An inelastic-damage micromechanical model based on the wing- and secondary-cracking mechanisms under dynamic loading

Abstract

For most rock materials, there exists a coupling between inelastic deformations caused by crack displacements on micro-crack faces and damage evolution due to nucleation and growth of wing- and secondary-cracks. While rock material is subjected to dynamic loading, the interaction between micro-cracks plays an important role in materials behavior. The self-consistent homogenization scheme is implemented in this paper to consider micro-cracks interaction and determine the equivalent mechanical properties of micro-cracked rock deteriorated by damage evolution. The aim of this article is to develop a self-consistent based micromechanical damage model by taking into account the wing- and secondary-cracking mechanisms accompanied by inelastic strains caused by crack displacements under dynamic compressive loading. While stress intensity factors in tensile and in-plane shear modes at flaw tips exceed the material fracture toughness in modes I and II, respectively, wing- and secondary-cracks are sprouted and damage evolution occurs. For closed cracks, an appropriate criterion for the secondary-crack initiation is proposed in this paper. Moreover, the evolution rule for the secondary-crack is determined based on the principles of dynamic fracture mechanics. The developed model algorithm is programmed in the commercial finite difference software environment for numerical simulation of rock material to investigate the relationship between the macroscopic mechanical behavior and the microstructure. The fracture toughness parameters of the rock samples are experimentally determined. The rock microstructure parameters (average initial length and density of flaws) are studied using scanning electron microscopy. In order to verify the developed model, a series of numerical simulations are carried out to numerically reproduce the Split-Hopkinson pressure bar test results. The numerical simulation results are in agreement with the experimental data. The simulation results demonstrate that the developed micromechanical model can adequately reproduce many features of the rock behavior such as softening in post-peak region, damage induced by wing- and secondary-cracks and irreversible deformations caused by crack displacements on micro-cracks. Furthermore, the softening behavior of rock material in the post-peak region is affected by considering inelasticity and the secondary-cracking mechanisms. Therefore, the rock sample simulation with the coupled inelastic-damage model can increase inelastic deformations in the post-peak region as a result of irreversible strains caused by crack displacements on micro-cracks. The simulation by considering the secondary-crack mechanism leads to an increase in the microcracking process and damage in rock material.