COMPLAS 2023

A Consistent Phase-Field Formulation for Ionic Transport and Reactions within Electrolyte-Filled Fractures

  • Hageman, Tim (Imperial College London)
  • Martínez-Pañeda, Emilio (Imperial College London)

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Phase-field models have become ubiquitous in recent years for modelling fracture propagation. They are able to include cracks with complex paths, while simplifying the numerical implementation compared to other methods. However, their integration with other relevant physical phenomena is often based on assumed interactions. For instance for ionic diffusion within cracks, a commonly used model assigns an experimentally determined diffusion coefficient (dependent only on the phase-field parameter) \cite{Wu}, with little regard for the actual physics and geometry contributing to this diffusion. While this is a valid approach for well-conducting cracks, it has been shown that even small changes in geometry can have a significant impact on the environmental conditions generated within cracks \cite{Hageman}, and as such, not including the effects of the crack geometry can potentially induce large errors. Here, a model will be presented for the diffusion of ions within the fracture phase-field framework. By deriving the governing equations for a geometric representation of the fracture before distributing this formulation in agreement with the phase-field model, the physical dependence on the geometry of the fracture can be retained. Specifically, the relevance of surface and volume reactions is conserved and the diffusion model is directly linked to the displacement jump across the interface. The derived formulation is applied to the case of hydrogen embrittlement, and by comparison to discrete simulations it is shown that this method is able to accurately capture the relevant phenomena.