Modelling of thermal processes in the cutting insert with a protective coating

Self-Similar Mode of Metals Fragmentation under Severe Plastic Deformation

“…It is evident that the positions of the extrema in the effective synergetic potential (18), which separate the modes of metal fragmentation at SPD, do not depend on the noise intensity . Note also that expression (19) derived in the framework of the Stratonovich approach is somewhat different from its counterpart derived in the framework of the Itô calculus.…”

“…Let us derive an equation for the stationary values of the GB density ℎ . It is determined from a necessary condition for the existence of extrema in distribution density (16) or effective potential (18):…”

“…However, it is worth noting that the synergetic potential (18) and, accordingly, the distribution density (ℎ ) [Eq. (16)] acquire another form owing to the renormalization of the effective noise intensity (ℎ ).…”

“…In work [19], stationary solutions of the effective synergetic potential (18) and the formation of phase diagrams with the help of the Stratonovich calculus were studied. This approach of stochastic integration was used in this work as well, because its aim was not reduced to the study of only the formation of stationary SMC or NC structures, but it also included the study of the peculiarities in the evolution of ℎ during SPD.…”

“…To describe the process of metal structure fragmentation, a generalized thermodynamic model was developed in works [11][12][13][14][15][16][17][18]. This model combines the methods of the classical non-equilibrium thermodynamics and the Landau theory of phase transitions.…”