Over the last few decades, rechargeable lithium-ion batteries have been extensively used in portable instruments due to their high energy density and low self-discharge rate. Recently, lithium-ion batteries have emerged as the most promising candidate for electric vehicles and stationary energy storage. However, the maximum energy that lithium-ion batteries can store decreases as they are used because of various irreversible degradation mechanisms. Lithium-ion batteries are complex systems to understand, and various processes and their interactions are responsible for the degradation over time. The mechanical integrity and stability of the electrode layers inside the battery highly influence the battery performance, which makes it a necessity to characterize the mechanical behavior of electrode active layers for mesoscopic and macroscopic level modeling.

In papers 1 and 2, the macroscopic mechanical behavior of active layers in the electrodes is investigated using U-shape bending tests. The active layers are porous and a different tensile and compressive behavior is captured by performing tests on single side coated dry specimens. The experiments reveal that the active layer is stiffer in compression as compared to tension. The compressive stiffness increases with bending strain whereas the tensile stiffness is almost independent of the bending strain. A very low value of modulus of the active layer (1-5 GPa) is measured in comparison to the metal foils (70-110 GPa) and the active particles (50-200 GPa) which shows that the electrode properties are governed majorly by the binders present in the active layers.  The time-dependent and hysteresis effects are also captured by the method which circumvents the flaws of many other test methods presented in the literature.  

In paper 3, we present a multiscale homogenization method that couples mechanics and electrochemistry at the particle, electrode, and battery scales. The active materials of lithium-ion battery electrodes exhibit volume change during lithium intercalation or deintercalation. A lithium concentration gradient develops inside particles, as well as inside the active layer. The developed stress due to deformations further affects solid diffusion.  We utilized models that have already been developed to couple particle and electrode layer levels. The mechanical coupling between the electrode and the battery level is achieved by homogenization of the layered battery using three-dimensional laminate theory.  By application of the model, we demonstrate that the stresses on all considered scales can be predicted from the homogenized model. It is furthermore demonstrated that the effects of external battery loadings like battery stacks, casings, and external pressure can be captured by the model. The model can also capture the effect of various electrochemical cycling rates and mechanical parameters like layer thicknesses, stiffnesses, and swelling properties. The presented multi-scale model is fast, accurate and the efficiency of the method is demonstrated by comparisons to detailed finite element computations where each layer is individually modeled. 

The applications of Li-ion batteries in the electronics and vehicle industry is increasing at a very rapid pace. This is primarily due to superior properties such as high specific energy storage and power as well as wider operation temperature ranges. Additional potential for improved properties is connected to capacity losses with time and the thereby resulting limitations of lifetime of batteries. The lifetime of a battery is strongly related to the mechanical and chemical degradation of the active material of electrodes during repeated electrochemical reactions at charging and discharging. To identify this phenomenon from a mechanical perspective, the mechanical properties of the electrode active layers should be characterized. Additionally, with the aid of mechanical properties, realistic electro-chemo-mechanical models should be developed to comprehend the mechanisms causing capacity fade.

In the first part of this thesis, macroscopic material properties of the active layers of Li-ion battery electrodes were measured with a unique bending test technique. Contrary to methods previously used; it is capable to overcome the challenges that were encountered in other traditional testing techniques. In papers 1 and 2 this bending test technique (U-shaped bending test), is used to characterize the elastic and viscoelastic behavior of NMC cathodic and graphite anodic active layers, respectively. By using single-sided thin electrode specimens in U-shape bending tests, it was possible to distinguish tensile and compressive elastic and viscoelastic behavior of the electrode active materials. The tensile Young’s moduli of cathodic and anodic active layers are found as 0.73 GPa and 1 GPa, respectively. On the other hand, the compressive Young’s moduli show a stiffening behavior at increasing strains. Stiffnesses between 1.3 GPa and 2.8 GPa for the cathodic active layer, and between 1 GPa and 3.8 GPa for the anodic active layer were recorded. This compressive behavior of the electrode active layers is expected as a result of the porous nature of the materials. In addition, the viscoelastic behavior of the electrode active layers is expressed through Prony series. It was observed that the behavior can be described by a short term (minutes) and a long term (hours, days) relaxation.

In paper 3, a statistical representative volume element is introduced to predict the elastic properties of a dry cathodic electrode active layer. A porous cathodic electrode active layer that is composed of NMC active particles and polymeric binder material with conductive carbon additives is modeled as a face-centered-cubic structure. Several particle-binder and particle-particle interaction conditions are repeated 50 times with random orientations. Based on the statistics for each interaction case, Young’s modulus is estimated. The results show a good agreement with the experimental findings from Paper 1. Furthermore, particle-particle and particle-binder contact force distributions are calculated for 3% of particle swelling. The characteristics of the force distributions are correlated with the typical material failures in the active layer such as particle cracking and binder debonding. The statistical data obtained here are also used to improve an analytical model that was previously derived to estimate the elastic properties of active porous layers. The analytical model, complemented by the statistical results, showed an excellent agreement with the finite element simulations.

Over the last few decades, rechargeable lithium-ion batteries have been extensively used in portable instruments due to their high energy density and low self-discharge rate. Recently, lithium-ion batteries have emerged as the most promising candidate for electric vehicles and stationary energy storage. However, the maximum energy that lithium-ion batteries store decreases as they are used because of various irreversible degradation mechanisms. The mechanical properties of the electrode layers inside the battery highly influence the battery's performance. There is, however, a fundamental lack of understanding of the mechanical properties of electrodes and how they evolve during electrochemical cycling, which makes it a necessity to characterize their mechanical behavior for mesoscopic and macroscopic level modeling. Lithium-ion batteries are complex systems to understand, and various processes and their interactions make battery modeling challenging. This thesis contributes to understanding the mechanical behavior of electrodes in lithium-ion batteries and provides methods for the design and efficient modeling of battery systems.

        In Paper A and Paper B, the macroscopic mechanical behavior of active layers in the electrodes is investigated using U-shape bending tests. The active layers are porous and a different tensile and compressive behavior is captured by performing tests on single side coated dry electrodes. The experiments reveal that the active layer is stiffer in compression as compared to tension. The compressive stiffness increases with bending strain whereas the tensile stiffness is almost independent of the bending strain. A very low value of modulus of the active layer (1-5 GPa) is measured in comparison to the metal foils (70-110 GPa) and the active particles (50-200 GPa) which shows that the electrode properties are governed majorly by the binders present in the active layers. The time-dependent and hysteresis effects are also captured by the method which circumvents the flaws of many other test methods presented in the literature.  

        Paper C focuses on characterizing the layer-level evolution of mechanical and electrochemical properties of a Ni-rich positive electrode during early-stage electrochemical cycling, along with complementary cross-section analyses to understand the relationship between macroscopic and microscopic changes. Macroscopic constitutive properties were measured using the U-shaped bending test method developed in papers A and B, which revealed that the compressive modulus was primarily influenced by the porous structure and binder properties. It decreased notably with electrolyte wetting but increased with cycling and aging. Electrochemical impedance spectra showed an increase in local resistance near the particle-electrolyte interface with early-stage aging, which was likely due to secondary particle grain separation and carbon black redistribution. Cross-section analyses reveal significant variations in particle properties between pristine and cycled samples, including particle swelling, compression of the binder phase, and increased particle contact, contributing to the rise in the elastic modulus of the porous layer during cycling.

        In Paper D and Paper E, we present a multiscale homogenization method that couples mechanics and electrochemistry at the particle, electrode, and battery scales. The active materials of lithium-ion battery electrodes exhibit volume change during lithium intercalation or deintercalation. A lithium concentration gradient develops inside particles, as well as inside the active layer. The developed stress due to deformations further affects solid diffusion.  We utilized models that have already been developed to couple particle and electrode layer levels. Electric vehicle battery packs consist of numerous battery modules, each of which includes multiple battery cells composed of electrode, separator, and current collector layers. A finite element model capable of capturing stresses at the layer level would need to be very large to account for all the details. The mechanical coupling between the electrode and the battery level is achieved by homogenization of the layered battery using three-dimensional laminate theory, which greatly reduces the number of finite elements required for stress simulations in batteries. After obtaining a homogenized solution, layer-level stresses can be determined in a post-processing step. The method accurately predicts stresses on various scales and captures the effects of external battery loadings, cycling rates, and mechanical parameters. The efficiency of the method is demonstrated by comparing it to detailed finite element computations. The simulations indicate that layer-wise stresses, such as pressure, can be predicted as functions of position and time, providing insights into the inhomogeneous aging state of the battery.

Under de senaste decennierna har uppladdningsbara litiumjonbatterier använts flitigt i bärbara instrument på grund av deras höga energitäthet och låga självurladdningshastighet. Just nu ses en kraftig ökning av eldrivna fordon. Den maximala energin som litiumjonbatterier kan lagra minskar dock med tiden på grund av olika irreversibla nedbrytningsmekanismer. De mekaniska egenskaperna hos elektrodskikten inuti batteriet påverkar här i hög grad batteriets prestanda. Det finns dock en bristande kunskap om elektrodernas mekaniska egenskaper och hur de utvecklas under elektrokemisk cykling. Behovet av nya experimentella och teoretiska metoder för karaktärisering på mikro- och makroskalor är stort. Litiumjonbatterier är komplexa system att förstå, och olika processer och deras interaktioner gör batterimodellering utmanande. Denna avhandling bidrar till en ökad förståelse av elektrodernas mekaniska beteende i litiumjonbatterier. Även metoder för design och effektiv modellering av batterisystem presenteras.

        I de bilagda rapporterna A och B undersöks det makroskopiska mekaniska beteendet hos aktiva skikt i elektroder med hjälp av böjprovning med U-formade provstavar. De aktiva skikten är porösa och skillnader i drag- och tryckbeteende fångas upp genom att utföra tester på ensidigt belagda torra elektroder. Experimenten visar att det aktiva lagret är styvare i kompression jämfört med dragning. Kompressionstyvheten ökar med töjningsnivån medan dragstyvheten är nästan oberoende av töjning. De uppmätta E-modulerna för det aktiva skiktet (1-5 GPa ) är låga i jämförelse med metallfolierna (70-110 GPa ) och de aktiva partiklarna (50-200 GPa ) vilket visar att elektrodegenskaperna huvudsakligen styrs av bindemedlen som finns i de aktiva skikten. Tidsberoende effekter och hystereser fångas också upp av den använda mätmetoden som även kringgår de begränsningar som alternativa testmetoder uppvisar. 

        I rapport C karakteriseras utvecklingen av mekaniska och elektrokemiska egenskaper som funktion av antalet laddningscykler i en positiv elektrod. För att bättre förstå orsaken till förändringar av egenskaper genomfördes parallella mikroskopiundersökningar. Makroskopiska konstitutiva egenskaper uppmättes med den böjprovningsmetod som utvecklades i rapporterna A och B. Resultaten visar att kompressionsmodulen främst påverkas av den porösa strukturen och bindemedlets egenskaper. Styvheten minskade märkbart efter vätning med elektrodvätska och därpå följande torkning. Med ökande antal laddningscykler ökade styvheten åter i jämförelse med denna referensnivå. Elektrokemiska impedansspektra visade på en ökning av lokal resistans nära partikel-elektrolytgränsytorna vid tidig åldring, vilket sannolikt berodde på sekundär kornseparation i elektrodpartiklarna samt omfördelning av kolpartiklar i bindemedlet. Mikroskopianalyser visade på betydande variationer i partikelegenskaper mellan virgina och cykliska prover. Förändringar i partikelstorlek och form kunde konstateras vilka kunde korreleras till utvecklingen av kompressionsstyvhet i den porösa elektroden. 

        I rapporterna D och E presenteras en flerskalig homogeniseringsmetod som kopplar mekanik och elektrokemi på partikel-, elektrod- och batteriskala. De aktiva materialen i litiumjonbatteriets elektroder uppvisar volymförändringar vid laddning och urladdning. En gradient i koncentrationen av litium utvecklas såväl inuti partiklar som inom elektrodskiktet under laddning eller urladdning. Dessa gradienter leder till mekaniska spänningar som i sin tur påverkar diffusionen av litium. För modellering av diffusion och därtill hörande litiumkoncentrationer applicerades är väl etablerad modell från litteraturen. Batteripaket för elfordon består av ett stort antal batterimoduler, som var och en innehåller flera battericeller vilka i sin tur består av många elektrod-, separator- och metallskikt. En finit elementmodell som kan fånga spänningar på skiktnivåer skulle behöva vara mycket stor för att ta hänsyn till alla variationer på små skalor. I rapporterna D och E utvecklas i stället en modell för homogenisering av det skiktade batteriet med hjälp av tredimensionell laminatteori. På detta sätt kan antalet frihetsgrader och därigenom beräkningskostnad för en finit elementmodell kraftigt reduceras. Baserat på en homogeniserad lösning kan spänningar på skiktnivå bestämmas i efterhand. Metoden förutsäger spänningar på olika skalor och fångar effekterna av laddningshastighet, extern mekanisk belastning och de ingående skiktens mekaniska egenskaper. Metodens effektivitet demonstreras genom att jämföra den med detaljerade finita elementberäkningar. Simuleringarna indikerar att skiktspänningar, såsom tryck, kan förutsägas som funktioner av position och tid, vilket ger insikter om åldrande i olika deler av ett batteri.