Another heat-transfer analogy for modeling chemo-mechanically coupled hydrogen diffusion processes in metals

  • Dyck, Alexander (Karlsruhe Institute of Technology (KIT))
  • Gisy, Johannes (Karlsruhe Institute of Technology (KIT))
  • Groß, Leonhard (Karlsruhe Institute of Technology (KIT))
  • Böhlke, Thomas (Karlsruhe Institute of Technology (KIT))

Please login to view abstract download link

Modeling and simulating hydrogen diffusion in metals in chemo-mechanically coupled processes is important for understanding e.g. embrittlement processes. The topic has been addressed in various publications, see e.g. \cite{Barrera,Diaz,Fernandez,Gobbi}, where an analogy between the heat-transfer and diffusion equation was used to solve derived models using the commercial finite-element solver ABAQUS. \\ In the classic formulation of the diffusion equation, the chemical degree of freedom is the concentration of hydrogen in lattice sites. Exploiting the analogy between heat-transfer equation implemented in ABAQUS and derived diffusion equation, the ABAQUS built-in coupled temperature-displacement procedure can be used to simulate chemo-mechanically coupled processes. However, several drawbacks exist with this approach. First, it is necessary to numerically approximate gradients of several quantities, which requires a new implementation whenever elements are changed, e.g. from tetrahedral to hexagonal. In addition, so called open systems, i.e. system being exposed to an atmosphere with a constant hydrogen partial pressure, can not readily be simulated. In \cite{DiLeo} a different chemical degree of freedom was chosen, namely the chemical potential, which circumvents these drawbacks. An implementation in ABAQUS was presented, making use of a user-defined-element. A drawback of user-defined-elements is the cumbersome implementation and the fact, that many built-in functionalities of ABAQUS can not easily be used, e.g. Neumann boundary conditions and visualization of results. \\ To bridge this gap, the goal of this talk is to present a novel implementation, allowing to exploit the heat-transfer analogy to simulate chemo-mechanically coupled processes using the chemical potential as degree of freedom. Therefore, we derive model equations in a consistent thermodynamic framework, present the analogy to the heat-transfer equation and our implementation. We discuss several examples, including the commonly studied blunting crack tip \cite{DiLeo,Fernandez}, to prove the validity of the proposed implementation.