Correlating the internal length in strain gradient plasticity theory with the microstructure of material

The internal length is the governing parameter in strain gradient theories which among other things have been used successfully to interpret size effects at the microscale. Physically, the internal length is supposed to be related with the microstructure of the material and evolves during the deformation. Based on Taylor hardening law, we propose a power-law relationship to describe the evolution of the variable internal length with strain. Then, the classical Fleck–Hutchinson strain gradient theory is extended with a strain-dependent internal length, and the generalized Fleck–Hutchinson theory is confirmed here, by comparing our model predictions to recent experimental data on tension and torsion of thin wires with varying diameter and grain size. Our work suggests that the internal length is a configuration-dependent parameter, closely related to dislocation characteristics and grain size, as well as sample geometry when this affects either the underlying microstructure or the ductility of the material.