Determination of constitutive properties of thin metallic films on substrates by spherical indentation using neural networks

Abstract The indentation test has been developed into a popular method for investigating mechanical properties of thin films. However, there exist only some empirical or semi-analytical methods for determining the hardness and Young’s modulus of a film from pyramidal indentation of the film on a substrate, where the deformation of film and substrate is subjected to be elastic–plastic. The aim of the present paper is to show how constitutive properties and material parameters may be determined by using a depth-load trajectory which is related to a fictitious bulk film material. This bulk film material is supposed to possess the same mechanical properties as the real film. It is assumed that the film and the substrate exhibit elastic–plastic material properties with nonlinear isotropic and kinematic hardening. The determination of the depth-load trajectory of the bulk film is a so-called inverse problem. This problem is solved in the present paper using both the depth-load trajectory of the pure substrate and the depth-load trajectory of the film deposited on this substrate. For this, use is made of the method of neural networks. Having established the bulk film depth-load trajectory, the set of material parameters entering in the constitutive laws may be determined by using e.g. the method proposed by Huber and Tsakmakis (Huber, N., Tsakmakis, Ch., 1999. Determination of constitutive properties from spherical indentation data using neural networks. Part II: plasticity with nonlinear isotropic and kinematic hardening. J. Mech. Phys. Solids 47, 1589–1607).

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