In this study, an analytical model is proposed in order to determine the indentation depth of pop-in appearing in the loading process and investigate the effects of the C-film thickness of the C/a-Si composite film on the parameters of the indentation depth of pop-in, the inclined face angle, and the Si-substrate semiangle shown at the substrate after finishing indentation. This model is developed on the basis of the elastoplastic deformation model for the specimen in combination with the concept of applying a virtual indenter with a variable semiangle to the Si substrate. From good agreement between the predicted value and the experimental result, the present model is proved to be trustworthy in the predictions of the indentation depth of pop-in varying with the C-film thickness. Due to a higher gradient demonstrated in the stress of the composite film and stress of the Si-substrate verse indentation depth, a specimen with a thinner C-film is easier to reach the pop-in as compared to that shown in a thicker C-film. The present model is applicable for hard film/substrate specimen as occurring the pop-in behavior in nanoindentations.
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