved to be superior since it is the most sensitive in capturing the material properties.

Effect of Microstructural Interfaces on the Mechanical Response of Crystalline Metallic Materials

Advances in nano-scale mechanical testing have brought about progress in the understanding of physical phenomena in materials and a measure of control in the fabrication of novel materials. In contrast to bulk materials that display size-invariant mechanical properties, sub-micron metallic samples show a critical dependence on sample size. The strength of nano-scale single crystalline metals is well-described by a power-law function, σαD^-n, where D is a critical sample size and n is a experimentally-fit positive exponent. This relationship is attributed to source-driven plasticity and demonstrates a strengthening as the decreasing sample size begins to limit the size and number of dislocation sources. A full understanding of this size-dependence is complicated by the presence of microstructural features such as interfaces that can compete with the dominant dislocation-based deformation mechanisms. In this thesis, the effects of microstructural features such as grain boundaries and anisotropic crystallinity on nano-scale metals are investigated through uniaxial compression testing. We find that nano-sized Cu covered by a hard coating displays a Bauschinger effect and the emergence of this behavior can be explained through a simple dislocation-based analytic model. Al nano-pillars containing a single vertically-oriented coincident site lattice grain boundary are found to show similar deformation to single-crystalline nano-pillars with slip traces passing through the grain boundary. With increasing tilt angle of the grain boundary from the pillar axis, we observe a transition from dislocation-dominated deformation to grain boundary sliding. Crystallites are observed to shear along the grain boundary and molecular dynamics simulations reveal a mechanism of atomic migration that accommodates boundary sliding. We conclude with an analysis of the effects of inherent crystal anisotropy and alloying on the mechanical behavior of the Mg alloy, AZ31. Through comparison to pure Mg, we show that the size effect dominates the strength of samples below 10 μm, that differences in the size effect between hexagonal slip systems is due to the inherent crystal anisotropy, suggesting that the fundamental mechanism of the size effect in these slip systems is the same.

Fabrication, Characterization, And Deformation of 3D Structural Meta-Materials

Current technological advances in fabrication methods have provided pathways to creating architected structural meta-materials similar to those found in natural organisms that are structurally robust and lightweight, such as diatoms. Structural meta-materials are materials with mechanical properties that are determined by material properties at various length scales, which range from the material microstructure (nm) to the macro-scale architecture (μm – mm). It is now possible to exploit material size effect, which emerge at the nanometer length scale, as well as structural effects to tune the material properties and failure mechanisms of small-scale cellular solids, such as nanolattices. This work demonstrates the fabrication and mechanical properties of 3-dimensional hollow nanolattices in both tension and compression. Hollow gold nanolattices loaded in uniaxial compression demonstrate that strength and stiffness vary as a function of geometry and tube wall thickness. Structural effects were explored by increasing the unit cell angle from 30° to 60° while keeping all other parameters constant; material size effects were probed by varying the tube wall thickness, t, from 200nm to 635nm, at a constant relative density and grain size. In-situ uniaxial compression experiments reveal an order-of-magnitude increase in yield stress and modulus in nanolattices with greater lattice angles, and a 150% increase in the yield strength without a concomitant change in modulus in thicker-walled nanolattices for fixed lattice angles. These results imply that independent control of structural and material size effects enables tunability of mechanical properties of 3-dimensional architected meta-materials and highlight the importance of material, geometric, and microstructural effects in small-scale mechanics. This work also explores the flaw tolerance of 3D hollow-tube alumina kagome nanolattices with and without pre-fabricated notches, both in experiment and simulation. Experiments demonstrate that the hollow kagome nanolattices in uniaxial tension always fail at the same load when the ratio of notch length (a) to sample width (w) is no greater than 1/3, with no correlation between failure occurring at or away from the notch. For notches with (a/w) > 1/3, the samples fail at lower peak loads and this is attributed to the increased compliance as fewer unit cells span the un-notched region. Finite element simulations of the kagome tension samples show that the failure is governed by tensile loading for (a/w) < 1/3 but as (a/w) increases, bending begins to play a significant role in the failure. This work explores the flaw sensitivity of hollow alumina kagome nanolattices in tension, using experiments and simulations, and demonstrates that the discrete-continuum duality of architected structural meta-materials gives rise to their flaw insensitivity even when made entirely of intrinsically brittle materials.

Design, Fabrication, and Mechanical Property Analysis of 3D Nanoarchitected Materials

Recent developments in micro- and nanoscale 3D fabrication techniques have enabled the creation of materials with a controllable nanoarchitecture that can have structural features spanning 5 orders of magnitude from tens of nanometers to millimeters. These fabrication methods in conjunction with nanomaterial processing techniques permit a nearly unbounded design space through which new combinations of nanomaterials and architecture can be realized. In the course of this work, we designed, fabricated, and mechanically analyzed a wide range of nanoarchitected materials in the form of nanolattices made from polymer, composite, and hollow ceramic beams. Using a combination of two-photon lithography and atomic layer deposition, we fabricated samples with periodic and hierarchical architectures spanning densities over 4 orders of magnitude from ρ=0.3-300kg/m³ and with features as small as 5nm. Uniaxial compression and cyclic loading tests performed on different nanolattice topologies revealed a range of novel mechanical properties: the constituent nanoceramics used here have size-enhanced strengths that approach the theoretical limit of materials strength; hollow aluminum oxide (Al₂O₃) nanolattices exhibited ductile-like deformation and recovered nearly completely after compression to 50% strain when their wall thicknesses were reduced below 20nm due to the activation of shell buckling; hierarchical nanolattices exhibited enhanced recoverability and a near linear scaling of strength and stiffness with relative density, with E∝ρ^1.04 and σy∝ρ^1.17 for hollow Al₂O₃ samples; periodic rigid and non-rigid nanolattice topologies were tested and showed a nearly uniform scaling of strength and stiffness with relative density, marking a significant deviation from traditional theories on “bending” and “stretching” dominated cellular solids; and the mechanical behavior across all topologies was highly tunable and was observed to strongly correlate with the slenderness λ and the wall thickness-to-radius ratio t/a of the beams. These results demonstrate the potential of nanoarchitected materials to create new highly tunable mechanical metamaterials with previously unattainable properties.

Test particle motion in a Lorentz gas

This is a two-part thesis concerning the motion of a test particle in a bath. In part one we use an expansion of the operator PLe^it(1-P)LLP to shape the Zwanzig equation into a generalized Fokker-Planck equation which involves a diffusion tensor depending on the test particle's momentum and the time.

In part two the resultant equation is studied in some detail for the case of test particle motion in a weakly coupled Lorentz Gas. The diffusion tensor for this system is considered. Some of its properties are calculated; it is computed explicitly for the case of a Gaussian potential of interaction.

The equation for the test particle distribution function can be put into the form of an inhomogeneous Schroedinger equation. The term corresponding to the potential energy in the Schroedinger equation is considered. Its structure is studied, and some of its simplest features are used to find the Green's function in the limiting situations of low density and long time.

Radiation from a short electric dipole antenna in a hot uniaxial plasma

The effects of electron temperature on the radiation fields and the resistance of a short dipole antenna embedded in a uniaxial plasma have been studied. It is found that for ω < ω_p the antenna excites two waves, a slow wave and a fast wave. These waves propagate only within a cone whose axis is parallel to the biasing magnetostatic field B_o and whose semicone angle is slightly less than sin ^(-1) (ω/ω_p). In the case of ω > ω_p the antenna excites two separate modes of radiation. One of the modes is the electromagnetic mode, while the other mode is of hot plasma origin. A characteristic interference structure is noted in the angular distribution of the field. The far fields are evaluated by asymptotic methods, while the near fields are calculated numerically. The effects of antenna length ℓ, electron thermal speed, collisional and Landau damping on the near field patterns have been studied.

The input and the radiation resistances are calculated and are shown to remain finite for nonzero electron thermal velocities. The effect of Landau damping and the antenna length on the input and radiation resistances has been considered.

The radiation condition for solving Maxwell's equations is discussed and the phase and group velocities for propagation given. It is found that for ω < ω_p in the radial direction (cylindrical coordinates) the power flow is in the opposite direction to that of the phase propagation. For ω > ω_p the hot plasma mode has similar characteristics.

Strength of tantalum at high pressures through Richtmyer-Meshkov laser compression experiments and simulations

Strength at extreme pressures (>1 Mbar or 100 GPa) and high strain rates (106-108 s-1) of materials is not well characterized. The goal of the research outlined in this thesis is to study the strength of tantalum (Ta) at these conditions. The Omega Laser in the Laboratory for Laser Energetics in Rochester, New York is used to create such extreme conditions. Targets are designed with ripples or waves on the surface, and these samples are subjected to high pressures using Omega’s high energy laser beams. In these experiments, the observational parameter is the Richtmyer-Meshkov (RM) instability in the form of ripple growth on single-mode ripples. The experimental platform used for these experiments is the “ride-along” laser compression recovery experiments, which provide a way to recover the specimens having been subjected to high pressures. Six different experiments are performed on the Omega laser using single-mode tantalum targets at different laser energies. The energy indicates the amount of laser energy that impinges the target. For each target, values for growth factor are obtained by comparing the profile of ripples before and after the experiment. With increasing energy, the growth factor increased.

Engineering simulations are used to interpret and correlate the measurements of growth factor to a measure of strength. In order to validate the engineering constitutive model for tantalum, a series of simulations are performed using the code Eureka, based on the Optimal Transportation Meshfree (OTM) method. Two different configurations are studied in the simulations: RM instabilities in single and multimode ripples. Six different simulations are performed for the single ripple configuration of the RM instability experiment, with drives corresponding to laser energies used in the experiments. Each successive simulation is performed at higher drive energy, and it is observed that with increasing energy, the growth factor increases. Overall, there is favorable agreement between the data from the simulations and the experiments. The peak growth factors from the simulations and the experiments are within 10% agreement. For the multimode simulations, the goal is to assist in the design of the laser driven experiments using the Omega laser. A series of three-mode and four-mode patterns are simulated at various energies and the resulting growth of the RM instability is computed. Based on the results of the simulations, a configuration is selected for the multimode experiments. These simulations also serve as validation for the constitutive model and the material parameters for tantalum that are used in the simulations.

By designing samples with initial perturbations in the form of single-mode and multimode ripples and subjecting these samples to high pressures, the Richtmyer-Meshkov instability is investigated in both laser compression experiments and simulations. By correlating the growth of these ripples to measures of strength, a better understanding of the strength of tantalum at high pressures is achieved.

Strength, Deformation and Fracture in Metallic Nanostructures

An understanding of the mechanics of nanoscale metals and semiconductors is necessary for the safe and prolonged operation of nanostructured devices from transistors to nanowire- based solar cells to miniaturized electrodes. This is a fascinating but challenging pursuit because mechanical properties that are size-invariant in conventional materials, such as strength, ductility and fracture behavior, can depend critically on sample size when materials are reduced to sub- micron dimensions. In this thesis, the effect of nanoscale sample size, microstructure and structural geometry on mechanical strength, deformation and fracture are explored for several classes of solid materials. Nanocrystalline platinum nano-cylinders with diameters of 60 nm to 1 μm and 12 nm sized grains are fabricated and tested in compression. We find that nano-sized metals containing few grains weaken as sample diameter is reduced relative to grain size due to a change from deformation governed by internal grains to surface grain governed deformation. Fracture at the nanoscale is explored by performing in-situ SEM tension tests on nanocrystalline platinum and amorphous, metallic glass nano-cylinders containing purposely introduced structural flaws. It is found that failure location, mechanism and strength are determined by the stress concentration with the highest local stress whether this is at the structural flaw or a microstructural feature. Principles of nano-mechanics are used to design and test mechanically robust hierarchical nanostructures with structural and electrochemical applications. 2-photon lithography and electroplating are used to fabricate 3D solid Cu octet meso-lattices with micron- scale features that exhibit strength higher than that of bulk Cu. An in-situ SEM lithiation stage is developed and used to simultaneously examine morphological and electrochemical changes in Si-coated Cu meso-lattices that are of interest as high energy capacity electrodes for Li-ion batteries.