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.
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
We develop a new hierarchical dislocation-grain boundary (GB) interaction model to predict the mechanical behavior of polycrystalline metals at micro and submicro scales by coupling 3D Discrete Dislocation Dynamics (DDD) simulation with the Molecular Dynamics (MD) simulation.At the microscales,the DDD simulations are responsible for capturing the evolution of dislocation structures;at the nanoscales,the MD simulations are responsible for obtaining the GB energy and ISF energy which are then transferred hierarchically to the DDD level.In the present model,four kinds of dislocation-GB interactions,i.e.transmission,absorption,re-emission and reflection,are all considered.By this methodology,the compression of a Cu micro-sized bi-crystal pillar is studied.We investigate the characteristic mechanical behavior of the bi-crystal compared with that of the single-crystal.Moreover,the comparison between the present penetrable model of GB and the conventional impenetrable model also shows the accuracy and efficiency of the present model.
In this paper,the micromorphic theory and the second gradient theory are proposedwhere the micromorphic model can be reduced to the second gradient model with the vanishing relative deformation between macrodeformation gradient and microdeformation.Analytical solutions for the simple shear problem in the case of a general small strain isotropic elasticity micromorphic model and the second gradient model are presented,respectively.Besides,uniaxial tension of a constrained layer with two different boundary conditions is also analytically solved.Finally,the micromorphic theory is implemented numerically within a two-dimensional plane strain finite element framework by developing two isoparametric elements.
