In Situ Measurements of Strains in Composite Battery Electrodes during Electrochemical Cycling

The cyclic stress in lithium-ion battery electrodes induced by repeated charge and discharge cycles causes electrode degradation and fracture, resulting in reduced battery performance and lifetime. To investigate electrode mechanics as a function of electrochemical cycling, we utilize digital image correlation (DIC) to measure the strains that develop in lithium-ion battery electrodes during lithiation and delithiation processes. A composite graphite electrode is cycled galvanostatically (with constant current) in a custom battery cell while optical images of the electrode surface are captured in situ. The strain in the electrode is computed using an in-house DIC code. On average, an unconstrained composite graphite electrode expands 1.41 % during lithiation and contracts 1.33 % during delithiation. These strain values compare favorably with predictions based on the elastic properties of the composite electrode and the expansion of graphite-lithium intercalation compounds (G-LICs). The establishment of this experimental protocol will enable future studies of the relationship between electrode mechanics and battery performance.     

Strain Evolution in Lithium Manganese Oxide Electrodes

Lithium manganese oxide, LiMn₂O₄ (LMO) is a promising cathode material, but is hampered by significant capacity fade due to instability of the electrode-electrolyte interface, manganese dissolution into the electrolyte and subsequent mechanical degradation of the electrode. In this work, electrochemically-induced strains in composite LMO electrodes are measured using the digital image correlation (DIC) technique and compared with electrochemical impedance spectroscopy (EIS) measurements of surface resistance for different scan rates. Distinct, irreversible strain variations are observed during the first delithiation cycle. The changes in strain and surface resistance are highly sensitive to the electrochemical changes occurring during the first cycle and correlate with prior reports of the removal of the native surface layer and the formation of cathode-electrolyte interface layer on the electrode surface. A large capacity fade is observed with increasing cycle number at high scan rates. Interestingly, the total capacity fade scales proportionately to the strain generated after each lithiation and delithiation cycle. The simultaneous reduction in capacity and strain is attributed to chemo-mechanical degradation of the electrode. The in situ strain measurements provide new insight into the electrochemical-induced volumetric changes in LMO electrodes with progressing cycling and may provide guidance for materials-based strategies to reduce strain and capacity fade.     

Analysis and Artifact Correction for Volume Correlation Measurements Using Tomographic Images from a Laboratory X-ray Source

The effects of three artifacts (reconstruction, beam hardening and temperature of the X-ray tube) associated with the use of a lab tomograph are analyzed in terms of their induced biases for Digital Volume Correlation (DVC) from a series of reconstructed volumes acquired successively. The most detrimental effect is due to spurious dilatational strains induced by temperature variations in the tomograph. If they are not accounted for, any quantitative kinematic measurement is impossible for strain levels below 0.5%.     

Real-Time Stress Measurement in SiO<Subscript>2</Subscript> Thin Films during Electrochemical Lithiation/Delithiation Cycling

Oxide coatings have been shown to improve the cyclic performance of high-energy density electrode materials such as Si. However, no study exists on the mechanical characterization of these oxide coatings. Here, thin film SiO₂ electrodes are cycled under galvanostatic conditions (at C/9 rate) in a half-cell configuration with lithium metal foil as counter/reference electrode, with 1 M LiPF₆ in ethylene carbonate, diethyl carbonate, dimethyl carbonate solution (1:1:1, wt%) as electrolyte. Stress evolution in the SiO₂ thin film electrodes during electrochemical lithiation/delithiation is measured in situ by monitoring the substrate curvature using a multi-beam optical sensing method. Upon lithiation SiO₂ undergoes extensive inelastic deformation, with a peak compressive stress of 3.1 GPa, and upon delithiation the stress became tensile with a peak stress of 0.7 GPa. A simple plane strain finite element model of Si nanotube coated with SiO₂ shell was developed to understand the mechanical response of the core-shell type microstructures under electrochemical cycling; measured stress response was used in the model to represent SiO₂ constitutive behavior while Si was treated as an elastic-plastic material with concentration dependent mechanical properties obtained from the literature. The results reported here provide insights and quantitative understanding as to why the highly brittle SiO₂ coatings are able to sustain significant volume expansion (300%) of Si core without fracture and enhance cyclic performance of Si reported in the literature. Also, the basic mechanical properties presented here are necessary first step for future design and development of durable Si/SiO₂ core shell structures or SiO₂-based electrodes.     

In-situ Analysis of Laminated Composite Materials by X-ray Micro-Computed Tomography and Digital Volume Correlation

The complex mechanical behaviour of composite materials, due to internal heterogeneity and multi-layered composition impose deeper studies. This paper presents an experimental investigation technique to perform volume kinematic measurements in composite materials. The association of X-ray micro-computed tomography acquisitions and Digital Volume Correlation (DVC) technique allows the measurement of displacements and deformations in the whole volume of composite specimen. To elaborate the latter, composite fibres and epoxy resin are associated with metallic particles to create contrast during X-ray acquisition. A specific in situ loading device is presented for three-point bending tests, which enables the visualization of transverse shear effects in composite structures.     

In situ 3D Synchrotron Laminography Assessment of Edge Fracture in Dual-Phase Steels: Quantitative and Numerical Analysis

The mechanical performance of automotive structures made of advanced high strength steels (AHSS) is often seen reduced by the presence of cut edges. An attempt is made to assess and quantify the initial damage state and the damage evolution during mechanical testing of a punched edge and a machined edge via a recently developed 3D imaging technique called synchrotron radiation computed laminography. This technique allows us to observe damage in regions of interest in thin sheet-like objects at micrometer resolution. In terms of new experimental mechanics, steel sheets having sizes and mechanical boundary conditions of engineering relevance can be tested for the first time with in situ 3D damage observation and quantification. It is found for the investigated DP600 steel that the fracture zone of the punched edge is rough and that needle-shape voids at the surface and in the bulk follow ferrite-martensite flow lines. During mechanical in situ testing the needle voids grow from the fracture zone surface and coalesce with the sheared zone. In contrast, during in situ mechanical testing of a machined edge the damage starts away from the edge (～800μm) where substantial necking has occurred. Three-dimensional image analysis was performed to quantify the initial damage and its evolution. These data can be used as input and validation data for micromechanical damage models. To interpret the experimental findings in terms of mechanical fields, combined surface digital image correlation and 3D finite element analysis were carried out using an elasto-plastic constitutive law of the investigated DP steel. The stress triaxiality and the accumulated plastic strain were calculated in order to understand the influence of the edge profile and the hardening of the cutting-affected zone on the mechanical fields.     

Three-dimensional Analysis of an In Situ Double-torsion Test by X-ray Computed Tomography and Digital Volume Correlation

The double-torsion (DT) test is commonly used to characterize the slow crack growth behavior of brittle materials. However, it relies on several mechanical hypotheses which still need to be deeply tackled. Measuring the full 3D displacement field experimentally through in situ experiments would improve the understanding of the mechanical behaviour. A dedicated experimental set-up was designed to perform in situ tests in a X-ray Computed Tomography (XCT) scanner on a porous brittle ceramic which is optically opaque. The analysis of the three-dimensional images with Digital Volume Correlation (DVC) allows a first study of the global kinematics and the stable crack growth propagation. This experimental and numerical methodology presents a strong potential for a future deep understanding of this complex mechanical test.     

Failure Mechanisms of Plasterboard in Nail Pull Test Determined by X-ray Microtomography and Digital Volume Correlation

To design lightweight plasterboard and optimize the compromise between thermal resistance and mechanical strength, it is important to characterize its strength as assessed with the normative “Nail pull” test. Understanding the phenomenology of this test is the key to identifying the limiting factor in terms of load carrying capacity. In this work, the degradation mechanisms of lightweight plasterboard are analyzed via tests conducted in situ in a laboratory tomograph. Through the analysis of the kinematics by digital volume correlation, the different mechanisms at play up to failure mechanism have been identified, i.e., quasi-elastic regime, failure of the roller coating layer, core compaction and core failure. The compaction of the core by the collapse of porosity in compression is recognized as the limiting factor in terms of compressive strength and tearing resistance.     

In-situ Strain Field Measurement and Mechano-electro-chemical Analysis of Graphite Electrodes Via Fluorescence Digital Image Correlation

Background

Mechano-electro-chemical coupling during the ion diffusion process is a core factor to determine the electrochemical performance of electrodes. However, relationship between the mechanics and the electrochemistry has not been clarified by experiments.

Objective

In this work, we conduct an in situ, visual, comprehensive characterization of strain field and Li concentration distribution to further explore the mechano-electro-chemical relationship.

Methods

The digital image correlation characterized by fluorescent speckle and active optical imaging is developed. Combined with electrochromic-based Li concentration detection, the spatiotemporal evolution of in-plane strain and Li concentration of a graphite electrode during the lithiation and delithiation processes are measured and displayed visually via a dual optical path acquisition system.

Results

The visual results show that in-plane strain and Li concentration possess a spatially non-uniform gradient distribution along the radial direction (i.e., diffusion path) with large values outside and small values inside, and that both present obvious temporal segmentation. And mechano-electro-chemical coupling analysis reveals that the in-plane strain is not always linearly related to the concentration and infers that a high strain limits the diffusion and lithiation. The strain–concentration evolution exhibits obvious asymmetric differences between lithiation and delithiation, wherein three equations are fitted to approximately represent the evolution process between in-plane strain and concentration during the lithiation and delithiation processes

Conclusions

This work overcomes the difficulties of fine strain measurements and collaborative concentration characterization during the electrochemical process, and provides an effective experimental method and data support for further exploration of mechano-electro-chemical coupling.

     

Viscoplastic response of electrode particles in Li-ion batteries driven by insertion of lithium

Constitutive equations are derived for the viscoplastic behavior of a host medium driven by diffusion of guest atoms. With reference to the trapping concept, two states of a guest atom are distinguished: mobile and immobilized (due to alloying with the host matrix). This allows propagation of a sharp interphase to be described between regions rich and poor in guest atoms. The model is applied to study the mechanical response of a spherical electrode particle in a Li-ion battery. Ability of the constitutive equations to capture basic phenomena observed in anode particles under lithiation is demonstrated by numerical simulation.     

Application of Moiré Interferometry to the Characterization of Orthotropic Materials in the Antisymmetric Configuration using the Virtual Fields Method

Moiré interferometry is an effective full-field deformation measurement technique and has been utilized for mechanical behavior analysis of materials and structures. For isotropic materials, Moiré patterns can be obtained by performing standard tests, such as, tensile and bending tests, to calculate the displacement and strain. Then, the mechanical properties can be characterized. However, standard tests are not sufficient to characterize the mechanical parameters of anisotropic materials due to the complexity of their material properties. Thus, in this work, Moiré interferometry was combined with the Virtual Fields Method to obtain the four in-plane elastic constants (Q₁₁, Q₂₂, Q₁₂, and Q₆₆) of orthotropic materials in the form of a diametrically compressed disk. Firstly, according to finite element method simulation results, optimized parameters can be achieved when the principal direction of the material does not coincide with the loading direction, making the loading configuration antisymmetric. Therefore, Moiré interferometry experiment was simulated to demonstrate the feasibility of measurement in the antisymmetric configuration. Finally, the Q₁₁, Q₂₂, Q₁₂ and Q₆₆ values of a unidirectional carbon fiber composite were measured in a real Moiré interferometry experiment using the proposed method, yielding results that agreed closely with those obtained using the strain gauges.     

Digital Volume Correlation: Review of Progress and Challenges

3D imaging has become popular for analyzing material microstructures. When time lapse series of 3D pictures are acquired during a single experiment, it is possible to measure displacement fields via digital volume correlation (DVC), thereby leading to 4D results. Such 4D analyses have been performed for almost two decades. The present paper aims at reviewing the achievements of and challenges faced by such measurement technique. Ex-situ and in-situ experiments are discussed. A general and unified DVC framework is introduced. Various sources of measurement bias and uncertainties are analyzed. The current challenges are studied and some propositions are given to address them.     

Growths of mechanical elasticity and electrical conductance of graphene nanoplatelet/poly(lactic acid) composites under strong electric field: correlation with time evolution of higher order structure of graphene nanoplatelets

For a composite of poly(lactic acid) containing graphene nanoplatelets (GNPs) at a low concentration (0.34 vol%), this study examined growths of mechanical and electrical properties under an alternating current (AC) electric field, focusing on field-induced GNP structures governing those properties. The composite was subjected to the AC field (60 Hz) of various intensities E for various times t _E at 190 °C. A fraction of randomly oriented GNPs was aligned by the field and then connected into columns, as suggested from optical microscopy. This structural evolution led to qualitatively similar growths of low-frequency storage modulus and static electrical conductivity. The key quantity for understanding this growth was a time t _E* for occurrence of short circuit that detected formation of GNP columns conductively bridging the electrodes. The growths of both modulus and conductivity for various E were summarized as functions of a reduced variable, t _E/t _E*, confirming the growths commonly reflected the evolution of the GNP columns. However, the modulus grew fast and leveled off by t _E/t _E* ~ 1, whereas the conductivity kept growing gradually even at t _E/t _E* > 1. This difference was discussed in relation to the matrix chains and leftover GNPs out the column.     

On the Accuracy of Elastic Strain Field Measurements by Laue Microdiffraction and High-Resolution EBSD: a Cross-Validation Experiment

Determining the accuracy of elastic strain measurements in plastically deformed alloys is an experimental challenge. To develop a novel cross-validation procedure, a controlled elasto-plastic strain gradient was created in a stainless steel single crystal by four point bending deformation. The corresponding elastic strain field was probed, with an intragranular spatial resolution, in-situ by Laue microdiffraction and ex-situ by High Resolution EBSD. Good agreement is found for the two independent measurements and the predictions of a mechanical model, at plastic strains below 0.5 %. The accuracy of the measurements is estimated at 3.2 × 10^{? 4}.     

Large amplitude oscillatory shear rheology of three different shear-thickening particle dispersions

We present a large amplitude oscillatory shear rheology (LAOS) investigation of three different shear-thickening particle dispersions - fumed silica in polyethylene oxide (FLOC), fumed silica in polypropylene glycol (HydroC), and cornstarch in water (JAM). These systems shear-thicken by three different mechanisms - shear-induced formation of particle clusters flocculated by polymer bridging, hydrocluster formation, and jamming. The viscoelastic non-linearities of the three fluids were studied as a function of strain and strain-rate space through the use of Lissajous-Bowditch curves and local nonlinear viscoelastic moduli of an oscillatory shear cycle. The nonlinear behaviors of the three fluids were compared and contrasted to understand the nonlinear shear-thickening mechanism of each. Both HydroC and JAM dispersions were found to exhibit strong strain stiffening of the elastic moduli and strain thickening of the loss moduli behavior associated with possible hydrocluster formation and particle jamming. However, the FLOC dispersion, in contrast, showed strong strain softening and strain thinning behavior at large strain amplitudes associated with yielding of the microstructure. The expected thickening of the loss modulus of FLOC in LAOS with increasing strain was not observed even though viscosity of FLOC was found to shear-thicken in steady-shear measurements. This disagreement is likely due to very large strain amplitudes required for shear-thickening to occur by shear-induced polymer bridging mechanism. The hypothesis was confirmed through stress growth experiments. Conversely, the HydroC and JAM dispersions required relatively small applied strains for shear-thickening to occur by hydrocluster and jamming mechanism. The comparison of local intra-cycle nonlinearity through Lissajous-Bowditch plots and nonlinear viscoelastic parameters indicated that the elastic nonlinearities of all three systems are primarily driven by a strong dependence on the magnitude of the applied strain-rates within an oscillatory cycle rather than the amplitude of the applied strain. A close inspection of the LAOS data reveals strong differences in the viscoelastic nonlinearities of these three different shear-thickening dispersions which can be used to create a nonlinear rheological fingerprint for each and offers valuable new insights into the nonlinear dynamics associated with each of the shear-thickening mechanisms.     

<Emphasis Type="Italic">In-situ</Emphasis> Full Field Measurements During Inter-Facial Debonding in Single Fiber Composite Under Transverse Load

The fibre/matrix interfacial damage mechanisms of fiber-reinforced composites (FRCs) are investigated for single-fiber composites under transverse load. A stereo microscope setup is used for 3D digital image correlation during in-situ quasi-static tests of single-fiber standard dog-bone specimens. Macro-fibers (0.9 mm diameter) with radically different interfacial bonding with the epoxy matrix are used. Damage appears to initiate with fiber debonding at the free surface along the tensile direction. The crack then propagates around the interface while slightly growing along the fiber until a lateral crack initiates on the debonded free surface, provoking specimen failure. The final failure mechanisms appears to be different for strong and weak fiber/matrix bonding. 3D DIC is used to provide precise measurements of displacements, strains, and out-of-plane displacement during the whole test. Quantitative differences in the displacement fields are measured in the cases of strong and weak bonding between the fiber and matrix. 3D DIC with macro-fibers is shown to be a promising technique to provide a better understanding of the damage mechanisms in a single-fiber composite and to determine interfacial toughness of a specific fibre/matrix couple in order to perform accurate modeling of damage in FRCs. Displacement, strain, and confidence field results for each pixel from each experiment and at each time step are also provided for detailed comparison with simulation results.     

Diffusion induced stresses in buckling battery electrodes

Highly networked nanostructured battery electrode materials offer the possibility of achieving both rapid battery charge–discharge rates and high storage capacity. Recently, lithium ion battery (LIB) electrodes based on a 2-D honeycomb architecture were shown to undergo remarkable and reversible morphological changes during the lithiation process. Charge–discharge rates in 3-D composite electrode have also been shown to benefit from sandwiching the electrolytically active material between highly conductive ion and electron transport pathways to reduce electrical resistance and solid-state diffusion lengths. In the present work we simulate and analyze the observed morphological changes in honeycomb electrodes, with and without the presence of conductive pathways, during the lithiation–delithiation process. Diffusion induced stresses are analyzed for such structures undergoing elastic–plastic deformation during cycling. The results show that such a periodic, nanostructured electrode geometry allows for the presence of buckling-like deformation modes, which effectively reduce the resulting mechanical stresses that lead to electrode failure.     

Investigation of the Tensile Behavior of Recycled Asphalts in the Small-Strain Domain with the Grid Method

Under mechanical loading, asphalt mixtures exhibit in their bulk heterogeneous strain fields characterized by localized gradients concentrated within the binder. Measuring such fields constitutes a challenge for the full-field measurement methods currently used in the experimental mechanics community. This is particularly true when the objective is to measure strains in the linear viscoelastic domain, which is characterized by low strain levels (about some 200 με). In the present study, the strain distribution is measured on the surface of several recycled asphalt pavements (RAP) subjected to direct tensile tests. Four asphalt mixtures incorporating respectively 0%, 20%, 40% and 100% of RAP are studied. The tests are performed using a servo-controlled machine for rheological tests (MAER) and the local strain fields are measured using the Grid Method (GM). Out-of-Plane Motions (OPM) and camera noise are the main causes of disturbance that significantly affect the strain measurements. A method is proposed here to compensate the OPM. It is specially dedicated to bituminous mixtures. Sensor noise is filtered over time to improve the measurement resolution. Obtained results indicate that such compensations allow the use of GM to obtain quantitative measurements of the asphalt deformation in the small-strain domain. Finally, the behavior of the different samples are compared and the effect of RAP inclusion on the local strain distribution is observed and characterized.     

A theory and a simulation capability for the growth of a solid electrolyte interphase layer at an anode particle in a Li-ion battery

A major mechanism for electrochemical aging of Li-ion batteries is the growth of a solid electrolyte interphase (SEI) layer on the surface of anode particles, which leads to capacity fade and also results in a rise in cell resistance. We have formulated a continuum theory for the growth of an SEI layer—a theory which accounts for the generation of the attendant growth stresses. The theory has been numerically implemented in a finite-element program. This simulation capability for SEI growth is coupled with our previously published chemo-mechanical simulation capability for intercalation of Li-ions in electrode particles. Using this new combined capability we have simulated the formation and growth of an SEI layer during cyclic lithiation and delithiation of an anode particle, and predicted the evolution of the growth stresses in the SEI layer. The evolution of the stress state within the SEI layer and at the SEI/anode-particle interface for spherical- and spheroidal-shaped graphite particles is studied. This knowledge of the local interfacial stresses provides a good estimate for the propensity of potential delamination of an SEI layer from an anode particle.     

Phase-field model for the two-phase lithiation of silicon

As an ideal anode material, silicon has the highest lithium-ion capacity in theory, but the broader application is limited by the huge volumetric strain caused by lithium insertion and extraction. To better understand the physical process and to resolve the related reliability issue, enormous efforts have been made. Recent experiments observed sharp reaction fronts in both crystalline and amorphous silicon during the first lithiation half-cycle. Such a concentration profile indicates that the process is likely to be reaction limited. Based on this postulation, a phase-field model is developed and implemented into a finite-element code to simulate the coupled large inelastic deformation and motion of the reaction front in a silicon electrode. In contrast to most existing models, the model treats both volumetric and deviatoric inelastic deformation in silicon as a direct consequence of the lithiation at the reaction front. The amount of deviatoric deformation is determined by using the recently developed kinetic model of stress-induced anisotropic reaction. By considering the role of stress in the lithiation process, this model successfully recovers the self-limiting phenomenon of silicon electrodes, and relates it to the local geometry of electrodes. The model is also used to evaluate the energy-release rate of the surface crack on a spherical electrode, and the result suggests a critical size of silicon nanoparticles to avert fracture. As examples, the morphology evolution of a silicon disk and a Si nanowire during lithiation are also investigated.