Executive Summary : | Objective: Material fracture could set off catastrophic effects, importance is naturally accorded to predicting fracture with high precision under various loading conditions. Cracks typically imply material discontinuities and, therefore, problems of crack initiation or propagation do not directly fall under the ambit of continuum formulations without warranting a special treatment. At present, fracture mechanics based methods are being used for prediction of life and thus for scheduling inspection and repair. Fracture mechanics approach has obvious disadvantages like it is not capable of predicting crack initiation life. Problem of crack branching, stress corrosion and crack growth have to be dealt one at a time in an adhoc approach. The phase-field method, which has of late attracted interest, has the ability to predict spontaneous emergence and propagation of cracks with the added attraction of mathematical simplicity. Here, cracks are represented using a supplementary continuous scalar field variable called the phase-field (order) parameter, s ? [0, 1] used to distinguish between the damaged and undamaged parts of the material. This proposal is aimed at the development of methodologies to predict crack initiation and crack growth of structural components under fatigue loading. Summary: An approach based on phase-field modelling which can be used for a scientific prediction of crack initiation life and stable crack propagation life in structural components. Phasefield approach differs from fracture mechanics based methods where the crack is modelled discretely as it takes a small piece of the crack boundary, smooths it, and then approximates the fracture surface. It uses a diffusive crack approach instead of modelling the discontinuities of the crack. The diffusive crack zone is determined by a scalar variable that interpolates between either the broken or the unbroken state of the material. The phase-field variable will take the value 0 inside the crack surface and 1 away from the crack surface, therefore this variable, c, is only on the set [0,1]. Two of the proposed benefits of this approach are that the crack no longer has to follow a predetermined path which is seldom known in real-word problems and the solution is mesh independent after mesh of certain length scale. Crack nucleation, crack propagation under cyclic load and crack branching models based on phase-field approach near crack tip degradation of materials that can account for fracture growth under cyclic loads below the Griffith threshold. Gradual degradation near the crack tip has to be incorporated due to a cyclic load through a flow equation that decreases spatially. The degradation is obtained by varying parameters controlling the fracture toughness in the vicinity of the crack tip, with the phase and displacement fields relaxed to an energy minimum at each time step. The proposed approach is phenomenological and it is capable of reproducing the Paris’ law. Phase-field fatigue crack growth is obtained by introducing a dissipative term in the equation of generalized behavior. In addition to reproducing the Paris’ law, the proposed approach can be used to model the growth of multiple cracks in arbitrarily complex geometries under varied loading conditions. |