Micro-bending of metallic crystalline foils by non-local dislocation density based crystal plasticity finite element model

Abstract A non-local dislocation density based crystal plasticity model, which takes account of the microstructure inhomogeneity, was used to investigate the micro-bending of metallic crystalline foils. In this model, both statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) are taken as the internal state variables. The strain gradient hardening in micro-bending of single-grained metal foils was predicted by evolution of GNDs. The predicted results were compared with the micro-hardness distribution of the previous micro-bending experiments of CuZn37 α-brass foils with coarse grains and fine grains. Comparison of the simulated dislocation densities distribution of SSDs and GNDs with the experimental results shows that different micro-hardness distribution patterns of the coarse and fine grain foils can be attributed to the corresponding SSDs and GNDs distributions. The present model provides a physical insight into the deformation mechanism and dislocation densities evolution of the micro-bending process.

[1]  Dierk Raabe,et al.  A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations , 2006 .

[2]  W. L. Chan,et al.  Experimental studies of plastic deformation behaviors in microheading process , 2012 .

[3]  J. Vlassak,et al.  Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments , 1998 .

[4]  Lining Sun,et al.  Effects of specimen size on flow stress of micro rod specimen , 2009 .

[5]  M. Fu,et al.  The size effect on micro deformation behaviour in micro-scale plastic deformation , 2011 .

[6]  Guo Bin.  Hybrid Micro-forming Processes and Quality Evaluation of Micro-double Gear , 2009 .

[7]  Huajian Gao,et al.  Mechanism-based strain gradient plasticity— I. Theory , 1999 .

[8]  Bin Guo,et al.  Effect of die cavity dimension on micro U deep drawing behaviour with T2 foil , 2009 .

[9]  Athanasios Arsenlis,et al.  Modeling the evolution of crystallographic dislocation density in crystal plasticity , 2002 .

[10]  James R. Rice,et al.  Strain localization in ductile single crystals , 1977 .

[11]  Xianghuai Dong,et al.  An effective semi-implicit integration scheme for rate dependent crystal plasticity using explicit finite element codes , 2012 .

[12]  Hinnerk Hagenah,et al.  Size effect on springback behavior due to plastic strain gradient hardening in microbending process of pure aluminum foils , 2010 .

[13]  Vasily V. Bulatov,et al.  On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals , 2004 .

[14]  M. Merklein,et al.  Determination of material intrinsic length and strain gradient hardening in microbending process , 2011 .

[15]  U. F. Kocks,et al.  Physics and phenomenology of strain hardening: the FCC case , 2003 .

[16]  Ulf Engel,et al.  Microforming—from basic research to its realization , 2002 .

[17]  M. Fu,et al.  Studies of the interactive effect of specimen and grain sizes on the plastic deformation behavior in microforming , 2012 .

[18]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[19]  M. Fu,et al.  Experimental and simulation studies of micro blanking and deep drawing compound process using copper sheet , 2013 .

[20]  Jian Cao,et al.  Crystal plasticity-based forming limit prediction for FCC materials under non-proportional strain-path , 2010 .

[21]  Reinhard Pippan,et al.  Mechanical properties of micro-sized copper bending beams machined by the focused ion beam technique , 2005 .

[22]  Bin Guo,et al.  Key Problems in Microforming Processes of Microparts , 2007 .

[23]  W. Brekelmans,et al.  Size effects in miniaturized polycrystalline FCC samples: Strengthening versus weakening , 2006 .

[24]  S. Graça,et al.  Determination of dislocation density from hardness measurements in metals , 2008 .

[25]  B. Guo,et al.  Polycrystalline model for FE-simulation of micro forming processes , 2011 .

[26]  Anthony G. Evans,et al.  A microbend test method for measuring the plasticity length scale , 1998 .

[27]  M. Gurtin,et al.  On the characterization of geometrically necessary dislocations in finite plasticity , 2001 .

[28]  Ri-chu Wang,et al.  Texture evolution of extruded AZ31 magnesium alloy sheets , 2009 .

[29]  B. Kinsey,et al.  Deformation size effects due to specimen and grain size in microbending , 2010 .

[30]  Jian Cao,et al.  Analysis of microbending of CuZn37 brass foils based on strain gradient hardening models , 2012 .

[31]  P. Franciosi,et al.  The concepts of latent hardening and strain hardening in metallic single crystals , 1985 .

[32]  Ying-hong Peng,et al.  Simulation of texture evolution during plastic deformation of FCC, BCC and HCP structured crystals with crystal plasticity based finite element method , 2011 .

[33]  Esteban P. Busso,et al.  Discrete dislocation density modelling of single phase FCC polycrystal aggregates , 2004 .

[34]  Norman A. Fleck,et al.  A phenomenological theory for strain gradient effects in plasticity , 1993 .

[35]  M. Ashby,et al.  Strain gradient plasticity: Theory and experiment , 1994 .

[36]  M. Fu,et al.  Geometry and grain size effects on the fracture behavior of sheet metal in micro-scale plastic deformation , 2011 .