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.
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Acknowledgements
This work was performed in the framework of the state assignment (reg. No. AAAA-A16-116121410009-8) and under partial financial support by the grant of the Russian Foundation for Basic Research (project No. 17-08-01085).
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Dudin, D., Keller, I. (2021). On the Spectrum of Relaxation Times in Coupled Diffusion and Rheological Processes in Metal Alloys. In: dell'Isola, F., Igumnov, L. (eds) Dynamics, Strength of Materials and Durability in Multiscale Mechanics. Advanced Structured Materials, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-030-53755-5_3
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