Mechanical response and failure mechanism of circular inclusion embedded in brittle materials under dynamic impact

Inclusions are prevalent in both natural and synthetic materials. Gaining a comprehensive understanding of their dynamic response and interaction with the surrounding matrix is essential in fundamental mechanics and engineering applications. This study aims to achieve such understanding through theoretical analysis, experimental investigations, and numerical simulations, focusing on the dynamic destruction of inclusions and the underlying mechanisms. Firstly, the circumferential, radial, and shear stresses around elastic heterogeneous inclusions were derived by the wave function expansion and Duhamel integration methods. Subsequently, a set of experiments on sandstone specimens containing three types of inclusions (plaster, epoxy resin, cement) were conducted utilizing the Split Hopkinson Pressure Bar (SHPB) system in conjunction with high-speed photography and Digital Image Correlation (DIC) techniques to obtain the surface deformation of inclusion specimens. Eventually, a series of Finite Element Method (FEM) numerical simulations adopted suitable materials were also carried out to investigate the fracture process of inclusion and matrix under dynamic impact. The results demonstrate that the stress distributions and fracture mode of matrix and inclusion are highly dependent on the physical and mechanical properties of the inclusions and the surrounding matrix, specifically, density ρ, elastic modulus E, Poisson's ratio v, and strength. With an increase in the E and v, there is a reduction in the concentration of circumferential stress, while the radial and shear stresses experience an increase. The experimental and numerical results corroborated the theoretical findings and indicated that the localized dynamic stress concentrations induced by wave scattering around the inclusions directly dominated both local and overall specimen failure. Due to the dissimilarities in elastic parameters and strength between the inclusion and the matrix, the stress state of the inclusion and the interface is not homogeneous. Under dynamic loading, the weaker inclusion experiences tensile cracking at both ends of the loading, and as the mechanical properties (ρ, E, v, and strength) of the inclusion rise, a transition from tensile- hybrid-shear failure occurs within the inclusion. The findings of this study help us understand the dynamic failure mechanisms of dissimilar inclusions in brittle material.