PSI - Issue 61

İmren Uyar et al. / Procedia Structural Integrity 61 (2024) 195 – 205 İ. Uyar, E. Gürses / Structural Integrity Procedia 00 ( 2019) 000 – 000

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separator. The surrounding polymer matrix is assumed to consist of a bi-continuous polymer base doped with positive electrode particles, such as LiFePO 4 , enabling it to function as the positive electrode within the battery cell. The matrix is infused with an electrically conductive material, such as carbon black, to enhance electrical conduction within the matrix. In this cell design, the single fiber battery cells operate in parallel. The key benefit of this design concept is the notably reduced distance between electrodes (Asp and Greenhalgh, 2014). Over the course of a rechargeable battery's functional life, the individual fibers within it experience numerous cycles of ion intercalation and deintercalation (corresponding to charging and discharging). During the process of ion intercalation and deintercalation, the fibers undergo repeated cycles, causing an uneven expansion. The framework is suitable for electrode materials that undergo large volume changes during charge-discharge cycles. This irregular expansion can lead to the development of mechanical stresses, which have the potential to create micro-damage within the fibers. Most of the work has focused on isolated active particles, so various assumptions have been made to disregard the surrounding phases. Varna et al. (2014) studied radial cracks and arc-shaped cracks in the fiber region. High hoop stresses during deintercalation can initiate radial crack growth in the fibers. However, radial cracks do not affect ion diffusion as they only occur in the radial direction. Concerning arc cracks, when there is a high level of radial tensile stress, arc-shaped cracks can begin by deflecting away from the end of the radial crack and then spreading in the circumferential direction. These arc-shaped cracks act as a barrier that obstructs the movement of ions through their exposed surfaces, which impacts the diffusion process (Varna et al., 2014). In their study (2015), Miehe and Dal proposed a framework suitable for electrode materials that undergo large volume changes during charge-discharge cycles. Klinsmann and colleagues (2016) utilized the phase field method to simulate the formation and expansion of cracks. Their approach incorporated a crack growth model tailored for idealized particles, and they examined the impact of particle size and charging rate on crack stability. Additionally, the researchers applied the phase field model to electrode particles to explore fatigue cracking, drawing similarities between intercalation deintercalation cycles and fatigue damage, as highlighted by Martínez-Pañeda et al. (2022). This paper investigates the monolithically coupled finite element simulation of electro-chemo-elastic media. It then integrates this analysis with the phase field method in a staggered manner for the crack formation in the fiber region. High-concentration gradients at the fiber surface induce mechanical stresses, potentially leading to crack initiation and growth. Such cracks can reduce fiber mechanical properties and lithium-ion diffusivity, thus impacting battery performance. The phase field fracture model is used to study damage mechanisms in a coupled system by simulating center and arc-shaped crack growth. A staggered solution scheme and phase field equation are used to solve the system, and previous numerical examples from the literature are reanalyzed to validate the proposed theory. Nomenclature stress tensor m aterial’s bulk modulus total strain tensor 0 diffusion coefficients of anions and cations ℎ chemical strain tensor normalized ionic concentration elastic strain tensor chemical potential ̅ prescribed surface displacements ̅ 0 prescribed ionic concentration ̅ prescribed surface tractions phase field variable displacement vector + history variable mass flux length scale parameter 0 Reference ionic concentration viscous term 2. Mathematical modeling 2.1. Electrochemical-Mechanical Coupling A physics-based model describing the electrochemical behavior of composite structures is explained here. The analysis begins by focusing on the fiber region and employing simplified equation sets for a finite element approach