Abstract
It is well-known that the creep equation obtained by the modified θ projection [2] describes well from the primary creep region to the tertiary creep region. However, unlike the power law such as that applied by the Bailey-Norton method, the stress variables and temperature variables are not found in the equation coefficients. Therefore, the users of this equation must find functions containing temperature variables and stress variables to display the equation coefficients. Thus, among the three coefficients A, α, and B included in the equation of the modified θ projection, the rate constant α, which exerts the largest influence on the curvature and the minimum creep strain rate of the creep curve [3], was selected as the object of investigation. Moreover, by considering the Cr-Mo-V steel and the Ni-based superalloy as examples, the expression of α was investigated. As a result, it was found that the discrete cosine transform and series can be applied not only to the coefficients of the creep equation but also to the creep equation itself. It is very important that the Fourier transform, which is considered to be applicable only to periodic functions, can be applied to non-periodic functions like a creep equation or its coefficients without apodizing such as windowing [9].
Highlights
The modified θ projection, which is one of the creep equations, is often used to predict the creep damage rate at each temperature and pressure of gas turbine materials by using interpolation and extrapolation
1) If the calculated value must be consistent with the value at all measured points, and if a waving phenomenon such as a sine curve does not occur, the N-Spline function of Eq (3) is suitable for the expression of the rate constant α, which is included in the modified θ projection (Eq (1)) for the creep constitutive equation
2) If the calculated value does not need to coincide completely with the measured value, and an accurate estimation must be made in the region above the middle stress, the modified θ projection type of Eq
Summary
The modified θ projection, which is one of the creep equations, is often used to predict the creep damage rate at each temperature and pressure of gas turbine materials by using interpolation and extrapolation. As described later, the values of α obtained by interpolation from the linear relationship in the high stress range are plotted far away from the measured values, in comparison with other expected values that can be calculated without using the natural logarithm. In order to apply the nonlinear least square method to the measured values, it was necessary to find a function similar to the curve drawn with the measured values and minimize the sum of the squares of the residuals. In this paper, we present the various expressions for α calculated without using the natural logarithm to achieve a more accurate interpolation prediction.
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