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

The indentation test has been developed into a popular method for investigating mechanical properties of thin ®lms. However, there exist only some empirical or semi-analytical methods for determining the hardness and Youngʹs modulus of a ®lm from pyramidal indentation of the ®lm on a substrate, where the deformation of ®lm 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 ®ctitious bulk ®lm material. This bulk ®lm material is supposed to possess the same mechanical properties as the real ®lm. It is assumed that the ®lm and the substrate exhibit elastic±plastic material properties with nonlinear isotropic and kinematic hardening. The determination of the depth-load trajectory of the bulk ®lm 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 ®lm deposited on this substrate. For this, use is made of the method of neural networks. Having established the bulk ®lm 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