Additive Gaussian Noise Effect on Phase Diagram of Metal’s Fragmentation Modes during Severe Plastic Deformation

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. Namely, in the latter variant, the terms that involve the interaction with the fluctuations of (these are two terms in Eq.…”

“…Expression (1) for the internal energy density differs from the initial one [11][12][13][14] by the presence of the last term, which describes the self-consistent behavior of the GB density ℎ and the dislocation density ℎ . According to it, the additive noise transforms into the multiplicative one [19]. The minus sign in front of this term ensures the formation of stationary states (the maximum of the thermodynamic or synergetic potential) and reflects the Le Chatelier principle.…”

“…The deterministic force (ℎ ) and the effective intensity of fluctuations √︀ (ℎ ) of the random variable are formulated as follows [19]:…”

“…Its transformation makes it possible to obtain an equation that determines the positions of stationary states [19],…”

“…KHOMENKO, 2019 both the formation conditions and the stability of the formed submicrocrystalline (SMC) or nanocrystalline (NC) boundary (stationary) structures. At the same time, the proposed theory considers the influence of fluctuations of the main parameters (noise), which can substantially change the evolution of the system in some cases and even lead to the appearance of new states [16,[19][20][21][22]that cannot be realized in the deterministic case [11][12][13][14][23][24][25].…”