A two phase elastic–plastic self-consistent model for the accumulation of microstrains in Waspaloy

Abstract A two phase self-consistent scheme for the accumulation of elastic lattice strains in the nickel-base superalloy Waspaloy is presented. The microstructure is idealised as a set of randomly orientated anisotropic grains which are assumed to be spherical and embedded within a homogenous effective medium which is assigned the properties of the bulk. Each grain is modelled as a medium with the properties of identically aligned cubic γ -Ni with a spherical inclusion of γ ′-Ni 3 Al. The γ ′ is treated as an elastic anisotropic solid, and the γ is modelled as an elastic–plastic single crystal according to the Taylor–Bishop–Hill plasticity theory. The diffraction elastic constants and microstrains accumulated are compared with those found experimentally using neutron diffraction, as previously reported by Stone et al . The predictions are found to be adequate, and in particular the shift of load, as reflected in the microstrain, from the matrix to the precipitate between 3 and 10% plastic strain is reproduced. The implications of these results for the development and use of Reitveld-derived schemes for the measurement of bulk residual stress at spallation sources are discussed.