Shape evolution of an initially circular precipitate growing by diffusion in an applied stress field

The diffusional growth of a precipitate transforming under applied stress is analyzed to determine the shape evolution of the precipitate. The analysis is based on linearizing the precipitate shape about a circle. Because of applied stresses, a circle is a stable shape only when the shear moduli of the precipitate and the surrounding matrix are identical. Otherwise, one finds a non-circular base shape that depends on the applied stress and the elastic constants of both phases. For small precipitate sizes, the progression of growing base shapes are not self-similar, but define a path of fastest growing shapes. The base shapes become unstable at a critical radius and that depends on the elastic fields. In particular, the critical radius can be affected by elastic even when the shear moduli of the precipitate and matrix are equal.