crack growth

Summary:

Recent developments in eXtended Finite Element Method (XFEM) opened new avenues through crack propagation problems. However, in most researches, exact porosities are not considered or are just replaced with some circular pores. This means the effects of the shape, location, and arrangement of the porosities are less evaluated. In this study, by considering the porosity as an elliptical pore, parameters such as elliptical shape, relative location, and arrangement of pores are studied. The results revealed that this kind of considerations can improve the accuracy of crack growth modeling through porous media.

The shape and location of a pore have a significant effect on the cracks' growth and propagation in porous media. Due to the concentration of stress around these discontinuities, tensile cracks are created and coalesced leading to the final failure in the sample. Since these kinds of tests in pore-scale are practically hard to implement in the laboratory, numerical computation of these behaviors is of great importance to correctly understand this phenomenon. In recent years, the use of XFEM, which eliminates the need for remeshing along the crack path, has been extensively developed and used by many researchers. However, due to the complex shape of the porous structure, even in numerical modeling, they either are not considered or their shape is assumed to be circular. We, in this study, will go a step forward in this limitation by assuming an elliptic shape for porosities.

Methodology and Approaches:

In this article, the effect of shape, location, and arrangement of elliptical porosity on crack growth is numerically modeled. By placing these porosities beside and in front of the crack, the stress distribution, stress intensity factor variation, and maximum resistance of the sample are investigated.

The results showed that for the equal size of pores if the vertical elliptical pore is located in front of the crack, its destructive effect is about 20% more than the horizontal elliptical pore. Also, when the porosity is located beside the crack, by increasing the angle between the horizontal axis with the direction of the large ellipse diameter (here we call it α), the stress intensity factor decreases from 1 to 0.94 and reduces the crack propagation in the porous sample. In addition, we defined the angle between the horizontal axis and the line joining the centers of the two porosities as β and evaluated the effect of the porosity shape and its location on crack growth in more complex models (i.e., models containing two elliptical porosities). By increasing the α and β from 0o to 90o, the maximum strength of the sample decreases by 18.12%, and the von Mises stress value increases from 0.154 to 0.922 MPa. However, the results revealed that the effect of β on crack growth is greater than α.

Summary:

The recent developments in the Extended Finite Element Method (XFEM) opened new avenues for crack propagation problems. However, its ability to predict the crack path in the micro-scale medium of real porous rock is questionable. In this work, we compare two strategies and introduce one as the best strategy to use the XFEM for such a purpose in Abaqus Software. We demonstrate our claim by comparing numerical results with the analytical solution and experimental test.

Crack growth has always been one of the major challenges in rock mechanics. Although pores, joints, and fractures are the most critical structures controlling cracks initiation and propagation, their spatial distribution and geometrical effects are not still well-understood. In this study, we aim to numerically model the crack growth in real porous rock.

Methodology and Approaches:

We use the extended finite element method (XFEM), which has recently attracted more attention due to its ability to estimate the discontinuous deformation field by using special shape functions. Since direct use of the XFEM does not lead to an accurate result, two different strategies are considered for applying the XFEM on a porous model to simulate the crack propagation.

Our results showed that applying several different partitions and enrich them individually lead to more logical results than to allocate reduced elastic modulus to porosity. We used this strategy to evaluate the XFEM both analytically and experimentally as a possible numerical solution. Thus, two simple models were constructed, both numerically and experimentally (Granite): i. a sample with one void and one crack, and ii. a sample with two voids and one crack between them. Analytical solutions for the stress intensity factor revealed that the XFEM modeling can compute this parameter with an error of less than 5%. On the other hand, experimental results showed that the XFEM with partitioning strategy can predict the correct crack growth path comparative to the experimental results. Accordingly, digital images of Berea sandstone were used as a real reservoir rock and, then, this method was implemented to simulate multi-crack propagation through the exact medium of rock.

The dimension of underground structure is a key factor in its stability. Rock blotting has important effect in rock mechanic projects. It increases the stability of rock blocks. The performance of rock bolt is depending on the quality of its set up. Quality of its set up is determined by pull out test method. Numerical simulation is other method for determination of rock blotting behavior. In this paper, the effect of tensile loading on the “Y” shape joint is determined using FRANC2D. The angularity of large joint tail (β) changes from 0° to 90° with increment of 45°. The angularity of small joint tail related to large joint tail (α) changes from 20° to 160° with increment of 20°. The spacing between joint and loading place change from 2a to 4a with increment of “a” which “a” is the length of large joint tail. Totally 52 model were simulated. In the case of horizontal joint the crack growth length is maximum and vertical joint has minimum effect on the crack growth. When the angularity of large joint tail related to horizontal was 45°, the maximum of crack growth was occurred. The maximum of crack growth from small joint tail was occurred when it is in horizontal configuration. The maximum number of small joint tail growth occurred when its angularities related to horizontal axis was 45°.