โ Scribed by D. Ivlev
No coin nor oath required. For personal study only.
THE BOOK presents a fundamental treatise on mechanics of brittle fracture and is almost entirely based on the author's original research. As far as I know, a considerable part of the contents is published for the first time and hence is not reflected in existing journals and monographs. The book seems to sum up the author's investigations of [1961][1962][1963][1964][1965][1966][1967][1968][1969][1970][1971] (the preface states it was completed in 197 I). It should be noted that the book evoked great interest of the scientific world: the edition was sold out in a few days and now the book is quite rare.
The monograph consists of eight chapters, three appendixes and a list of works (361 sources).
Chapter I deals with the author's classification of all possible models of behaviour of solids and fluids from the point of view of general cybernetics. The chapter also analyses in general the functioning of various constructions under critical conditions of fracture and gives a brief review of principal works on fracture mechanics (approximately up to 1960).
Chapter 2 gives an account of the quantum mechanics approach and different approximate methods in calculating surface energy, cohesion energy and theoretical strength of solids. For instance, by the chemical composition and elastic constants of glass, the author calculates its surface energy, which is in striking coincidence with test data. Moreover, on the basis of his method the author predicts the decrease of surface energy of glass in water by 20-30%, which also agrees well with the experiments. The results of calculations for some crystals (HzO, C, AI, a-Fe, T-Fe, Cu, NaCI and some others) are tabulated. The point of view accepted in Chapter 2 is discrete-automistic as distinct from those in other chapters.
Chapter 3 presents a scrupulous investigation of the crack-tip vicinity in solids with due regard for various factors in the framework of the theory of elasticity. At first the author suggests a general method of investigating singular points of arbitrary boundary problems in mathematical physics. The 'method is based upon group-invariance considerations and helps the author, in particular, to get the rigorous proof of the Sent-Venant classic principle. The elastic field is studied in the vicinity of a thin alien inset, either plastic or elastic. Considering the general case of the plane problem of the anisotropic theory of elasticity, the author draws the representations generalizing the well-known ones by Lekhnizky. The generalization made it possible to find the stress and strain field in the vicinity of a crack in any anisotropic body. The chapter also presents the problem of a crack which issues from the boundary of two different elastic media at any arbitrary angle. On the basis of some original rigorous solutions the author considers the elastic field in the crack vicinity subjected to the influence of the following factors: finiteness of deformations, physical non-linearity, the distinctions of initial cavity from the mathematical cut, inertia force, etc.
Chapter 4 suggests an accurate approach to mechanics of brittle fracture (functional and energy methods), which makes it possible to determine the critical state of a cracked quasibrittle body, judging by stress intensity factors known to the researcher. In particular the author considers curvilinear cracks and these with trajectory kinks; finds general conditions for stability and instability of cracks; studies the structure of plastic zones in the crack-tip vicinity; discusses some methods of experimental determination of fracture toughness, etc. The chapter contains approximate theoretical estimation of fracture toughness and engineering strength of the main types of materials (metals, alloys, composites, ceramics, glass). Theoretical estimation of K~ value is also given for through cracks in thin metal plates and agrees well with lest data. Unexpected, but quite logical is the application of fracture mechanics to the rock burst problem in excavations, which helped the author to formulate the common criterion of the rock burst emergence in terms of the stress intensity factors along the edges of excavations.
Chapter 5 investigates general energetics of the continuum with discontinuity surface of displacement. In the beginning the author introduces the notion of vector energy flux, the physical essence of which is revealed when considering moving energy springs or drains (point, linear, surface and volume) in continuum. From this point of view moving cracks and dislocations represent linear drains of energy. Then follows the formulation of the physical theory of such objects based on the notion of three-dimensional vector F of energy flux and on the concept of constant specific energy dissipation in the drain track within the limits of the fixed model of a body. On these grounds the author analyses the motion of cracks (including the initial and steady motion) in non-linear elastic, plastic-elastic and visco-elastic bodies. Of interest is the conclusion that ideal plasticity and viscosity models are incorrect from the standpoint of local fracture criteria: ruptures along the front of a crack in such bodies under critical conditions exceed by far the dimensions of super-fine structure of the crack tip typical for the model of the body under discussion. On the basis of a simple non-local criterion the author considers sub-critical growth of a through crack in a plate under monotonous loading. The following author's conclusion is of some interest too: for slowly growing cracks in solids the mechanism of local fracture at the crack tip is quite different from the purely energetical mechanism considered in this chapter.
Chapter 6 is dedicated to the author's theory of the growth of fatigue cracks in inert medium, its comparison with the test data and to the solution of some concrete problems for various conditions of loading (periodic, random, combined). As far as I know, this theory is nowadays the only rational physical theory enabling the description of empirical data on the common grounds and with the minimum amount of new physical constants.
Chapter 7 investigates various mechanisms of environmental effects upon the sub-critical growth of cracks under stationary and variable Ioadings: local hydrogen embrittlement, the chemical mechanism of growing various corrosion films, the electrochemical mechanism of micro-tunnel dissolving of some metal in the crack-opening, general kinetic mechanism, adsorption mechanism, etc. The author also deals with developing cracks in burning solid fuel, in rock, etc. All these problems are studied on the basis of the strict mathematical analysis of physics and chemistry laws (diffusion equation, chemical and electrochemical kinetics, Folmer's equation, etc) and some complementary natural assumptions. As a result the author obtains diagrams of the dependence of crack growth velocity on the stress intensity factor characteristic for the given mechanism, estimates the boundaries of critical regimes (e.g. K1scc), etc.
Chapter 8 deals with the following problems: the theory of explosion effect (with the detailed solution for the case of camouflet explosion), the theory of [ire boring, self-sustaining fracture of brittle bodies in the vicinity of cavities, fracture due to the collision of brittle bodies, errosion of solids, optical fracture, etc. All the results mentioned belong to the author.
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