Ductile damage Cam-Clay plasticity and fracture modeling of shale based on nano-characterization experiment

Abstract:

A finite strain ductile damage formulation of Modified Cam-Clay (MCC) plasticity has been developed in order to model the observed elastoplastic behavior of shale at nano- to micro-scales. Nano-indentation combined with both 2D and 3D imaging was performed on a sample of Woodford shale. Significant plastic deformation was observed in the nano-indentation testing, and nano-scale resolution FIB-SEM imaging of the post-indented regions has revealed that the plastic deformation is accompanied by extensive micro-fracture of the shale's highly heterogeneous micro-structure.

A spatial tensor that is similar to Eshelby's energy momentum tensor is shown to be energy conjugate to the plastic velocity gradient under large inelastic volume strain. These results are cast in MCC framework drawing on the concept of continuum damage. The resulting formulation provides a connection between density (porosity), elastic (and plastic) moduli, and micro damage/healing. Nonlinear finite element modeling is used for implementation of the constitutive model in simulation of both laboratory-scale and nano- to micro-scale experiments. The results show that the model is able to predict the inception and propagation of micro-fractures around inhomogeneities, as well as capture the resulting behavior observed at the much larger laboratory scale.