EXPLORATION OF FRACTURE ANISOTROPY, MULTISCALE MECHANICS AND DYNAMIC FRACTURE THROUGH PHASE-FIELD METHOD

Abstract

Understanding fracture behaviour is essential for designing critical components. Complexity of the problem often necessitates numerical modelling of the material and structure, rather than analytical investigation. Of the different numerical methods for modelling fracture, phase-field method (PFM) has been proved to be a robust approach. The ability of this method to capture complexities for fracture process such as crack initiation, propagation, branching and merging distinguishes this method from other alternatives such as extended finite element method (X-FEM), cohesive zone method, gradient enhanced damage models etc. PFM finds applications in myriads of mechanics problems, such as brittle fracture, quasi-brittle fracture, ductile fracture, fracture in heterogeneous materials, etc. In this thesis, we explore PFM in studying fracture behaviour in architected materials and metals under quasi-static and dynamic loading. In an attempt to efficiently model fracture in architected lattice materials a phase-field fracture model for shallow beams, an assemblage of which forms the lattice, is proposed. This approach introduces a simple hypothesis for the variation of phase-field across the beam crosssection along with the standard Euler-Bernoulli type kinematic assumptions to reduce the three-dimensional problem to a one-dimensional one. Subsequently, a computational approach is proposed to determine the direction-dependent fracture toughness of architected materials. To enable a straightforward determination of the macroscopic toughness of the homogenized material, the principles of multiscale mechanics and phase-field modelling of fracture is used. The most important feature of the computational scheme is the loading arrangement which ensures the crack propagation along a macroscopic straight line in the same direction as the initial notch, irrespective of the material’s orientation. Forcing the crack propagation in a specific direction, we extract the toughness of the homogenized material in that direction by utilizing the equivalence of dissipation in micro and macro scales. Incorporation of direction-dependent fracture toughness requires a suitable phase-field fracture model, multi-phase-field formalism being one such candidate. However, the existing formulation in the literature consists of a few significant inconsistencies which we bring out next and propose a consistent multi-phase-field theory. The proposed model introduces a new degradation function which leads to an unambiguous definition of damage, and an analytical expression for modelled fracture toughness. Finally, dynamic fracture in metals is studied. A non-equilibrium thermodynamics model of viscoplasticity coupled with damage is presented. Keeping in view the experimentally observed failure mode transitions, e.g. brittle to ductile, under dynamic loading condition, the emphasis of the present work has been to endow the formulation with capability of modelling such transitions in a physically consistent manner. Within a framework of internal variables, the current formulation tracks the effect of isotropic viscoplasticity with accumulated plastic strain, and a scalar phase field variable traces the degradation of the material caused by either tensile cracking or shear-induced failure.