Deformation as a measure of conformality deviation

Abstract

The plane vector field for solid with constant deformation is considered. The formulae for components of the field are given. Linear character of a displacement fields and its evolution is shown at the example of plastic flow of base metal of welded joint in the neck region. Two consequent vector fields give the summary field as their sum. The high-cyclic fatigue of welded joints of Fe-17Cr-0.8Ti-0.08C steel was used to analyze. The criteria of deviation the vector field from the field, which components can be described by analytical functions, are considered. It is shown that summary declination of these criteria from the Cauchy–Riemann equations is closed to deformation. Therefore, only non-linear components of the deformation can satisfied to Cauchy–Riemann equations for the next conformal transformation.The plane vector field for solid with constant deformation is considered. The formulae for components of the field are given. Linear character of a displacement fields and its evolution is shown at the example of plastic flow of base metal of welded joint in the neck region. Two consequent vector fields give the summary field as their sum. The high-cyclic fatigue of welded joints of Fe-17Cr-0.8Ti-0.08C steel was used to analyze. The criteria of deviation the vector field from the field, which components can be described by analytical functions, are considered. It is shown that summary declination of these criteria from the Cauchy–Riemann equations is closed to deformation. Therefore, only non-linear components of the deformation can satisfied to Cauchy–Riemann equations for the next conformal transformation.