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

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.

Morphology of γ Precipitates in Ni-Rich γ'-Ni3 (Al,Ta)

The microstrueture of a commercial nickel-base alloy normally consists of a coherent, cuboidal precipitate of γ’ (alloyed Ni3Al) in a matrix of γ (Ni solid solution). Recently, Ham et al., working with the ternary alloy 78Ni-l8Al-4Ti (a/o), have shown that by appropriate heat treatment a completely novel microstrueture can be developed, in which the matrix is γ’ and the precipitate is platelet γ. The present study represents an extension of this work, and reports some new findings on precipitation of γ in γ’ in alloys similar in composition to the Ni-Al-Ti alloy but with Ta replacing Ti.The alloys used were solutionized in the range 2200-2400°F and aged at l600°F for 24hrs (giving ∼ 10 vol. percent of γ in γ’). According to our most recent findings, unlike the binary system, the solubility of γ’ for γ reaches a maximum at ∼ 2200°F in these alloys.