The solution of complex problems of strength in many branches of industry
and science is impossible without a knowledge of fracture processes. Last 50
years demonstrated a great interest to these problems that was stimulated
by their immense practical importance. Exact methods of solution aimed at
finding fields of stresses and strains based on theories of elasticity, plasticity,
creep, etc. and a rough appreciation of strength provide different results
and this discrepancy can be explained by the fact that the fracture is a complex
problem at the intersection of physics of solids, mechanics of media and
material sciences. Real materials contain many defects of different form and
dimensions beginning from submicroscopic ones to big pores and main cracks.
Because of that the use of physical theories for a quantitative appreciation of
real structures can be considered by us as of little perspective. For technical
applications the concept of fracture in terms of methods of continuum mechanics
plays an important role. We shall distinguish between the strength of
a material (considered as an element of it – a cube, for example) and that of
structures, which include also samples (of a material) of a different kind. We
shall also distinguish between various types of fracture: ductile (plastic at big
residual strains), brittle (at small changes of a bodies’ dimensions) and due
to a development of main cracks (splits).
Here we will not use the usual approach to strength computation when the
distribution of stresses are found by methods of continuum mechanics and then
hypotheses of strength are applied to the most dangerous points. Instead, we
consider the fracture as a process developing in time according to constitutive
equations taking into account large strains of unsteady creep and damage
(development of internal defects). Any stage of the structures’ deformation
can be supposed as a dangerous one and hence the condition of maximum
allowable strains can be used. But more convenient is the application of a
criterion of an infinite strain rate at the moment of beginning of unstable
deformation. This approach gives critical strains and the time in a natural
way. When the influence of the latter is small, ultimate loads may be also
