Lower-order strain gradient plasticity theory with variable length scales

Abstract A fixed value of the material length scale is unrealistic. Different problems may require different values. This chapter addresses the proper modifications required for the full utility of the gradient plasticity theories in solving the size effect problems. It is shown that the current gradient plasticity theories do not give sound interpretations of the size effects in microbending and microtorsion tests if a definite and fixed length-scale parameter is used. A generalized lower-order gradient plasticity model with a nonfixed length-scale parameter is developed based on dislocation mechanics. A physically based relation for the length-scale parameter as a function of the course of deformation and the material microstructural features is addressed. The present model gives good predictions of the size effect in microbending tests of thin films and microtorsion tests of thin wires.