Rock Dynamic Fracture Toughness Research Articles

The Loading Rate Effect on the Fracture Toughness of Marble Using Semicircular Bend Specimens

A series of dynamic fracture experiments on semicircular bend (SCB) marble specimens were conducted to characterize the loading rate effect using the INSTRON testing machine and the modified SHPB testing system. The fracture toughness of the marble specimens was measured from a low loading rate to a high loading rate (10-3~106 MPa·m1/2s-1). The results show that the fracture toughness will increase with the loading rate. Since the fracture toughness at a magnitude of 10-3 MPa·m1/2s-1 is regarded as the static fracture toughness, the specific value of DI F f (the dynamic increase factor of fracture toughness) can be obtained at the other loading magnitudes from dynamic fracture tests. To describe the variation in DI F f from low to high loading rates, a new continuous model of DI F f was put forward to express the quantitative relation between the loading rate and rock dynamic fracture toughness. It is shown that the new DI F f model can accurately describe the loading rate effect on the dynamic fracture testing data for rock materials.

Testing Method of Rock Dynamic Fracture Toughness Using Large Single Cleavage Semicircle Compression Specimens

Abstract Dynamic fracture toughness is an important material parameter that can be applied in the prediction of a cracked structure’s stability under dynamic loads. Large single cleavage semicircle compression specimens were used to evaluate rock dynamic fracture toughness by a drop weight impact test system. Crack propagation gauges, which consist of a group of fine wires, were glued along a crack propagation path to measure crack propagation speed and propagation time. The finite difference code Autodyn (ANSYS, Canonsburg, PA) was used to simulate the crack propagation path and to analyze the crack propagation mechanism. A group of gauge points were set up along the propagation path, and the stresses at these points were calculated and analyzed. The dynamic stress intensity factors were calculated by numerical models using the finite element code ABAQUS (Dassault Systèmes, Vélizy-Villacoublay, France). Finally, the dynamic fracture toughness, including initiation toughness and propagation toughness, was determined according to crack propagation speed and propagation time. The results show that crack propagation speed varies during dynamic propagation under impact loads, and the propagation toughness is inversely proportional to the crack propagation speed. In addition, the phenomena of cracks temporarily arresting could be observed during crack dynamic propagations.

Dynamic Fracture Test of Laurentian Granite Subjected to Hydrostatic Pressure

Dynamic fracture failure of rocks subjected to static hydrostatic pressure is commonly encountered in deep underground rock engineering. The static fracture behavior of rocks under hydrostatic stress has been well studied in the literature. However, it is desirable to investigate the dynamic fracture failure of rocks under various hydrostatic pressures. In this study, a triaxial split Hopkinson pressure bar (SHPB) system is used to measure the dynamic fracture toughness of rocks under five hydrostatic pressures. The results show that dynamic fracture toughness under a certain hydrostatic pressure enhances with the increase of the loading rate, and the dynamic fracture toughness at the similar loading rate increases with the hydrostatic pressure due to the closure of microcracks in rocks. An empirical formula is proposed to describe the influences of the loading rate and the hydrostatic pressure on the rock dynamic fracture toughness.

Study of mode I crack dynamic propagation behaviour and rock dynamic fracture toughness by using SCT specimens

AbstractTo study crack dynamic propagation behaviour and rock dynamic fracture toughness, a single cleavage triangle (SCT) specimen was proposed in this paper. By using these specimens and a drop‐weight test system, impact experiments were conducted, and the crack propagation velocity and the fracture time were measured by using crack propagation gauges. To examine the effectiveness of the SCT specimen and to predict the test results, finite difference numerical models were established by using AUTODYN code, and the simulation results showed that the crack propagation path agrees with the test results, and crack arrest phenomena could happen. Meanwhile, by using these numerical models, the crack dynamic propagation mechanism was investigated. Finite element code ABAQUS was applied in the calculation of crack dynamic stress intensity factors (SIFs) based on specimen dimension and the loading curves measured, and the curves of crack dynamic SIFs versus time were obtained. The fracture toughness (including initiation toughness and propagation toughness) was determined according to the fracture time and crack speeds measured by crack propagation gauges. The results show that the SCT specimen is applicable to the study of crack dynamic propagation behaviour and fracture toughness, and in the process of crack propagation, the propagation toughness decreases with crack propagation velocity, and the crack arrest phenomena could happen. The critical SIF of an arrest crack (or arrest toughness) was higher than the crack propagation toughness but was lower than the initiation toughness.

Study of rock dynamic fracture toughness by using VB-SCSC specimens under medium-low speed impacts

Dynamic fracture toughness, including initiation toughness, propagation toughness and arrest toughness, are important parameters for describing fracture behavior of rock materials. In order to study these parameters, a new V-shaped bottom single cleavage semi circle (VB-SCSC) specimen which has the arrest function for propagating cracks was proposed in this paper. The arrest function of this specimen is produced by the compressive waves set off from the two inclined bottoms, and the horizontal components of these compressive waves have the confining action on the propagating cracks. The experiments were performed by using a low & medium speed impact test system, and the crack propagation time and propagation speed were measured by using crack propagation gauges (CPG). The angle of the two inclined bottoms of the VB-SCSC specimens was designed as 120° or 150°, and both types of specimens have the arrest function on the propagating cracks. The finite difference code AUTODYN was applied in the simulation of crack propagation path, and the finite element code ABAQUS was applied in the calculation of stress intensity factors. Finally the dynamic fracture toughness was determined by using experimental-numerical method. The results show that the VB-SCSC specimen can be used to measure not only the initiation and propagation toughness, but also the arrest toughness. In the process of crack propagation, the crack may arrest for a period, and the arrest toughness is higher than both the initiation toughness and propagation toughness.

A new Method for Measuring Mode-I Dynamic Fracture Toughness of Rock under Blasting Loads

Blasting excavation method by using explosive is still widely applied in mining and quarrying, and therefore, rock dynamic fracture toughness under blasting loads is one of the most concerned subjects in rock dynamics. In this paper, blasting experiments by using detonators and cement mortar specimens with a mode-I crack were conducted. The crack initiation time was determined by the strain signal recorded by a signal conditioner. The pressure acting on the hole was obtained by the strains measured from the two strain gauges near the hole, and then the pressure was applied as the dynamic boundary condition of the hole in the subsequent numerical calculation by using ANSYS code. The crack tip open displacements were calculated and applied in the determination of crack tip dynamic intensity factors KI, and accordingly the curve of KI versus time was obtained. The dynamic toughness was determined according to the time of crack initiation.

Steady-state optimization model and practical design of the fracture network system in tight sand gas reservoirs

Abstract Based on steady-state seepage theory in porous media and the Galerkin method, a finite element model of seepage field in a stimulated reservoir volume of a horizontal well was established. The relationship between fracture conductivity and production under different fractured drainage volumes was studied. For shale gas reservoir, the productivity will increase as the fractured drainage volume enlarges. However for tight sand gas reservoir, this study revealed that the fractured drainage volume should be maintained in the mid-small scale (0.1≤FCI≤0.25) with highly conductive main fractures. For certain fracture network morphology, there exists a critical value or optimal value of SRV curve. The production increase slows down when SRV exceeds its critical value. Cluster spacing and number of clusters for horizontal well fracturing can be determined by critical value of SRV and FCI value. The paper studied the operational conditions for the creation of small and medium-scale fracture network. Firstly, analytical solution of pressure inside the fracture is derived from fracture dynamics of rocks. Pump rate of fracturing fluid, viscosity, rock dynamic fracture toughness, elastic modulus, Poisson's ratio, in-situ stress, natural fracture parameters are input parameters to this analytical solution. Optimized pump rate for small to medium-scale fracture network was derived from the dynamic expanding condition of fracture network.

Research on Improving the Test Effectiveness of Rock Dynamic Fracture Toughness

Some problems of testing rock dynamic parameters in the SHPB experiment were analyzed and the relevant measures were proposed, which included how to determining the fracture time and the dynamic load etc. Based on the dynamic fracture experiment in the SHPB system with flattened Brazilian disc made of marble, the strain gauge technique to get the accurate fracture time was applied, and the different pulse shaper were adopted to get more precise wave data. The effective test methods of determining rock dynamic fracture toughness were discussed.

Effect of the Stress Balance on Determination of Rock Dynamic Fracture Toughness Using Holed-Cracked Flattened Brazilian Disc

Based on the experimental and FEM analysis, it was discussed that the stress balance was not a necessary condition for determining rock dynamic fracture toughness accurately using holed-cracked flattened Brazilian disc. The dynamic stress distribution modes of disc sample with time change were analyzed from the early loading stage to continued loading process. It was proved that the fracture time may occur before the balance of stress was achieved. It was not necessary meet the condition of the stress balance using the experiment combined with numerical method. We could get dynamic fracture toughness, according to the dynamic stress intensity factor of the crack tip and fracture time.

Measurement of mode I and mode II rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar

In order to find an effective and convincing method to measure rock dynamic fracture toughness for mode I and mode II, cracked straight through flattened Brazilian disc specimens of marble, which were geometrically similar for three size, were diametrically impacted by split Hopkinson pressure bar on the flat end of the specimen with three load angle respectively. History of stress intensity factors (KI(t) for opening mode I, and KII(t) for sliding mode II), mode mixture ratio (KI(t)/KII(t)), as well as mode I and mode II dynamic fracture toughness at crack initiation (KId and KIId) were determined with the experimental–numerical method. It is found that there is a unique size effect for dynamic fracture test with the specimens, the mode mixture ratio is not solely determined by load angle (the angle between load direction and crack line) as in the static loading; the pure mode II load angle is 19° for the ϕ50mm specimen, however it is 10° for the ϕ130mm and ϕ200mm specimens; the mode II load angle decreases with increment of specimen size. Realization of pure mode II is justified by the mode mixture ratio approaching zero, it can be realized under certain load angle and loading rate for the specimen of specified size. KIId is generally greater than KId. Both KId and KIId increase with increment of specimen size, and this trend for KIId is more remarkable than that for KId.

Erratum to: Rock Dynamic Fracture Toughness Tested with Holed-Cracked Flattened Brazilian Discs Diametrically Impacted by SHPB and its Size Effect

Dynamic fracture initiation toughness of marble was tested using two types of the holed-cracked flattened Brazilian disc (HCFBD) specimens, which were diametrically impacted at the flat end of the disc by the split Hopkinson pressure bar (SHPB) of 100 mm diameter. One type of the discs is geometrically similar with different outside diameter of 42 mm, 80 mm, 122 mm and 155 mm respectively, and with crack length being half the diameter; another type of the discs has identical 80 mm diameter and different crack length. Issues associated with determination of the stress wave loading by the SHPB system and the crack initiation time in the disc specimen were resolved using strain gage technique. The stress waves recorded on the bars and the disc failure patterns are shown and explained. The tested dynamic fracture toughness increases obviously with increasing diameter for the geometrically similar HCFBD specimens. It changes moderately for the one-size specimens of identical diameter and different crack length. The size effect of rock dynamic fracture toughness is mainly caused by the fracture process zone length l and fracture incubation time τ, the latter being an additional influencing factor for the dynamic loading as compared with the counterpart static situation. Hence a method is proposed to determine a unique value for the dynamic fracture initiation toughness, the approach takes average of the local distribution and time history for dynamic stress intensity factor in the spatial-temporal domain, which is defined by l and τ jointly. In this way the dynamic size effect is minimized.

Rock Dynamic Fracture Toughness Tested with Holed-Cracked Flattened Brazilian Discs Diametrically Impacted by SHPB and its Size Effect

Rock Dynamic Fracture Toughness Tested with Holed-Cracked Flattened Brazilian Discs Diametrically Impacted by SHPB and its Size Effect