An Investigation of Non-linear Stress-strain Behavior of Thin Metal Films
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An Investigation of Non-linear Stress-strain Behavior of Thin Metal Films
N. Huber, T. Dietz, E. Tyulyukovskiy Forschungszentrum Karlsruhe, Institut für Materialforschung II, Postfach 3640, D-76021 Karlsruhe, Germany ABSTACT Non-linear stress-strain curves of various films with thickness of one to four microns were determined from nanoindentation experiments with a Berkovich indenter. The measured loaddepth data are analysed using a method based on neural networks. An inverse mapping of depthdependent dimensionless hardness and stiffness data yields the material parameters describing a non-linear elastic-plastic stress-strain curve of the Armstrong-Frederick type. Suppositions for the application of this method are a sufficiently different hardness between film and substrate, and hardness and stiffness data available in a depth range of 10 to 200% of the film thickness. For all films considered a significant thickness dependence in strength has been observed. In addition, a remarkable influence of the substrate material on the strength of the film material was found and has been confirmed by focussed ion beam microscopy.
INTRODUCTION The stress-strain behavior of thin metal films is of significant importance for the design and reliability assessment of micro-electronic and micro/nano-mechanical systems. Only a few methods allow the measurement of the true stress-strain behaviour of films with thicknesses of and below one micrometer. Of practical relevance are micro tensile testing, micro cantilever deflection, and nanoindentation [1]. Among them nanoindentation is the most popular method for mechanical characterization of thin film properties, but the analysis methods are commonly restricted to hardness and modulus. Generally finite element simulations are required in order to perform a more sophisticated analysis and to extract information on the tensile behavior of the film material. Only a few analysis methods have been proposed for the identification of the stress-strain behavior of thin films from nanoindentation data. For a plastic film modelled with a power law hardening rule on an elastic substrate dimensionless scaling functions have been proposed for determining Young’s modulus, yield strength and strain hardening exponent from nanoindentation curves [2]. In [3] a neural network software was presented, which has been trained to solve the inverse problem of material parameter identification for elastic-plastic film and substrate materials. Theoretical suppositions for the application of this method are a sufficiently different hardness between film and substrate, and available hardness and depth data for a depth range from 10% to 200% of the film thickness in order to break the self similarity of the pyramidal indent and to provide sufficient information on the stress-strain behavior of the film material. The present work aims to (a) demonstrate the applicability of the neural network software for various film/substrate systems under practical conditions, (b) to investigate its limitations, and (
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