In order to understand and predict the fracture behaviour of polycrystalline materials from a fundamental perspective, it is important to first investigate plastic deformation at a crack tip in a ductile single crystal. In this context, it may be noted that when the crack opening displacement is much less than the grain size, the crack tip fields are entirely contained in a single grain. Further, some key structural components are being fabricated in single crystal form. For example, blades in high pressure turbines of jet engines are made of single crystals of Nickel-based superalloys. In view of the above considerations, a combined experimental and computational study of the crack tip stress and strain fields in FCC single crystal is carried out in the present work. The effect of constraint level, which is characterized by the T-stress under mode I, plane strain small scale yielding conditions, on the near-tip response is first analyzed for a crystal orientation in which the crack plane coincides with (010) and ¯the crack front lies along[101]direction. A family of finite element solutions are generated by employing a boundary layer approach within continuum crystal plasticity framework. The results show that the near-tip deformation field, especially the development of kink and slip shear bands, is sensitive to the constraint level. On imposition of negative T-stress, a significant drop in the hydrostatic stress level is noticed in the region ahead of the tip. This suggests loss of crack tip constraint with negative T-stress, which is akin to isotropic plastic solids. The reason for the loss of crack tip constraint is traced to the occurrence of an elastic sector near the notch tip. The results also show that a two-parameter (such as K-T or J-Q) characterization of near-tip fields is necessary to accommodate different constraint levels in FCC single crystals. The results of the boundary layer formulation are used to guide the construction of asymptotic solutions near the crack tip corresponding to various constraint levels in elastic-perfectly plastic FCC single crystal. Two families of alternate asymptotic solutions are constructed by introducing an elastic near-tip sector. These families of stress fields are parameterized by the normalized opening stress ahead of the tip, τA22/τo, where τo is the critical resolved shear stress, and a quantity (p) which characterizes the coordinates of the point where elastic unloading commences in stress plane. The results show that the stress distribution corresponding to each member of these families, as well as the trajectories in stress plane as the crack tip is traversed, agree well with finite element results for a certain value of T-stress. In order to validate the above numerical and analytical solutions, the nature of crack tip deformation in aluminium single crystals is examined experimentally in a high constraint three point bend (TPB) specimen and in a low constraint single edge notch tensile (SENT) geometry. These experiments provide evidence, based on in-situ Electron Back Scattered Diffraction (EBSD) of the existence of kink shear bands (involving lattice rotation) exactly as predicted by Rice [J.R. Rice, Mech. Mater. 6 (1987) 317] and the present finite element analysis. The experimental investigation of a low constraint SENT geometry is also supplemented by 3D finite element computations based on continuum crystal plasticity. These computational results enable assessment of 3D effects near the tip. Finally, the effects of different lattice orientations (especially ones for which the slip systems are not symmetric with respect to the notch line) on the near-tip fields are studied pertaining to various constraint levels. The results obtained for different orientations show that the near-tip deformation field is sensitive to the constraint level. The stress distribution and the size and shape of plastic zone near the notch tip are also strongly influenced by the level of T-stress. It is clearly established that ductile single crystal fracture geometries, would progressively lose stress triaxiality with increase in negative T-stress irrespective of lattice orientation. Also, the near-tip field is shown to be part of a family which can be characterized by two parameters (such as K – T or J - Q).

The failure mechanism in ductile materials involves void nucleation, their growth and subsequent coalescence to form the fracture surface. The voids are generated due to fracture or debonding of second phase particles or at slip band intersections. The triaxial stress field prevailing around a crack tip and in the necking region strongly influences the growth of these voids. In the initial stages of deformation, these microscale voids are often sufficiently small so that they exist entirely within a single grain of a polycrystalline material. Further, single crystals are used in high technology applications like turbine blades. This motivates the need to study void growth in a single crystal while investigating ductile fracture. Thus, the objectives of this work are to analyze the interaction between a notch tip and void as well as the growth and coalescence of a periodic array of voids under different states of stress in ductile FCC single crystals. First, the growth of a cylindrical void ahead of a notch tip in ductile FCC single crystals is studied. To this end, 2D plane strain finite element simulations are carried out under mode I, small scale yielding conditions, neglecting elastic anisotropy. In most of these computations, the orientation of the FCC single crystal is chosen so that notch lies in the (010) plane, with notch front along the [101] direction and potential crack growth along [101]. This orientation has been frequently observed in experimental studies on fracture of FCC single crystals. Three equivalent slip systems are considered which are deduced by combining three pairs of 3D conjugate slip systems producing only in-plane deformation. Attention is focused on the effects of crystal hardening, ratio of void diameter to spacing from the notch on plastic flow localization in the ligament connecting the notch and the void as well as their growth. The results show strong interaction between slip shear bands emanating from the notch and angular sectors of single slip forming around the void leading to intense plastic strain development in the ligament. However, the ductile fracture processes are retarded by increase in hardening of the single crystal and decrease in ratio of void diameter to spacing from the notch. In order to examine the effect of crystal orientation, computations are performed with an orientation wherein the three effective slip systems are rotated about the normal to the plane of deformation. A strong influence of crystal orientation on near-tip void growth and plastic slip band development is observed. Further, in order to study the synergistic, cooperative growth of multiple voids ahead of the notchtip, an analysis is performed by considering a series of voids located ahead of the tip. It is found that enhanced void growth occurs at higher load levels as compared to the single void model. Next, the growth and coalescence of a periodic array of cylindrical voids in a FCC single crystal is analyzed under different stress states by employing a 2D plane strain, unit cell approach. The orientation of the crystal studied here considers [101] and [010] crystal directions along the minor and major principal stress directions, respectively. Three equivalent slip systems, similar to those in the notch and void simulations are taken into account. Fringe contours of plastic slip and evolution of macroscopic hydrostatic stress and void volume fraction are examined. A criterion for unstable void growth which leads to onset of void coalescence is established. The effects of various stress triaxialities, initial void volume fraction and hardening on void growth and coalescence is assessed. It is observed that plastic slip activity around the void intensifies with increase in stress triaxiality. The macroscopic hydrostatic stress increases with deformation, reaches a peak value and subsequently decreases rapidly. An increase in stress triaxiality enhances the macroscopic hydrostatic stress sustained by the unit cell and promotes void coalescence. The stress triaxiality also has a profound effect on the shape of the void profile. The values of critical void volume fraction and critical strain, which mark onset of void coalescence, decrease within crease in stress triaxiality. However, the onset of void coalescence is delayed by increase in hardening and decrease initial void volume fraction.

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.