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By the use of the Griffith model, the propagation of a crack in a solid subjected to a cyclic loading is studied. It is assumed that all the energy lost per cycle in the Bauschinger process is transferred to the crack to increase its size.The paper is divided in two parts, the first dealing with materials which do not undergo work-hardening and the second with materials subjected to said phenomenon during cyclic loading. Notwithstanding the crude approximation of this model, it is shown that the main features of fatigue phenomena are accounted for.

The second quantization of the phonon field allows a theory to be developed which gives the reticular centre displacements, produced by vacancy formation. The theory is based on Bravais lattices, and a detailed calculation is carried out for the Debye approximation.Numerical results for argon at 50 "K are compared with those of previous theories.Par un calcul de seconde quantization on dtudie la distorsion d'un rbseau cristallin autour d'une vacance. La thhorie est appliquire aux cristaux de Bravais en employant l'approximation de Debye. Les resultats numdriques pour un cristal d'argon B 50 "K sont cornpards B ceux des theories prhckdentes.where r is the distance of the atom from the defect point, v the atomic volume, and a a dimensionless constant, related to the material properties. However, equation (1) is an unsatisfactory solution, because elasticity theory fails in the immediate neighbourhood of the vacancy, i.e. just in the region which gives the most important contribution to scatterings and relaxation energy. The first attempt to account for the lattice discrete nature, in a static model, was made by KANZAKI [6], for a f.c.c. lattice. His method, based on expansion of the atom displacements in normal lattice coordinates, can be used both for vacancies and interstitials. An iterative procedure, leading to successive solutions of linear algebraic equation systems, has been formulated by TEWORDT [ 7 ] . It requires the use of a large electronic computer, and, moreover, may be regarded as an attempt to give numerical rather than analytical solutions.