# An Alternative Method of Calibration and Prediction for The Theta-Projection Model

#### Abstract

The combustion induced high temperature-stress conditions of industrial gas turbines used in power generation causes turbine blades to wear and break after prolonged use. The need to predict turbine blade service life is ever increasing, leading to the development of several constitutive prediction models. It is necessary to design components for high-temperature/high-stress service such that creep failure does not occur during service life. For this reason, it is important to accurately predict creep life and understand the behavior of creep deformation leading to rupture. Several models have been expanded upon to improve their effectiveness for use with particular parametric data. One such model, popular for its flexibility, is the theta-projection model. The theta-projection model, developed by R. W. Evans in response to the point-prediction limitations of previous models, excels at fitting the graphical form of creep deformation plotted with time. The method of application proposed by Evans for interpolating and extrapolating predictions of creep deformation requires that the model constants be optimized using a least-square non-linear scheme with respect to an error function. These numerically optimized constants are used to establish an interpolation and extrapolation formula of temperature and stress. Once the interpolation/extrapolation formula has been established, theta constants can be derived for any temperature-stress condition. Though this form of numerical optimization generates constants that produce excellent fits to experimental data, the principal issue is that the numerical optimization process does not produce constants with a trend that is conducive to the interpolation/extrapolation formula. Using the proposed interpolation function, variations from constant to constant cause imprecise predictions. To address this prediction issue, three alterations to the theta projection method are proposed. Firstly, it is necessary to implement a method of calibration that produces a consistent, physically realistic trend of theta constants for use in prediction. An analytical approach to calibration is used to derive theta constants with respect to the experimental data used in calibration. As the behavior of the data changes with temperature and stress, so do the theta constants in a similar, more consistent manner. Secondly, an alternative interpolation/extrapolation function that relies on rupture time rather than temperature and stress is used to make predictions. The rupture time of test data follows a pattern as stress and temperature change. The theta-rupture time relationship results in more precise predictions than the original theta-stress/temperature relationship. Thirdly and finally, it is necessary to relate the rupture time to temperature and stress so that any prediction at desired conditions can be made. The Wilshire model includes an equation relating rupture time to temperature and stress. Applying this Wilshire equation is the final step in the modified theta-projection method. The modified theta-projection method is demonstrated using a database of creep deformation data for Alloy P91. It is determined that the method provides more reliable calibration, better functionalization, and predictions that are on par with the original theta method while requiring less constants to be calibrated.

#### Subject Area

Materials science|Mechanical engineering

#### Recommended Citation

Perez, Jimmy Jesus, "An Alternative Method of Calibration and Prediction for The Theta-Projection Model" (2019). *ETD Collection for University of Texas, El Paso*. AAI13885587.

https://digitalcommons.utep.edu/dissertations/AAI13885587