Physical mesomechanics of materials

Abstract

The basic principles of the physical mesomechanics of materials are formulated. This new scientific discipline relates the physics of plasticity (the micro level), the mechanics of a deformable solid (the macro level), and physical materials science. Plastic deformation and subsequent failure of a loaded solid develops as the successive evolution of shear-stability loss at the micro, meso, and macro levels. The deformation laws at the different scale levels are scale-invariant. To study the deformation mechanisms at the meso level, engineering viewing methods may be used. It is shown that, in deformable materials, a basic stress concentrator always appears at the point of application of an external load; this plays the fundamental role in the meso-level development of deformation. The basic carriers of plastic flow at the meso level are volume elements of various sizes; their motion occurs by a shear+rotation mechanism. In a structurally inhomogeneous medium, stress mesoconcentrators arise at internal boundaries; these form dissipative substructures and result in fragmentation of the material at the meso level. Electron-microscopic data on the basic types of meso-level substructures for high-strength materials indicate that, at the substructure boundaries, high-energy states that are in structural disequilibrium are formed at the substructure boundaries; these states are characterized by crystal-lattice curvature of up to 1 deg/μm and a high disclination density. A new structural state is observed: a substructure with a continuum disclination density, characterized by crystal-lattice curvature of up to 40 deg/μm. The methodological aspects of a unified theory of a deformable solid are discussed, and a theoretical approach that may be used to model the deformation and failure of materials with a complex internal structure at different scale levels, on the basis of continuum-mechanics methods, is proposed. This approach allows defining equations for the description of plastic deformation at the micro, meso, and macro levels to be written, taking account of the contribution of the accumulated strain at the lower levels to the strain at the upper levels. The theoretical results are in good agreement with experimental data.