Experimental investigation on the creep behaviors of shale using nanoindentation technique and fractional constitutive models

Viscoelasticity is a key mechanical feature of shale that can influence a variety of oil and gas engineering issues. To describe the time-dependent creep behavior of shale at nano-scale, the nanoindentation technique was used. Moreover, Maxwell and Zener fractional derivative models were applied for the fitting data and the applicability and the accuracy of these fractional viscoelastic models are discussed. Moreover, the creep difference on samples with different mineral compositions may be compared using Energy Dispersive Spectra (EDS) mapping techniques. The experimental results indicate that there is a better match between fitting values and measured values versus time by fractional models compared to traditional viscoelastic models. Furthermore, fitting parameter changes with different holding times were investigated. The results demonstrate that the fractional Zener model yield the highest RMSE and R2, indicating the optimal fitting results. The fractional Maxwell model likewise provides an excellent fit to the data and takes the least amount of time to compute, however, the creep response is infinite. In addition, both elastic parameters and fractional derivatives decrease while viscous parameters increase along with a reduction of Young's modulus and hardness, indicating microdamage accumulation induced by the viscoelastic behavior of shale. Comparing the results of clay-rich and quartz-rich samples showed reduced stiff shale creep, but creep-induced deformation led to more obvious deformation and mechanical strength reduction. This study not only investigates the use of nanoindentation in the creep analysis of composite shale but also shows that fractional models can be used to characterize shale viscoelasticity.