A potential for higher-order phenomenological strain gradient plasticity to predict reliable response under non-proportional loading

Andrea Panteghini, Lorenzo Bardella, Christian F. Niordson

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Abstract

We propose a plastic potential for higher-order (HO) phenomenological strain gradient plasticity (SGP), predicting reliable size-dependent response for general loading histories. By constructing the free energy density as a sum of quadratic plastic strain gradient contributions that each transitions into linear terms at different threshold values, we show that we can predict the expected micron-scale behaviour, including increase of strain hardening and strengthening-like behaviour with diminishing size. Furthermore, the anomalous behaviour predicted by most HO theories under non-proportional loading is avoided. Though we demonstrate our findings on the basis of Gurtin (Gurtin 2004 J. Mech. Phys. Solids 52, 2545-2568, doi:10.1016/j.jmps.2003.11.002) distortion gradient plasticity, adopting Nye's dislocation density tensor as primal HO variable, we expect our results to hold qualitatively for any HO SGP theory, including crystal plasticity.
Original languageEnglish
Article number20190258
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume475
Issue number2229
Number of pages21
ISSN1364-5021
DOIs
Publication statusPublished - 2019

Keywords

  • Strain gradient plasticity
  • Non-proportional loading
  • Cyclic plasticity
  • Dislocation density tensor
  • Size effect
  • Finite-element method

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