Title: Microstructural patterning in time-dependent non-convex crystal plasticity
Other Contributors: GEERS M.g.d.
Citation: 11th. GAMM-Seminar on Microstructures p. 15
Publisher: University of Duisburg-Essen
Publication Year: 2012
JRC N°: JRC68615
URI: http://www.uni-due.de/imperia/md/content/mechanika/gamm_seminar_microstructures_2012.pdf
Type: Articles in periodicals and books
Abstract: Microstructures in materials generally originate from a non-convex free energy, whereby the evolution is controlled by the kinetics underlying the physical processes governing the patterning. Special examples thereof are microstructures in metals and dislocation microstructures in particular, which have been an interesting research topic for the materials science community for decades. This paper analyses the intrinsic role of non-convexity in the formation and evolution of deformation microstructures, in close comparison to classical phase field approaches for microstructure evolution. Special emphasis is given on the role of kinetics that control the time dependent evolution in a deformation microstructure. For this purpose, a non-convex rate dependent strain gradient plasticity framework is used to recover plastic slip patterning in metal crystals. The non-convexity is treated as an intrinsic property of the free energy of the material. Departing from explicit expressions for the free energy and the dissipation potential, the non-convex strain gradient crystal plasticity model is derived in a thermodynamically consistent manner, including the accompanying slip law. For the numerical solution of the problem, the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by solving simultaneously the linear momentum balance and the resulting slip evolution equation. The slip law differs from classical ones in the sense that it naturally includes a contribution from the non-convex free energy term, which enables patterning of the deformation field. The formulation of the computational framework is partially dual to a Ginzburg Landau type of phase field modeling approach. The essential difference resides in the fact that a strong coupling exists between the deformation and the evolution of the plastic slip, whereas in the phase field type models the governing fields are only weakly coupled. The derivations and implementations are first done in a transparent 1D setting [1], which allows for a thorough mechanistic understanding. The extension to 2D and multiple slip is presented as well, whereby the non-convexity originates from the slip system interaction.
JRC Directorate:Energy, Transport and Climate

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