Study on new creep equation using discrete cosine transform for high temperature materials

Hideo Hiraguchi

doi:10.1016/j.heliyon.2019.e02619

Abstract

For an equation representing creep strain-time relationship curves of high temperature materials, the equations which represent from the primary creep region to the tertiary creep region using exponential functions such as the modified θ projection [3] have already been proposed. However, the estimated values by the modified θ projection don't necessarily coincide with the measured values, and deviations occur between the estimated values and the measured values [8]. Then in this paper, we propose a new creep equation using the Discrete Cosine Transform (DCT). According to this equation, all the estimated values coincide with the measured values and each interpolated value between the measured points gives a reasonable value. Therefore it is possible to express a creep curve quite well from the primary creep region to the tertiary creep region by using the DCT.

Highlights

IntroductionEquations using power law such as Bailey-Norton method [1, 2] (Eq 1) and exponential functions like the modified θ projection [3] (Eq 2) have already been proposed as equations representing creep strain-time relationship curves of high temperature materials for such as boilers and turbines
We propose an unprecedented new equation using the discrete cosine transform that can express from the primary creep region to the tertiary creep region instead of the above Eqs. (1) and (2)
From the results of this research and the author's previous published papers [8, 9], it was found that the discrete cosine transform and series, which is an improved version of the Fourier transform, is suitable for the creep equation and the creep strain rate equation

Summary

Introduction

Equations using power law such as Bailey-Norton method [1, 2] (Eq 1) and exponential functions like the modified θ projection [3] (Eq 2) have already been proposed as equations representing creep strain-time relationship curves of high temperature materials for such as boilers and turbines. It is known to display the entire creep curve from the primary creep region to the tertiary creep region. We propose an unprecedented new equation using the discrete cosine transform that can express from the primary creep region to the tertiary creep region instead of the above Eqs. The content of this research is a slightly modified version of what was presented at the 56th Symposium on Strength of Materials at High Temperatures of the Society of Materials Science, Japan in 2018 [9]

Ni based superalloy

About discrete cosine transform

Application to creep equation

Calculation and consideration of creep strain rate

Stress dependence of discrete cosine transform

Discussion and conclusion