COMPLAS 2023

Coupling Discrete Dislocation Dynamics and Phase Field for First Strain Gradient Materials

  • Budnitzki, Michael (Forschungszentrum Jülich GmbH)
  • Strobl, Rachel (Forschungszentrum Jülich GmbH)
  • Sandfeld, Stefan (Forschungszentrum Jülich GmbH)

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Gaining insight into the interaction of lattice defects, such as dislocations and phase boundaries, is crucial to the understanding of the deformation behavior of multi phase materials at nano scale. In classical elasticity theory the stress-field of a dislocation is characterized by a 1/r-type singularity. When considered together with an Allen-Cahn-type phase-field description for microstructure evolution, this singularity leads to unbounded driving forces for the order parameter, resulting in non-physical predictions for the interaction between dislocations and defects like phase-, twin- or grain-boundaries. Previously, we developed a framework [1] that consistently couples first strain gradient elasticity, which regularizes the dislocation core, to an Allen-Cahn-type evolution of the phase microstructure. In this work we combine this formulation with 2D discrete dislocation dynamics (DDD) in order to investigate the interaction of mobile dislocations with phase boundaries driven by either thermal or mechanical loading. The coupled problem is solved using the finite element library FEniCS. We use this implementation to show the effect of dislocations on the evolution of the phase microstructure as well as the influence of phase boundaries on the motion of dislocations. [1] Budnitzki, M., Sandfeld, S., 2021. A model for the interaction of dislocations with planar defects based on Allen–Cahn type microstructure evolution coupled to strain gradient elasticity. Journal of the Mechanics and Physics of Solids 150, 104222. https://doi.org/10.1016/j.jmps.2020.104222