POSSIBLE MECHANISMS OF ENERGY DISSIPATION IN THE TRANSITION FROM REVERSIBLE DEFORMATION TO IRREVERSIBLE

Physically observed mechanisms of transition from reversible deformation to irreversible do not have an adequate mathematical model in the mechanics of a deformed solid. An attempt is made to describe the observed phenomena on the basis of the energy principles of mechanics. Two models are considered, the first of which provides for a two-stage picture of a uniform strain with linear stretching of a homogeneous sample with isotropic properties. At the first stage, the generally accepted equations of motion in the form of Lagrange are used, the relationship between longitudinal and transverse deformations determines the Poisson’s ratio. After reaching the critical state, the deformation remains uniform with the equations of motion similar to those adopted in the first stage, but the ratio of transverse and longitudinal deformations varies, facilitating the return of the volume of particles to their original value. In this case, the energy of the particles, determined by the change in their volume and shape, decreases, the excess part is released as heat to the surrounding space. In the second model, the material of the deformable body is assumed to be an ideal rigid-plastic medium, for which the initial undeformed state becomes plastic when the tangential stresses reach a critical value. The position of the shear planes is determined from the extreme principles of the theory of plasticity. The most probable is sliding along planes, the normals to which are oriented at an angle of 45° to the axis of maximum normal stress. It is shown that, due to the change in the stress state scheme after the formation of primary slip bands, several other families of slip planes can be successively formed. Moreover, a shift in the second, and then in the third and other families, requires less energy. But the simultaneous existence of several slip planes is impossible, since a reduction in effort leads to the termination of sliding along the initial plane. Thermal sources on slip planes result in energy dissipation, reduction in effort and further development of deformation requires an increase in effort to a critical value corresponding to the beginning of the first stage. Both models are consistent with the experimentally observed mechanisms of irreversible deformation, in particular when static stretching under the conditions of planar deformation, fracture of samples most often occurs at an angle of about 21°.

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