Chapter 3
On the Spectrum of Relaxation Times
in Coupled Diffusion and Rheological
Processes in Metal Alloys
Dmitry Dudin and Ilya Keller
Abstract The paper is concerned with studying the relaxation times of coupled
diffusion and rheological processes in metals within the framework of a linear model,
which takes into account elastic and viscous bulk and shear modulus. Here, we
consider the spatial perturbations of a homogeneous stationary solution of field equations for a one-dimensional model problem, in which only the diffusion and rheological relations remain nontrivial. The study made allowed us to obtain the asymptotic
expressions for the coefficients of interdiffusion at vanishingly small and infinitely
large characteristic lengths of perturbations, as well as the dependences on the ratios
of the elastic to viscous moduli. Consideration for the material elasticity leads to the
appearance of an additional relaxation time, which is responsible for the diffusion
mechanism. In this case, conventional thermal diffusion can be accompanied by fast
diffusion or it can exist against the background of slow diffusion, depending on the
ratio of the characteristic values of the elastic and thermal energies. A viscous shear
flow in the region of small wavelengths of spatial perturbations plays a key role in
the mechanism of interdiffusion in a binary alloy, in which vacancy diffusion is not
taken into account. The relation between the diffusion and rheological processes is
maintained by stresses. The method can be used for qualitative analysis of much
more complex, coupled diffusion-rheological systems.
Keywords Metal alloys · Interdiffusion · Rheological processes · Stresses ·
Coupled processes · Asymptotics · Perturbation analysis
D. Dudin
Perm National Research Polytechnic University, Perm, Russia
e-mail: dmitryovj@yandex.ru
I. Keller (B)
Institute of Continuous Media Mechanics of the UB RAS, Perm, Russia
e-mail: kie@icmm.ru
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_3
41
On the Spectrum of Relaxation Times
in Coupled Diffusion and Rheological
Processes in Metal Alloys
Dmitry Dudin and Ilya Keller
Abstract The paper is concerned with studying the relaxation times of coupled
diffusion and rheological processes in metals within the framework of a linear model,
which takes into account elastic and viscous bulk and shear modulus. Here, we
consider the spatial perturbations of a homogeneous stationary solution of field equations for a one-dimensional model problem, in which only the diffusion and rheological relations remain nontrivial. The study made allowed us to obtain the asymptotic
expressions for the coefficients of interdiffusion at vanishingly small and infinitely
large characteristic lengths of perturbations, as well as the dependences on the ratios
of the elastic to viscous moduli. Consideration for the material elasticity leads to the
appearance of an additional relaxation time, which is responsible for the diffusion
mechanism. In this case, conventional thermal diffusion can be accompanied by fast
diffusion or it can exist against the background of slow diffusion, depending on the
ratio of the characteristic values of the elastic and thermal energies. A viscous shear
flow in the region of small wavelengths of spatial perturbations plays a key role in
the mechanism of interdiffusion in a binary alloy, in which vacancy diffusion is not
taken into account. The relation between the diffusion and rheological processes is
maintained by stresses. The method can be used for qualitative analysis of much
more complex, coupled diffusion-rheological systems.
Keywords Metal alloys · Interdiffusion · Rheological processes · Stresses ·
Coupled processes · Asymptotics · Perturbation analysis
D. Dudin
Perm National Research Polytechnic University, Perm, Russia
e-mail: dmitryovj@yandex.ru
I. Keller (B)
Institute of Continuous Media Mechanics of the UB RAS, Perm, Russia
e-mail: kie@icmm.ru
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_3
41