Quasi-Relaxation Transforms, Meromorphic Curves and Hereditary Integrals of the Stress-Deformation Tensor to Metallic Specimens
- 1 Department of Research in Mathematics and Engineering, Tecnológico de Estudios Superiores de Chalco, Mexico, Russia
- 2 Baikov Institute of Research in Metallurgy and Material Sciences, Mexico, Russia
- 3 Baikov Institute of Research in Metallurgy and Material Sciences, Mexico, Russia
Abstract
Into the study of quasi-relaxation, in the past researches it has been concluded that the condition of meta-stability in the metallic specimen is given by the plasticity explained by the plastic energy in the process of the quasi-relaxation. It is calculated through quasi-relaxation functional of this energy to obtain a spectra in the space D(σ – ε; t) , that induces the existence of functions φ( t ), and Ψ( t ), related with the fundamental curves of quasi-relaxation given by σ( t ), with their poles in , which is got in the maximum of stress given by σ0 = σ1 . Also the tensor of plastic deformation that represents the plastic load during the application of specimen machine, cannot be obtained without poles in the space D(σ; t) , corresponding the curves calculated into the space D(σ – ε; t) , by curves that in the kinetic process of quasi-relaxation are represented by experimental curves in coordinates log σ – t . This situation cannot be eluded, since in this phenomena exist dislocations that go conform fatigue in the nano-crystalline structure of metals. From this point of view, is necessary to obtain a spectral study related to the energy using functions that permits the modeling and compute the states of quasi-relaxation included in the poles in the deformation problem to complete the solutions in the space D(σ – ε; t) , and try a new method of solution of the differential equations of the quasi-relaxation analysis. In a nearly future development, the information obtained by this spectral study (by our integral transforms), will be able to give place to the programming through the spectral encoding of the materials in the meta-stability state, which is propitious to a nano-technological transformation of materials, concrete case, some metals.
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