Phase Field Modelling of Indentation-Induced Crack Systems in Glass

  • Gibb, Alwin (Technical University of Darmstadt)
  • Tsakmakis, Aris (Technical University of Darmstadt)
  • Müller, Ralf (Technical University of Darmstadt)
  • Weiß, Marie-Louis (Technical University of Darmstadt)
  • Seel, Matthias (Technical University of Darmstadt)
  • Trauth, Anna (Technical University of Darmstadt)

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Based on a regularized formulation of Griffith’s theory, the phase field approach to brittle fracture provides a powerful framework to capture complex crack phenomena such as crack initiation, branching and kinking. In contrast to classical concepts of linear elastic fracture mechanics, phase field models can naturally handle arbitrarily complex multiaxial stress states. To account for the tension-compression-asymmetry in brittle fracture, as well as crack-closure, the elastic free energy density is commonly decomposed into a crack driving (tensile) and a non-driving (compressive) part. This energy decomposition is often based on a volumetric-deviatoric [1] or a spectral [2] split of the strain tensor, both of which correctly reproduce the stress response for Mode I cracks. However, these two popular models predict unrealistic crack patterns in indentation problems, where the stress field in the vicinity of the indenter is highly multiaxial and involves not only compressive stresses but also shear stresses. Consequently, the aim of this work is to investigate the material responses according to alternative formulations of crack driving forces. Furthermore, all driving forces considered within this work are derived in a thermodynamically consistent manner and are based on well-known brittle failure hypothesis such as the Rankine or Drucker-Prager criteria. By incorporating contact between a rigid indenter and the glass sheet, the proposed model is capable of predicting the characteristic crack system in blunt indentation experiments. References: [1] Amor, H. et al., Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments, Journal of the Mechanics and Physics of Solids, 57(8), 1209-1229, 2009. [2] Miehe, C. et. al., Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, International Journal for Numerical Methods in Engineering, 83(10), 1273-1311, 2010.