Qingyuan Wang

The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results

Abstract The flattened Brazilian disc specimen is proposed for determination of the elastic modulus E , tensile strength σ t and opening mode fracture toughness K IC for brittle rocks in just one test. This paper is concerned with the theoretical analysis as well as analytical and numerical results for the formulas. According to the results of stress analysis and Griffiths strength criteria, in order to guarantee crack initiation at the centre of the specimen, which is considered to be crucial for the test validity, the loading angle corresponding to the flat end width must be greater than a critical value (2 α ⩾20°). The analysis shows that, based on the recorded complete load–displacement curve of the specimen (the curve should include the ‘fluctuation’ section after the maximum load), E can be determined by the slope of the section before the maximum load, σ t by the maximum load, and K IC by the local minimum load immediately subsequent to the maximum load. The relevant formulas for the calculation of E , σ t , K IC are obtained, and the key coefficients in these formulas are calibrated by finite-element analysis. In addition, some approximate closed-form formulas based on elasticity are provided, and their accuracy is shown to be adequate by comparison with the finite-element results.

More accurate stress intensity factor derived by finite element analysis for the ISRM suggested rock fracture toughness specimen—CCNBD

More accurate stress intensity factor derived by finite element analysis for the ISRM suggested rock fracture toughness specimen-CCNBD

Recalibration and Clarification of the Formula Applied to the ISRM-Suggested CCNBD Specimens for Testing Rock Fracture Toughness

The cracked chevron-notched Brazilian disc (CCNBD) was proposed by the International Society for Rock Mechanics (ISRM) to test the mode I (opening mode) fracture toughness of rock. The test method has been vigorously discussed and debated, despite being the subject of intensive research for decades. The minimum (critical) dimensionless stress intensity factors affiliated with the formula for calculating the fracture toughness using CCNBD specimens with different geometric parameters remain elusive and complex. The matter cannot be resolved by simply replacing the diameter in the original formula with the radius, as claimed by several authors. In this paper, the formula is fundamentally improved, as wide-ranging minimum dimensionless stress intensity factors pertaining to diversified CCNBD geometries are recalibrated by three-dimensional finite element analysis, and an expression with tabulated coefficients is obtained through curve-fitting the data obtained from the numerical calibration. The present results are shown to be more accurate than those in the literature. Furthermore, the importance of the reasonability of the results is highlighted; a comprehensive comparison of different values shows that the upper bounds of minimum stress intensity factors are violated by the above claim. The confusion resulting from the claim is, thus, clarified conclusively.

Effect of Confining Pressure on Stress Intensity Factors for Cracked Brazilian Disk

An analytical model, verified by the finite element method, is developed to study the effect of confining pressure on stress intensity factors for the cracked Brazilian disk. The closed-form expressions for stress intensity factors under both confining pressure and diametric forces are obtained based on the weight function method. The results show that the confining pressure has no effect on the mode II stress intensity factor; however, the mode I stress intensity factor decreases with the increase of confining pressure and the change may be above 100% for a large confining pressure. In addition, the effect of confining pressure on the loading condition of pure mode II crack is also investigated. It is shown that the critical loading angle for pure mode II crack decreases as the confining pressure increases. Depending on the magnitude of confining pressure, the failure problem of a disk may be no longer a pure fracture problem. These results have established the theoretical foundation to measure the fracture toughness of materials under confining pressure.