Engineering Transactions, 5, 4, pp. 457-478, 1957

Zaprawa, Opóźnienie Sprężyste i Naprężenia Resztkowe w Ujęciu Dynamicznej Teorii Plastyczności

J. Madejski

In the author's previous papers on the model taken as a basis was «dynamical theory of plasticity» that of a homogeneous continuum. In the present paper, a non-homogeneous «honeycomb» model is analyzed. It is assumed that both substances are solutions capable, under certain circumstances, of separating or absorbing some components of the solution. It is further assumed that the kinetics of this phenomemon determines the equation of monomolecular chemical reaction (2.2). The corresponding thermal effect may be result of heat transfer from the outside or of internal friction. In the latter case, isothermal and irreversible changes of state of a solid are possible. By application of the principles of the «dynamical theory of plasticity» for each component separately, it is found that the model considered is subjected to work hardening (i.e. an increase of the elastic limit in the sense of Dinnik- Stromeyer-Buchnee) and reveals elastic after-effect, deformation due to cold working and residual stresses. The physical interpretation of the «honeycomb» model is as follows. Real metals are in practice alloys of polycrystalline structure. If the structure shows no distinct texture the material may be considered to be macroscopically quasi-isotropic. Considering the structure of the material as mosaic paltterned (dendritic grains divided by «hard» intercrystalline substance) the grains can be treated as «honey» and the intercrystalline substance as «wax». Both substances should be considered as solutions. In this case diffusion of certain components from one solution to the other and vice versa is possible. This is connected with changes of the proportions of «wax» and «honey» in the aggregate as a whole.
Assuming that an increase of the quantity of «wax» results in an extension of the layers of intercrystalline matter, and much less in a growth of their thickness, it may be concluded that such a phenomenon will provoke fragmentation of the grains, i.e. fine-granulation. This structural property is a result of work hardening. It should be emphasized that the above considerations remain unaffected even in the case of zero value 'of the true elastic limit of single crystallites.

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