scholarly journals Fundamentals of a continuum theory of dislocations

2006 ◽  
Author(s):  
Thomas Hochrainer ◽  
Michael Zaiser
Keyword(s):  
Continuum Theory ◽  
Continuum Theory Of Dislocations

scholarly journals Influence of Dislocations on the Spatial Variation of Microstructure in Martensites

2011 ◽  
Vol 465 ◽  
pp. 77-80
Author(s):  
Roman Gröger ◽  
Turab Lookman
Keyword(s):  
Free Energy ◽  
Local Density ◽  
Parent Phase ◽  
Mean Field ◽  
Continuum Theory ◽  
Energy Functional ◽  
Cubic Symmetry ◽  
Macroscopic Models ◽  
Multiphase Materials ◽  
Continuum Theory Of Dislocations

The continuum theory of dislocations, as developed predominantly by Kröner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy functional to develop a mean-field mesoscopic model of materials with dislocations. The order parameters that represent the distortion of the parent phase (often of cubic symmetry) are written in terms of elastic strains which are themselves coupled by incompatibility constraints. Since the “strength” of the incompatibility depends on the local density of dislocations, the presence of dislocations affects the evolution of the microstructure and vice versa. An advantage of this formulation is that long range anisotropic interactions between dislocations appear naturally in the formulation of the free energy. Owing to the distortion of the crystal structure around dislocations, their presence in multiphase materials causes heterogeneous nucleation of the product phase and thus also shifts of the transformation temperature. This novel field-theoretical approach is very convenient as it allows to bridge the gap in studying the behavior of materials at the length and time scales that are not attainable by atomistic or macroscopic models.

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