A conventional theory of mechanism-based strain gradient plasticity

The indentation size effect in the spherical indentation of iridium: A study via the conventional theory of mechanism-based strain gradient plasticity

The micro-indentation experiments have shown that the indentation hardness depends not only on the indentation depth hut also on the indenter tip radius. In fact, the indentation hardness displays opposite dependence on the indentation depth h for a sharp, conical indenter and for a spherical indenter, decreasing and increasing, respectively, with increasing h. We have developed an indentation model based on the theory of mechanism-based strain gradient plasticity to study the effect of indenter tip radius. The same indentation model captures this opposite depth dependence of indentation hardness, and shows the opposite depth dependence resulting from the different distributions of strain and strain gradient underneath a conical indenter and a spherical indenter. We have also used the finite element method to study the indentation hardness for a spherical indenter as well as for a conical indenter with a spherical tip. It is established that the effect of indenter tip radius disappears once the contact radius exceeds one half of the indenter tip radius.

The Influence of Indenter Tip Radius on the Micro-Indentation Hardness

Nix and Gao established an important relation between microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments (indentation depths in the micrometer range), but it does not always hold in nanoindentation experiments (indentation depths approaching the nanometer range). We have developed a unified computational model for both micro- and nanoindentation in an effort to understand the breakdown of the Nix–Gao relation at indentation depths approaching the nanometer scale. The unified computational model for indentation accounts for various indenter shapes, including a sharp, conical indenter, a spherical indenter, and a conical indenter with a spherical tip. It is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The unified computational model for indentation indeed shows that the Nix–Gao relation holds in microindentation with a sharp indenter, but it does not hold in nanoindentation due to the indenter tip radius effect.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0884291400087458

Indenter tip radius effect on the Nix–Gao relation in micro- and nanoindentation hardness experiments

On fracture in finite strain gradient plasticity

The theory of mechanism-based strain gradient (MSG) plasticity involves two material length parameters, namely the intrinsic material length land the mesoscale cell size le, which are on the order of a few microns and 0.1 μm, respectively. Prior studies suggest that lehas essentially no effect on the macroscopic quantities, but it may affect the local stress distribution. We demonstrate in this paper that there is a boundary layer effect associated with lein MSG plasticity, and the thickness of the boundary layer is on the order of l2ebig/l. By neglecting this boundary layer effect, a stress-dominated asymptotic field around a crack tip in MSG plasticity is obtained. This asymptotic field is valid at a distance to the crack tip between leand l(i.e., from 0.1 μm to a few microns). The stress in this asymptotic field has an approximate singularity of r−2/3, which is more singular than not only the HRR field in classical plasticity but also the classical elastic Kfield (r−1/2). The stress level in this asymptotic field is two to three times higher than the HRR field, which provides an alternative mechanism for cleavage fracture in ductile materials observed in experiments.

Ming Li

Papers

The boundary-layer effect on the crack tip field in mechanism-based strain gradient plasticity