Bauschinger and size effects in thin-film plasticity due to defect-energy of geometrical necessary dislocations  

作　　者：Zhan-Li Liu · Zhuo Zhuang · Xiao-Ming Liu · Xue-Chuan Zhao · Yuan Gao Department of Engineering Mechanics, School of Aerospace, Tsinghua University, 100084 Beijing, China 

出　　处：《Acta Mechanica Sinica》2011年第2期266-276,共11页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (10772096)

摘　　要：The Bauschinger and size effects in the thinfilm 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.The Bauschinger and size effects in the thinfilm 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.

关 键 词：Thin film · Crystal plasticity · Defect energy · Back stress · Size effect 

分 类 号：O484.2[理学—固体物理]