Approximation of the Strain Field Associated With an Inhomogeneous Precipitate—Part 2: The Cuboidal Inhomogeneity

Abstract

The modified equivalency and integral equation methods for determination of the constrained strain field associated with a precipitate that has undergone a dilatational stress-free transformation strain as developed in Part 1, are applied to the case of a cuboidal inhomogeneity within an isotropic matrix. Agreement between the two methods is good for small and moderate differences in the shear moduli between precipitate and matrix. For large differences in the shear moduli, some divergence is observed in that fluctuations in the constrained strain field become quite pronounced near the cube edge and corner when considering the integral equation method. Although some error is inevitable due to the cutoff of higher-order terms in the Taylor series expansion, the modified equivalency method yields fair results under such circumstances. With the latter method, the constrained strain field of a cuboid is analyzed as a function of position and orientation. Although the strain field behaves as expected in the central regions of the cube in that the harder the precipitate the larger the constrained strain, its behavior becomes complicated as the precipitate-matrix interface is approached, demonstrating a strong dependency on precipitate rigidity. As a result, the dilatation in the inhomogeneous cuboidal precipitate is found not to be a constant as contrasted with the homogeneous case.