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| Titel |
Generalization of the slip line field theory for temperature sensitive visco-plastic materials |
| VerfasserIn |
Martin Paesold, Max Peters, Klaus Regenauer-Lieb, Manolis Veveakis, Andrew Bassom |
| Konferenz |
EGU General Assembly 2015
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250108321
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| Publikation (Nr.) |
 EGU/EGU2015-8071.pdf |
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| Zusammenfassung |
| Geological processes can be a combination of various effects such as heat
production or consumption, chemical reactions or fluid flow. These individual
effects are coupled to each other via feedbacks and the mathematical analysis
becomes challenging due to these interdependencies. Here, we concentrate solely on
thermo-mechanical coupling and a main result of this work is that the coupling
can depend on material parameters and boundary conditions and the coupling is
more or less pronounced depending on theses parameters. The transitions from
weak to strong coupling can be studied in the context of a bifurcation analysis.
classically, Material instabilities in solids are approached as material
bifurcations of a rate-independent, isothermal, elasto-plastic solid. However,
previous research has shown that temperature and deformation
rate are important factors and are fully coupled with the mechanical
deformation. Early experiments in steel revealed a distinct
pattern of localized heat dissipation and plastic deformation
known as heat lines. Further, earth materials, soils, rocks and
ceramics are known to be greatly influenced by
temperature with strain localization being strongly affected by
thermal loading. In this work, we provide a theoretical framework
for the evolution of plastic deformation for such coupled systems,
with a two-pronged approach to the prediction of localized
failure. First, slip line field theory is employed to
predict the geometry of the failure patterns and second,
failure criteria are derived from an energy bifurcation analysis.
The bifurcation analysis is concerned with the local energy balance of a material and
compares the effects of heat diffusion terms and heat production terms where
the heat production is due to mechanical processes. Commonly, the heat is
produced locally along the slip lines and if the heat production outweighs
diffusion the material is locally weakened which eventually leads to failure.
The effect of diffusion and heat production is captured by a dimensionless
quantity, the Gruntfest number, and only if the Gruntfest number is larger than
a critical value localized failure occurs. This critical Gruntfest number
depends on boundary conditions such as temperature or pressure and hence this
critical value gives rise to localization criteria. We find that the results of
this approach agree with earlier contributions to the theory of plasticity but
gives the advantage of a unified framework which might prove useful in
numerical schemes for visco-plasticity. |
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