A Novel Metamodeling Approach for Time-Temperature Parameter Models

The classic approach to the prediction of stress-rupture involves using time-temperature parameters. Since 1952 with the introduction of the Larson-Miller parameter, many different time-temperature parameters have been introduced. There have been several attempts to generalize the many time-temperature models into a single “metamodel”. A common approach is to use a pre-defined stress-parameter function that is force fit to the submodels leading to biased predictions. In this study, a novel metamodeling approach is applied to derive a single metamodel that incorporates twelve time-temperature parameters (eight existing and four new time-temperature parameter models are exploited). This metamodel allows the instantaneous and efficient evaluation of all twelve submodels simultaneously. The metamodel and twelve submodels are evaluated against four isotherms of alloy P91 stress-rupture data in the form of time-temperature parameterization isostress lines, points of convergence, and master curves for each model. A statistical analysis of the uncertainty of stress-rupture predictions with respect to the experimental uncertainty of the experimental database is performed. A key characteristic of time-temperature parameters is the regression analysis of stress versus the calculated parameter. An analysis of stress-parameter functions is performed to determine the optimal function that produces physically realistic predictions. Finally, a guideline to the selection of the most physically realistic time-temperature parameter and stress-parameter function for a given material is presented.