Fracture size effect in ultrananocrystalline diamond: Applicability of Weibull theory
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X. Xiao, O. Auciello,b) and J.A. Carlisle Materials Science Divisions, Argonne National Laboratory, Argonne, Illinois 60439 (Received 18 March 2006; accepted 29 June 2006)
An analysis of size effects and doping on the strength of ultrananocrystalline diamond (UNCD) thin films is presented. The doping was achieved by the addition of nitrogen gas to the Ar/CH4 microwave plasma. The strength data, obtained by means of the membrane deflection experiment (MDE) were interpreted using Weibull statistics. The validity and predictive capability of the theory were examined in conjunction with detailed fractographic and transmission electron microscopy microstructural analysis. The Weibull parameters were estimated nonlinear regression based on 480 tests when the specimen volume varied from 500 to 16,000 m3. Both undoped and doped UNCD films exhibited a decrease in strength with an increase in specimen size. A significant drop in strength was measured when the films were doped with nitrogen. Such a drop was almost independent of the percentage of doping. The results also showed that one can predict the fracture strength of a component possessing any arbitrary volume to within ±3%. Moreover, the failure mode of UNCD was found to be volume controlled. We also report changes in Young’s modulus as a function of doping for n-doped UNCD thin films.
I. INTRODUCTION
Failure of brittle materials is caused by the unstable propagation of microcracks that initiate at surface or volume defects. Typically, such defects exhibit a random distribution of size, orientation, and location. At the millimeter or larger size scale, where microstructure details are averaged, material strength does not strongly depend upon the size and shape of the test specimen. Other characteristics of the system such as the size of the process zone ahead of a crack tip become dominant. However, at the micron and sub-micron scale, where the number of defects can be greatly reduced by decreasing the size of the interrogated volume or surface, fracture strength is strongly size dependent. This size effect can be explained by the statistical theory first proposed by Weibull.1,2 This theory describes strength variability in brittle materials by means of well-defined statistical parameters. Hence,
a)
Address all correspondence to this author. e-mail: [email protected] b) This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of articles authored by editors, please refer to http://www.mrs.org/ jmr_policy. DOI: 10.1557/JMR.2007.0137 J. Mater. Res., Vol. 22, No. 4, Apr 2007
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knowledge of these material parameters, i.e., Weibull modulus and characteristic strength, is the first step in developing predictive capabilities in applications of interest, for instance, microelectromechanical systems (MEMS).3,4 The existence of size effect in brittle MEMS materials has been reported by LaVan et al.,5,6 Sharpe et al.,3,4,7 Espinosa et al.,8,9 Ba
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