Ming-Dong Wei

Numerical Assessment of the Progressive Rock Fracture Mechanism of Cracked Chevron Notched Brazilian Disc Specimens

The International Society of Rock Mechanics (ISRM) suggested cracked chevron notched Brazilian disc method falls into a major testing category of rock fracture toughness measurement by virtue of chevron notched rock samples. A straight through crack front during the whole fracturing process is assumed in the testing principle but is never assessed. In this study, the progressive rock fracture mechanism of cracked chevron notched Brazilian disc rock specimens is numerically simulated for the first time. Two representative sample types with distinct geometry of notch ligaments are modelled. The assumption of a straight through crack front for chevron notched fracture samples is critically assessed. The results show that not only the notch tip but also the saw-cut chevron notch cracks during the experiments. The straight through crack front assumption is never satisfied in the realistic rock fracture progress of chevron notched disc samples. In addition, the crack features prominent curved front, far from being straight. In contrast to the sample type with narrow notch ligament, the acoustic emission (AE) of the simulation on the sample with wide notch ligament depicts obvious biased fracturing of the prescript fracturing route of the notch. The numerically observed progressive fracture mechanism calls for more attention on how to accurately calibrate the critical dimensionless stress intensity factor for a better measurement of Mode I fracture toughness via chevron notched samples.

Numerical Observation of Three-Dimensional Wing Cracking of Cracked Chevron Notched Brazilian Disc Rock Specimen Subjected to Mixed Mode Loading

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by International Society for Rock Mechanics for measuring mode I fracture toughness of rocks. Subsequently, this specimen geometry has been widely extended to conduct mixed mode fracture tests on rocks as well. A straight through crack front during the fracturing process upon the root of the chevron notch is assumed in the testing principle, but has never been thoroughly evaluated before. In this study, for the first time, the progressive rock fracture mechanism of the CCNBD rock specimen under mixed mode loading is numerically simulated. Specimens under representative mixed mode loading angles are modelled; and the assumption of the straight through crack front growth is critically assessed. The results show that not only the notch tip but also the saw-cut chevron notch cracks during the experiments, yielding a prominent twisted front, far from being straight. The crack front never grows up to the root of the notch ligament and the straight through crack front assumption is never satisfied in the realistic rock fracture progress of this chevron notched specimen subjected to mixed mode loads. In contrast, the fracture progress features typical three-dimensional wing cracking towards the loading ends. The numerically observed progressive fracture mechanism reveals that the measuring principle of mixed mode fracture tests employing CCNBD specimens is significantly violated and the measures of both modes I and II fracture toughness are uncertain.

Experimental and Numerical Study on the Cracked Chevron Notched Semi-Circular Bend Method for Characterizing the Mode I Fracture Toughness of Rocks

The cracked chevron notched semi-circular bending (CCNSCB) method for measuring the mode I fracture toughness of rocks combines the merits (e.g., avoidance of tedious pre-cracking of notch tips, ease of sample preparation and loading accommodation) of both methods suggested by the International Society for Rock Mechanics, which are the cracked chevron notched Brazilian disc (CCNBD) method and the notched semi-circular bend (NSCB) method. However, the limited availability of the critical dimensionless stress intensity factor (SIF) values severely hinders the widespread usage of the CCNSCB method. In this study, the critical SIFs are determined for a wide range of CCNSCB specimen geometries via three-dimensional finite element analysis. A relatively large support span in the three point bending configuration was considered because the fracture of the CCNSCB specimen in that situation is finely restricted in the notch ligament, which has been commonly assumed for mode I fracture toughness measurements using chevron notched rock specimens. Both CCNSCB and NSCB tests were conducted to measure the fracture toughness of two different rock types; for each rock type, the two methods produce similar toughness values. Given the reported experimental results, the CCNSCB method can be reliable for characterizing the mode I fracture toughness of rocks.

DEM investigation on fracture mechanism of the CCNSCB specimen under intermediate dynamic loading

The cracked chevron notched semi-circular bending (CCNSCB) method falls into a significant testing category of chevron notched specimens for measuring the mode I fracture toughness, of which the progressive fracture mechanism deserves to be further assessed under intermediate dynamic loading rate (IDLR). In this study, the discrete element method (DEM) is adopted to depict the three-dimensional fracture processes of the CCNSCB specimens subjected to different IDLRs considering different supporting spans. The results demonstrate that the crack front of the CCNSCB specimen with any loading condition is prominently curved, which violates the straight-through crack propagation assumption and may induce some errors in the fracture toughness measurements. For each IDLR, the peak force of the CCNSCB specimen evidently increases with decreased supporting span, and the effect of loading rate on this parameter is more prominent for a smaller supporting span. For a relatively large span, the crack grows restrictively in the notched ligament, which conforms to the ideal assumption of the fracture process and contributes to an accurate measurement of the mode I fracture toughness. Thus, a large supporting span is suggested for the semi-circular bend tests. Additionally, the critical crack length and peak force are found dependent on the loading rate, and they are larger for the higher loading rate. Thus, the critical crack length determined under quasi-static conditions is not strictly suitable for the specimens under different IDLRs, especially for the much higher IDLR. This study calls for more attention on how to accurately determine the fracture toughness via chevron notched samples.

A Further Improved Maximum Tangential Stress Criterion for Assessing Mode I Fracture of Rocks Considering Non-singular Stress Terms of the Williams Expansion

Previous studies showed that the modified maximum tangential stress (MMTS) criterion considering two stress terms (containing r−1/2 and r1/2) of the well-known Williams series expansion can better assess the mode I fracture toughness (KIc) of rocks than the traditional maximum tangential stress (MTS) criterion. However, this study indicates that in some cases, only using the two stress terms cannot fully describe the tangential stress at the critical distance for rock specimens, and the higher order, non-singular stress terms can also play important roles in the tangential stress. The MMTS fracture criterion might still induce non-negligible errors for assessing mode I rock fracture. Thus, we propose a further improved MTS (FIMTS) criterion. The FIMTS criterion emphasizes that the number of non-singular stress terms used in a MTS-based criterion should be carefully chosen according to the following principle: the tangential stress at the critical distance can be accurately described using the selected stress terms. Mode I fracture tests on two kinds of rocks are conducted using a newly proposed V-notched short rod bend (VNSRB) specimen. The specimen- or loading-configuration-dependence of KIc indicated by the experimental data is theoretically assessed using the traditional MTS, the MMTS and the FIMTS criteria, and the last criterion is shown to be the best. Therefore, considering non-singular stress terms of the Williams expansion can better assess mode I fracture of rocks. Our study calls for more attention to the effects of non-singular stress terms on mode I fracture of rocks, especially for small-size specimens and for rocks with relatively large critical distances.