Assessment of mechanical properties using instrumented indentation and inverse methods

The present work deals with the determination of mechanical properties of materials using instrumented indentation techniques. The main advantage of indentation testing is that it is relatively simple to perform and does not need any special and time-consuming sample preparation. Furthermore, the tests can be performed on very small volumes and samples. However, the determination of mechanical properties from simple indentation tests is not as straightforward. This is mainly due to the many nonlinearities encountered (large and non-homogeneous deformations, contact involving friction, plasticity) which prevent a complete analytical treatment. In this work, two inverse methods are presented which permit to determine the stress-strain behaviour of materials from the analysis of the indentation response which could be applied both at the micro- and nanometre range. The first method is based on the use of conical indenters characterized by different included half-angles θ. The inverse algorithm developed in this work permits to attribute a representative strain value er to each indenter geometry. The corresponding representative stress value εr is calculated from the curvature of the loading curve. In this manner, it is possible to construct a stress-strain curve in a point-wise manner. The second method relies on finite element simulations which are controlled by an external optimization program. The materials stress-strain behaviour is assumed to follow a given constitutive law and the parameters of the constitutive law are then adjusted in a manner such as to reconstruct the experimental data as accurately as possible. The two stress-strain methods are validated on a series of bulk Al and Cu based alloys as well as UV LIGA Ni based coatings. For this, the stress-strain curves as well as the relevant tensile parameters (Young's modulus E, yield stress σy, hardening coefficient n) obtained experimentally are compared to the stress-strain curve and material parameters obtained with the two inverse methods. Both methods have permitted to estimate the stress-strain behaviour of bulk metallic materials tested here. The respective advantages and disadvantages of the two methods are put into evidence and possible further extensions and improvements are discussed in the final part of this work.