Strain-Dependent Variation of Critical Resolved Shear Stress: A Quantized Crystal Plasticity Analysis
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Date
2016-05
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The Ohio State University
Abstract
Nanocrystalline (NC) metals are metals comprised of numerous crystals (grains) that are smaller than 100 nm in diameter, on average. They have been an intense focus of research, due to several desirable mechanical properties, including high strength and high wear resistance. The classical Hall-Petch relationship between strength and grain size does not apply, suggesting that the underlying deformation physics is different in NC metals. This study uses the finite element method to explore how a variation in critical resolved shear stress (CRSS) at the nanocrystalline scale affects the macroscopic mechanical response of a NC metal. The model expands on prior work that is predicated on the phenomena whereby a dislocation loop propagates across a grain unimpeded by pinning sites, but is pinned instead by the grain boundary. The nature of this slip event means that each event is accompanied by a quantized change in strain that scales as the inverse of the grain size. The values for strain and the behaviors are mathematically constrained by the critical resolved shear stress, which has a distribution within a polycrystalline sample that is dependent on the size of the grain. This distribution, which is asymmetric, does not change over the previous simulation’s runs, and is a key factor to capturing the reversible plasticity in cyclic tension/compression tests. This analysis considers three fundamentally different behaviors: strain hardening, softening, or a mixture of the two. The CRSS increases if hardening is introduced. Hardening also extends the transition from fully elastic to fully plastic behavior and it reduces the recoverable plastic deformation upon unloading. Softening creates an ultimate tensile strength followed by a gradual softening during straining. The clear trends in full width at half max (FWHM) of the diffraction peaks prove the model is suitable to be used in time-dependent hardening/softening laws compared to experimental creep data for NC Ni. The peak position varies greatly based on the position of the diffraction group in the grain.
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Keywords
Finite Element Analysis, Nanocrystalline metals, Quantized Crystal Plasticity