G. S. Pisarenko over many years was engaged in intensive investigations in the new and promising area, which he qualified as the strength of materials and structural elements under extreme conditions. Those operating conditions were characteristic of many structural elements of novel equipment in engineering industries, which were progressing rapidly during the second half of the 20th century.All this called for creation of new materials such as high-temperature steels and alloys, high-strength titanium and aluminum alloys, composite ceramic and cermet materials, including heat-shielding ones, refractory metals and alloys, carbon-graphite materials, etc.Designing of structures from the above materials is impossible without knowledge of their strength and deformability characteristics and the regularities in the in-service behavior of structures. Moreover, it is important not only to determine the characteristics of some particular properties of materials under certain conditions but also to develop the criteria of their ultimate state that would make it possible to calculate the strength and life of real structures using the results obtained in testing laboratory specimens and taking into account the structure geometry, stress state, size, and other factors.The development of the ultimate state criteria of materials is a challenging scientific problem. In attacking it one should consider the great number of different mechanisms of deformation and fracture of materials (for instance, plastic deformation, creep, cyclic, low-and high-cycle fatigue, thermal fatigue, corrosion cracking, wear, frettingcorrosion, erosion, etc.) occurring in operation and resulting in various conditions of the ultimate state (failure).Furthermore, it is necessary to take into account the large variety of materials used in engineering and significant difference in their behavior under mechanical, thermal, and themomechanical loading, as well as some peculiar features of real materials such as scatter in properties, the presence of manufacturing and in-service defects, instability of properties in the course of long-term operation, particularly under conditions of radiation embrittlement, specific state of the material surface layer, etc.330