Taylor-based nonlocal theory of plasticity: Numerical studies of the micro-indentation experiments and crack tip fields

Recent advances in strain gradient plasticity have provided a means to quantitatively characterize the experimentally observed size effect at the micron and submicron scales. The introduction of strain gradients in the constitutive model has increased the order of governing equations and therefore require additional boundary conditions in some theories of strain gradient plasticity. Is it possible to develop a micro-scale plasticity theory that preserves the structure of classical plasticity? The Taylor-based nonlocal theory (TNT) of plasticity (Int. J. Solids Struct. 38 (2001), 2615) was developed from the Taylor dislocation model for this purpose. We have proposed a finite element method for TNT plasticity, and have applied it to study micro-indentation experiments. The micro-indentation hardness predicted by TNT plasticity agrees very well with the indentation hardness data. We have also studied the crack tip field in TNT plasticity, and have found that the stress level in TNT plasticity is significantly higher than that in classical plasticity. This provides an alternative mechanism for cleavage fracture in ductile materials observed in Elssner et al.'s experiments (Scripta Metall. Mater. 31 (1994) 1037).