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Journal of Elasticity
Erschienen in: Journal of Elasticity 2/2016

18.09.2015

On the Effect of Elastic Distortions on the Kinetics of Diffusion-Induced Phase Transformations

verfasst von: Fernando P. Duda, G. Tomassetti

Erschienen in: Journal of Elasticity | Ausgabe 2/2016

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Abstract

We derive the evolution equation for a sharp concentric interface in a two-phase elastic solid of spherical shape. The solid is immersed in a reservoir of interstitial species whose diffusion triggers phase transformation. We find that mismatch strain accelerates phase–transformation processes that initiate at the center of the specimen, and slows down those that begin at the boundary.
Vorheriger Artikel Estimates of Nonlinear Elastic Constants and Acoustic Nonlinearity Parameters for Textured Polycrystals
Nächster Artikel Kinking Instability in the Torsion of Stretched Anisotropic Elastomeric Filaments

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Fußnoten
1
When writing constitutive equations governing a field, the index \(\phi\) equals \(\alpha\) or \(\beta\) according the whether the field is evaluated in the region occupied by the \(\alpha\) or by the \(\beta\) phase.
 
2
If the diffusing species is an interstitial, the mobility of each phase is proportional to concentration. Thus, \(m_{\phi}=c_{\phi}\bar{m}_{\phi}\) with \(\bar{m}_{\phi}\) a constant that depends on the particular phase \(\phi=\alpha, \beta\). Such explicit dependence does not play any role as long as (4) holds true.
 
3
In writing the third of (10) we are neglecting the pressure that the environment exerts on the body.
 
4
We remark that the Maxwell condition (11) may be interpreted as a balance statement localized at the interface \(\mathbf{n}\cdot\llbracket\mathbf{C}\rrbracket\mathbf{n}=0\), involving the configurational stress \(\mathbf{C}=\omega\mathbf{I}-\nabla\mathbf{u}^{T}\mathbf{S}\) (see [6]). If one adopts this point of view, then implicit in (11) is the assumption that the interface be dissipationless and structureless. This assumption may well be relaxed, as in [7], where surface energy and dissipation are ascribed to the interface.
 
5
This quantity coincides with the normal velocity, since the interface is a sphere.
 
6
It is argued in [4] (see also [5]) that a problem with the linearization (17) is that it pollutes the thermodynamic structure of the system. This is the motivation for the different path taken in [4] — a path we follow in the present paper — based on taking \(\mu\) as independent variable and on stipulating (3).
 
7
Given that the mechanical effects of phase transformation are essentially those engendered by elastic misfit, we assume for simplicity that the stiffness in either phase is the same. This approximation delivers fairly accurate results in many situations, such as for instance the hydrating process of a metallic particle [22].
 
8
Here we rule out unbounded solutions of (37).
 
9
Namely, \(\langle \!\!\langle a\rangle \!\!\rangle =\frac{a(\varrho+)+a(\varrho-)}{2}\).
 
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Metadaten
Titel
On the Effect of Elastic Distortions on the Kinetics of Diffusion-Induced Phase Transformations
verfasst von
Fernando P. Duda
G. Tomassetti
Publikationsdatum
18.09.2015
Verlag
Springer Netherlands
Erschienen in
Journal of Elasticity / Ausgabe 2/2016
Print ISSN: 0374-3535
Elektronische ISSN: 1573-2681
DOI
https://doi.org/10.1007/s10659-015-9539-0

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