Mathematical model for high-temperature metal fatigue

Abstract

Results are analyzed for studying the thermal fatigue of metal for power engineering and production equipment using mechanical unloading theory with clear separation of the stages of crack generation and growth. Experimental data are provided for specimens of corrosion-resistant steels subjected to tensioncompression with different holding periods at a specific temperature and constant strain and without holding periods.Many domestic units of power generation and production equipment operate in a regime of high temperature heating during start-up followed by leveling of the temperature to a working regime, then cooling during shutdown. In these cases, a requirement arises for evaluating material resistance to high-temperature fatigue.This problem, starting with the first overseas studies [1, 2] has received a lot of attention, although up to now it has not been finally resolved. A considerable contribution to experimental research of long-term cyclic strength of metals has been contributed by domestic scientists [3][4][5].A qualitative jump in studies of high-temperature fatigue of metals is connected with the development of failure mechanics with a clear separation of the stages of crack generation and growth of the crack formed. Studies of short (fine) cracks has shown that the rate of their development is proportional to the area of the plastic hysteresis loop, and also elastic strain energy corresponding to crack opening. In the field of low-cycle fatigue, crack opening coefficients approximate to one and it is necessary to consider elastic strain. In view of this, it is possible to conclude that the scales of total strain in the field of low-cycle fatigue are more informative than scales of plastic strain, particularly for materials with low fracture toughness.It has been established that a considerable proportion of the endurance of smooth specimens during fatigue comprises the period of small crack generation with a depth of the order of the grain size. Experiments have shown that in the first stage of fatigue, when in sliding planes there is development of a shear microcrack, its rate may be considered as constant. In [6], it was noted that with this assumption it is possible to obtain for a smooth specimen a Coffin−Manson equation based on experimental data for growth of long cracks.These conclusions, obtained in studying fatigue in the normal temperature range, may be also be extended to hightemperature fatigue. As confirmation of this it is possible to cite data in [7], where the first and second stages of crack growth are considered in corrosion-resistant steel 316 at 550°C. The average grain size equals 40 µm. Specimens were tested in variable-sign bending with monitoring of strain, and also with periods under load of one hour, and here tension was provided in the upper generating line of a specimen (Fig. 1).It follows from analysis of data in Fig. 1 that the initial crack growth occurs at a constant rate (line ---). After reaching a crack length of the order of two average grain diameters (80 µm) th...