Simplified elastic models for disk-shaped precipitates

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A procedure is presented to calculate the elastic displacement fields found in the early stages of coherent precipitation in age hardenable alloys. The procedure is designed for a subsequent calculation of X-ray diffraction profiles. Displacement fields from precipitates of finite size having local order may be examined with reduced computer times. Point sources consisting of a doublet combined with a spherical field are distributed over the plane of a disk shaped precipitate. The relative strength of this combination is adjustable; however, the total strength is scaled to be in agreement with lattice parameter data. An empirical correction for elastic anisotropy, is guided by Green's function calculations. Examples are given for calculating fields from single disks and stair step pairs. These calculations may be carried out with reduced computer time. This is made possible by reducing a large number of uniformly distributed point sources to an optimum number having weighted strengths and special locations throughout the plane of a disk. In order to assess directional effects and more readily relate the displacements to diffraction data, projected displacements are used. The tetragonality of the interplanar d-spacings is examined within zones of severe deformation located in the immediate vicinity of the precipitate.

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