Internal length scale and grain boundary yield strength in gradient models of polycrystal plasticity: How do they relate
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Katerina E. Aifantis Lab of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece; and Department of Civil Engineering-Engineering Mechanics, University of Arizona, Tucson, AZ 85721, USA
Jochen Senger and Daniel Weygand Institute for Applied Materials IAM, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany
Michael Zaisera) University of Erlangen, Department of Materials Science and Engineering, Institute for Materials Simulation WW8, Fürth 90762, Germany (Received 30 May 2014; accepted 11 August 2014)
Gradient plasticity provides an effective theoretical framework to interpret heterogeneous and irreversible deformation processes on micron and submicron scales. By incorporating internal length scales into a plasticity framework, gradient plasticity gives access to size effects, strain heterogeneities at interfaces, and characteristic lengths of strain localization. To relate the magnitude of the internal length scale to parameters of the dislocation microstructure of the material, 3D discrete dislocation dynamics (DDD) simulations were performed for tricrystals of different dislocation source lengths (100, 200, and 300 nm). Comparing the strain profiles deduced from DDD with gradient plasticity predictions demonstrated that the internal length scale depends on the flow-stress-controlling mechanism. Different dislocation mechanisms produce different internal lengths. Furthermore, by comparing a gradient plasticity framework with interfacial yielding to the simulations it was found that, even though in the DDD simulations grain boundaries (GBs) were physically impenetrable to dislocations, on the continuum scale the assumption of plastically deformable GBs produces a better match of the DDD data than the assumption of rigid GBs. The associated effective GB strength again depends on the dislocation microstructure in the grain interior.
I. INTRODUCTION
Address all correspondence to this author. e-mail: [email protected] This paper has been selected as an Invited Feature Paper. DOI: 10.1557/jmr.2014.234
phenomenologically or physically based. Fleck et al.1 used the phenomenological strain gradient (SG) couple stress theory to explain the size effect observed in torsion experiments, and later reformulated and updated the theory, 11,13,14 for instance, to accommodate the requirement of thermodynamic consistency.11 The so-called-mechanism-based SG theory was proposed by Nix, Gao, and Huang et al. 5,10 to explain a series of experiments related to size effects; a systematic exploration of size effects using the SG theory can also be found in Ref. 18. Recently, a multilayer SG plasticity model has been used to model the strain burst or stress drop phenomena in micropillar compression. 19,20 A common feature of all these formulations is the prefactor of the SG, which for reasons of dimensional consistency must have the dimension of (an internal) length. The physical origin of the gradient term has already been discussed;21,22 however, the origin of this internal l
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