Scale effects in microindentation of ductile crystals

Abstract

Indentation testing has long been a standard test used to classify all types of materials. In the past several decades the scale of indentation testing has moved into the micron and even sub-micron range. For many types of materials, at these small length scales, the hardness of the material measured by the indentation test depends on the depth of the indentation. This indentation size effect was not observed at the larger length scales. Because indentation testing with conical or pyramidal indenter tips is geometrically similar, the existence of a size effect was surprising. Since the size effect associated with microindentation was discovered, many theories about its cause have been proposed. Several of the theories suggest that the source of the indentation size effect is experimental error. Such factors as inaccurate measurement of the contact area, indenter tip deformities, improper surface preparation, lateral movement of the indenter tip, inhomogeneity of the material, compliance of the test fixture, anisotropic deformations, thermal drift, and noise have been cited as areas where experimental error may play a role in the size effect. Another group of theories suggests that there are actual physical causes for the size effect. Some of the proposed physical causes of the size effect are friction between the specimen and the indenter tip, elastic recovery of the indent, material pile-up and sink- in, work-hardened surface material, oxidized surface layers, and variation of material parameters due to the stress state of the material. One area that has received some attention recently as a possible cause of the indentation size effect is hardening resulting from geometrically necessary dislocations (GNDs). GNDs arise due to curvature in the crystalline lattice from gradients of plastic shear strain. As the indentation depth decreases, the relative strain gradients within the test specimen increase.

(cont.) These relative increases in strain gradients cause increased levels of GND densities which in turn cause increased material hardening. This increased hardening is observed as the indentation size effect. A material model has been developed that explicitly incorporates the geometrically necessary dislocation hardening within a crystal plasticity framework (Dai, 1997; Dai et al., 2000). This model has been used to conduct a two-dimensional finite element study of the indentation size effect. Additionally, the effects of strain rate and friction on the indentation size effect were studied. It was found that the GND hardening accounted for the indentation size effect of work-hardened and annealed copper very well. Further, a series of plots of the contours of the geometrically necessary dislocation density and deformation resistance clearly indicated the relative decrease of the GND density and deformation resistance for increasingly larger indentation depths. It was found that for strain-rate sensitive material, variation of strain-rate during the indentation process could also cause a substantial indentation size effect. To eliminate the size effect due to strain-rate, it is necessary to use an exponential tip displacement/time curve during the indentation test. Three cases of friction were studied; no friction, mild friction, and strong friction. All of the friction cases produced very close to the same indentation hardness/depth curves, indicating that, for the large-angle indenter tip used in the simulation, friction had a very small effect.

(cont.) Further research in this area should include the effects of indenter tips of different angles and cases of non-symmetry between the indenter tip and the crystalline slip planes. Both variation of indenter tip angles and crystalline and indenter tip non-symmetry can be studied in a two-dimensional model. A three-dimensional model could be used to study indentation contact area with respect to material pile-up and sink-in, verify the GND density results from the two-dimensional model, and further study the effects of indentation strain-rate and friction on microindentation.