Phase-field Modeling of Void Formation: Non-Classical Nuclei and the Role of Plastic Flow

  • Pendl, Kevin Ayrton (Graz University of Technology)
  • Hochrainer, Thomas (Graz University of Technology)

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High vacancy concentrations in crystals, caused by, e.g., severe plastic deformation, can promote void nucleation well before macroscopic ductile fracture. Predicting nucleation in this regime remains difficult because classical nucleation theory prescribes idealized nucleus geometries and sizes, while the relevant chemical driving forces and mechanical fields are strongly coupled and evolve with the microstructure. Phase-field models (PFMs) offer a promising alternative by formulating the problem in terms of a free energy associated with the underlying phase transition, into which chemical and mechanical effects can be incorporated in a unified way. In our previous work, we developed a PFM for void formation in single crystals that couples conserved vacancy diffusion (Cahn–Hilliard) and non-conserved void evolution (Allen–Cahn), while chemo-mechanical coupling is introduced via eigenstrains representing lattice relaxation upon atom removal [1]. Within this formulation, the critical (non-classical) void nucleus is a saddle point of the coupled free-energy functional. We computed this barrier-defining configuration using gentlest ascent dynamics (GAD) [2], without prescribing the nucleus shape. Here we briefly summarize the GAD-based derivation and discuss how mechanics and model parameters influence critical nucleus morphology. Motivated by large-deformation ductile fracture, we then outline an extension to finite strains for the application of the governing equations in the multi-physics environment DAMASK [3]. Preliminary DAMASK-based simulations indicate that plastic flow qualitatively modifies nucleation behavior compared to the purely elastic case, emphasizing the importance of strong chemo-mechanical coupling between defect chemistry and inelastic deformation during early-stage damage initiation. The resulting framework is intended to support controlled numerical experiments on void formation under coupled diffusion, stress, and plastic flow. [1] K. A. Pendl and T. Hochrainer. Coupling stress fields and vacancy diffusion in phase-field models of voids as pure vacancy phase. Comput. Mater. Sci., 224:112157, 2023. [2] K. A. Pendl and T. Hochrainer. Non-classical critical void nuclei from a vacancy-based chemo-mechanical phase-field model. Model. Simul. Mater. Sci. Eng., 33(5):055009, 2025. [3] F. Roters et al. DAMASK. Comput. Mater. Sci., 158:420–478, 2019.