Two-dimensional analysis on elastic strain energy due to a uniformly eigenstrained supercircular inclusion in an elastically anisotropic material

In Ni-base alloys, the shape of gamma' precipitates with purely dilatational misfit strains often becomes an intermediate shape between the sphere and cuboid. The present study provides a new two-dimensional model to understand the elastic strain energy caused by the intermediate precipitate shape. A two-dimensional inclusion problem is solved for an inclusion shape described by (x(1)(2)/a(2))(p/2) + (x(2)(2)/a(2))(p/2) less than or equal to 1 (p greater than or equal to 2). This shape that may be called a supercircle becomes a circle and a square when p = 2 and p --> infinity, respectively. intermediate shapes between the circle and square can be expressed by choosing appropriate values of p. Using the two-dimensional Green function of elasticity, the elastic states are examined for an infinitely extended material containing a uniformly eigenstrained supercircular inclusion. Anisotropic elastic moduli of cubic crystals are considered as those of the material containing the supercircular inclusion. The averaged Eshelby tensors of the supercircular inclusions are calculated as a function of p and the anisotropic elastic moduli. Using the averaged Eshelby tensors calculated, the elastic strain energy due to the supercircular inclusion with purely dilatational eigenstrains and its variation with the shape change from circular to square are discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.