The objective of this thesis is to study the fracture behavior of bulk metallic glasses. For this purpose, detailed finite element investigation of the mode I and mixed mode (I and II) stationary crack tip fields under plane strain, small scale yielding conditions is carried out. An implicit backward Euler finite element implementation of the Anand and Su constitutive model [Anand, L. and Su, C., 2005, J. Mech. Phys. Solids 53, 1362] is used in the simulations. The effects of internal friction (μ), strain softening, Poisson's ratio (ν) and elastic mode mixity (Me) on the near-tip stress and deformation fields are examined. The results show that under mode I loading, a higher μ leads to a larger normalized plastic zone size and higher plastic strain level near the notch tip, but causes a substantial decrease in the opening stress. The brittle crack trajectories and shear band patterns around the notch are also simulated. An increase in ν reduces the extent of plastic zone and plastic strain levels in front of the notch tip. The results from mixed mode simulations show that increase in the mode II component of loading dramatically increases the maximum plastic zone extent, lowers the stresses and significantly enhances the plastic strain levels near the notch tip. Higher μ causes the peak magnitudes of tensile tangential stress to decrease. The implications of the above results on the fracture response of bulk metallic glasses are discussed. The possible variations of fracture toughness with mode mixity predicted by employing two simple fracture criteria are examined. Finally, mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass are performed. It is found that the fracture toughness increases with Me and Jc under mode I is higher than that under mode II loading by a factor of 4. The operative failure mechanism and fracture process zone size are discerned based on observations of incipient crack growth and fractographs. Lastly, a fracture criterion is proposed which predicts the experimentally observed variation of fracture toughness with mode mixity.

An understanding of crack tip fields and fracture mechanisms in single crystals can help in developing better polycrystalline alloys and manufacturing processes. To this end, the effects of loading rate, material inertia and strain rate sensitivity on crack tip fields and their influence on fracture mechanisms in FCC single crystals are examined in this work by performing finite element analysis. It is shown that, in the absence of inertial effects, high loading rates elevate the stresses ahead of a crack tip and decrease the plastic strains in rate dependent single crystals. Also, it is found that the quasi-static near-tip stress field can be adequately characterized by the energy release rate J and a constraint parameter Q. Similar two-parameter characterization is possible even under dynamic loading. It is observed that if a suitable reference solution is used, the role of inertia manifests as a loss of constraint with increasing loading rate irrespective of strain rate sensitivity and lattice orientation. Thus, at very high loading rates, inertial effects oppose the role of rate sensitivity and cause a decrease in stresses near the tip. The relative influence of these two factors depends on rate sensitivity index. For a mildly rate dependent single crystal, the predicted cleavage fracture toughness remains constant up to a certain loading rate and thereafter increases sharply. On the other hand, for a strongly rate dependent single crystal, fracture toughness drops initially up to a certain loading rate beyond which it increases marginally. The loss of crack tip constraint is found to retard the ductile fracture mechanisms of void growth and coalescence. However, this is dependent on lattice orientation. In-situ experimental observation of void growth near a notch tip also shows strong orientation dependence. In addition, 3D finite element results indicate though-thickness dependence of equivalent plastic slip and hydrostatic stress leading to variations in void growth along the thickness direction of the specimens. The predicted load-displacement curves, lattice rotation, slip traces and void growth using finite element analysis are found to be in good agreement with the experimental observations. Thus, the present study has provided an understanding of the role of several factors such as constraint level, rate sensitivity, material inertia, lattice orientation and 3D effects on the mechanics of fracture of ductile single crystals.

The presented dissertation thesis is focused, as the title suggests, on the analysis of stress state aspects of quasi-brittle fracture. That means the fracture of composite materials with cement matrix (such as concrete, mortar, plaster, etc.), ceramics and other composites. Used methods are based on the theory of multi-parameter linear elastic fracture mechanics, which highlights the importance of considering of several initial terms of Williams power series, approximating the stress and displacement fields in a cracked body, within conducted fracture analyses. Determination of values of coefficients of terms of this series, recalculated into the shape functions serving in most of the conducted stress state analyses, is performed via the so called over-deterministic method. Another tool for the problem solving is nonlinear fracture mechanics, represented primarily by the cohesive crack model, namely the crack band model implemented in the used ATENA software. For the backward reconstruction of stress field in the cracked bodies the application ReFraPro is used. The analytical part deals with various aspects of wedge-splitting test – from the boundary conditions, though various possibilities of nodal selection (required as input variables for the over-deterministic method) up to the advanced (automated) analysis of numerical model. Special chapter includes atypical test specimens designed for adjusting of various levels of constraint of stress and deformation at the propagating crack tip. The study of this geometry and also the subsequent detail analysis reveals important information for real experiments. Backward reconstruction of stress field presents analysis on suitable possibilities of nodal selections as inputs into the procedure of approximation of the crack tip fields and answers the question of the necessity of application of the multi-parameter linear elastic fracture mechanics for certain fracture analyses of specimens from quasi-brittle materials. The th