A finite element study on the hardness of carbon nanotubes-doped diamond-like carbon film
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e hardness of the carbon nanotubes (CNTs)-doped diamond-like carbon (DLC) films is modeled by a nanoindentation finite element analysis. A three-dimensional (3D) formation where CNTs are modeled as transverse isotropy is compared with a two-dimensional (2D) analysis with isotropic CNTs. The results showed that for small CNTs volume fraction, the overall hardness of CNTs/ DLC/Si composites is controlled by the elastic modulus along the indentation direction. For vertical CNTs-doped DLC films, the hardness in 3D analysis is close to that in 2D analysis if the isotropic elastic modulus is taken as the long-axis direction. However, for horizontal CNTs-doped DLC films, the hardness in 3D and in 2D is similar if the 2D isotropic elastic modulus is taken as the short-axis direction of the 3D elastic modulus. As a result, for small CNTs volume fraction, the hardness of CNTs/DLC/Si composites can be modeled by a 2D isotropic inclusion as long as the elastic modulus is chosen properly. The hardness in CNTs/DLC/Si composites depends on the orientation of CNTs and the volume fraction. The mechanisms in hardness enhancement for different CNT orientations are explained by shear stress and the effective projected area. The issues like interface strength and indentation size effect are also addressed in terms of CNT orientations.
I. INTRODUCTION
High hardness, low friction coefficient, chemical inertness, biocompatibility, and wear resistance are good properties associated with diamond-like carbon (DLC) films. To further improve the properties, carbon nanotubes (CNTs) have been doped into DLC films. The elastic modulus of CNTs is at the order 1–3 TPa,1 which is 1,000 times higher than high-strength steel alloys.2 They also exhibit superior electrical and thermal properties.3 Research on CNTs doping is popular in the field of polymer composites for its effectiveness in improving the electrical, mechanical, and thermal properties,4 as well as in the field of metal matrix composites.5,6 The matrix can be either soft or ductile. For hard matrix like ceramics, many new strengthening mechanisms such as CNT collapse and shear banding occur.7 Recently, CNTs have been included in DLC films to increase toughness,8 reduce friction coefficient,9 or lower residual stress.10 However, the discrepancy in hardness of CNTs/DLC composites seems to depend on CNT orientations. For vertically grown CNTs-doped DLC films, the overall hardness is reduced compared to undoped ones,8 while for horizontal dispersed CNTs-doped DLC films, the overall hardness is increased.9 This phenomenon poses the question of exactly how the hardness in CNTs-doped
DLC films is affected by CNT orientation. In this work, we address this question by carrying out a nanoindentation to calculate the hardness of CNTs-doped DLC films on silicon substrates via three-dimensional (3D) and twodimensional (2D) finite element analysis. The effects of modulus anisotropy, CNT orientation, interface strength, and indentation size effect (ISE) on hardness and associated mechanisms are questions to be address
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