The Bauschinger and size effects in the thin-film plasticity theory arising from the defect-energy of geometrically necessary dislocations were analytically investigated in this paper. Firstly, this defect-energy was deduced based upon the elastic interactions of coupling dislocations (or pile-ups) moving on the closed neighbouring slip plane. This energy was a quadratic function of the geometrically necessary dislocation 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 was obtained, which just played the role of back stress in the kinematic hardening model. Then this back-stress hardening model was 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 showed a reverse dependence upon the film thickness h. By comparing it with discrete-dislocation simulation results, the length scale L was determined, which was just several slip-plane spacings, and agreed well with the present physical interpretation of the defect energy. The Bauschinger effect after unloading was 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 were quantified and qualitatively compared with experiment results.

Bauschinger and Size Effects in Thin-Film Plasticity Due to Defect-Energy of Geometrical Necessary Dislocations. Z.L.Liu, Z.Zhuang, X.M.Liu, X.C.Zhao, Y.Gao: Acta Mechanica Sinica, 2011, 27[2], 266-76