Inverse method for parameter optimisation in superalloy tertiary creep equations

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

Characterization of superalloy tertiary creep by inverse modeling

The design of new alloys for high-temperature engineering applications frequently requires the rapid characterization of material mechanical behavior, particularly creep resistance. Such information is ordinarily extracted by conducting a series of time-consuming and costly experiments under uniform load or stress. To expedite material prototyping we have developed a technique that allows estimation of the stress-dependence of material behavior from a single, short-duration, tensile test performed under non-uniform stress. The approach involves inverse modeling of experiments conducted using a novel tensile testpiece with a concave gauge-length profile. Temporal strain and post-deformation spatial strain distribution are simulated using a well-founded mechanistic creep damage model, and agreement between model results and experimental data is optimized by systematic perturbation of model parameters. This inverse strategy has been validated by examining high temperature tertiary creep in three generations of nickel superalloy single-crystal materials, but has wider application to materials characterization generally

Parameter optimisation in constitutive equations for hot forging

Various methods for parameter optimisation in constitutive equations applied to the hot deformation of a popular alpha-beta titanium alloy have been examined. The use of direct search and gradient methods are shown to be effective, even with a limited dataset, and reliable confidence limits can be computed in each case. However, a hybrid approach, whereby genetic algorithms are used to find an initial parameter starting point, and then a direct search (simplex) method is applied to obtain a global minimum, is particularly promising. For comparison, an artificial neural network approach, which does not require the use of any constitutive equations, has also been implemented

Modeling and measurement of residual stresses in a forged IN718 superalloy disc

The residual stresses present in a quenched IN718 aeroengine compressor disc forging have been characterized using neutron diffraction and the results compared to those obtained from a finite element (FE) model for the quenching process. The ~40 kg forging had a diameter of ~400 mm and a maximum thickness of ~45mm. Neutron path lengths of up to 60 mm were required to record strain components at the deepest points within the material. The residual hoop and radial stresses measured are generally compressive at the surface, up to 600 MPa and tensile at depth, up to 400 MPa, whilst the radial stresses are generally small. The deviatoric stresses are generally <150 MPa. FE model predictions of the residual stress are reasonable agreement with the measured values

Creep-constitutive behavior of Sn-3.8Ag-0.7Cu solder using an internal stress approach

The experimental tensile creep deformation of bulk Sn-3.8Ag-0.7Cu solder at temperatures between 263 K and 398 K, covering lifetimes up to 3,500 h, has been rationalized using constitutive equations that incorporate structure-related internal state variables. Primary creep is accounted for using an evolving internal back stress, due to the interaction between the soft matrix phase and a more creep-resistant particle phase. Steady-state creep is incorporated using a conventional power law, modified to include the steady-state value of internal stress. It is demonstrated that the observed behavior is well-fitted using creep constants for pure tin in the modified creep power law. A preliminary analysis of damage-induced tertiary creep is also presented