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Intragranular deformation patterning through non‐convex rate dependent strain gradient crystal plasticity
Author(s) -
Yalçinkaya Tuncay
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210389
Subject(s) - convexity , slip (aerodynamics) , plasticity , regular polygon , crystal plasticity , materials science , mechanics , hardening (computing) , strain hardening exponent , geometry , lattice (music) , mathematics , physics , composite material , thermodynamics , layer (electronics) , financial economics , economics , acoustics
Abstract A rate dependent strain gradient crystal plasticity framework is presented where the displacement and the plastic slip fields are considered as primary variables. These coupled fields are determined on a global level by solving simultaneously the linear momentum balance and the slip evolution equation, which is derived in a thermodynamically consistent manner. The formulation is based on the 1D theory presented in Yalcinkaya et al. (2011), where the patterning of plastic slip is obtained in a system with non‐convex energetic hardening through a phenomenological double‐well plastic potential. In the current multi‐dimensional multi‐slip analysis the non‐convexity enters the framework through a latent hardening potential presented in Ortiz and Repettto (1999) where the microstructure evolution is obtained explicitly via a lamination procedure. The current study aims the implicit evolution of deformation patterns due to the incorporated physically based non‐convex potential. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)