Inverse method for parameter optimisation in superalloy tertiary creep equations

Abstract

A new methodology has been devised for the optimisation of material parameters in equations that govern the tertiary creep deformation of single crystal superalloys. Such information is ordinarily extracted by conducting a series of mechanical experiments over a range of appropriate environmental conditions, e.g. at various fixed stresses and temperatures. However, the current technique allows material behaviour to be characterised from a limited number of tests of short duration performed under non-uniform stress. A strategy is presented in which the time dependent strain response under a distributed stress gradient is measured using a novel testpiece geometry incorporating a concave gauge length profile. Spatial strain distribution is determined by accurate post-deformation measurement of specimen shape. Both spatial and temporal deformation are then simulated using a well founded mechanistic damage model, and the agreement between model results and experimental data is optimised by systematic perturbation of model parameters using the Nelder - Mead direct search method, i.e. an inverse modelling approach is applied. The overall strategy has been successfully validated for SRR99 by direct comparison with a database of more conventional tensile creep data, but it has the potential for broad application in cost effective and efficient prototyping of new materials generally.