On the shape evolution of a two-dimensional coherent precipitate with a general misfit strain

For a coherent precipitate in two dimensions, any misfit strain, i.e. stress-free transformation strain is expressed with two principal terms of epsilon and eta. Therefore, all the transformation problems can be divided into three cases, (a) a purely dilatational case with epsilon = eta; (b) a tetragonal case of opposite signs with epsilon eta less than or equal to 0; and (c) a tetragonal case of same signs with epsilon(eta) > 0. For case (a) with purely dilatational misfit strain, if elastic anisotropy is uniform, a soft particle takes on a plate-like shape along an elastically soft direction. A hard particle, however, tends to take on a shape of high symmetry with edges parallel to elastically soft directions. A homogeneous particle tends to follow the hard particle case in the early stage of evolution, but eventually changes to the pattern of a soft particle. For case (b) with tetragonal misfit strain of opposite signs, there exists always a preferred orientation at an angle of tan(-1) ( -eta/epsilon)(1/2) With respect to a principal direction. This is true whether the particle is soft or hard, i.e. regardless of inhomogeneity. The third case (c), a misfit strain of same signs with epsilon eta > 0, represents a combination of the previous two. A hard particle of this case tends to change its morphology from a plump shape to a somewhat elongated one with its major axis parallel to the preferred orientation due to the tetragonal part of opposite signs. A soft particle becomes a plate lying along a direction between an elastically soft direction and the preferred orientation. (C) 2000 Elsevier Science S.A. All rights reserved.