Fields of plastic deformation in indented bilayers: comparison between kinematic calculations and experimental data obtained at scales ranging from one centimetre to ten nanometres

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Abstract
A simple incremental kinematic model (IKM) has been used to calculate the variations of indentation pressure Pm and shape of the plastic field with depth, in bilayers, the indentation angle being 35 degrees . For films softer or harder than the substrate, and for an adhesive or frictionless contact, the model's predictions were compared with experimental results at various scales of test. The IKM describes quite well the shape of the plastic fields observed directly in millimetre scale tests on plasticine blocks. In agreement with its predictions, the measured hardness remained equal to the intrinsic hardness of the film until it was fully penetrated, whatever the ratio of film to substrate hardnesses, the friction or the scale of the indent (in plasticine or in thin metallic bilayers). However, for depths greater than the film thickness, the calculated variations of Pm did not fit the observations, except in the few cases where the bilayers were fully plastic.

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