A Diffusive crack model for fiber reinforced polymer composites

Aksu Denli, Funda
Recently, classical fracture mechanics approaches based on Griffith type sharp crack topologies have left the stage to diffusive crack approaches or the so called phase field models. Crack initiation and propagation is based on the variational principles for energy minimization leading to symmetric set of algebraic equations. In this thesis, which is the first attempt to model failure of engineered composites using an anisotropic crack phase–field approach, Fiber Reinforced Polymer (FRP) specific anisotropic phase field model is developed in the light of the previous studies on isotropic brittle materials and anisotropic materials like biological tissues. It started with the continuous formulation of the variational principle for the multi-field problem manifested through the deformation map and the crack phase-field at finite strains which leads to the Euler–Lagrange equations of the coupled problem. In particular, the coupled balance equations derived render the evolution of the anisotropic crack phase-field and the balance of linear momentum. In addition, a novel energy-based anisotropic failure criterion is proposed which regulates the evolution of the crack phase-field. Distinct failure processes for the ground matrix and the fibers are modelled by additively decomposing the energetic force, driving force for the damage, into isotropic and anisotropic parts. Distinct fracture energies were introduced for isotropic and anisotropic parts and anisotropic damage field interpretation is used for the dispersed damage field. In addition, an anisotropic geometric resistance expression has been added to the theory, which regulates the crack length scale distribution in different directions, to ensure that geometric constraints are taken into account in the direction of crack propagation. The coupled problem is solved using a one-pass operator-splitting algorithm composed of a mechanical predictor step that updates the displacement field and a crack evolution step that updates the damage field. Representative numerical examples are devised for crack initiation and propagation in Carbon-Fiber-Reinforced Polymeric (CFRP) composites. Model parameters are obtained by fitting the set of experimental data reported in the literature to the predicted model response; the finite element results capture the effect of anisotropy in stiffness and strength both qualitatively and quantitatively. The proposed approach and its algorithmic implementation validated by Mixed Mode Bending (MMB) test results of APC2-prepreg unidirectional (UD) laminate. The success of the model in capturing different modes of failure and the ability to simulate interface effects have been demonstrated for double fix–end supported CFRP composite beam subjected to transverse load.