By Gerard G. Emch
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Extra info for Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Physics & Astronomical Monograph)
Stored dislocations can be divided into two groups: statistically stored dislocations (SSDs) and GNDs. SSDs are generated by trapping each other in a random way and believed to be dependent on effective plastic strain. On the other hand, GNDs are the stored dislocations that relieve plastic-deformation incompatibilities within the material caused by nonuniform dislocation slip. The density of GNDs is directly proportional to the gradients of effective plastic strain, and their presence causes additional storage of defects and, Fig.
3 Schematic plot of variations in GND and SSD densities with indentation depth using a sharp (a) and spherical indenter (b) hardness . On the other hand, the experimental study of  with a sharp indenter demonstrated that the total GND density below the indents decreased with decreasing indentation depth. This observation contradict the strain-gradient theories attributing size-dependent material properties to GNDs. Abu Al-Rub and Voyiadjis  interpreted the size effect in hardness experiments with a spherical indenter in a different way.
Some authors argued that the size dependence of material’s mechanical properties resulted from an increase in strain gradients inherent to localized zones, which necessitated the presence of geometrically necessary dislocations resulted in additional hardening . The characteristic features of deformation in metals are formation, motion and storage of dislocations. According to a Taylor’s hardening rule, dislocation storage is responsible for material hardening. Stored dislocations can be divided into two groups: statistically stored dislocations (SSDs) and GNDs.