# Hui-Chia Yu

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Research Items (32)

- Aug 2018

Rate-dependent Reversal of Lithium Concentration During Intercalation into LixFePO4 Nanoparticles - Volume 24 Supplement - Wei Zhang, Lijun Wu, Hui-Chia Yu, Jianming Bai, Yimei Zhu, Katsuyo Thornton, Feng Wang

Nanoparticulate electrodes, such as LixFePO4, have unique advantages over their microparticulate counterparts for the applications in Li-ion batteries because of the shortened diffusion path and access to nonequilibrium routes for fast Li incorporation, thus radically boosting power density of the electrodes. However, how Li intercalation occurs locally in a single nanoparticle of such materials remains unresolved because real-time observation at such a fine scale is still lacking. We report visualization of local Li intercalation via solid-solution transformation in individual LixFePO4 nanoparticles, enabled by probing sub-angstrom changes in the lattice spacing in situ. The real-time observation reveals inhomogeneous intercalation, accompanied with an unexpected reversal of Li concentration at the nanometer scale. The origin of the reversal phenomenon is elucidated through phase-field simulations, and it is attributed to the presence of structurally different regions that have distinct chemical potential functions. The findings from this study provide a new perspective on the local intercalation dynamics in battery electrodes.

- Jan 2018

Nanoparticulate electrodes, such as LixFePO4, have unique advantages over their microparticulate counterparts for the applications in Li-ion batteries because of the shortened diffusion path and access to nonequilibrium routes for fast Li incorporation, thus radically boosting power density of the electrodes. However, how Li intercalation occurs locally in a single nanoparticle of such materials remains unresolved because real-time observation at such a fine scale is still lacking. We report visualization of local Li intercalation via solid-solution transformation in individual LixFePO4 nanoparticles, enabled by probing sub-angstrom changes in the lattice spacing in situ. The real-time observation reveals inhomogeneous intercalation, accompanied with an unexpected reversal of Li concentration at the nanometer scale. The origin of the reversal phenomenon is elucidated through phase-field simulations, and it is attributed to the presence of structurally different regions that have distinct chemical potential functions. The findings from this study provide a new perspective on the local intercalation dynamics in battery electrodes.

- Aug 2016

Grain boundaries have a major impact on material properties, but explicit consideration of the complex geometries of grain structures in simulations poses a challenge. In this paper, we present a general method for incorporating the effect of grain boundaries based on the Smoothed Boundary Method (SBM). By using multiple domain parameters to define the domains of different grains, this method circumvents time-consuming mesh generation steps that are associated with finite element calculations involving complex microstructures. To validate the approach, we evaluate the accuracy of the SBM against the sharp interface method. The capabilities of this approach were demonstrated through simulations of surface and grain boundary diffusion, as well as those of electrochemical impedance spectroscopy. This method is applicable to many material systems in which grain boundaries play a crucial role.

- Jan 2016

Electrochemical processes in high-energy electrode materials often involve diffusion of multiple species and solid-state phase transformations. Some of these phase transformations involve breaking and rearranging ionic bonds and are referred to as conversion reactions (e.g., the lithium and iron difluoride conversion reaction: 2Li+ + 2e− + FeF2 → 2LiF + Fe). The phase transformations during conversion processes are governed by fundamental thermodynamics and kinetics in a similar manner to metallurgical systems. In this work, we developed a phase-field model that tracks atomic fractions of three constituent species to simulate the morphological evolution of different phases. The simulations demonstrate that conversion proceeds via a two-stage process consisting of lithiation and decomposition stages, whereas the reconversion process consists of a single-stage delithiation. This asymmetry in evolution paths of conversion and reconversion is likely responsible for the voltage hysteresis commonly observed during lithiation-delithiation cycling of conversion materials.

- Jun 2015

Several electrode materials, such as LiFePO4, have a thermodynamic driving force toward phase separation. However, phase separation inside the electrode particles can be suppressed when the particles are nanosized. In this case, each individual particle remains monophasic, but phase separation can occur between particles via Li redistribution. Here, we investigate the dynamics of Li redistribution when the equilibrium potential is size dependent. We perform simulations of the charge-discharge cycle in a two-particle cell and in a 65-particle agglomerate. The difference in particle equilibrium potentials can lead to an asymmetry between lithiation and delithiation of an electrode, in which the order of transformation of the particles during lithiation and delithiation is reversed. This effect is more significant at low currents but almost negligible at high currents.

- Apr 2015

Nanosized, carbon-coated LiFePO4 (LFP) is a promising
cathode for Li-ion batteries. However, nano-particles are problematic for
electrode design, optimized electrodes requiring high tap densities, good
electronic wiring, and a low tortuosity for efficient Li diffusion in the
electrolyte in between the solid particles, conditions that are difficult to
achieve simultaneously. Using in situ energy-dispersive X-ray diffraction,
we map the evolution of the inhomogeneous electrochemical reaction in
LFP-electrodes. On the first cycle, the dynamics are limited by Li
diffusion in the electrolyte at a cycle rate of C/7. On the second cycle,
there appear to be two rate-limiting processes: Li diffusion in the
electrolyte and electronic conductivity through the electrode. Three-dimensional modeling based on porous electrode theory shows that this change in dynamics can be reproduced by reducing the electronic conductivity of the composite electrode by a factor of 8 compared to the first cycle. The poorer electronic wiring could result from the expansion and contraction of the particles upon cycling and/or the formation of a solid-electrolyte interphase layer. A lag was also observed perpendicular to the direction of the current: the LFP particles at the edges of the cathode reacted preferentially to those in the middle, owing to the closer proximity to the electrolyte source. Simulations show that, at low charge rates, the reaction becomes more uniformly distributed across the electrode as the porosity or the width of the particle-size distribution is increased. However, at higher rates, the reaction becomes less uniform and independent of the particle-size distribution.

Nanoparticles with a tendency to phase separate interact with each other during a process of either intraparticle phase separation (occurring inside the particle) or interparticle phase separation (occurring between particles). In this paper, we examine a half-cell consisting of two particles to systematically analyze the particle interactions and their resulting voltage response at different insertion currents. The kinetics of the interactions between nanoparticles is studied for cases in which particles undergo interparticle and intraparticle phase separation. Our results indicate that the interactions between particles in a cell containing only particles that undergo intraparticle phase separation are similar to those in a cell containing only particles that undergo interparticle phase separation. In both cases, sequential transformation occurs at low currents, whereas a simultaneous transformation occurs at high currents. However, such transformation dynamics changes in cases where the cell contains a mixture of particles that undergo interparticle and intraparticle phase separations, which exhibits more complex dynamics.

- Aug 2014

Elucidating the role of interparticle Li transport and multi-particle (de)lithiation kinetics in nanoparticulate two-phase electrode materials such as LiFePO4 is a challenging task because of the small temporal and spatial scale associated with the process. Often, the relevant processes that determine the kinetics of (dis)charging an electrode are assumed to be exclusively those associated with Li transport to and from the counter-electrode, without a consideration of interactions between particles. However, the redistribution of Li between nanoparticles can have a strong influence on the overall cell rate performance. Using a continuum model to simulate the lithiation kinetics of a porous aggregate of LiFePO4 nanoparticles, we demonstrate the impact of cell architecture (in terms of ionic and electronic connectivities between active particles) and cycling rate on the multi-particle (de)lithiation kinetics. Specifically, the connectivity between particles is shown to have a strong effect on “interparticle phase separation,” a process by which active particles undergo additional cycling (charge during the overall discharge) and amplified reaction rates. We show that interparticle phase separation can be reduced or eliminated by improving (“homogenizing”) the connectivity between particles. Extensive comparisons to experimental literature and insights toward improving the performance of nanoparticulate electrodes are also provided.

- May 2014

Much of current research in electrochemical energy storage is devoted to new electrode chemistries and reaction mechanisms that promise substantial increases in energy density. Unfortunately, most high capacity electrodes exhibit an unacceptably large hysteresis in their voltage profile. Using a first-principles multi-scale approach to examine particle level dynamics, we identify intrinsic thermodynamic and kinetic properties that are responsible for the large hysteresis exhibited by many high capacity electrodes. Our analysis shows that the hysteresis in the voltage profile of high capacity electrodes that rely on displacement reactions arises from a difference in reaction paths between charge and discharge. We demonstrate that different reaction paths are followed (i) when there is a large mismatch in ionic mobilities between the electrochemically active species (e.g. Li) and displaced ionic species and (ii) when there is a lack of a thermodynamic driving force to redistribute displaced ions upon charging of the electrode. These insights motivate the formulation of design metrics for displacement reactions in terms of fundamental properties determined by the chemistry and crystallography of the electrode material, properties that are now readily accessible with first-principles computation.

In nanoparticulate phase-separating electrodes, phase separation inside the
particles can be hindered during their charge/discharge cycles even when a
thermodynamic driving force for phase separation exists. In such cases,
particles may (de)lithiate discretely in a process referred to as mosaic
instability. This instability could be the key to elucidating the complex
charge/discharge dynamics in nanoparticulate phase-separating electrodes. In
this paper, the dynamics of the mosaic instability is studied using Smoothed
Boundary Method simulations at the particle level, where the concentration and
electrostatic potential fields are spatially resolved around individual
particles. Two sets of configurations consisting of spherical particles with an
identical radius are employed to study the instability in detail. The effect of
an activity-dependent exchange current density on the mosaic instability, which
leads to asymmetric charge/discharge, is also studied. While we show that our
model reproduces the results of a porous-electrode model for the simple setup
studied here, it is a powerful framework with the capability to predict the
detailed dynamics in three-dimensional complex electrodes and provides further
insights into the complex dynamics that result from the coupling of
electrochemistry, thermodynamics, and transport kinetics.

Materials that undergo a lithium conversion reaction often accommodate more than one Li per transition metal, and are promising candidates for high-capacity electrodes for lithium batteries. However, little is known about the mechanisms involved in the conversion process, the origins of the large polarization during electrochemical cycling, and why some materials are reversible (e. g., FeF2) while others are not (e. g., CuF2). We investigated the conversion reaction of metal fluorides, FeF2 and CuF2, to better understand the mechanisms underlying their contrasting electrochemical behavior. Lithium conversion of FeF2 results in the formation of an interconnected network of small iron nanoparticles (< 5nm), which may provide a pathway for electron transport and a high interfacial area between the Fe and LiF phases. Conversely, lithium conversion of CuF2 results in the formation of large isolated Cu particles, which may partially explain the poor reversibility in the CuF2 system.

Expectations for the next generation of lithium batteries include greater energy and power densities along with a substantial increase in both calendar and cycle life. Developing new materials to meet these goals requires a better understanding of how electrodes function by tracking physical and chemical changes of active components in a working electrode. Here we develop a new, simple in-situ electrochemical cell for the transmission electron microscope and use it to track lithium transport and conversion in FeF(2) nanoparticles by nanoscale imaging, diffraction and spectroscopy. In this system, lithium conversion is initiated at the surface, sweeping rapidly across the FeF(2) particles, followed by a gradual phase transformation in the bulk, resulting in 1-3 nm iron crystallites mixed with amorphous LiF. The real-time imaging reveals a surprisingly fast conversion process in individual particles (complete in a few minutes), with a morphological evolution resembling spinodal decomposition. This work provides new insights into the inter- and intra-particle lithium transport and kinetics of lithium conversion reactions, and may help to pave the way to develop high-energy conversion electrodes for lithium-ion batteries.

- Oct 2012

The Kirkendall effect stems from the imbalance of atomic diffusion fluxes in a crystalline solid. Vacancy generation and annihilation, which compensate for the unbalanced fluxes, result in deformation that is experimentally observed as the motion of fiducial markers in a diffusion couple that can be approximated as a one-dimensional system. In multiple dimensions, such deformation occurs along both the directions parallel to and normal to the primary diffusion direction. In this article, we present a model that couples unbalanced interdiffusion and the resulting plastic deformation. One- and two-dimensional simulations are conducted with the analytically calculated diffusion coefficients of a thermodynamically ideal random alloy; the result shows that the ratio of the diffusion fluxes of the atomic species equals the ratio of atomic hop frequencies, which leads to the final volume ratio also given approximately by the hop frequency ratio if the initial volume ratio is equal. Moreover, the result also demonstrates that the conventional interdiffusion model fails to describe the Kirkendall void growth dynamics. For numerical implementation, we reformulate the diffusion equation to the smoothed boundary form and solve it within the deforming body governed by steady-state Navier-Stokes equation. This work demonstrates that the presented method can be a useful tool for studying Kirkendall-effect-induced deformation.

Ni coarsening in Ni-yttria stabilized zirconia (YSZ) solid oxide fuel cell
anodes is considered a major reason for anode degradation. We present a
predictive, quantative modeling framework based on the phase-field approach to
systematically examine coarsening kinetics in such anodes. The initial
structures for simulations are experimentally acquired functional layers of
anodes. Sample size effects and error analysis of contact angles are examined.
Three phase boundary (TPB) lengths and Ni surface areas are quantatively
identified on the basis of the active, dead-end, and isolated phase clusters
throughout coarsening. Tortuosity evolution of the pores is also investigated.
We find that phase clusters with larger characteristic length evolve slower
than those with smaller length scales. As a result, coarsening has small
positive effects on transport, and impacts less on the active Ni surface area
than the total counter part. TPBs, however, are found to be sensitive to local
morphological features and are only indirectly correlated to the evolution
kinetics of the Ni phase.

In this article, we describe an approach for solving partial differential
equations with general boundary conditions imposed on arbitrarily shaped
boundaries. A continuous function, the domain parameter, is used to modify the
original differential equations such that the equations are solved in the
region where a domain parameter takes a specified value while boundary
conditions are imposed on the region where the value of the domain parameter
varies smoothly across a short distance. The mathematical derivations are
straightforward and generically applicable to a wide variety of partial
differential equations. To demonstrate the general applicability of the
approach, we provide four examples herein: (1) the diffusion equation with both
Neumann and Dirichlet boundary conditions; (2) the diffusion equation with both
surface diffusion and reaction; (3) the mechanical equilibrium equation; and
(4) the equation for phase transformation with the presence of additional
boundaries. The solutions for several of these cases are validated against
corresponding analytical and semi-analytical solutions. The potential of the
approach is demonstrated with five applications: surface-reaction-diffusion
kinetics with a complex geometry, Kirkendall-effect-induced deformation,
thermal stress in a complex geometry, phase transformations affected by
substrate surfaces, and a self-propelled droplet.

- Feb 2011

Coarsening of the nickel phase is known to occur in solid oxide fuel cell (SOFC) anodes consisting of Ni and yttria-stabilized zirconia (YSZ). However, the exact nature of the coarsening process is not known, nor how it affects three-phase boundaries (TPBs) and the resulting electrochemical performance. We apply a phase-field approach to simulate the microstructural evolution of Ni–YSZ anode functional layers. An experimentally obtained three-dimensional reconstruction of a functional layer from an anode-supported SOFC is used as the initial microstructure. The evolution of the microstructure is characterized quantitatively by examining the TPB density, interfacial area per unit volume, and tortuosity versus time. The assumed TPB contact angles are found to have a strong effect on the microstructural evolution; in particular, reducing the contact angle of nickel on YSZ yields less TPB reduction.

- Jan 2011
- 219th ECS Meeting

The total measured overpotential of a porous SOFC electrode is governed by a complex mixture of rates, including heterogeneous catalysis, interfacial charge transfer, bulk and surface ion transport and gaseous diffusion. In order to better understand the role of microstructure in mediating these rates, our group has been developing detailed microkinetic models (based on finite-element analysis), which employ various 3D representations of the electrode microstructure. These 3D representations span a range of complexity, from pseudoparticles (such as rods or spheres) to solid meshes generated from 3D images of the microstructure (based on 3D FIB-SEM reconstructions). These models have been used to explore where and under what circumstances the fine details of the microstructure matter to performance, and where macrohomogeneous approximations can be made without loss of accuracy. We have used these models to aid interpretation of linear (EIS) and nonlinear (NLEIS) impedance response of single-phase porous mixed conducting SOFC cathodes.

- Feb 2010

We describe a formalism to predict diffusion coefficients of substitutional alloys from first principles. The focus is restricted to vacancy mediated diffusion in binary substitutional alloys. The approach relies on the evaluation of Kubo-Green expressions of kinetic-transport coefficients and fluctuation expressions of thermodynamic factors for a perfect crystal using Monte Carlo simulations applied to a cluster expansion of the configurational energy. We make a clear distinction between diffusion in a perfect crystal (i.e. no climbing dislocations and grain boundaries that can act as vacancy sources) and diffusion in a solid containing a continuous distribution of vacancy sources that regulate an equilibrium vacancy concentration throughout. A variety of useful metrics to characterize intermixing processes and net vacancy fluxes that can result in the Kirkendall effect are described and are analyzed in the context of thermodynamically ideal but kinetically non-ideal model alloys as well as a realistic thermodynamically non-ideal alloy. Based on continuum simulations of diffusion couples using self-consistent perfect-crystal diffusion coefficients, we show that the rate and mechanism of intermixing in kinetically non-ideal alloys is very sensitive to the density of discrete vacancy sources.

In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential equation is valid and smoothly but rapidly varying values on the boundary where boundary conditions are imposed is used to modify the original differential equations. The mathematical derivations are straight forward, and generically applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions, (2) the diffusion equation with surface diffusion, (3) the mechanical equilibrium equation, and (4) the equation for phase transformation with additional boundaries. The solutions for a few of these cases are validated against corresponding analytical and semi-analytical solutions. The potential of the approach is demonstrated with five applications: surface-reaction diffusion kinetics with a complex geometry, Kirkendall-effect-induced deformation, thermal stress in a complex geometry, phase transformations affected by substrate surfaces, and a self-propelling droplet. Comment: A better smooth algorithm has been developed and tested, will soon replace Eq. 58 in page 16. We have also developed a level-set moving boundary SBM method, and it will replace the Navier-Stokes-Cahn-Hilliard type domain parameter tracking method in Section 5.2

- Oct 2009

We examine binary substitutional diffusion in cylindrical diffusion couples in which free surfaces are considered explicit vacancy sources and sinks. The central region of the cylinder is initially occupied by an atomic species with a larger hop frequency, while the outer region is occupied by another atomic species with a smaller hop frequency. Equilibrium vacancy concentration is maintained at free surfaces that serve as vacancy sources and sinks. In the crystal, diffusion is governed by the standard diffusion equations with analytically evaluated diffusion coefficients. The void growth dynamics and hollow cylinder formation stemming from the Kirkendall effect are simulated. Our results show that the Kirkendall void growth involves two competing factors. One is the net inward vacancy flux that favors void growth. The other is the Gibbs–Thomson effect that favors void shrinkage. We compute the critical initial radius for void growth above which the Kirkendall effect dominates over the Gibbs–Thomson effect. The fully grown void radius and the elapsed time to the fully grown size are also predicted for different fast-diffuser volume fractions and fast-to-slow diffuser atomic hop frequency ratios.

- Jan 2009

The Kirkendall effect stems from the difference between the exchange rates of the atomic species and vacancies in a substitutional alloy. Vacancies, which mediate diffusion, are generated and eliminated at their sources and sinks, resulting in lattice shift and deformation. In the conventional model, these vacancy sources and sinks are assumed to be distributed everywhere in a solid and maintain vacancy concentration at a constant, uniform equilibrium value throughout the solid. In this thesis work, we propose a new, rigorous model of interdiffusion by considering explicit and localized vacancy sources and sinks such as free surfaces and grain boundaries. Vacancy concentration only remains at its equilibrium value at these explicit sources and sinks. In the bulk of a grain, vacancies are conserved and must diffuse in the same manner as atomic species.
This model was first applied to one-dimensional planar and quasi-one-dimensional cylindrical systems. The results demonstrated that explicit consideration of vacancy diffusion leads to different dynamics and final states compared with what the conventional model would predict. Two-dimensional simulations of the concentration evolution in a solid containing a grain boundary demonstrated that the interdiffusion process changes from fast-mode diffusion to slow-mode diffusion as the interdiffusion region becomes farther away from a grain boundary. In order to simulate interdiffusion and the Kirkendall-effect-induced deformation in two dimensions, we extended a smooth boundary method to impose generalized boundary conditions at the solid surfaces. This method was first applied to the traditional interdiffusion model coupled with a linear visco-plastic deformation model. Expansion, contraction, bending, as well as a complex combination of these types of deformations were studied. The new method was also applied to our rigorous model to simulate interdiffusion and resultant shape changes of a single crystalline solid.

- Oct 2008

A set of coupled diffusion equations is numerically solved to demonstrate that grain boundary diffusion is significantly enhanced when diffusing atomic species have dissimilar atomic hop frequencies in the bulk. The model is based on a rigorous treatment of two-component substitutional diffusion where vacancies are treated as an additional species. By examining the concentration fields and the eigenvalues of the diffusivity matrix, the origin of the enhanced grain boundary diffusion is explained in terms of the Kirkendall effect.

- Dec 2007

We investigate vacancy-mediated diffusion in a binary substitutional alloy by explicitly accounting for discrete vacancy sources and sinks. The regions between sources and sinks are treated as binary crystals with a perfect lattice structure containing a dilute concentration of vacancies. The sources and sinks are assumed ideal, maintaining an equilibrium vacancy concentration in their immediate vicinity. Diffusion within the perfect lattice is described with a diffusion-coefficient matrix determined by kinetic Monte Carlo simulations for a binary, thermodynamically ideal alloy in which the components have different vacancy-exchange frequencies. Continuum simulations are performed for diffusion couples with discrete grain boundaries acting as vacancy sources and sinks. Effective grain coarsening due to the Kirkendall effect is observed even in the absence of Gibbs-Thomson driving forces. As in standard ternary systems, uphill diffusion is observed. We also find that the drift of the lattice frame of reference as a result of the Kirkendall effect increases with the source/sink density. Upon increasing the density of vacancy sources and sinks, we recover the conventional treatment of substitutional diffusion, which assumes a dense and uniform distribution of vacancy sources and sinks that maintain an equilibrium vacancy concentration throughout the solid. The inverse Kirkendall effect, where the slower component segregates at grain boundaries acting as vacancy sinks, is also observed in the simulations.

- Jun 2005

Vacancies in a solid may coalesce into nanoscale voids and further self-organize into a regular pattern. We incorporate free energy of mixing, interfacial energy and elastic energy into a Cahn-Hilliard type nonlinear diffusion equation. The free energy of mixing drives spinodal decomposition. The total interfacial energy drives coarsening. The surface misfit at the void/solid interface limits the coarsening process, and induces anisotropic diffusion in an elastically anisotropic solid. The dynamic process of void coalescence and self-ordering are demonstrated by numerical simulations. Surface misfit and elastic anisotropy are found to play a significant role in inducing ordered nanostructures.

- Apr 2005

Experiments show that vacancies in solids may coalesce into voids and self-organize into a superlattice. The voids have diameters around 10 nm and spacing of tens of nanometers. This paper develops a phase-field model to study this behavior, which incorporates the free energy of mixing, interfacial energy and elastic energy. Vacancy diffusion is described by a Cahn–Hilliard type nonlinear diffusion equation, which couples the vacancy distribution field and the stress field. The reduction of the mixing energy drives spinodal decomposition. The reduction of the interfacial energy drives void coarsening. The long-range elastic interaction and elastic anisotropy significantly affect superlattice formation and may essentially limit void coarsening.

- Jan 2005

Self-organized crack patterns have drawn intensive attention recently. For instance, regular micro-cracks appear on certain polymer materials spread on substrates when drying. These cracks are generally conceived originating from the competition of two effects, i.e. cohesion force between molecules and adhesion forces between molecules and substrates. This paper develops a phase field model to study the formation and growth of crack patterns of a thin film attached to an elastic substrate. We treat the thin film as a superficial object, and specify the excess surface energy for the object. The variation of the surface energy density with the variation of the strain defines surface stress. When cracks form in the film, the surface stress is nonuniform, deforms the substrate, and reduces the total energy. This energy reduction constitutes a driving force for crack nucleation and growth. The model consists of two fields: a concentration field C, and a displacement field u. The former phase-field parameter describes the coverage of substrate surface with film molecules, and has values between zero and one. The latter represents the elastic field in the substrate. A phase boundary in our model is represented by a concentration gradient, an approach analogous to the work of Cahn and Hilliard on spinodal decomposition. With this approach we avoid solving a moving boundary value problem which would require tracking the boundary numerically. Our model is a dynamic model and the material system can generate whatever crack patterns it favors. A nonlinear diffusion equation couples the concentration field in the film and the stress field in the substrate. An efficient spectral method is developed to solve the problem efficiently. The simulations have revealed remarkably rich dynamics in the crack pattern formation process, and produced results consistent with experiments.

- Jan 2004
- ASME 2004 International Mechanical Engineering Congress and Exposition

Experiments show that vacancies in a solid may coalesce into voids and self-organize into a super-lattice. The voids have diameters around 10 nm and spacing of tens of nanometers. This paper develops a thermodynamic model to explain and simulate the remarkable phenomena. We incorporate free energy of mixing, interface energy and elasticity into a continuous phase field model. It is well known that the total interface energy reduces when the voids grow larger. Simulations show that elastic anisotropy may limit the coarsening. Starting from randomly distributed vacancies, the process of coalescence and void lattice formation demonstrates rich dynamics. Long-range elastic interaction and elastic anisotropy are found to play a significant role that determines the self-assembled super-lattice.

- Jul 1998

Effects of low-energy impact loading and thermal cycling on fatigue behavior of carbon fiber reinforced epoxy (carbon/epoxy)
laminates are examined. A low-energy of 0.62 Joules was adopted to impact carbon/epoxy laminates prior to thermal cycling
exposure and fatigue test. The temperature ranged between 60 and −60 °C for thermal cycling and the stress ratio of 0.1 with
a frequency of 3 Hz for fatigue loading were used. Impact performances were tested on the virgin specimens and the thermal-cycling
exposure specimens. Residual tensile strength and fatigue tests were performed on the laminate composites after being subjected
to thermal cycling. The relationship between tensile strength reduction and fatigue performance after thermal cycling was
investigated. Stiffness degradation during fatigue testing was monitored; the differences in stiffness for these three composites
(virgin specimens, low-energy impacted specimens, low-energy impacted and thermal-cycling exposure specimens) were compared
and the coupling effects of low-energy impact and thermal fatigue were studied. Furthermore, the S-N curves were also plotted
and the variation was compared on the aforementioned three composites. SEM was used to examine the difference in fracture
morphologies on the composites with and without suffering low-energy impact and thermal fatigue.

Current institution

- Department of Materials Science and Engineering
- Ann Arbor, Michigan, United States

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