The Stress Evolution Of Layered Si Electrode During Lithiation And Delithiation: Modified Stoney Formula And Finite Element Simulation

Silicon(Si)is a highly promising materials electrode in lithium-ion batteries for its highest capacity,however,the large volume expansion and high stress are the major bottlenecks for the application of Si electrodes.The cracking and delamination caused by stress directly lead to mechanical degradation in Si electrodes.Studying the stress evolution of Si electrode during lithiation and delithiation is important to improve and predict the material properties,optimize the electrode structure,Experiments based on substrate curvature method(SCM)is developed for stress measurement of Si thin film in multi-layer battery,which has many merits such as simplicity,easy operation and high accuracy.The Stoney formula serves as a cornerstone of experimental work in which stress values are inferred from curvature measurement.However,the classical Stoney formula has lots of assumptions,such as linear-elastic,small deformation and so on.Even in the case of curvature bifurcation the classical Stoney formula cannot be used.At present,for the layered electrode the relationship between stress and curvature is still lack of research in the process of lithiation and delithiation,such as large deformation.So studying the modified formula is necessary to accurately forecast the average stress of Si thin film electrode for large deformation.In this thesis,we propose a modified Stoney equation to facilitate experimental studies of stress evolution in film/substrate system,using both analytical method and finite element method(ABAQUS software)during the cycles of lithiation and delithiation.Using this user-defined heat transfer subroutine UMATHT and existing coupled deformation and heat transfer module in ABAQUS,the coupled deformation and mass diffusion can be realized in ABAQUS.The properties of Si film materials and the thickness of Si electrode depending on composition are considered during charging and discharging.Reasonable finite element model providing numerical solution is set up to verify the accuracy of the modified formula of Stoney.The main work and results of this thesis are as follows:1.We begin with a simple test of temperature load to test the accuracy of the analytical solution of the modified Stoney equation and critical bifurcation point.Secondly,the simulation of Si pure elastic electrodes is to verify the accuracy of the modified Stoney equation in the process of lithiation.2.Then,the model is extended to inelastic and the average stress evolution is studied during charging and discharging in Si thin films.In this part,the volume expansion is set up to 370%corresponding to the capacity of 3580mAh/g in simulations.The nonlinear elastic response is successfully simulated through finite element analyses accompanied by the increasing in-plane size and Lithium ion concentration.In this case the stress errors from the classic Stoney formula increase gradually but the revised formula for large deformation has a high degree of accuracy.The accuracy of the classic Stoney formula is affected by electrode size and large deformation(high-order curvature),yield strength,etc.Finally,with regard to bifurcation,we take the effects of edge size,yield stress and SOC(state of charge)into consideration and give the critical bifurcation condition of the electrode model.The theory of critical bifurcation point providing certain theory basis to avoid curvature bifurcation.3.Finally,the island Si thin film electrodes is also discussed in this thesis.On the basis of previous experiments,correction scheme is proposed and verified through finite element analysis(FEA).