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Modelling the plastic deformation of nanostructured metals with bimodal grain size distribution.pdf

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Modelling the plastic deformation of nanostructured metals with bimodal grain size distribution

International Journal of Plasticity 30–31 (2012) 166–184Contents lists available at SciVerse ScienceDirect International Journal of Plasticity journal homepage: www.elsevier .com/locate / i jp lasModelling the plastic deformation of nanostructured metals with bimodal grain size distribution Linli Zhu a, Jian Lu b,? aDepartment of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China bDepartment of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong, Chinaa r t i c l e i n f o Article history: Received 12 April 2011 Received in final revised form 5 September 2011 Available online 8 October 2011 Keywords: Bimodal grain size distribution Strain gradient Strength Ductility Strain hardening0749-6419/$ - see front matter 2011 Elsevier Ltd doi:10.1016/j.ijplas.2011.10.003 ? Corresponding author. Tel.: +852 3442 9811; fa E-mail address: jianlu@.hk (J. Lu).a b s t r a c t Rendering a bimodal grain size distribution in nanostructured materials has been proved to effectively achieve both higher strength and higher ductility, which is based on the ansatz that large grains provide hardening ability and small grains provide larger yield stress. Here we propose a theoretical model focusing on the behaviour of nano/microcracks, which nucleate in the nano/ultrafine grained phase and stop at the boundary of large grains during the plastic deformation. We found that nano/microcracks do not lead to cata- strophic failure; instead, they induce the back stress for the strain hardening and also the variation of the mechanical behaviour in the nano/ultrafine grained phase. With the aid of the modified mean field approach, the stress–strain relationship of the bimodal met- als can be derived by combining the constitutive relations of the nano/ultrafine grained phase and the coarse grained phase. Numerical results show that the proposed model can successfully describe the enhanced strength and ductility of the bimodal me