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.

Magnesium alloys, owing to their low density and high specific strength, are potential candidates for structural applications in automotive and aerospace industry. While considerable research effort has been devoted in recent years to understand deformation twinning in these alloys and Mg single crystals, only few studies have been conducted on their fracture behavior. This issue assumes importance since some investigations have shown that Mg alloys may possess low fracture toughness (less than Al alloys). Therefore, a combined experimental and numerical study of fracture in Mg single crystals under mode-I loading is performed in this work. The fracture experiments are conducted using three point bend(TPB) specimens inside a scanning electron microscope(SEM) stage equipped with specially designed fixtures. Three crystallographic orientations are considered where c-axis [0001] is along the normal to the flat surface of the notch in the first two orientations, while in the third it is aligned with the notch front. In-situ electron back scattered diffraction (EBSD) observations are made in the region around the notch root to monitor the evolution of tensile twinning on the specimen free surface. Along with EBSD, optical metallography, fractography and surface profilometry are also performed on the specimens to obtain a comprehensive understanding on the micromechanics of fracture in Mg single crystals. From the EBSD data, it is noticed that all the orientations show profuse tensile twinning of {1012}-type. Further, in the first two orientations, basal and prismatic slip traces are identified along with secondary basal slip inside the twins. The growth of the most prominent twin is monitored as a function of load and it is found that its width saturates at around 120 -150 μm, while twins continue to nucleate farther away to accommodate plastic deformation. The 3D nature of twinning is examined by comparing distribution of twin traces and the average twin volume fraction at the free surface and the mid-plane. It is noted that in all the orientations crack initiation occurs before the attainment of peak load and the crack grows stably along twin-matrix interface. Further, zigzaging of the crack path occurs due to deflection of the crack at the twin-twin intersections. It is found that profuse tensile twinning is an important energy dissipating mechanism that enhances the toughness of the material. Indeed, the experimental results show that the energy release rate J versus load histories corroborate with evolution of average twin volume fraction around the notch root. In order to gain further insights on the mechanics of fracture in Mg single crystals, 3D finite element simulations are carried out using a crystal plasticity framework, which includes crystallographic slip and twinning. The predicted load-displacement curves, slip traces and tensile twinning activity from finite element analysis are in good corroboration with the experimental observations. The numerical results are used to understand the 3D nature of the crack tip stress, plastic slip and twin volume fraction distributions near the notch root. The occurrence of tensile twinning in all three orientations is rationalized from the distribution of nor-mal stress ahead of the notch tip. In particular, compressive normal stress beyond the plastic hinge point causes out-of-plane bulging that is accompanied by tensile twinning for the third orientation in which the c-axis is aligned along the specimen thickness. The above behavior emphasizes the importance of tensile twinning since this orientation has relevance to polycrystalline Mg alloys that have a basal texture.