A critical assessment of theories of strain gradient plasticity

Theories to extend plasticity to the micron scale have been in existence for over a decade, complemented by a growing body of experimental data. Here, materials and mechanics aspects of two prominent strain gradient theories of plasticity, due to Nix and Gao and to Fleck and Hutchinson, are assessed within the context of simple bending. Differences between the theories are highlighted. The theories predict different trends relative to the size dependence of initial yielding and rate of hardening. The dislocation mechanics underpinning the two theories is addressed. Distinctions between lower-order theories and higher-order theories are also drawn, emphasizing the flexibility of higher-order theories to solve problems for a wide range of boundary conditions, especially those where, locally, the dislocations are blocked (pile up) and the plastic strain is zero.