A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries

Cui, Zhiwei; Gao, Feng; Qu, Jianmin

doi:10.1016/j.jmps.2012.03.008

Cited by 300 publications

(194 citation statements)

References 32 publications

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“…The unlithiated domain is modeled as an isotropic, elastic material, whose stress and strain rates obey the classical Hooke's law with two material constants, Young's modulus Y and Poisson's ratio ν. The lithiated phase is modeled by an isotropic elastic, perfectly, 65 or rate-dependent plastic material, 67,70,[73][74][75][76][77] with phase-dependent elastic constants. Note that the ratedependent plasticity introduces an additional time scale characterizing the stress relaxation, and thus may affect stress generation.…”

Section: Governing Equationsmentioning

confidence: 99%

Chemomechanical modeling of lithiation-induced failure in high-volume-change electrode materials for lithium ion batteries

Zhang

2017

npj Comput Mater

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The rapidly increasing demand for efficient energy storage systems in the last two decades has stimulated enormous efforts to the development of high-capacity, high-power, durable lithium ion batteries. Inherent to the high-capacity electrode materials is material degradation and failure due to the large volumetric changes during the electrochemical cycling, causing fast capacity decay and low cycle life. This review surveys recent progress in continuum-level computational modeling of the degradation mechanisms of high-capacity anode materials for lithium-ion batteries. Using silicon (Si) as an example, we highlight the strong coupling between electrochemical kinetics and mechanical stress in the degradation process. We show that the coupling phenomena can be tailored through a set of materials design strategies, including surface coating and porosity, presenting effective methods to mitigate the degradation. Validated by the experimental data, the modeling results lay down a foundation for engineering, diagnosis, and optimization of high-performance lithium ion batteries.

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Section: Governing Equationsmentioning

confidence: 99%

Chemomechanical modeling of lithiation-induced failure in high-volume-change electrode materials for lithium ion batteries

Zhang

2017

npj Comput Mater

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“…Since then, some researchers [12][13][14][15][16][17] had made a series of studies of diffusion-induced stresses in coatings and had come up with experiments and numerical models to analyse coating-substrate debondment. Also, in recent research work, models for coating-substrate debondment involving diffusion-induced stresses, developed by Nguyen et al [18], Prawoto et al [19,20], Cui et al [21], Yang and Li [22] and Rusanov [23] are based on various numerical methods and techniques. It is worth noting that the occurrence of residual stress in coating-substrate systems due to thermal expansion mismatch is unavoidable in practice.…”

Section: Introductionmentioning

confidence: 99%

Optimisation of interface roughness and coating thickness to maximise coating–substrate adhesion – a failure prediction and reliability assessment modelling

Nazir

Khan

Stokes

2015

Journal of Adhesion Science and Technology

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A mathematical model for failure prediction and reliability assessment of coating-substrate system is developed based on a multidisciplinary approach. Two models for diffusion and bending of bi-layer cantilever beam have been designed separately based on the concepts of material science and solid mechanics respectively. Then, these two models are integrated to design an equation for debonding driving force under mesomechanics concepts. Mesomechanics seeks to apply the concepts of solid mechanics to microstructural constituent of materials such as coatings. This research takes the concepts of mesomechanics to the next level in order to predict the performance and assess the reliability of coatings based on the measure of debonding driving force. The effects of two parameters i.e. interface roughness and coating thickness on debonding driving force have been analysed using finite difference method. Critical/ threshold value of debonding driving force is calculated which defines the point of failure of coating-substrate system and can be used for failure prediction and reliability assessment by defining three conditions of performance i.e. safe, critical and fail. Results reveal that debonding driving force decreases with an increase in interface roughness and coating thickness. However, this is subject to condition that the material properties of coating such as diffusivity should not increase and Young's modulus should not decrease with an increase in the interface roughness and coating thickness. The model is based on the observations recorded from experimentation. These experiments are performed to understand the behaviour of debonding driving force with the variation in interface roughness and coating thickness.

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“…12,15,18,19,21,24 Based on nonequilibrium thermodynamics, Zhao et al 15,21 considered the coupled large plastic deformation and lithiation in a spherical Si electrode. Bower et al 12,18 developed a theoretical framework to incorporate finite deformation, diffusion, plastic flow, and electrochemical reaction in lithiation of Si electrodes.…”

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confidence: 99%

A Phase-Field Model Coupled with Large Elasto-Plastic Deformation: Application to Lithiated Silicon Electrodes

Chen

Fan

Hong

et al. 2014

J. Electrochem. Soc.

108

105

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A phase-field model, accounting for large elasto-plastic deformation, is developed to study the evolution of phase, morphology and stress in crystalline silicon (Si) electrodes upon lithium (Li) insertion. The Li concentration profiles and deformation geometries are co-evolved by solving a set of coupled phase-field and mechanics equations using the finite element method. The present phase-field model is validated in comparison with a non-linear concentration-dependent diffusion model of lithiation in Si electrodes. It is shown that as the lithiation proceeds, the hoop stress changes from the initial compression to tension in the surface layer of the Si electrode, which may explain the surface cracking observed in experiments. The present phase-field model is generally applicable to high-capacity electrode systems undergoing both phase change and large elasto-plastic deformation. As a promising anode material for lithium (Li)-ion batteries, 1-3 the theoretical Li capacity of Silicon (Si) is 4200 mAh/g (corresponding to the lithiated phase of Li 4.4 Si), which is one order of magnitude larger than the commercialized graphite anode.1,2 Recent experiments revealed that the lithiation of crystalline Si (c-Si) occurs through a two-phase mechanism, i.e., growth of lithiated amorphous Li x Si (aLi x Si, x ∼ 3.75) phase separated from the unlithiated c-Si phase by a sharp phase boundary of about 1 nm thick.4-8 An abrupt change of Li concentration across the amorphous-crystalline interface (ACI) gives rise to drastic volume strain inhomogeneity. The resulting high stresses induce plastic flow, fracture, and pulverization of Si electrodes, thereby leading to the loss of electrical contact and limiting the cycle life of Li-ion batteries. [9][10][11] Electrochemically driven mechanical degradation in high-capacity electrodes has stimulated enormous efforts on the development of chemo-mechanical models to understand how the stress arises and evolves in lithiated Si electrodes.12-15 These chemo-mechanical models often treated the lithiation-induced stress as the diffusion-induced stress by considering Li diffusion in a solid-state electrode that results in the change of composition from its stoichiometric state. Deviation from stoichiometry usually results in a volume change that generates stress if the Li distribution is non-uniform. Early chemo-mechanical models only involved a unidirectional coupling. Namely, the diffusioninduced mechanical stress was considered, whereas the effect of mechanical stress on diffusion was ignored. Both experimental and computational studies, however, have shown that the mechanical stresses play an important role in the lithiation kinetics of Si electrodes. 4,6,16,17 Recently, fully coupled chemo-mechanical models were developed to incorporate the mechanical stress into the chemical potential. [18][19][20][21][22] In these models, the local stress modulates lithiation kinetics (reaction rate and diffusivity), 4,6,23 and in turn, lithiation kinetics regulates the stress generation in lithiated ...

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A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries

Cited by 300 publications

References 32 publications

Chemomechanical modeling of lithiation-induced failure in high-volume-change electrode materials for lithium ion batteries

Chemomechanical modeling of lithiation-induced failure in high-volume-change electrode materials for lithium ion batteries

Optimisation of interface roughness and coating thickness to maximise coating–substrate adhesion – a failure prediction and reliability assessment modelling

A Phase-Field Model Coupled with Large Elasto-Plastic Deformation: Application to Lithiated Silicon Electrodes

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