Since the ISO standards for four major hardness scales were revised in 2005, the indirect verification has been considered as the mainstream of the traceability chain of hardness. In the recommended procedure of ISO, the uncertainty of hardness machine should be estimated and added to the combined uncertainty of hardness measurement value. The equation to calculate this uncertainty component was introduced according to the rectangular distribution of bias of hardness machines. However, if the error propagation is investigated in detail, the uncertainty of hardness machines should be obtained by considering the probability distributions of the uniformity of hardness reference block, the repeatability and the bias of hardness machine. In addition, the distribution of verification results should be calculated after some hardness machines are screened out by the maximum permissible values requested in ISO. In this paper, the probability distribution of the hardness machines, which passed in the indirect verification, are obtained by means of the Monte Carlo method. Since a calibration value of hardness is obtained only by measuring a specimen, it is not possible to separate the uncertainties of hardness machine and hardness block. Then the result of indirect verification is affected by the uniformity of reference block. The relation between the distribution of passed hardness machines and the uniformity of reference blocks is presented for several hardness scales. In addition, the guideline to estimate the uncertainty of the measured hardness values can be verified by means of the Monte Carlo method.

Analysis of indentation depth dependence of elastic modulus of soft films on silicon substrate measured by nanoindentation was studied. The experimental results were compared with two existing models that describe the effects of the substrate on elastic modulus of layered solid. Saha-Nix model that is the recent modification of King model agreed well with the experimental results to a certain limit of the indentation depth. It was found that the depth limit which Saha-Nix model is valid depended almost linearly on the relative elastic modulus of the film to the substrate Ef/Es. We further introduced an additional scaling parameter that is a linear function of Ef/Es in Saha-Nix model. The improved model was applied to porous silica low-k films. The model predicted a constant intrinsic elastic modulus of the film up to a depth of 30 % of the film thickness.

The influences of indenter micro-geometry on the micro-hardness performance in the film/substrate system are discussed. Experimental results verify the force required to produce hardness indents for thin films, the measurement of the size of plastic zone cross-sections of the indents, and the characterisation of the indenters. It was found that the deformation is highly localised beneath the indenter and failures in the corners of pyramidal indenters occurred.

Hardness measurement methods for rubber and plastics are described in the standards ISO 7619-1, ISO 7619- 2, ISO 868 and ISO 48. Rising requirements for the accuracy of this hardness measurement have led to the result that the users of rubber hardness testers and also metrology experts who deal with their calibration need a calibration method to check the overall function of the testers acknowledged by a standard. Therefore extensive experiments were conducted in a cooperation between the Physikalisch - Technische Bundesanstalt (PTB) in Braunschweig (Germany) and the ZAG Ljubljana (Slovenia). The results have been used as a basis for the elaboration of the relevant international standard ISO 18898 which was published in 2006. In this standard direct verification methods are laid down. An indirect verification method using rubber hardness reference blocks, which is also applicable for the verification of hardness testers, is presented in this paper. At present hardness reference blocks are available only for some of the hardness scales which are used for rubber materials. Suchwise, Shore A, IRHD N and IRHD M reference blocks are available in the market. During the verification process the hardness tester is calibrated by using rubber hardness reference blocks. The evaluation of the repeatability and the error of the hardness testers including the uncertainty of measurement of the calibration results is given in this paper.

In order to perform traceable hardness measurements using Rockwell Hardness Indenters, the indenter must conform to the requirement of ISO 6508-3 standard. The standard defines specifications for the geometric parameters for this type of indenter. Conformance to this standard is of particular importance to all calibration laboratories which operate in accordance with ISO/IEC 17025. At present there is no facility in South Africa with the capability of calibrating indenters for conformance to ISO 6508-3. This situation is being addressed through a series of studies currently being conducted at the National Metrology Institute of South Africa. The following parameters are calibrated using the µCMM. ISO 6508-3 specifies a radius of 200 µm with an uncertainty of ± 5 µm for Rockwell Hardness Indenter tips. Also specified in the ISO standard is the cone perpendicularity between the axis of the diamond cone to the axis of the indenter holder, with a specification of ± 0,03°. The last part of the ISO standard which was investigated states: “The surface of the cone and the spherical tip shall blend in a truly tangential manner.” All these parameters were measured and associated uncertainties calculated to prove conformance with ISO 6508-3 for the calibration of hardness indenters.