Constraint Effects On Stationary Crack Tip Fields In Ductile Single Crystals

Abstract

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).