Numerical simulation of fatigue crack propagation in heterogeneous geomaterials under varied loads using displacement discontinuity method

Heterogeneous brittle geomaterials are highly susceptible to cyclic loads.They contain inherent flaws and cracks that grow under fatigue loads and lead to failure.This study presents a numerical model for analyzing fatigue in these materials based on the two-dimensional(2D)boundary element method and linear elastic fracture mechanics.The process is formulated by coupling the displacement discontinuity method with the incorporation technique of dissimilar regions and the governing equations of fatigue.The heterogeneous media are assumed to consist of materials with different properties,and the interfaces are assumed to be completely bonded.In addition,the domains include multiple cracks exposed to constant and variable amplitude cyclic loads.The stress intensity factor is a crucial parameter in fatigue analysis,which is determined using the displacement field around crack tips.An incremental crack growth scheme is applied to calculating the fatigue life.The growth rate values are employed to estimate the length of crack extension when there are multiple cracks.The interaction between cracks is considered,which also includes the coalescence phenomenon.Finally,various structures under different cyclic loads are examined to evaluate the accuracy of this method.The results demonstrate the efficiency of the proposed approach in modeling fatigue crack growth and life estimation.The behavior of life curves for the heterogeneous domain was as expected.These curves illustrate the breakpoints caused by utilizing discrete incremental life equations.At these points,the trend of the curves changed with the material properties and fatigue characteristics of the new material around the crack tips.

Cracks coalescence mechanism and cracks propagation paths in rock-like specimens containing pre-existing random cracks under compression

The mechanism of cracks propagation and cracks coalescence due to compressive loading of the brittle substances containing pre-existing cracks （flaws） was modeled experimentally using specially made rock-like specimens from Portland Pozzolana Cement （PPC）. The breakage process of the specimens was studied by inserting single and double flaws with different inclination angles at the center and applying uniaxial compressive stress at both ends of the specimen. The first crack was oriented at 50＆#176; from the horizontal direction and kept constant throughout the analysis while the orientation of the second crack was changed. It is experimentally observed that the wing cracks are produced at the first stage of loading and start their propagation toward the direction of uniaxial compressive loading. The secondary cracks may also be produced in form of quasi-coplanar and/or oblique cracks in a stable manner. The secondary cracks may eventually continue their propagation in the direction of maximum principle stress. These experimental works were also simulated numerically by a modified higher order displacement discontinuity method and the cracks propagation and cracks coalescence were studied based on Mode I and Mode II stress intensity factors （SIFs）. It is concluded that the wing cracks initiation stresses for the specimens change from 11.3 to 14.1 MPain the case of numerical simulations and from 7.3 to 13.8 MPa in the case of experimental works. It is observed that cracks coalescence stresses change from 21.8 to 25.3 MPa and from 19.5 to 21.8 MPa in the numerical and experimental analyses, respectively. Comparing some of the numerical and experimental results with those recently cited in the literature validates the results obtained by the proposed study. Finally, a numerical simulation was accomplished to study the effect of confining pressure on the crack propagation process, showing that the SIFs increase and the crack initiation angles change in this case.

Numerical analysis of confinement effect on crack propagation mechanism from a flaw in a pre-cracked rock under compression

In many situations rocks are subjected to biaxial loading and the failure process is controlled by the lateral confinement stresses. The importance of confinement stresses has been recognized in the literature by many researchers, in particular, its influence on strength and on the angle of fracture, but still there is not a clear description for the influence of confining stress on the crack propagation mechanism of rocks. This paper presents a numerical pro- cedure for the analysis of crack propagation in rock-like ma- terials under compressive biaxial loads. Several numerical simulations of biaxial tests on the rock specimen have been carried out by a bonded particle model （BPM） and the influ- ence of confinement on the mechanism of crack propagation from a single flaw in rock specimens is studied. For this purpose, several biaxial compressive tests on rectangular spec- imens under different confinement stresses were modeled in （2 dimensional particle flow code） PFC2D. The results show that wing cracks initiate perpendicular to the flaw and trend toward the direction of major stress, however, when the lat- eral stresses increase, this initiation angle gets wider. Also it is concluded that in addition to the material type, the initiation direction of the secondary cracks depends on confine- ment stresses, too. Besides, it is understood that secondary cracks may be produced from both tensile and shear mechanisms.

Fracture analyses of different pre-holed concrete specimens under compression

Crack propagation processes in specially prepared concrete discs and rectangular specimens containing a single cylindrical hole or multiple holes of varying diameters have been studied both experimentally and numerically. In this research, the cracks coalescence paths in Brazilian disc and rectangular specimens made from rock-like material containing multi-holes are investigated. These concrete specimens are specially prepared from an appropriate mixture of Portland Pozzolana Cement （PPC）, fine sands, and water. The pre-holed Brazilian discs and rectangular specimens are experimentally tested under compression. The breakage load in the ring type disc specimens containing an axial hole with varying diameters is measured and the distribution of the induced lateral stress is obtained. The mechanism of cracks propagation in the wall of the ring type specimens is also stud- ied. In the case of multi-hole Brazilian disc and rectangular specimens, the cracks propagation and cracks coalescence are also investigated. These experiments are numerically modeled by a modified higher order displacement discontinuity method. It has been shown that the corresponding experimental and numerical results are in good agreement with each other. The results presented in this research vali date the accuracy and applicability of these crack analyses procedures.

Simulation of crack coalescence mechanism underneath single and double disc cutters by higher order displacement discontinuity method

The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics(LEFM) concepts and the maximum tangential stress criterion are used to investigate the micro crack propagation and its direction underneath the excavating discs. A higher order displacement discontinuity method with quadratic displacement discontinuity elements is used to estimate the stress intensity factors near the crack tips. Rock cutting mechanisms under single and double type discs are simulated by the proposed numerical method.The main purposes of the present modeling are to simulate the chip formation process of indented rocks by single and double discs.The effects of specific disc parameters(except speed) on the thrust force Ft, the rolling force Fr, and the specific energy ES are investigated. It has been shown that the specific energy(energy required to cut through a unit volume of rock) of the double disc is less than that of the single disc. Crack propagation in rocks under disc cutters is numerically modeled and the optimum ratio of disc spacing S to penetration depth Pd(i.e. S/Pd ratio) of about 10 is obtained, which is in good agreement with the theoretical and experimental results cited in the literature.

On the accuracy of higher order displacement discontinuity method(HODDM) in the solution of linear elastic fracture mechanics problems

The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example problems from the fracture mechanics literature(with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode Ⅰ and Mode Ⅱ SIFs for these problems using HODDM are in excellent agreement with analytical results(reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort(with less than 400 nodes) than the XFEM and the modified XFEM(which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.

Numerical Crack Analysis of Blunt Rock Indenters by an Indirect Boundary Element Method

Linear elastic fracture mechanics principles are widely applied for the analysis of crack problems in rock fracture mechanics. Rock indentation is an important and complicated problem among rock engineering issues. In this paper, in addition to the fracture criterion of maximum tangential stress adjacent to crack tip, the higher order displacement discontinuity method (which is a version of the indirect boundary element method) has been used for modeling the crack propagation mechanism under blunt indenters. In order to achieve more accurate results, higher order boundary elements i.e. quadratic elements, has been used to calculate displacement discontinuities and also to reduce the singularities of stress and displacement fields near the crack tip, the special crack tip elements has been used to calculate the stress intensity factors (SIF) at the crack tips. In this modeling, the effect of crack angle on stress intensity factors has been investigated. The numerical results of stress intensity factors obtained from some example problems were compared to the theoretical and experimental results cited in the literature which always show a percentage error less than one percent. The simulated results may pave the way for increasing the efficiency of mining and drilling by improving the design of tools and indentation equipments.

A thermo-mechanical simulation for the stability analysis of a horizontal wellbore in underground coal gasification

The stability analysis of horizontal wells is essential for a successful underground coal gasification(UCG)operation.In this paper,a new 3D coupled thermo-mechanical numerical modeling is proposed for analyzing the stability of UCG horizontal wells.In this model,the effect of front abutment stresses,syngas pressure,syngas temperature and thermal stresses is considered to predict the mud weight window and drilling mud pressure during UCG process.The results show that the roof caving in UCG panel has a greatest impact on the stability of horizontal well.Moreover,when the time of coal gasification is increased,the well convergence increases and for more stability it is necessary to increase the drilling mud pressure.This research was carried out on the M2 coal seam in Mazino coal deposit(Iran).The results showed that the mud weight window for horizontal well drilling is between 0 and 33 MPa.The appropriate stress for the maximum stability of the horizontal well,taking all the thermal and mechanical parameters into account,is 28 MPa.The suggested numerical method is a comprehensive and consistent way for analyzing the stability of horizontal wells in UCG sites.

脆性材料I型(张开)-断裂韧性测定的PFC2D和试验研究:一种新方法

在本文研究中,通过利用优势边缘缺口盘型(END)试样,确定了石灰石的断裂韧性,提出了一种新的石灰石归一化相应力、高相变的计算方法.采用柔性有限元法(FEM)对试样的I型(张开)-断裂韧性进行了精确计算,并得到了相应实用公式.在试验中,还使用含缺口巴西圆盘(NBD)试件,测试了END程序的准确性.为了在数值上重现这些测试并验证断裂韧性测量的正确性,还对END测试进行了离散元分析.数值模拟结果与实验结果吻合良好.然而,END研究所确定的韧性水平低于NBD测试规定的韧性水平,这是因为END石灰石样品中的缺口具有均匀的拉伸应力分布.

Comparison of indirect boundary element and finite element methods A case study:Shiraz-Esfahan railway tunnel in Iran

Because of the high importance of transportation tunnels,most precise analyses of stress concentration and displacement around them are essential to provide safety of them as much as possible.Recently,various numerical methods such as finite element method(FEM),discrete element method(DEM),finite difference method(FDM)and boundary element method(BEM)have been used extremely in geosciences problems,but among these numerical methods,BEM has been used less than others because the computational algorithm is not so straightforward.This paper suggests the implementation of the indirect boundary element method(IBEM)as a formulation of BEM to analyze displacement around Shiraz-Esfahan railway tunnel in Zagros Mountains southwest of Iran.For this purpose,this tunnel has been modeled numerically using two-dimensional fictitious stress method(TWOFS)algorithm.To validate the results,they were compared with FEM results as a commonly used numerical method.Results of current theoretical study have shown that the presented approach using IBEM is reasonably accurate and can be used for analysis of displacement in geosciences problems.In rock mechanics,for problems with a low ratio of boundary surface to volume,FEM is not very well suited and may be cumbersome,but use of such a proposed IBEM approach can be particularly attractive.

Experimental and Numerical Study of Shear Fracture in Brittle Materials with Interference of Initial Double Cracks

A simultaneous experimental and numerical study of shear fracture of concrete-like materials is carried out using Brazilian disc specimens with initial double edge cracks and fourpoint bending beam specimens with double edge-notches.The interference effects of two cracks/notches are investigated through varied ligament angles and crack lengths.It is shown that shear fracturing paths change remarkably with the initial ligament angles and crack lengths.The cracked specimens are numerically simulated by an indirect boundary element method.A comparison between the numerical results and the experimental ones shows good agreement.