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 super alloy with a high volume fraction of gamma'. The structure is modeled as a simple cubic array of gamma' cubes separated by thin sheets of gamma'. During rafting, the gamma' particles are constrained to remain tetragonal prisms. For tension along a cube axis, the driving force is proportional to the product of the tension delta, the fractional difference delta of lattice parameters of gamma' and gamma and the fractional difference m of their elastic constants C(11)- C(12). As in the calculation of Pineau for an isolated spheroid, needles are formed when this product sigma delta m is positive. Two- and three-dimensional systems behave similarly. The initial plastic strain in gamma' is anelastic and in principle reversible. When the plastic strain exceeds m delta, platelets perpendicular to the stress axis are formed if the product sigma delta is negative.