Search

Homophase misorientation spaces are investigated with a focus on the effect of symmetry operations on their topology and their minimum embedding dimensions in Euclidean space. Whereas the topology of rotation space is well established and requires a minimum of five variables for a one-to-one and continuous mapping, the spaces of orientations and misorientations are quotient spaces of the rotation space and are obtained by applying various equivalence relations. The equivalence relations for orientation spaces only involve the rotational symmetries of the underlying crystals. These spaces are classified under the three-dimensional manifolds called the spherical 3-manifolds, which have a non-trivial fundamental group, are not simply connected spaces, and do not embed in three-dimensional Euclidean space. In the case of homophase misorientation spaces, however, in addition to rotational symmetry operations there is a further 'grain exchange symmetry', which is shown to simplify the topology considerably. In some important cases this symmetry also reduces the number of Euclidean dimensions required to embed these misorientation spaces. The homophase misorientation spaces for the dihedral point groups D2(222), D4(422) and D6(622), the tetrahedral point group T(23), and the octahedral group O(432) are all found to be embeddable in only three dimensions, two dimensions less than required for rotations. Hence, these misorientation systems can be represented using three variables in a one-to-one and continuous manner. [ABSTRACT FROM AUTHOR]

A combined program of experiments and simulations is used to study the problem of cyclic indentation loading on metallic glasses. The experiments use a spherical nanoindenter tip to study shear band formation in three glasses (two based on Pd and one on Fe), after subjecting the glass to cycles of load in the nominal elastic range. In all three glasses, such elastic cycles lead to significant increases in the load required to subsequently trigger the first shear band. This cyclic hardening occurs progressively over several cycles, but eventually saturates. The effect requires cycles of sufficient amplitude and is not induced by sustained loading alone. The simulations employed a new shear transformation zone (STZ) dynamics code to reveal the local STZ operations that occur beneath an indenter during cycling. These results reveal a plausible mechanism for the observed cyclic hardening: local regions of confined microplasticity can develop progressively over several cycles, without being detectable in the global load-displacement response. It is inferred that significant structural change must attend such microplasticity, leading to hardening of the glass. [ABSTRACT FROM AUTHOR]