Modeling of fatigue behaviors of rock materials subjected to cyclic loads with fractional-order plastic flow rule

Abstract

Compressive cyclic loads induce a progressive failure in rock materials, and the long-term stability can not be guaranteed by the strength under monotonic load. To this end, the present study aims at establishing an elastoplastic fractional fatigue damage model for predicting the accumulative deformation of rock materials in a unified framework. A fractional-order plastic flow rule is introduced to describe volume transformation of rock sample from compression to expansion, eliminating the need for plastic potential functions. And a hardening function with an equivalent plastic shear strain is adopted. Concerning the fatigue effects, the progressive deterioration of material due to cyclic loads is intricately linked to microstructural degradation, depicted by a convolution law. In the context of creep deformation, loading cycle serves as an equivalent time measure, connecting the plastic deformation with the fatigue damage. In order to verify the accuracy, the proposed model is numerically implemented by a returning mapping procedure simulate the mechanical responses of three types of rocks in both uniaxial and triaxial cyclic tests. Comparative analysis with associated fatigue model is also provided to evaluate the accumulative deformation and damage evolution of concerned rocks.