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A variational phase-field model For ductile fracture with coalescence dissipation

Abstract

A novel phase-field model for ductile fracture is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling mechanism between plasticity and fracture by degrading the fracture toughness as the equivalent plastic strain increases. The proposed model is compared with a recent alternative where plasticity and fracture are strongly coupled. Several representative numerical examples motivate specific modeling choices. In particular, a linear crack geometric function provides an “unperturbed” ductile response prior to crack initiation, and Lorentz-type degradation functions ensure that the critical fracture strength remains independent of the phase-field regularization length. In addition, the response of the model is demonstrated to converge with a vanishing phase-field regularization length. The model is then applied to calibrate and simulate a three-point bending experiment of an aluminum alloy specimen with a complex geometry. The effect of the proposed coalescence dissipation coupling on simulations of the experiment is first investigated in a two-dimensional plane strain setting. The calibrated model is then applied to a three-dimensional calculation, where the calculated load-deflection curves and the crack trajectory show excellent agreement with experimental observations. Finally, the model is applied to simulate crack nucleation and growth in a specimen from a recent Sandia Fracture Challenge.

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Notes

  1. 1.

    Also sometimes referred to as the local fracture dissipation function in the phase-field for fracture related literature, despite its energetic nature in the thermodynamic framework.

  2. 2.

    It can also be interpreted as the critical energy release rate depending on the context.

  3. 3.

    We refer to \(\alpha (d)\) as the crack geometric function to keep it consistent with previous works. This should not be confused with the energetic processes considered in this work.

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Acknowledgements

This research was supported by a research grant to Duke University from Sandia National Laboratories. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration, USA under contract DE-NA0003525.

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Correspondence to John E. Dolbow.

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Hu, T., Talamini, B., Stershic, A.J. et al. A variational phase-field model For ductile fracture with coalescence dissipation. Comput Mech 68, 311–335 (2021). https://doi.org/10.1007/s00466-021-02033-1

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Keywords

  • Phase-field models
  • Ductile fracture
  • Plasticity
  • Three-point bending