Fractal characteristic of fracture in glass or single crystals of quartz by 3D micro X-ray CT measurement

摘要

We analyzed the fractal characteristic of fracture geometry of experimentally fractured borosilicaternglass and single crystals of quartz samples using 3D micro X-ray Computed Tomography (CT)rntechniques. The fracture experiments were performed at the confining pressure (P_c) of 300 MPa andrnuniaxial compression under nominal axial strain rate of 5.0×10~(-4)/s using a Griggs apparatus with arnlead confining medium. Then the space distributions of fractures using a Box-Counting method werernmeasured for each micro X-ray CT image sliced both perpendicular and parallel to the direction ofrnmaximum compressive stress (XY-planes, YZ-planes and ZX-planes. The space distributions ofrnfractures showed a power-law distribution. The scaling exponents (D_(BC)) of the correlation of thernfractures space distributions in YZ-planes and ZX-planes ranged uniformly. Otherwise D_(BC) of thernspace distributions of fracture patterns in XY-planes increased toward the sides of each sample,rnespecially D_(BC) of the the glass sample fractured at P_c = 300 Mpa (GLS-300) increased suddenly fromrn1.1 to 1.9 toward the highly fractured bottom side. The relation between D_(BC) of GLS-300 and thernlogarithm of the area distortion ε in XY-planes showed a positive correlation in the range of high arearndistortion ε > 1. The heterogeneous distribution of DBC possibly shows heterogeneous distribution ofrnfracture energy. DBC in the range of low area distortion ε < 1 showed the constant behaviors in thernrange of 1.1 < D(BC) < 1.2 and can be ragarded as the background D_(BC) by the elastic deformation beforernthe destruction. Our result implies the presence of heterogeneity in fracturing energy densityrndistribution even in highly homogeneous glass samples, which lay on the background DBC. Thereforernwe should consider the inhomogeneity and anisotropy of the fracture space distribution in case ofrncomparison with the fractal dimensions of different analyzing directions or locations.