Life Fraction Hardening Applied to a Modified Theta Projection Creep Model for a Nickel-Based Super-Alloy
This paper presents the application of a life fraction hardening rule to the analytical calculation of creep in hot section components. Accurate prediction of creep is critical to assuring the mechanical integrity of heavy-duty, industrial gas turbine (IGT) hardware. The accuracy of such predictions depend upon both the creep models assumed and how those models are implemented in a finite element solution. A modified theta projection creep model for a nickel-based super alloy was presented in a previous paper as an accurate simulation of creep behavior [1]. Application of such a user defined creep law depends upon definition of a hardening rule in the form of either an explicit or an implicit integration scheme in order to calculate incremental strains during any time increment. Time hardening is the simplest and least computationally intensive of the two most common hardening rules, but does not correctly show the effect of changing stresses or temperatures. Strain hardening may provide the most accurate solution, but the creep models are too complex to invert, which results in highly iterative and computationally intensive solutions. A life fraction hardening rule has been presented in other works [2] as a compromise between time hardening and strain hardening. Life fraction hardening is presented here as a highly efficient and accurate means of calculating incremental creep strain when applied to a modified theta projection creep model. A user creep subroutine was defined using a state variable to represent the strain life fraction at any time. By using the time to tertiary creep as the denominator for the life fraction, no new material constants are needed to relate to creep failure. The start of tertiary creep is effectively considered to be a failure. Additional design insight can be provided through the inclusion of other state variables to calculate temperature margins at current conditions. Material testing with changing stress levels will be used to help validate the technique. A simplified example of the technique is presented in the paper. More accurate creep predictions allow our company to improve the structural integrity of its turbine blades and vanes.Copyright © 2014 by Alstom Technologie AG
Effect of Temperature Variation on the Long-Time Rupture Strength of Steels

 This paper presents a method of computing the factor of safety of a structural member with reference to a stated life, when operating under stress at high temperature when the temperature varies or when the stress varies moderately according to some definite pattern. The formulas presented herein are based on the supposition that the expenditure of each particular fraction of the life span at elevated temperature is independent of and without influence upon the expenditure of all other fractions of the life to rupture. The author makes no claim that this assumption is wholly true. The suggested procedure is offered simply to provide a means for making engineering estimates with some greater validity than always to assume that the worst conditions are present all the time. The desirability of taking account of certain additional influences which may differ from one material to another is recognized.
Deformation and fracture at elevated temperatures
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