A strain gradient crystal plasticity analysis of grain size effects in polycrystals

The influence of grain size on yield and flow stress in polycrystalline metals is analyzed using a strain gradient crystal plasticity theory with an internal material length scale. The numerical solutions are obtained with the finite element method considering a polycrystal modeled by 40 individually oriented grains in a unit cell, each having three planar slip systems. An energy potential that penalizes crystallographic slip at grain boundaries is included in the analyzes. The polycrystal is subjected to plane strain tension for various grain sizes and higher order boundary conditions at the grain boundaries. An increase in flow stress with decreasing grain size, d, was obtained on the form d − n , with n in the range 0.82 to 1.25 at initial yield and in the range 0.77 to 1.09 after 0.1 logarithmic strain.