Some issues concerning the use of a single, material specific length scale parameter in theories of higher order strain gradient plasticity

Higher order strain gradient plasticity theories extend conventional ones with a view to explain the observed elevation of plastic flow stress in micron-sized structures. The essential elements of this modifications are the definition of a measure of plastic strain gradients, introduction of a conjugate higher order stress and introduction of one or more length scale parameters. We adopt a particular elasto-viscoplastic version of the higher order strain gradient theory based on a single scalar length scale parameter, formulate a large deformation based Finite Element model capable of handling strain gradients and higher order boundary conditions and simulate for three different materials, two sets of experiments where size effects manifest. The experiments differ in the level of plasticity that is induced during deformation — ranging from the order of the yield strain to approximately ten times its value. The materials, namely Cu, Al and Ni, have grain sizes that differ widely. We determine the scalar length scale parameter by demanding that the simulations match the experimental load deformation responses closely. The results indicate that single, scalar length scale parameter based higher order strain gradient theories cannot describe experimental observations across a wide range of geometries, boundary conditions, and plastic strain levels. The length scale is not intrinsic to the material but depends on the level of plastic strain induced by the deformation and also possibly on the number of grains involved in the deformation.