Gradient plasticity theory with a variable length scale parameter

The definition and magnitude of the intrinsic length scale are keys to the development of the gradient plasticity theory that incorporates size effects. However, a fixed value of the material length-scale is not always realistic and different problems could require different values. Moreover, a linear coupling between the local and nonlocal terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings. This work addresses the proper modifications required for the full utility of the current gradient plasticity theories in solving the size effect problem. It is shown that the current gradient plasticity theories do not give sound interpretations of the size effects in micro-bending and micro-torsion tests if a definite and fixed length scale parameter is used. A generalized gradient plasticity model with a non-fixed length scale parameter is proposed based on dislocation mechanics. This model assesses the sensitivity of predictions to the way in which the local and nonlocal parts are coupled (or to the way in which the statically stored and geometrically necessary dislocations are coupled). In addition a physically-based relation for the length scale parameter as a function of the course of deformation and the material microstructural features is proposed. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and micro-torsion tests of thin wires.