@article {Liu2020-tk,
	title = {A comparison study of the unloading behavior in shale samples in nanoindentation experiments using different models},
	journal = {Journal of Petroleum Science and Engineering},
	volume = {186},
	year = {2020},
	pages = {106715},
	abstract = {Recently, nanoindentation has become an increasingly popular method for geomechanical analysis of rock samples in petroleum industry. Unloading curves of shale samples from the nanoindentation, which are considered as the pure elastic response, are used to determine the mechanical properties such as Young\&$\#$039;s modulus. In order to find a suitable model to characterize the unloading behavior of shale samples, in this study, we collected one Bakken Shale sample and performed nanoindentation tests on aliquots. First, the characteristics of the unloading curves were analyzed and then parameters such as: contact displacement and Young\&$\#$039;s modulus, based on two different prominent models (Oliver-Pharr model and Zeng-Chiu model) were calculated. Finally, values obtained from these two models were compared. The results showed that the unloading curves from the shale samples are nonlinear while Oliver-Pharr and Zeng-Chiu models both can be applied to represent the unloading curves. The mean Young\&$\#$039;s modulus from Oliver-Pharr model is around 1.2 times the value from Zeng-Chiu model. Using the Mori-Tanaka method, the upscaled Young\&$\#$039;s modulus value (32.14 GPa) from the Oliver-Pharr model is slight larger than the value from Zeng-Chiu model (28.70 GPa). In conclusion, the Oliver-Pharr model and Zeng- Chiu model can be both applied to study the unloading behavior of the nanoindentation curves.},
	keywords = {Model comparison, Nanoindentation, Shale samples, Unloading curve},
	author = {Kouqi Liu and Mehdi Ostadhassan and Xiaomeng Xu}
}
