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International Journal of Mechanical Sciences (00207403)290
Solid-state batteries are promising candidates for the next-generation energy storage technology, as they circumvent the cyclic stability and safety issues of the traditional liquid-electrolyte Li-ion technology. Solid electrolytes are less reactive and enable using Li-metal anodes, increasing the energy density of battery cells. However, Li dendrites nucleating at pores, grain boundaries, and cracks, particularly when the current density exceeds a critical level, have been found to penetrate the solid electrolyte, resulting in short circuit and battery failure. While existing fracture mechanics-based models of dendrite usually examine Li-filled cracks, recent experiments have shown that a Li dendrite formed inside a crack can induce fracture growth well before filling it. This work aims to develop a model for this largely unexplained behaviour by considering a Li dendrite as it grows inside a crack from an initially small nucleus. The model couples solid electrolyte deformation, stress-driven Li diffusion along the dendrite-electrolyte interface, and stress-dependent Butler-Volmer kinetics of Li deposition into the crack. A finite element formulation developed for solving the governing equations is applied to two types of solid electrolytes to examine simultaneous evolution of the stress profile, dendrite thickness profile, dendrite length, and the stress intensity factor. By considering a realistic range of model parameters, it is shown that dendrite thickening, as compared to lengthening, promoted by a lower interfacial diffusivity, a higher interfacial resistance, and a higher applied current density, can mediate crack growth before dendrite fills the crack. Both assumptions and predictions of the model are discussed with reference to the existing literature, and model predictions are compared to the experiments. © 2025
Journal of the Mechanics and Physics of Solids (00225096)174
Point defect distribution in the vicinity of discontinuities plays important role in the transport properties of nonstoichiometric ionic solids. Here, considering dopants and oxygen vacancies as the major point defects in doped ceria, we develop a Monte Carlo model to examine how the stress field of edge dislocations affect point defect distribution in their surroundings. Point defects are considered to interact with the elastic stress field of dislocations due to their misfit volume, and the electrostatic interaction between the point defects is also taken into account. In contrast with a prevalent theory of chemo-mechanical equilibrium in solid solutions, the model developed here is consistent with classical elasticity in that the point defects do not interact through their self-stress fields. Stress effects both on the defect distribution, and on the electric potential, are examined for a single dislocation as well as a periodic array of like dislocations. In agreement with previous atomistic simulations, the model predicts that electrostatic interactions drive enrichment or depletion of defects of both types on either the compressive or tensile side of edge dislocations depending on the ionic radius of the dopant. The stress field of an array of like dislocations periodic in the direction of the Burgers vector is shown to result in different bulk defect concentrations and bulk electric potentials on the opposite sides of the array, whereas for an array with repeat direction normal to the Burgers vector, defect enrichment and depletion emerge in alternate regions limited to the vicinity of the dislocations. © 2023 Elsevier Ltd
Construction and Building Materials (09500618)369
The cement production process produces enormous amounts of carbon dioxide (CO2). Hence, using new types of cement, like ternary cement, which contains calcined clay, limestone, and cement clinker, can significantly reduce the CO2 emissions of the cement industry and even increase the mechanical properties and durability of samples. This paper investigates the cement mortar's mechanical and durability characteristics, containing ceramic waste powder (CWP) and limestone powder (LSP) as partial cement substitution. Samples with 5, 10, and 15 % LSP and 10, 20, and 30 % (by weight of cement) CWP as cement substitutes were produced. The mortar specimen tests were performed after 7, 28, and 90 days of curing in the water pool, then compressive strength and alkali-silica reaction (ASR) tests were evaluated. Furthermore, setting time test, thermogravimetric analyses, X-ray diffraction analyses, and scanning electron microscopy (SEM) of cement paste were carried out. The ternary cement mortar containing 10 % CWP and 15 % LSP has the highest compressive strength. Also, the ternary cement mortar containing 30 % CWP and 15 % LSP shows the lowest compressive strength (decreased by 8.5 % compared to the reference sample). In addition, the mix containing 20 % CWP and 15 % LSP has a lower ASR value than the control sample (52 % less). Eventually, SEM images showed the reference sample and the specimen containing 30 % CWP and 15 % LSP have the lowest and highest pores and cavities, respectively. © 2023 Elsevier Ltd
Computers and Mathematics with Applications (08981221)124pp. 163-187
Transient nonlinear problems play an important role in many engineering problems. Phase-field equations, including the well-known Allen-Cahn and Cahn-Hilliard equations, fall in this category, and have applications in cutting-edge technologies such as modeling the diffusion of lithium (Li) ions in two-phase electrode particles of Li-ion batteries. In this paper, a local meshless method for solving this category of partial differential equations (PDEs) is proposed. The Newton-Kantorovich scheme is employed to transform the nonlinear PDEs to an iterative series of linear ones which can be solved with the proposed method. The accuracy and performance of the method are examined in various linear and nonlinear problems, such as Laplace equation, three dimensional elasticity as well as some abstract mathematical equations with linear or nonlinear boundary conditions. The main focus of the work is on applying the proposed method in solution of the phase-field equations, including the Allen-Cahn and Cahn-Hilliard equations. In addition to homogeneous Neumann boundary condition which has been widely examined in the literature, we also employ a practical nonlinear, inhomogeneous Neumann boundary condition formulation specialized for modeling the diffusion of lithium ions in electrode particles of Li-ion batteries. The generalized-α method is used for time integration of diffusion-type equations to overcome the intrinsic stiffness of the phase-field equations. It is shown that the method is capable of capturing the main features of the phase-field models i.e. phase separation, coarsening and energy decay in closed systems. © 2022 Elsevier Ltd
International Journal of Solids and Structures (00207683)254
All-solid-state lithium (Li) batteries provide a promising pathway toward high energy and power density. Dendrite penetration through the solid electrolyte causing battery short-circuit, however, persists to be one of the challenges impeding their widespread application. Here, considering a pre-existing surface crack in the electrolyte initially filled with an infinitely thin layer of Li, and assuming Li deposit to behave in accordance with rigid-viscoplasticity, we seek for the steady state Li-filled crack opening profile that could potentially form at a given constant current density. Treating the chemical potential of Li ions in the electrolyte and the electric potential to be uniform along the crack face, the model accounts for the coupling between stress buildup in the dendrite, deposition rate, viscoplastic flow of Li deposit, and crack opening induced by electrolyte deformation using singular integral equations of fracture mechanics. The model establishes limiting conditions for crack growth before a steady state dendrite is reached, triggering a cycle of crack growth and dendrite elongation. Using material properties adopted from literature, the model predicts that the critical condition can be met for a microcrack at typical current densities. The effect of pressure applied to the cell is further discussed. © 2022 Elsevier Ltd
European Journal of Mechanics, A/Solids (09977538)91
Thermodynamics-based continuum models have been previously employed for examining how a solute atmosphere interacts with the stress field of various material defects in solids. However, recent studies suggest that the chemical potential used in prevalent continuum frameworks needs to be revised in the sense that the stress contribution to the chemical potential should arise only through the image stress field of the solutes, and the homogenized self-stress field of the solutes must hence be excluded from the chemical potential in a correct treatment. Here, adopting a statistical mechanics-based approach fully accounting for the image stress effects, we aim to present an investigation of the effect of a mode II loading on the interaction of a solute atmosphere with the stress field of a crack. Solute atmosphere is treated as a distribution of solute rods which extend indefinitely in the direction parallel to the crack front. Image stress effects both on the enthalpy of the solutes and on the stress intensity factors (SIFs) are taken into consideration. Monte Carlo simulations are utilized to find the equilibrium distribution of the solutes in the solid, and also to compute the ensemble average of the energy release rate (ERR) available for crack growth in the presence of an external loading. Effects of the system temperature, average solute concentration, and the loading intensity on the results are also examined. Simulation results suggest that the solute redistribution driven by mode II loading generates an additional mode II ERR for the crack growth. The results further indicate that the increase in the mode I ERR as caused by the solute redistribution induced by a mode I loading is weakened in the presence of a mode II loading. Since simulations are performed for a finite solid, the effects of solid dimensions and crack size on the results are also examined, and it is shown that the results remain insensitive to the geometric dimensions as long as the loading-induced SIFs at the crack tip and the solute concentration are kept unchanged. Effect of solute atmosphere on the maximum ERR for kinked crack growth is also examined. © 2021 Elsevier Masson SAS
Mechanics of Materials (01676636)172
It is well known that the presence of foreign solutes could critically affect fracture properties of the solid solutions of critical importance to many technological advances. It has been shown recently that a prevalent continuum theory widely applied to such systems is inconsistent with classical elasticity which predicts that two point defects in an isotropic unbounded solid do not interact, and interact only in a finite solid through image stresses arising due to the presence of the boundaries. Previous studies have shown that the image stresses resulting from an external boundary of a finite solid also generally raise the stress intensity factors (SIFs) induced by the solutes at a crack tip. Here, we examine the possibility that the increase in the SIFs by image stress effects together with variations in the configuration of mobile solutes around a crack tip could from time to time push the crack tip SIFs beyond the critical value required for crack growth, and hence cause subcritical crack growth over time. Incorporating crack growth criterion in kinetic Monte Carlo (KMC) simulations and fully accounting for the image stress effects, we investigate this possibility by examining how temperature, solute concentration, and the difference between the loading-induced SIF and the critical SIF could affect crack growth. In agreement with an analysis based on the central limit theorem presented for the limit of high temperatures, our simulations indicate that the probability of the Griffith-Irwin criterion being met among various solute configurations generally increases with increasing solute concentration. The model shows that, within a certain range of the loading-induced SIF below the critical SIF, the crack growth rate increases with solute concentration, and this effect becomes particularly more evident at larger temperatures. © 2022 Elsevier Ltd
International Journal of Solids and Structures (00207683)228
Although continuum frameworks have been developed in the past for studying how material defects behave in solid solutions, recent studies have demonstrated that the self-stress field of the solutes which enter the chemical potential in the prevalent continuum models must be excluded, and instead the image stresses included, in a correct treatment. Here, working within the framework of Gibbs canonical ensemble of statistical mechanics, and accounting for the image stresses of the solutes arising due to the presence of the boundaries, we examine the interaction between a solute atmosphere and a crack in the presence of an external loading. Relying on a plane strain model, the solute atmosphere is treated as a distribution of misfitting solute rods, infinitely long in the direction normal to the plane of analysis. Since solutes interact through their image stress fields and can move around in the solid, Monte Carlo simulations, fully accounting for both the energy of interaction between the solute rods and their interaction with the external loading, are performed to explore various configurations of the solute rods in the host, and to compute the temperature-dependent ensemble averages of the enthalpy, equilibrium solute distribution, and the energy release rate (ERR) of crack growth. It is shown that solute redistribution induced by a tensile loading of the solid results in an increase in the ERR. Our simulations further interestingly reveal that even in the limit of large temperatures where a nearly uniform solute distribution prevails, the interaction between the collective image stress field of the solutes and the stress field of the loading results in an added contribution to the ERR which, at a fixed average concentration and a fixed loading-induced stress intensity factor, does not fade away with increasing solid dimensions, and further strengthens both with the solute concentration and with the external loading. © 2021 Elsevier Ltd
International Journal of Mechanical Sciences (00207403)194
Phase separation arises in many materials systems as a result of solute intercalation. It is in particular known that the mechanical stresses resulting from phase separation in lithium-ion batteries can be large enough to cause formation of a variety of defects and degradation of the host electrode upon cycling. Fracture mechanics models have been previously developed for identifying the critical conditions which lead to the growth of a pre-existing crack in two-phase electrode particles. Relying on a cohesive zone model in combination with the distributed dislocation technique, this work examines critical conditions corresponding to the onset of crack formation in an initially crack-free two-phase electrode. Considering a phase separating planar electrode, we utilize a Cahn-Hilliard type phase field model for capturing evolution of the concentration profiles during both intercalation and deintercalation half-cycles. Crack formation in the electrode subject to the diffusion-induced stresses is considered to result from strain localization at the place of pre-existing defects or weaknesses in the material whose behavior is modelled using a linearly softening traction-separation law. Numerical solution of the governing equations allows identification of a flaw-tolerant electrode thickness below which crack formation in the electrode becomes suppressed in the sense that the maximum opening along the cohesive zone cannot reach the critical separation required for crack formation, and hence, failure in the electrode is predicted to be dominated by the theoretical strength of the material rather than by crack formation. Since in the limit of small surface fluxes, uniform axial stresses develop in the individual phases, results of the analyses are also examined with reference to the results which follow from the analysis of the planar structure subject to uniform tension. © 2020
Mechanics of Materials (01676636)152
It is well known that phase separation occurs in many intercalation materials as a result of solute intercalation. In lithium storage materials, phase separation induced by electrochemical cycling is known to intensify mechanical stresses in the host, and results in the emergence of a variety of defects causing mechanical degradation of the electrode particles. Treating two-phase electrode particles as a homogeneous material, fracture mechanics models have been previously developed for studying fracture of two-phase electrode particles. Recent theoretical and experimental studies, however, reveal that the elastic properties of the coexisting phases in the material could significantly differ due to their markedly different solute contents. This work aims to present a fracture mechanics study of the two-phase electrode particles accounting for the different elastic moduli of the phases. To this end, a planar composite core-shell model is utilized to examine how different elastic moduli of the phases could impact the stress intensity factors and the energy release rates associated with the pre-existing cracks in the particle. Our results reveal that although softening of the material as a result of phase change could result in stress relief in the electrode particle, however, it could still raise the energy release rate for pre-existing cracks, since a softened material behaves like a weakened deformational constraint ahead of a pre-existing crack. The model presented is also applied to the material systems exhibiting modulus change as a result of phase separation, and implications of the modulus change on the energy release rate for crack growth are also discussed. It is shown that although significant changes in the toughness of the material could arise due to the phase transformation, however, changes in elastic moduli could still raise the energy release rate for a crack whose tip is embedded in the phase with the lower toughness. © 2020 Elsevier Ltd
International Journal of Mechanical Sciences (00207403)183
It is well known that cycling induced capacity fading in phase transforming intercalation materials is critically linked to the severity of misfit strain between the phases which could result in the emergence of a variety of defects in the material. Here, adopting a planar model and making use of a well-established energy-based framework, we examine stability of a misfit dislocation lying at the phase boundary within a two-phase electrode particle. Within this framework, the stability criterion emerges as a result of competition between the work that must be done against the image forces with the work that is supplied by the phase transformation induced stresses, as the dislocation is pulled from free surface of the solid toward interior. A numerical model accounting for anisotropy of both misfit strain between the phases and elastic properties of the solid is developed. The model is in particular applied to the electrode particles of LiFePO4, a highly promising cathode material for lithium-ion battery applications in which misfit dislocations as a result of phase transformation have also been experimentally observed. The analysis is revealing of size effects on the stability of a misfit dislocation in the electrode particle. Most notably, it is shown that below a critical particle size, no misfit dislocation at the interphase can remain stable within the particle as it becomes energetically more favorable for the dislocation to be driven out of the particle through absorption by the free surfaces. Numerical estimates of the critical size are presented and discussed with reference to available experiments. Through providing a guideline for suppressing misfit dislocations, results of this work could have potentially important implications for disabling a wide range of dislocation-based fatigue mechanisms which could otherwise become active and result in capacity fading upon a large number of cycles. © 2020
Journal of the Mechanics and Physics of Solids (00225096)145
Solid solutions are of critical importance to many technological applications. While continuum frameworks have been developed and invoked in the past for studying behavior of solid solutions, recent studies point to the importance of image stresses in finite systems, and in particular, suggest that the homogenized self-stress field of the solutes, which enter the chemical potential in the prevalent continuum models, should be excluded in a correct treatment. The present work is concerned with the study of a solute atmosphere in the vicinity of a void in two-dimensional elasticity wherein the solute atmosphere is treated as a distribution of solute rods extended indefinitely normal to the plane of analysis. A statistical mechanics framework is adopted based on the Gibbs canonical ensemble, and the well-established path-independent integrals of solid mechanics are used for examining configurational forces on the void induced by the presence of a solute atmosphere. Numerical Monte Carlo simulations fully accounting for the interaction energy between the solute rods are used for calculation of the ensemble averages of the energy release rates associated with void translation and expansion, and semi-analytical solutions are further developed in the limit of dilute solute concentrations and large temperatures. Effect of interaction between the stress fields of a solute atmosphere and an external loading on the configurational forces is also investigated through both numerical and analytical calculations. It is shown that the interaction between the image stress field of a given concentration of solute rods and the stress field of an equi-biaxial loading results in an added contribution to the energy release rate of void expansion which does not fade away even when the solid dimensions grow indefinitely. Numerical simulations are further used to examine the effect of loading-induced solute redistribution on the energetic driving force for void expansion. © 2020 Elsevier Ltd
Journal of the Mechanics and Physics of Solids (00225096)133
Defect formation has been widely observed to occur in phase transforming intercalation materials of critical importance to many technological applications. In this work, relying on energy balance argument, we develop a planar particle model to investigate critical conditions for spontaneous dislocation formation in a single-crystalline phase transforming material. Dislocations self-energy is calculated assuming isotropic elasticity, and the work done by the background stress field during dislocation formation is examined based on bilayer and core-shell models of solute distribution. Considering well-known slip systems in cubic crystals, critical sizes are derived, as a function of transformation strain, below which dislocation formation is predicted to remain energetically suppressed throughout complete phase transformation, resulting in completely coherent phase transformation. Effect of the surface flux on the critical size is also examined using a moving interphase model. Minimum dislocation spacing is derived for an array of dislocations which could spontaneously form at the phase boundary when particle size exceeds the critical size. Numerical estimates of the critical size are presented for several materials systems, and the results are discussed with reference to the available experiments. Results of this work could have potentially important implications in terms of designing phase changing materials resistant against cyclic damage. © 2019
European Journal of Mechanics, A/Solids (09977538)74pp. 96-111
Phase separation has been widely observed in various energy storage systems, and is known to severely impact mechanical integrity and electrochemical performance in lithium intercalation materials. Core-shell type models have been extensively used for modeling diffusion, phase transformation, deformation, and stress generation in phase changing energy storage materials. The purpose of this work is to present a systematic fracture mechanics analysis of two-phase electrode particles with core-shell structure subject to deintercalation using both numerical and analytical models. Mechanical behavior of the host solid is assumed to follow small deformation linear elasticity, and geometry of the particles is considered to be cylindrical/spherical. A moving interphase model accounting for the effect of solution non-ideality is utilized in combination with the weight function method of fracture mechanics to numerically calculate stress intensity factors (SIFs) for pre-existing cracks at the particle surface. Further, an analytical solution in the limit of small surface fluxes and a semi-analytical solution in the presence of large surface fluxes are also developed for the maximum SIF which could arise for a pre-existing surface crack during a complete deintercalation half-cycle. Implication of the results in terms of prediction of a critical particle size to avoid fracture in two-phase electrode particles is also presented. Numerical results along with their comparison with analytical predictions are presented in terms of the concentration and stress profiles, maximum tensile hoop stress, and maximum SIFs for a range of two-phase regular solid solutions and subject to a broad range of surface deintercalation fluxes. We further examine the results of this work by considering a lithium deintercalation system whose thermodynamic behavior is considerably different from that of a regular solution, and the results found using analytical and numerical models are compared. © 2018 Elsevier Masson SAS
Journal of Power Sources (03787753)350pp. 127-139
It is well known that phase separation could severely intensify mechanical degradation and expedite capacity fading in lithium-ion battery electrodes during electrochemical cycling. Experiments have frequently revealed that such degradation effects could be substantially mitigated via reducing the electrode feature size to the nanoscale. The purpose of this work is to present a fracture mechanics study of the phase separating planar electrodes. To this end, a phase field model is utilized to predict how phase separation affects evolution of the solute distribution and stress profile in a planar electrode. Behavior of the preexisting flaws in the electrode in response to the diffusion induced stresses is then examined via computing the time dependent stress intensity factor arising at the tip of flaws during both the insertion and extraction half-cycles. Further, adopting a sharp-interphase approximation of the system, a critical electrode thickness is derived below which the phase separating electrode becomes flaw tolerant. Numerical results of the phase field model are also compared against analytical predictions of the sharp-interphase model. The results are further discussed with reference to the available experiments in the literature. Finally, some of the limitations of the model are cautioned. © 2017 Elsevier B.V.
Scripta Materialia (13596462)114pp. 142-145
In the past few decades, nanostructures of ceria have received significant attention for potential applications in a variety of technologies. Experiments have frequently shown that physical properties of ceria nanomaterials are strongly size-dependent. Here, by accounting for the highly non-linear coupling between electrical, chemical and mechanical driving forces, we develop a continuum model which allows us to investigate equilibrium distribution of defects in nanowires and nanotubes of ceria. It is shown that the model predicts strongly size-dependent non-stoichiometric composition, lattice constant and surface stresses in ceria nanostructures whose diameter is comparable with the Debye's length scale of the problem. © 2015 Elsevier B.V. All rights reserved.
International Journal of Solids and Structures (00207683)91pp. 157-168
High-capacity anodes hold great promise for the next-generation lithium-ion batteries. However, they are well known to suffer from mechanical failure during battery cycling. Among various nano-structured electrodes, nano-scale thin-film electrodes have been frequently observed to undergo fracture and delamination. In this work, we investigate the effect of nonlinear coupling between chemical and mechanical fields on the distribution of solute concentration and stress in a finite thin-film elastic electrode bonded to the surface of a thick chemically-inactive elastic substrate. The film is considered in chemical equilibrium with an external mass reservoir. It is demonstrated through numerical and analytical methods that chemo-mechanical coupling could lead to considerable solute segregation at the edges of the film. The coupling could also remarkably magnify the edge stress intensity factor beyond the classical predictions in the absence of coupling. Potential implications of the results in terms of prediction of a critical film thickness to avoid film delamination, and in terms of prediction of fatigue delamination growth are also discussed. © 2016 Elsevier Ltd.
Journal of the Mechanics and Physics of Solids (00225096)88pp. 1-11
Owing to its broad potential applications, nanostructured ceria has been subject of intense investigation in the past few decades. Experiments have demonstrated that various material properties of the nanostructured ionic solids including ceria vary with the feature size. Here, we present a theoretical study of the size effects on the composition, defect concentrations and stresses in free-standing nanoparticles of nonstoichiometric ionic solids. To this end, a continuum model is developed which accounts for the highly nonlinear coupling between mechanical, chemical and electrical driving forces, and their effects on the thermodynamic equilibrium of the defect species. It is demonstrated that the model, once applied to the case of ceria, predicts size-dependent defect concentrations and surface stresses. It is further shown that the theoretical predictions of the size effects on the composition and lattice parameter are in good agreement with the experimental observations. © 2015 Elsevier Ltd. All rights reserved.
Cheng, G.,
Miao, C.,
Qin, Q.,
Li, J.,
Xu, F.,
Haftbaradaran, H.,
Dickey, E.C.,
Gao, H.,
Zhu, Y. Nature Nanotechnology (17483387)10(8)pp. 687-691
Anelastic materials exhibit gradual full recovery of deformation once a load is removed, leading to dissipation of internal mechanical energy. As a consequence, anelastic materials are being investigated for mechanical damping applications. At the macroscopic scale, however, anelasticity is usually very small or negligible, especially in single-crystalline materials. Here, we show that single-crystalline ZnO and p-doped Si nanowires can exhibit anelastic behaviour that is up to four orders of magnitude larger than the largest anelasticity observed in bulk materials, with a timescale on the order of minutes. In situ scanning electron microscope tests of individual nanowires showed that, on removal of the bending load and instantaneous recovery of the elastic strain, a substantial portion of the total strain gradually recovers with time. We attribute this large anelasticity to stress-gradient-induced migration of point defects, as supported by electron energy loss spectroscopy measurements and also by the fact that no anelastic behaviour could be observed under tension. We model this behaviour through a theoretical framework by point defect diffusion under a high strain gradient and short diffusion distance, expanding the classic Gorsky theory. Finally, we show that ZnO single-crystalline nanowires exhibit a high damping merit index, suggesting that crystalline nanowires with point defects are promising materials for energy damping applications. © 2015 Macmillan Publishers Limited.
International Journal of Solids and Structures (00207683)58pp. 73-90
The inadequacy of traditional theory of elasticity in describing such a phenomenon as dispersion associated to a propagating wave with wavelength comparable to the intrinsic length of the medium of interest is well-known. Moreover, under certain circumstances it is incapable of capturing all the propagating waves. A remedy to such dilemmas is the employment of the more accurate higher order continuum theories which give rise to the appearance of at least one new characteristic length in the formulation. The experimental evidences as well as lattice dynamic analysis suggest that, although higher order continuum theories result in some improvements, but cannot fully overcome the above-mentioned dilemmas, unless the micro inertia term is included in the formulations. The current work addresses the elastodynamic fields of an anti-plane shear wave scattered by a micro-/nano-fiber embedded in an infinite matrix using couple stress theory with micro inertia term. Moreover, the formulations pertinent to the cases where the incident wave strikes an embedded micro-/nano-size circular cavity or a rigid immovable micro-/nano-fiber are also obtained. Within this theory, the appearance of a new length scale, so-called "dynamic characteristic length" stems from consideration of the micro inertia, which gives rise to physically realistic dispersion relations with characteristic resembling those observed in experiments. The effects of two different types of boundary conditions for the cases of elastic and rigid immovable fiber encountered within the present theory are discussed. By using this theory, the corresponding analytical expressions of the elastodynamic fields, total and differential scattering cross-sections, and the dynamic stress concentration factor are presented and their dependence on the characteristic lengths and frequency are examined. It has been shown that the effect of micro inertia term is more noticeable in higher frequencies. © 2014 Elsevier Ltd. All rights reserved.
Journal of Power Sources (03787753)288pp. 278-287
High-capacity anodes hold great promise for the next-generation lithium-ion batteries. However, such electrodes are known to suffer from mechanical degradation during battery cycling. One important failure mode commonly observed in thin-film electrodes is film delamination from the underneath current collector. Here, by accounting for the nonlinear coupling between the chemical and mechanical fields, we derive the stress intensity and solute segregation factors close to the edge of a thin elastic film which is bonded to the surface of a thick elastic substrate. The film is considered in chemical equilibrium with an external mass reservoir. While in the limit of extremely weak coupling, our formulation reduces to the classical delamination theory, the results indicate that the chemo-mechanical coupling leads to magnification of the stress intensity factor and solute segregation near the film edge. The effect of coupling on the solute and stress distribution in the film is discussed. Further, an analytical expression is derived for the edge stress intensity factor in the limit of extremely strong chemo-mechanical coupling, based on which a modified critical film thickness to avoid edge delamination is proposed. Potential implication of the results for fatigue delamination growth is also discussed. © 2015 Elsevier B.V. All rights reserved.
International Journal of Solids and Structures (00207683)56pp. 126-135
The coupling between solid state diffusion and mechanical stress arises in a number of important technological applications. The theory that describes such coupling is termed chemo-elasticity. In this paper, a solution approach is developed for two-dimensional chemo-elasticity problems. First, a coupled system of nonlinear partial differential equations is derived in terms of an Airy stress function and the solute concentration. Then, this coupled system of nonlinear equations is solved asymptotically using a perturbation technique. Finally, based on this approach, asymptotic solutions are obtained for three fundamental problems in two-dimensional chemo-elasticity, namely, a circular hole in an infinite plate under uniaxial tension, a straight edge dislocation and a disclination. ©2014 Elsevier Ltd. All rights reserved.
Journal of the Mechanics and Physics of Solids (00225096)71(1)pp. 1-14
In this study, we first demonstrate that the J-integral in classical linear elasticity becomes path-dependent when the solid is subjected to combined electrical, chemical and mechanical loadings. We then construct an electro-chemo-mechanical J-integral that is path-independent under such combined multiple driving forces. Further, we show that this electro-chemo-mechanical J-integral represents the rate at which the grand potential releases per unit crack growth. As an example, the path-independent nature of the electro-chemo-mechanical J-integral is demonstrated by solving the problem of a thin elastic film delaminated from a thick elastic substrate. © 2014 Elsevier Ltd.
Modelling and Simulation in Materials Science and Engineering (09650393)21(7)
It is well known that thin-film electrodes on substrates could fracture during lithium insertion/extraction above a critical film thickness. Recent studies have revealed that lithium could facilitate sliding at the interface between lithiated Si and the underlying substrate. In this paper, we investigate fracture in thin-film electrodes and derive the critical film thickness for fracture as a function of both the fracture toughness of the film and the sliding resistance of the interface. The analysis indicates that a slippery interface due to lithiation could significantly decrease the critical thickness for fracture. © 2013 IOP Publishing Ltd.
Journal of Power Sources (03787753)206pp. 357-366
Recent experiments have suggested that there is a critical size for patterned silicon (Si) thin film electrodes for delamination from a current collector during lithiation and delithiation cycling. However, no existing theories can explain this phenomenon, in spite of its potential importance in designing reliable electrodes for high-capacity lithium-ion batteries. In this study, we show that the observed delamination size effect can be rationalized by modeling thin film delamination in the presence of large scale interfacial sliding. A method is proposed to deduce the critical size for delamination based on the critical conditions for the nucleation and growth of edge or center cracks at the film-substrate interface under plane strain or axisymmetric conditions. Applications to lithiation of thin-film Si islands give results in excellent agreement with experimental observations. © 2012 Elsevier B.V. All rights reserved.
Journal of Applied Mechanics (00218936)79(3)
Mechanical stresses and failure are believed to be a major cause for the limited cycle life of lithium-ion batteries employing high capacity Si electrodes. Recent experiments have shown that patterned Si thin film electrodes on substrate exhibit improved cycling stability and substantial sliding at the film/substrate interface. To facilitate experimental studies of stress evolution in such systems, we have developed a modified Stoney equation which accounts for the effect of interfacial sliding on the relationship between curvature and stress in patterned thin films on substrate. © 2012 American Society of Mechanical Engineers.
Applied Physics Letters (10773118)100(12)
Analytical and numerical calculations are conducted to demonstrate a ratcheting mechanism of irreversible and accumulative deformation in patterned Si islands on substrates during lithiation/delithiation cycling. It is shown that ratcheting occurs as soon as one allows the yield stress of Si and/or the friction strength of the interface to vary from lithiation to delithiation half-cycles, and that this important failure mode can be avoided by simply reducing the lateral size of the islands below a critical length scale. The present study provides a feasible explanation for the experimentally observed ratcheting in fractured Si films on substrates. © 2012 American Institute of Physics.
Soni, S.K.,
Sheldon, B.W.,
Xiao, X.,
Verbrugge, M.W.,
Ahn, D.,
Haftbaradaran, H.,
Gao, H. Journal of the Electrochemical Society (00134651)159(1)
In this study, we report in situ measurements of lithium diffusion induced stress in patterned amorphous Si negative electrodes. This configuration was used as a model system to understand how the gap between islands can accommodate the large volume expansion and stress generation that occurs during the lithiation of Si. The effect of pattern size was studied systematically with 7 μm, 17 μm and 40 μm square islands. Experimentally measured stresses were then compared to a continuum model that describes stress accommodation due to interfacial sliding or plastic deformation in the underlying current collector. These results indicate that engineering an appropriately sized Si island is an effective method for mitigating lithiation-induced stress and mechanical degradation in Si based electrodes. © 2011 The Electrochemical Society.
Journal of Power Sources (03787753)196(1)pp. 361-370
Poor cyclic performance of electrodes in lithium-ion rechargeable cell batteries is calling for efforts to develop continuum models of diffusion under very large stresses and high solute concentrations. The present work is aimed to develop such a model based on input from atomistic simulations. We consider four fundamental features of highly nonlinear behavior associated with diffusion at high solute concentrations. First, the effect of solute-induced stresses on the activation energy of solute diffusion could be important. Second, the solute concentration may be subject to an upper limit if there exists a stoichiometric maximum concentration. Third, the strong influence of the change in local chemical environment on the interaction energy between solute and host atoms could play a significant role. Fourth, we include the effect of the solute concentration on the Young's modulus of the host material. A continuum model is developed and validated based on atomistic simulations of hydrogen diffusion in nickel. The influences of each feature above are clearly discussed through parametric studies. © 2010 Elsevier B.V.
Journal of Power Sources (03787753)196(3)pp. 1409-1416
The mechanical degradation of electrodes caused by lithiation and delithiation is one of the main factors responsible for the short cycle life of lithium-based batteries employing high capacity electrodes. In this report, we introduced a simple patterning approach to improve the cycling stability of silicon electrode, which is considered as the next generation negative electrode due to its high Coulombic capacity and low cost, but is limited by the mechanical degradation associated with large volume variations during cycling. The pattern design is based on the observation of a critical size for the crack gap in continuous films. An improvement in cycle life was noted when the pattern size was below the critical (7-10 μm) size, in which case the Si electrode patches adhered well to the Cu substrate after many cycles. By taking the plastic deformation in both Si thin film and substrate into consideration, the calculated crack spacing is consistent with experimental observations. Theoretical considerations gave a feasible explanation for the failure of Si pattern above the critical size. These results suggest a new approach to extend the cycle life of Si-based electrode materials using size to control and relax the stress due to lithiation and delithiation. © 2010 Elsevier B.V. All rights reserved.
Applied Physics Letters (10773118)96(9)
By introducing a coupling between internal stresses and activation energy for diffusion in the classical theory of diffusion induced stresses, a class of nonconventional solutions has been found for atomic intercalation into a solid electrode, indicative of a surface locking instability once the product between electrode dimension and charging rate exceeds a critical value. This finding may have important implications for the lithium ion battery technology. © 2010 American Institute of Physics.
The application of higher order continuum theories, with size effect considerations, have recently been spread in the micro and nano-scale studies. One famous version of these theories is the couple stress theory. This paper utilizes this theory to study the anti-plane problem of an elliptic nano-fiber, embedded in an infinite medium, both made of centrosymmetric isotropic material. In this framework, a characteristic length appears in the formulation, by which examination of the size effect is possible. This work presents an analytical solution for the proposed problem. Copyright © 2008 by ASME.
International Journal of Solids and Structures (00207683)46(16)pp. 2978-2987
It is well-known that classical continuum theory has certain deficiencies in predicting material's behavior at the micro- and nanoscales, where the size effect is not negligible. Higher order continuum theories introduce new material constants into the formulation, making the interpretation of the size effect possible. One famous version of these theories is the couple stress theory, invoked to study the anti-plane problems of the elliptic inhomogeneities and inclusions in the present work. The formulation in elliptic coordinates leads to an exact series solution involving Mathieu functions. Subsequently, the elastic fields of a single inhomogeneity in conjunction with the Mori-Tanaka theory is employed to estimate the overall anti-plane shear moduli of composites with uni-directional elliptic cylindrical fibers. The dependence of the anti-plane elastic moduli on several important physical parameters such as size, aspect ratio and rigidity of the fiber, the characteristic length of the constituents, and the orientation of the reinforcements is analyzed. Based on the available data in the literature, certain nano-composite models have been proposed and their overall behavior estimated using the present theory. © 2009 Elsevier Ltd. All rights reserved.
Composites Science and Technology (02663538)67(6)pp. 1073-1080
An exact thermoelasticity solution for a two-dimensional thick composite consisting of homogeneous and functionally graded layers is presented. The thermomechanical properties of functionally graded layers are assumed to vary exponentially through the thickness while the Poisson's ratio is taken to be constant. The heat transfer problem is solved under steady state condition accounting for the heat convection. Utilizing the stress function the governing equation reduces to a fourth order inhomogeneous partial differential equation which is solved exactly using Fourier series method. A comparative study is done between two sandwich structures with homogeneous and functionally graded coatings, respectively. The results reveal that stress concentration effects are eliminated and interfacial shear stress is reduced when a functionally graded coating is used. © 2006 Elsevier Ltd. All rights reserved.
