The thermodynamic driving force for rafting in superalloys

Abstract

Eshelby's energy-momentum tensor is used to provide an analytical expression for the driving force for rafting in the elastic regime in a superalloy with a high volume fraction of γ′. The structure is modelled as a simple cubic array of γ′ cubes separated by thin sheets of γ. During rafting, the γ′ particles are constrained to remain tetragonal prisms. For tension along a cube axis, the driving force is proportional to the product of the tension σ, the fractional difference δ of lattice parameters of γ′ and γ and the fractional differencem of their elastic constantsc11 – c12. As in the calculation of Pineau for an isolated spheroid, needles are formed when this productσδm is positive. Two- and three-dimensional systems behave similarly. The initial plastic strain in γ is anelastic and in principle reversible. When the plastic strain exceedsmδ, platelets perpendicular to the stress axis are formed if the product σδ is negative.