ICMCTF2006 Session E3-1: Determining Constitutive Relationships by Instrumented Indentation on Techniques

We present two instrumented indentation methods for determining yield stress and strain hardening coefficient of metalic coatings.

The first method is based on a series of indentations with conical indenters exhibiting different included angles. From parametric finite element simulations we have constructed, for each included angle, a dimensionless function relating the characteristic parameters of the indentation loading curve to the Young's modulus, the yield strength, and the strain hardening exponent.

The second method relies on inverse finite element simulations controlled by an automated fitting algorithm that is used to estimate elastic modulus, yield strength and hardening coefficient from spherical indentation load-displacement curves. It turns out that experimental load-displacement curves can be reproduced within convergence limits of the fitting algorithm without the correct set of material parameters of the constitutive model. The convergence could be improved by using starting values for the fitting procedure based on a Meyersâ?T analysis of the load displacement curves, but in order to obtain unambiguous results post-indentation surface topography were incorporated into the fitting scheme.

Both methods were applied to assess yield stress and strain hardening coefficients of electrodeposited Ni and NiCo coatings for UV-LIGA applications. In particular, the influence of of a post-annealing on the microstructure and on the mechanical properties of the coatings is investigated. Conical nanoindentation tips and spherical nanoindentation tips were used. The accuracy of both methods depending on the precision of the cone angles and on tip defects, respectively, is discussed. A comparison with microtensile tests on the same materials was performed to validate the results.

The complex deformation in indentation testing requires analysis methods that account for nonlinear material behaviour as well as nonlinearities induced by the contact problem. Depending on the generality of the constitutive model, indenter geometry and the specimen (bulk material or thin film), different suppositions need to be fulfilled to solve the inverese problem uniquely. Finally an inverse algorithm is needed to determine the material parameters under the assumption of a constitutive model.

The presentation gives an overview on recent finite element and neural network based approaches for the identification of material parameters and the determination of stress-strain behaviour for different constitutive models and indentation experiments. The importance of a properly chosen loading history, zero-point correction, and tip shape correction for imperfect spherical tips will be demonstrated.

TiC monolayers and Ti/TiN/TiC/TiCN multilayers were deposited onto AISI 4340 steel substrates at 300°C and 4.0x10^-2 mbar nitrogen/methane pressures by using a Pulsed-Laser Deposition technique. A Nd: YAG laser (1064 nm, 500 mJ and 7 ns), with a repetition rate of 10 Hz was used. Here we analyzed the difference in structure and morphology for single layers and multilayers structures deposited on stainless steel substrates. AFM analysis presented different morphologies; showing, that the single layer had an average grain size of 0.087 µm; while the multilayers exhibited grain sizes of 0.045 µm. Coating thicknesses were 1 µm, approximately, and monolayer average roughness was 0.21 µm; while a value of 0.15 µm was measured for multilayers. Under a 60 Kg maximum load applied in tension to evaluate the adhesion to the substrate, no detachment of the films was presented. Multilayers evidenced better impact resistance as compared with TiC single layer; this result is considered, bearing in mind that in multilayers propagation of fissures is slower, because the presence of layer inter-phases, lead to fissures strays in other directions. Slight corrosion specks are present; but mass loss was around 16 mg. in multilayers a value was lower than for the TiC single layer that was near 43 mg. Homogeneity, grain size, fracture resistance, corrosion resistance, and adhesion of the multilayers are suitable for mechanical applications of these types of coatings as shown in mechanical measurements. These results indicate that for engineering applications under corrosive environments, the use of this type of multilayered coatings on AISI 4340 steel, are highly recommended.

This work was supported by COLCIENCIAS under the program Excellence Center for Novel Materials, contract No. 0043-2005.