Modelling of fatigue damage in granitic rock by piezoelectric effect in quartz phase due to alternating current excitation

Abstract

This paper considers numerical modelling of hypothetical fatigue damage in granitic rock by alternating current (AC) excitation of piezoelectric properties of Quartz. For this end, a numerical method consisting of a rock mineral mesostructure model, an implicit time stepping scheme to solve the piezoelectro-mechanical problem, and a fatigue damage model was developed. The rock material was assumed to be heterogenous linear elastic and isotropic, save the Quartz piezoelectric properties, which are anisotropic. An evolution equation-based continuum scalar damage model based on an evolving back stress tensor and a moving Drucker–Prager type of endurance surface was applied to compute the damage inflicted by the AC excitation. The damage was computed in a post-processed mode, i.e., un-coupled to the material model, at this stage of investigations. Some preliminary axisymmetric simulations are presented with a rock mesotructure based on electron backscatter diffraction data. These simulations corroborate the hypothesis that fatigue damage can be induced on granitic rock by converse piezoelectric effect in the Quartz phase by sinusoidal alternating current. More specifically, fatigue damage was induced on a disc-shaped numerical rock sample at a voltage of 15 kV with 2.5 kHz of frequency.