This article is an analytical review of experimental and theoretical studies of creep and creep rupture strength of metals under unsteady complex stress states published over the past 60 years.The first systematic studies of the creep of metals under complex stress conditions were published in the late 50s and early 60s of the 20th century in the Soviet Union (L. M. Kachanov and Yu. N. Rabotnov) and Great Britain (A. E. Johnson). Pioneering work on creep rupture strength first appeared in the USSR (L. M. Kachanov and Yu. N. Rabotnov). Subsequently, Yu. N. Rabotnov developed the kinetic theory of creep and creep rupture strength, with the help of which it is possible to efficiently describe various features of the creep process of metals up to fracture under various loading programs. Different versions of the kinetic theory use either a scalar damage parameter, or a vector parameter, or a tensor parameter, or a combination of them. Following the work of M. Kachanov and Yu. N. Rabotnov mechanics of continuum destruction began to develop in Europe, in Asia, and then in the USA.The hypothesis of proportionality of stress deviators and deviators of creep strain rates is accepted as the main connection between the components of stress tensors and creep strains. When modeling experimental data, the proportionality coefficient in this dependence takes different forms. The main problem in the development of this direction is the difficulty in obtaining experimental data with arbitrary loading programs.This review provides the main results of studies conducted by scientists from different countries. Except Yu. N. Rabotnov and L. M. Kachanov, also a significant contribution to the development of the direction of science made by Russian scientists N. N. Malinin, A. A. Ilyushin, V. S. Namestnikov, S. A. Shesterikov, A. M. Lokoshchenko, Yu. P. Samarin, O. V. Sosnin, A. F. Nikitenko, et al.

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Ползучесть и длительная прочность металлов при нестационарных сложных напряженных состояниях (обзор)

Рассмотрено моделирование результатов испытаний металлов в условиях ползучести при нестационарном сложном напряженном состоянии. В качестве примера рассмотрены экспериментальные данные, полученные группой японских ученых при испытаниях трубчатых образцов из нержавеющей стали при температуре $650 ^{\circ}$С. В приведенной статье представлены результаты испытаний при четырех различных программах нагружения. Эти программы нагружения представляют собой различные комбинации кусочно-постоянных зависимостей касательного и нормального напряжений от времени. Проведено моделирование представленных данных с помощью теории упрочнения и теории течения, две используемые материальные константы определяются из условия минимального относительного интегрального расхождения экспериментальных и теоретических кривых ползучести. Проведено сопоставление результатов моделирования с результатами моделирования этих тех же экспериментальных данных, полученных другими исследователями с использованием других теорий. В этих других теориях использовано большое количество характеристик материала: от трех до девяти констант и дополнительно - одной материальной функции. Показано преимущество рассмотренных авторами данной статьи теории упрочнения и теории течения всего с двумя материальными константами в каждой по сравнению с другими использованными теориями.

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Моделирование ползучести металлов при нестационарном сложном напряженном состоянии

A mathematical model describing the unsteady creep of metals under complex loading is proposed. The results of numerical simulation of creep of St.304 steel in complex regimes of block multiaxial cyclic deformation are given. The numerical calculation results obtained are compared with the data of full-scale experiments. Creep is simulated in complex deformation processes accompanied by the rotation of main regions of stress, strain, and creep strain tensors.

State Equations of Unsteady Creep under Complex Loading

Modeling of non-stationary creep processes under multiple loading conditions by taking into account damage accumulation in a structural material

The behavior of metal tubular specimens under combined tension–torsion, torsion–compression and internal torsion pressures is studied experimentally. The tests are necessary for obtaining experimental data in order to study loss of stability and deformation of elastic–plastic shells caused by large deformations under complex stress conditions loaded along multi-link broken polygonal deformation trajectories, as well as for assessing the role of deformation anisotropy. In order to conduct tests under complex stress conditions (internal pressure loading in combination with other types of loading), the testing equipment was modified. Equipment of the test complex with a system for loading of tubular specimens with internal pressure ensures the conditions for achieving destructive stresses, caused by both internal pressure and torsion with tension. The Zwick/Roell Z100 testing machine equipped with the system generating internal pressure in hollow specimens makes it possible to expand significantly the types of tests on determining deformation and strength characteristics of materials. The results can be used to verify mathematical models and program codes for the numerical study of the processes of elastic–plastic deformation and loss of stability of shells of revolution under complex loading.

Experimental Studies of Elastic–Plastic Deformation of Structural Materials Under Conditions of Triaxial Loading

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Defining relations of transient creep under complex stress state

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A damaged medium model for describing the processof long-term strength of structural materials(metals and their alloys)

The main regularities of the degradation of structural materials (metals and alloys) resulting in a decrease in creep-rupture strength were investigated. A mathematical model describing the viscoplastic deformation and damage accumulation in polycrystalline structural alloys in creep was developed using the equations of the mechanics of damaged media. The paper presents the results of experimental studies of the short-term creep of 12Kh18N9 steel and VZh-159 high-temperature alloy at constant temperature and different stresses set in the samples and the results of experimental studies of creep recovery in some structural steels. Deformation and damage accumulation were studied numerically and the results were compared with the data of full-scale experiments.

I. V. Smetanin

Papers

Defining relations of transient creep under complex stress state

A damaged medium model for describing the processof long-term strength of structural materials(metals and their alloys)

Constitutive Relations of the Mechanics of a Damaged Medium for Evaluating the Creep-Rupture Strength of Structural Alloys