Length scale effect on mechanical behavior due to strain gradient plasticity

The characteristic material length scale l as introduced in the phenomenological theory of strain gradient plasticity by Fleck and Hutchinson [1] is crucial for the application of the theory. Three dislocation models are proposed in this paper for the derivation of the material length scales as there is a rational connection between dislocation theory and phenomenological theory. The length scale is determined as a function of material fundamental parameters and is independent of how the ‘overall effective strain’ is measured, or how the dislocations interact. The length scale is generally about 1.5 μm or less, agreeing with the observation that the size effect appears approximately at 1 μm and sub-micrometer levels for indentation deformations. The dislocation interaction is also discussed in the framework of strain gradient plasticity.