Archives
The value of can be significantly lower than
The value of can be significantly lower than the initial elastic modulus of the material containing no hydrogen, as <
Similarly to the equation for an ideal gas located in the pores and voids of a material, the constitutive equation describing the relationship between the pressure p and the density of the second medium has the form
where is the volume concentration of the mobile hydrogen particles, k is the Boltzmann constant, T is the absolute temperature of the mobile continuum.
We believe that the force R of the interaction between the mobile hydrogen particles and the lattice can be also described through the approach used for ideal gas flow. This allows to obtain the following representation for the quantity R:
The force of interaction can be regarded as a linear function of the difference between the particle speeds in the two-continuum medium. The parameter F(ɛ) (depends on the strain ɛ) is proportional to the area of the flow section and depends on the properties of the material, such as the parameters of the crystalline lattice, the surface area of crystalline grains, the ratio between this area and the grain volume, porosity, etc.
The source term J was taken in the form suggested in Ref. [31], i.e., similar to Eq. (1):
where α and β are the positive coefficients describing sorption and desorption of diffusely mobile hydrogen within the crystalline lattice from isosafrole channels.
To illustrate the role of these coefficients, the solution of the equations of particle balance may be used assuming that the volume density distribution of the bound and the mobile hydrogen particles is uniform [31]. This system of equations has the form
Let us impose the following initial conditions:
This means that in the initial moment of time there is no bound hydrogen in the material, while the diffusely mobile hydrogen has 
the concentration . In this case the solutions of the system (4) have the form:
The obtained time dependences are shown in Fig. 2. They demonstrate the process of hydrogen saturating the host medium and of the diffusely mobile hydrogen concentration decreasing to equilibrium values determined by the sorption and desorption coefficients. The parameters α and β must be found experimentally, as the sorption and desorption mechanism lie outside the scope of our discussion.
We should note that Eq. (4) describes the exchange of hydrogen particles with different binding energies (the bound and the mobile) on the condition that the mobile hydrogen particles have a zero speed. As follows from Eq. (3), this happens on the condition that , i.e. when transfer of mobile hydrogen particles is impossible. Obviously, in this case all diffusely mobile hydrogen is going to change its binding energy and add to the host medium particles on the condition that α > >β.
After substituting , и we can write the complete systems of equations for the one-dimensional case of a two-continuum medium in the following form:
Here
The obtained system of Eq. (5) is complete. At the same time, these equations are strongly non-linear, which is the reason why our further analysis is going to be restricted to the case of static uniaxial stress–strain.
We should note that the concept of a static stress state is rather arbitrary. It must be classified as a balance equation of a continuous medium (5). The assumption of static deformation allows to describe the movement of the second component by pure kinematic relations. In other words, the structural changes in the material over time are a dynamics of sorts. Therefore, it is natural to search for a solution to the problem in the following form: