A predictive strain-gradient model with no undetermined constants or length scales

A general meso‑scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc nume...

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Bibliographic Details
Published in:Journal of the mechanics and physics of solids 2020-12, Vol.145, p.104178, Article 104178
Main Authors: Zhou, G., Jeong, W., Homer, E.R., Fullwood, D.T., Lee, M.G., Kim, J.H., Lim, H., Zbib, H., Wagoner, R.H.
Format: Article
Language:English
Subjects:
Anelasticity
Bauschinger effect
Boundary conditions
Crystal Plasticity
Finite Element
GND
Harmonization
Heterogeneity
MATERIALS SCIENCE
Residual stress
Shape functions
Stagnation
Strain Gradient
Strain hardening
Stress distribution
Ta
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Summary:A general meso‑scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.
ISSN:0022-5096
1873-4782
DOI:10.1016/j.jmps.2020.104178