Flowcode 5 Full Crack

Failure of rock under impact loadings involves complex micro-fracturing and progressive damage. Strength increase and splitting failure have been observed during dynamic tests of rock materials. However, the failure mechanism still remains unclear. In this work, based on laboratory tests, numerical simulations with the particle flow code (PFC) were carried out to reproduce the micro-fracturing process of granite specimens. Shear and tensile cracks were both recorded to investigate the failure mode of rocks under different loading conditions. At the same time, a dynamic damage model based on the Weibull distribution was established to predict the deformation and degradation behavior of specimens. It is found that micro-cracks play important roles in controlling the dynamic deformation and failure process of rock under impact loadings. The sharp increase in the number of cracks may be the reason for the strength increase of rock under high strain rates. Tensile cracks tend to be the key reason for splitting failure of specimens. Numerical simulation of crack propagation by PFC can give vivid description of the failure process. However, it is not enough for evaluation of material degradation. The dynamic damage model is able to predict the stress-strain relationship of specimens reasonably well, and can be used to explain the degradation of specimens under impact loadings at macro-scale. Crack and damage can describe material degradation at different scales and can be used together to reveal the failure mechanism of rocks.

The interactions between defects are important in the behavior of brittle materials. The micromechanical interactions between a circular hole and a crack under uniaxial compression are investigated in this paper. Experiments of specimens containing a hole and a crack are conducted. Subsequently, Particle Flow Code 2D (PFC2D) is adopted to simulate the fracture behavior. The crack initiation, propagation and coalescence with a hole are investigated. The propagating cracks contain first cracks and secondary cracks. Both first cracks and secondary cracks will disturb the stress field and displacement field. The DEM simulation explains the initiation position of secondary cracks observed in experiments, which is not necessarily located at the crack tips or on crack surfaces, but possibly in the intact part of the specimen at a distance away from the pre-existing crack. The hole will influence the crack initiation stress of the pre-existing crack and attract the propagating cracks. The present research paves the way for using the DEM to simulate the micromechanical interactions between a hole and a crack.

The interactions between a crack and a circular hole in rocks have been studied previously [1]. However, the prior study focused on the fracture phenomena by experiments and did not analyze the inherent mechanism in-depth. Further, the interactions were interpreted by micromechanics [2]; however, the cracking behavior was ignored. The cracking process around a hole was examined in uniaxial compression tests in some papers and relative mechanism was interpreted [3,4]. Compared with the studies of specimens with a hole, there are much more research of specimens with pre-existing cracks in a brittle material. Wong and Einstein [5] observed and characterized the fracture behavior in gypsum and Carrara marble specimens containing a single crack under uniaxial compression and identified different crack types based on their geometry and propagation mechanism. Cracking behavior were investigated containing two parallel open flaws experimentally at macroscopic and microscopic level [6,7]. Specimens under the biaxial compression test were also investigated [8]. Not only open flaws, but also closed flaws in a brittle material had been studied [9]. Specimens with 3 and 16 cracks were made and tested in compression tests [10]. However, these investigations did not consider the situation containing both a crack and a hole.

Brittleness, which is generally viewed as a property (or ability) of solid material that ruptures with little appreciable permanent deformation, has long been considered approximately equivalent to fracability, because it shows empirical relevance to the possibility of crack propagation: reservoir comprising brittle rocks usually responds well to stimulation, whereas preexisting and hydraulic fractures tend to heal rather than to propagate in a less brittle reservoir. This is probably attributed to less energy consumed by the ductile deformation of brittle rock materials [2].

In summary, many brittleness indices currently popular in fracability evaluation for reservoir lacks mechanical relevance to the rock cracking process. On the other hand, the evaluation indices used in other areas (e.g., those used to estimate rock cuttability [13]) are usually inapplicable for reservoir fracability evaluation owing to the essential differences of physical meaning between brittleness and fracability. Thus far, few evaluation indices of rock fracability meet the following requirements [3]:

To address this issue, we propose a new evaluation index for rock fracability that we call the crack tolerance. See Section 2 for its definition. Section 3 and Section 4 show the experimental measurement of this new index and the corresponding numerical simulation results, respectively, to demonstrate the rationality of the index. Based on these analyses, the effects of several characteristics of the rock materials on the crack tolerance are discussed in Section 5.

Crack propagation in tensile mode is most common in hydraulic fracturing because the effect of hydraulic pressure imposed on the crack surface approximates remote tensile stress in nature; additionally, rocks have a much lower tensile strength than compressive and shear strengths. Thus, cracks easily propagate driven by an injected fluid. The principal stresses at a tensile crack tip can be described as [15]

where σ1 and σ2 are maximum and intermediate principal stresses, KI is tensile stress intensity factor, r and θ are polar radius and polar angle for polar coordinate system from the tip. Note that the minimum principal stress not listed here equals to zero. The range of FPZ (i.e., its size) is calculated based on the hypothesis that nonlinear deformation occurs within a region around crack tip when the local stress state satisfies a certain criterion (e.g., tensile strength criterion for rock materials, von Mises criterion for metal materials). The tensile cracks are assumed to propagate parallel to their own plane (i.e., θ = 0) when the σ1 reaches the tensile strength of the rock (σt), because the critical state of crack propagation is attained, which corresponds to the maximum size of the FPZ:

A large rc would indicate that micro-cracks are distributed within a large FPZ in front of a preexisting crack tip. It would also suggest a considerable number of micro-cracks within the FPZ because a preexisting crack will not propagate until the micro-crack density is high enough to reach a critical level [16]. Therefore, rc may characterize the maximum number of micro-cracks generated in the preparation stage for macroscopic crack propagation. In other words, rc can be used to indicate the ability of a rock to tolerate micro-cracks before crack unstable propagation. For this reason, we refer to rc as the crack tolerance. The crack morphology may also depend on the crack tolerance because a large rc would indicate an extensive distribution of micro-cracks, which would likely result in irregular and branch cracks.

The notched crack of each CCNBD specimen was created by a 1 mm thick circular diamond saw. To ensure cutting accuracy, the expected locations of the circular center and the initial and final chevron notched cracks were marked on each disk. We measured the actual values of the parameters shown in Figure 2a,b and confirmed that the dimensionless parameters α1 and αB of all CCNBD specimens were within the valid range (Figure 2c). The method reported by Fowell et al. [23] was used to calculate the KIC:

(a) Orthographic and (b) side profiles of a marble CCNBD specimen; (c) valid range for dimensionless parameters α1 and αB (outlined in gray) [23] and the distribution of parameter values for all of the prepared CCNBD specimens. Geometric parameters: diameter D = 75 mm, radius R = 37.5 mm, thickness B = 30 mm, saw radius Rs = 25 mm, initial chevron notched crack length a0 = 8.45 mm, and final chevron notched crack length a1 = 23.5 mm.

Each CCNBD or BD test (Figure 3a,b) was performed at a constant displacement rate of 0.06 mm/min by an MTS servo-control testing machine (series CMT) with a maximum loading force of 100 kN. This machine is equipped with an SNAS GDS-300 environmental chamber controlled by a WK650 controller (Figure 3c,d). These apparatuses permit environmental temperatures within the chamber up to 200 °C by electrical heaters (Figure 3b). To investigate the effect of temperature, several sandstone specimens were placed in the chamber at 75 or 125 °C for 1 h before the tests began, so that the notched crack propagated within rocks under higher temperatures. Other tests were performed at room temperature (~25 °C). The bedding planes of the shale specimens were set perpendicular (horizontal) or parallel (vertical) to the notched cracks to analyze the effect of the bedding orientation.

Mean tensile strength (brown), tensile fracture toughness (green), and crack tolerance (sienna) of the (a) marble A (diamond) and J (triangle), (b) shale (circle) with horizontal and vertical orientations and (c) sandstone (square).

Crack morphologies of (a,b) marble A and (c,d) J. The red dashed ellipses in (a) denote white patches around the notched crack tips.

The mean crack tolerance of the shale specimens was less with a vertical bedding orientation than with a horizontal orientation (Figure 4b). The tensile strength and fracture toughness displayed similar variation trends with bedding orientation. Similar results can be acquired based on the data from Wang [26]. With a vertical orientation, the main crack of the specimen propagated along the bedding planes (Figure 6a), which generated a smooth rupture surface (Figure 6b). In contrast, with a horizontal orientation, the main crack spanned across bedding planes, and the path with steps was more irregular (Figure 6c,d). This is because the main crack was offset or even bifurcated when it encountered a bedding plane. The branch cracks were captured by bedding planes and then propagated along them, thereby their morphologies were smooth. 2b1af7f3a8