Abstract The Bauschinger and size effects in the thin-film plasticity
theory arising from the defect-energy of geometrically necessary
dislocations (GNDs) are analytically investigated in this paper.
Firstly, this defect-energy is deduced based on the elastic
interactions of coupling dislocations (or pile-ups) moving on the
closed neighboring slip plane. This energy is a quadratic function
of the GNDs density, and includes an elastic interaction
coefficient and an energetic length scale L. By incorporating it
into the work-conjugate strain gradient plasticity theory of
Gurtin, an energetic stress associated with this defect energy is
obtained, which just plays the role of back stress in the
kinematic hardening model. Then this back-stress hardening model
is used to investigate the Bauschinger and size effects in the
tension problem of single crystal Al films with passivation
layers. The tension stress in the film shows a reverse dependence
on the film thickness h. By comparing it with
discrete-dislocation simulation results, the length scale $L$ is
determined, which is just several slip plane spacing, and accords
well with our physical interpretation for the defect-energy. The
Bauschinger effect after unloading is analyzed by combining this
back-stress hardening model with a friction model. The effects of
film thickness and pre-strain on the reversed plastic strain after
unloading are quantified and qualitatively compared with
experiment results.
Corresponding Authors:
Z.L. Liu
E-mail: liuzhanli@tsinghua.org.cn
Cite this article:
Z.L. -Liu,ZHUANG Zhu,LIU Xiao-Meng et al. Bauschinger and size effects in thin-film plasticity due to defect-energy of geometrical necessary dislocations[J]. Acta Mechanica Sinica, 2011, 27(2): 266-276.
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