Owing to continuous miniaturization, many modern high-technology applications such as medical and optical devices, thermal barrier coatings, electronics, micro- and nano-electro mechanical systems (MEMS and NEMS), gems industry and semiconductors increasingly use components with sizes down to a few micrometers and even smaller. Understanding their deformation mechanisms and assessing their mechanical performance help to achieve new insights or design new material systems with superior properties through controlled microstructure at the appropriate scales. However, a fundamental understanding of mechanical response in surface-dominated structures, different than their bulk behaviours, is still elusive. In this thesis, the size effect in a single-crystal Ti alloy (Ti15V3Cr3Al3Sn) is investigated. To achieve this, nanoindentation and micropillar (with a square cross-section) compression tests were carried out in collaboration with Swiss Federal Laboratories for Materials Testing and Research (EMPA), Switzerland. Three-dimensional finite element models of compression and indentation with an implicit time-integration scheme incorporating a strain-gradient crystal-plasticity (SGCP) theory were developed to accurately represent deformation of the studied body-centered cubic metallic material. An appropriate hardening model was implemented to account for strain-hardening of the active slip systems, determined experimentally. The optimized set of parameters characterizing the deformation behaviour of Ti alloy was obtained based on a direct comparison of simulations and the experiments. An enhanced model based on the SGCP theory (EMSGCP), accounting for an initial microstructure of samples in terms of different types of dislocations (statistically stored and geometrically necessary dislocations), was suggested and used in the numerical analysis. This meso-scale continuum theory bridges the gap between the discrete-dislocation dynamics theory, where simulations are performed at strain rates several orders of magnitude higher than those in experiments, and the classical continuum-plasticity theory, which cannot explain the dependence of mechanical response on a specimen s size since there is no length scale in its constitutive description. A case study was performed using a cylindrical pillar to examine, on the one hand, accuracy of the proposed EMSGCP theory and, on the other hand, its universality for different pillar geometries. An extensive numerical study of the size effect in micron-size pillars was also implemented. On the other hand, an anisotropic character of surface topographies around indents along different crystallographic orientations of single crystals obtained in numerical simulations was compared to experimental findings. The size effect in nano-indentation was studied numerically. The differences in the observed hardness values for various indenter types were investigated using the developed EMSGCP theory.

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.