COMPLAS 2023

Phase Field Modelling of Ductile Fracture in the Context of Continuum Damage Mechanics

  • Tsakmakis, Aris (Technische Universität Darmstadt)
  • Vormwald, Michael (Technische Universität Darmstadt)

Please login to view abstract download link

Phase field theories have been introduced in fracture mechanics, in order to capture the surface energy of cracks. The fundamental idea of those theories is to introduce an additional variable and its gradient in the constitutive functional modelling of the material response. The present work is concerned in more detail about applications in the context of fracture for ductile materials. The basic model of phase field theories for fracture originates from a generalization of the Griffith theory for brittle materials, where the relevant crack propagation mechanism is based on the debonding of atomic planes. Consequently, plastic deformations do not influence the fracture process and established results from classic elastoplasticity are not described adequately under cyclic loading conditions [1]. In continuum damage mechanics on the other hand, the phase field corresponds to the isotropic damage variable and reflects in a natural way the physical mechanisms of crack initiation and crack propagation for ductile materials. In principle, any gradient enhanced isotropic damage theory is a phase field theory. The aim of the present work is therefore to model the constitutive response of ductile materials within the context of continuum damage mechanics. Accordingly, an evolution equation for the phase field variable will be adopted, which depends on the rate of the plastic arc length [2]. Special attention for the proposed model needs to be paid to the appropriate thermodynamics framework. Here, non-conventional thermodynamics are adopted and thermodynamic consistency of the model is verified for the case, where the free energy function depends explicitly on the phase field variable and its gradient. Finally, the resulting constitutive and field equations for models exhibiting isotropic and kinematic hardening are discussed with reference to both one-dimensional homogeneous deformations and fracture mechanics specimens. Especially the effect of cyclic loading conditions is analyzed. REFERENCES [1] Tsakmakis A., Vormwald M., Thermodynamics and Analysis of Predicted Responses of a Phase Field Model for Ductile, Materials, 14(19):5842, 2021. [2] Tsakmakis A., Vormwald M., Phase field modelling of ductile fracture in the frameworks of non-conventional thermodynamics and continuum damage, International Journal of Solids and Structures, Vol. 262-263, 2023.