Analysis of Stress Relaxation Data by a Total Strain-Time Parametric Method

Abstract

A total strain-time parametric method representing long-time stress relaxation data with different total strains at specified temperatures has been proposed. Parametric analysis was made using the observed stress relaxation data up to about 10000hr for the total strains ranging from 0.10 to 0.25 percent on 1Cr-0.5Mo-0.25V, 12Cr-1Mo-1W-0.25V and 19Cr-9Ni-1.4Mo-1.4W-Nb high temperature bolting steels. The proposed total strain-time parameter (P_T) is as follows:
P_T=ε_T-b₀t^b₁ε_T^{a₀+a₁logt}
where ε_T is the total strain, t is the time, and a₀, a₁, b₀ and b₁ are constants.
The present parameter was deduced by the following analyses: (1) the plastic strain (ε_P) could be expressed by means of the equation, ε_P=kε_T^m (m and k are coefficients), because a linear correlation of the data points in the coordinates of log ε_P and logε_T was obtained; (2) both of the coefficients m and k in the above equation depended on time, and they were approximated by means of the respective equations, m=a₀+a₁logt and k=b₀t^b₁.
The observed stress relaxation data for each total strain, including the data of which the relaxation curves showed an inflection of a convex nature in a certain time range, were combined into a single correlation curve with the coordinates of the residual stress (σ_r) and the new parameter (P_T). The regression equation up to second degree, σ_r=c₀+c₁P_T+c₂P_T² (c₀ is a constant, c₁ and c₂ are the regression coefficients), was applied for the master relaxation data. The estimated relaxation curves for the specified total strain calculated from the regression equation showed good agreement with the observed ones.