A statistical model of hydride phase formation in hydrogenated metals under loading

Dynamics of Mechanical Systems with Variable Mass

“…inBažant et al (2008), where supporting arguments are consistently proved; see alsoBažant & Le (2008) andLe & Bažant (2010, 2011.…”

“…As a matter of fact, the initial motivation came from two recent papers by Bažant & Verdure (2007), and by Seffen (2008). In fact, a exciting discussion followed, as testimony a series of papers, published from 2008 on; see, e.g., Bažant et al (2008), Bažant & Le (2008), Beck (2007 and Le & Bažant (2010, 2011. Apart some differences on the consideration of a parameter known as the compaction factor, both authors ended up with two distinct equations of motion, derived by applying either the usual or the extended form of the Lagrange equation, Eq.…”

“…Here k is determined in terms of the material properties, D(ε) is the effective cross section of the flow of the second component Indeitsev and Osipova (2011). The larger is the deformation, the smaller is the quantity D, since it is more difficult for mobile hydrogen to move in strained medium.…”

A statistical model of hydrogen-induced fracture of metals

“…This model is based on the fact that the destruction process under the load is a first order phase transition [11][12][13][14], which is either negated or not taken into account in models [4][5][6][7][8][9][10]. Correspondingly, at the instant of fracture, the fractured and unfractured metal phases are in equilibrium.…”

“…Equating partial derivative to zero, we will derive the equilibrium distribution of hydrogen by chemical bonds of metal The coincidence of formula (4) with the Fermi dis tribution is associated with the fact that the filling numbers of hydrogen in chemical bonds can accept the values of either 0 or 1, which ensures the complete analogy of this system with the electron distribution by energies in metals. The relation between stress σ and relative deformation (elongation) in a two phase medium is known to have the form [12,13] …”