Моделювання процесів повзучості й тривалої міцності матеріалів

Abstract

Запропоновано модель для опису одновимірних неізотермічних процесів деформування, що враховує пошкодженість при повзучості для широких діапазонів напруження і температури. Уточнено області застосування параметричних методів для прогнозування тривалої міцності матеріалів. Подано методику для конкретизації запропонованих рівнянь стану та показано їх ефективність при описуванні повзучості матеріалів.

A model for describing one-dimensional nonisothermal deformation processes that considers the damage under creep for a wide range of stress and temperature is proposed. The influence of the stress state and temperature on the creep rate variation is taken into account by means of a scalar function of damage level, with all three specific portions of the creep curve being described. The Lemaitre and Plumtree model is used as an evolutionary relationship, considering that its parameters are stress- and temperature-dependent. Based on the relationships described by the stress-rupture curves, the procedure is proposed for specifying the parameters of the evolutionary equation. The application areas of the known parametric methods for predicting the stress-rupture strength of materials are specified based on the experimental investigations. It is shown that these methods allow extrapolating the creep-rupture life to the values that exceed the available experimental data by no more than a factor of 10 with accuracy sufficient for engineering purposes. To extend the prediction capabilities to 300 thousand hours or more on the basis of the test results of limited duration, a modified base diagram method is proposed. A linear dependence is proposed to approximate the residual function in terms of the base diagram method. In the case, where it is impossible to reduce the stress-rupture curves to a common curve, the residual function parameters are determined from the experimental data for one isotherm. In this case, its parameters are the functions of temperature. The advantages of this approach over the Larson–Miller, Orr–Sherby–Dorn, Manson–Succop, Trunin and other parameters are shown during the extrapolation of stress-rupture strength to long lifetimes. To describe the dependence of the creep strain rate on the stress, creep strain, damage level function and temperature, the relationship of the strain-hardening theory is used with the corresponding change of the stress value for the effective stress defined by Kachanov. The procedure is proposed for specifying the constitutive equations in terms of the strain distribution in creep and the stress-rupture curves. The obtained values of the parameters calculated at the fixed stress and temperature values are approximated using the smoothing-surface approximation. The efficiency of describing the creep processes is shown in the strain calculations for alloy 19Cr-18Co-4Mo-3Ti-3Al-B and steels 12Cr-18Ni-Mo, 21Cr-32Ni-Ti-Al. Good agreement is shown between the predicted and experimentally obtained data for quite wide ranges of working stress and temperature.