2015-Sustainable Industrial Processing Summit
SIPS 2015 Volume 1: Aifantis Intl. Symp. / Multiscale Material Mechanics
| Editors: | Kongoli F, Bordas S, Estrin Y |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2015 |
| Pages: | 300 pages |
| ISBN: | 978-1-987820-24-9 |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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Towards a Consistent Internal State Variable Theory of Inelasticity
Douglas Bammann1;1MISSISSIPPI STATE UNIVERSITY, Mississippis State, United States;
Type of Paper: Regular
Id Paper: 571
Topic: 1
Abstract:
A structure for an internal state viable description of inelastic deformation of crystals is developed. The deformation gradient is multiplicatively decomposed into an elastic deformation resulting from externally applied loads and the deformations associated with each density of defects to be included as internal state variables. The deformations associated with these defects or foreign atoms such as diffusing species, may further be decomposed into elastic and plastic parts depending upon the structure of the defect. In many cases, either the elastic or plastic part of a particular deformation gradient will be negligible, depending upon the situation. The appropriate strain-like variable associated with the defects is included in the free energy resulting in conjugate thermodynamic forces (internal stresses) that must be included in the dissipation inequality. In addition, these forces (stresses) are required to satisfy micro or meso scale linear and angular balance laws. All transport equations (e.g. heat conduction or diffusing species) are derived from a combination of the energy balance and these force balance laws. This is in contrast to classic state variable theories in which only temporal evolution equations were specified for the internal state variables. Constraint equations are required for the extra kinematic degrees of freedom that are introduced. These are based upon the physics of the associated defect density/state variable an example given by the flow rule or plastic velocity gradient based upon the Orowan equation relating plastic strain rate to mobile dislocation density and velocity. This structure leads to a natural length scale bridging as conjugate forces to the state variables are required to satisfy balance laws at their respective length scale and information is passed from scale to scale via the constraint equations.
Examples are given for the construction of such theories ranging from simple statistically stored dislocations, coupled transport theories for hydrogen and micropolar type theories for asymmetric defects.