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1.
Summary This paper presents a combination of the Boundary Element Method (BEM) and the cracked ring test to determine the mixed-mode
(I–II) fracture toughness of anisotropic rocks. The proposed BEM is used to accurately calculate the Stress Intensity Factors
(SIFs) of a cracked anisotropic plate. An anisotropic Hualien marble of Taiwan with a distinct foliation was selected to conduct
the cracked ring tests. Based on the measurement of the failure load during the test, the mixed-mode (I–II) fracture toughness
can be determined. Experimental results show that the radius ratio, inclination and crack angle significantly affect the fracture
toughness. The mode-I fracture toughness (K
IC
) is shown to decrease with the increase in hole diameter, whereas the mode-II fracture toughness (K
IIC
) increases with the increase in hole diameter when the crack angle β is equal to 0°. The experimental methods proposed have
the advantage that the material is easily prepared, the test procedure is simple, and the cost is low.
Correspondence: Chia-Hau Chen, Chao-Shi Chen, Department of Resources Engineering, National Cheng Kung University, 701 Tainan,
Taiwan 相似文献
2.
This paper presents a boundary element method (BEM) procedure for a linear elastic fracture mechanics analysis in two‐dimensional anisotropic bimaterials. In this formulation, a displacement integral equation is only collocated on the uncracked boundary, and a traction integral equation is only collocated on one side of the crack surface. A fundamental solution (Green's function) for anisotropic bimaterials is also derived and implemented into the boundary integral formulation so that except for the interfacial crack part, the discretization along the interface can be avoided. A special crack‐tip element is introduced to capture the exact crack‐tip behavior. A computer program using FORTRAN has been developed to effectively calculate the stress intensity factors of an anisotropic bimaterial. This BEM program has been verified to have a good accuracy with previous studies. In addition, a central cracked bimaterial Brazilian specimen constituting cement and gypsum is prepared to conduct the Brazilian test under diametral loading. The result shows that the numerical analysis can predict relatively well the direction of crack initiation and the path of crack propagation. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
3.
This paper presents a single‐domain boundary element method (BEM) for linear elastic fracture mechanics analysis in the two‐dimensional anisotropic material. In this formulation, the displacement integral equation is collocated on the un‐cracked boundary only, and the traction integral equation is collocated on one side of the crack surface only. A special crack‐tip element was introduced to capture exactly the crack‐tip behavior. A computer program with the FORTRAN language has been developed to effectively calculate the stress intensity factors of an anisotropic material. This BEM program has been verified having a good accuracy with the previous researches. Furthermore, by analyzing the different anisotropic degree cracks in a finite plate, we found that the stress intensity factors of crack tips had apparent influence by the geometry forms of cracks and media with different anisotropic degrees. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
4.
Mixed mode crack propagation in low brittle rock-like materials 总被引：3，自引：0，他引：3
Abdolhadi Ghazvinian Hamid Reza Nejati Vahab Sarfarazi Mir Raouf Hadei 《Arabian Journal of Geosciences》2013,6(11):4435-4444
Mixed mode fracture is quite common in rock structures. Numerous investigators have used the Brazilian disk specimens with a central crack for investigating modes I, II, and mixed fracture toughness in brittle materials. In this study, analytical, experimental, and numerical investigations were planned and performed on Central Straight Through Crack Brazilian Disk (CSCBD) specimens. Ranking of geometrical parameters effective on the value of stress intensity factors (SIFs) of CSCBD specimens were obtained using stochastic analysis. Furthermore, experimental tests were undertaken in order to evaluate the crack propagation in rock-like material of low brittleness. Finally, numerical modeling was performed to assess the effect of crack length on the failure mode of CSCBD specimens. Analytical analyses revealed that the inclination angle of the crack with respect to the diametrical load has the most important impact on the SIFs among the geometrical parameters of CSCBD specimen. Performed experimental and numerical analyses also confirmed the effect of inclination angle and crack length and their impact on the mode of failure of the tested specimen. 相似文献
5.
为了研究围压对巴西裂纹圆盘应力强度因子的影响,使用权函数方法得到了围压作用下巴西裂纹圆盘的应力强度因子,进而得到径向集中荷载与围压共同作用下的应力强度因子的计算公式。在此基础上,从理论上分析了围压对巴西裂纹圆盘应力强度因子的影响,分析结果表明：围压对II型应力强度因子无影响,纯围压作用下裂纹趋于闭合;围压和集中力共同作用下,I型应力强度因子随着围压的增大而减小。对比分析了数值分析与理论结果,分析表明,理论与数值结果吻合良好,从而表明了理论分析的正确性。此外,还研究了围压对纯II型裂纹加载条件的影响,结果表明,纯II型裂纹的临界加载角随着围压增大而减小,直至为0。因此,当围压较大时,加载角为0°左右所发生的断裂不一定全是纯I型断裂。 相似文献
6.
层理弱面对层状岩石的力学特性影响较显著，为了研究层理面特性对岩石断裂力学特性的影响，开展了具有不同层理方向的砂岩试样三点弯试验，探讨了砂岩断裂韧度及断裂模式的各向异性。之后基于有限元中的黏聚单元建立了数值模型，采用数值模拟方法研究了层理面强度对各层理角度试样断裂力学行为的影响规律。结果表明：层理方向影响下砂岩的断裂韧度及模式存在各向异性；同一层理方向试样的断裂韧度随层理面强度的增大而增大，且试样的层理面与加载方向夹角越小，断裂韧度受层理面强度变化影响越明显；试样的断裂模式不仅与层理面强度有关，还受层理倾角的控制，层理面与加载方向夹角θ = 0o试样断裂模式基本不受层理面强度影响，θ = 30o试样主要沿层理面张拉或剪切破坏，且沿层理面的破裂长度随层理面强度的降低逐渐增大；层理面强度较大时，θ = 45o试样主要沿层理面张拉破坏，θ = 60o～90o试样主要以贯穿层理的张拉破坏为主；层理面强度较小时，θ = 45o～90o试样均以沿层理面的剪切破坏为主，其中θ = 45o试样沿层理剪切长度最大。另外，通过数值模拟结果分析了层理面强度及方向对试样的起裂角及裂纹扩展路径产生的影响。该研究成果可作为层状岩石断裂力学理论的有益补充。 相似文献
7.
Mahmoud Behnia Kamran Goshtasbi Mohammad Fatehi Marji Aliakbar Golshani 《Arabian Journal of Geosciences》2014,7(7):2729-2737
In the present study, a boundary element method based on the higher order displacement discontinuity formulation is presented to solve the general problem of hydraulic fracture propagation in layered formations. Displacement collocation technique is employed to model the higher order displacement variation along the crack and the special crack tip element near its ends. The hydraulic fracture propagation and its interaction with the layer interface in non-homogenous rock materials are studied by the proposed semi-analytical (hybridized boundary element-boundary collocation) method. The maximum tangential stress criterion (or σ-criterion) of fracture mechanics considering different elastic constants (Young modulus and Poisson’s ratio) is used to obtain the fracture path. The fracture propagation from stiff to soft and soft to stiff media for cracks having different inclination angles is modeled, and the effects of elastic constants on the hydraulic fracture propagation is studied. The results show that if the hydraulic fracture originates in the stiffer layer, its capability to cross the layer increases and is vice versa for the softer material. The comparison of the results gained from the numerical method with those in the literature show a good performance of the method in the case of propagation of hydraulic fracture in layered formations. 相似文献
8.
In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second‐order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro–macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
9.
Rock strengths are directly influenced by the open or closed flaws widely distributed in rock masses. Extensive studies have been conducted on the propagations of open flaws in rocks. However, few concerns are paid on the propagation of closed flaws, the influence of the surface friction on the initiation and propagation of closed flaws should be investigated systematically. In present article, the crack initiation and propagation in rock like material subjected to compressive loads have been investigated. The effects of crack surface friction on crack initiation and propagation have been quantified with the help from extended finite element method which is efficient and accurate. Based on the analysis on stress distribution and propagation patterns, following results are obtained: Firstly, minor effects are exerted by crack surface friction on the stress distribution around the flaws when the flaws inclination angle is 30° and 45°. However, as the inclination angle increases to 60°, the effects are much more significant. Secondly, as the inclination angle ranges from 30° to 60°, the most favorable angle for crack propagation is 45°. Thirdly, the initiation location and angle of the wing cracks will not be influenced by the frictions. However, the propagation length will be greatly influenced by the friction and the inclination angle. 相似文献
10.
Summary This paper presents a systematic procedure for determining fracture toughness of an anisotropic marble using the diametral
compression test (Brazilian test) with a central crack on the discs. Additionally, a novel formulation to increase the accuracy
in Stress Intensity Factor (SIF) calculations using Boundary Element Method (BEM) is applied to determine the stress intensity
factors and the fracture toughness of anisotropic rocks under mixed-mode loading. The numerical results show that the SIFs
for both isotropic and anisotropic problems are in good agreement with those reported by previous authors. The marble with
clear white-black foliation from Hualien (in eastern Taiwan), was selected for the Brazilian tests. Diametral loading was
conducted on the Cracked Straight Through Brazilian Disc (CSTBD) specimens to evaluate their fracture toughness. In addition,
a new fracture criterion was developed to predict pure mode I, pure mode II or mixed mode (I–II) fracture toughness of the
anisotropic marble. The new fracture criterion is based on the examination of mode I, mode II and mixed mode (I–II) fracture
toughness for different crack angles and anisotropic orientation.
Authors’ address: Associate Professor Chao-Shi Chen, Department of Resources Engineering, National Cheng Kung University,
No. 1 Dasyue Rd., East District, Tainan 701, Taiwan 相似文献
11.
天然岩体内部含有微裂纹,其裂纹的发展贯通机制一直是岩石力学研究的热点问题。此外,岩体物理力学参数的空间变异性,也会影响其强度及破坏演化过程。本文采用了一种新的随机近场动力学方法(RPD),并对含缺陷岩体单轴压缩下的裂纹发展进行模拟,该方法结合了近场动力学方法在模拟裂纹发展及随机场方法在表征材料参数空间变异性方面的优势,使所建模型更接近真实岩体状态。利用MATLAB编程并依托含单一倾斜预制裂缝模型进行了计算程序的准确性验证。结果表明,所采用的随机近场动力学方法可以很好地模拟裂纹发展过程,预制裂缝倾角对后续裂纹发展有较大影响。此外,不考虑岩体物理力学材料参数空间变异性的存在时,会大大低估裂纹发展速度。 相似文献
12.
We propose a discrete element model for brittle rupture. The material consists of a bidimensional set of closed‐packed particles in contact. We explore the isotropic elastic behavior of this regular structure to derive a rupture criterion compatible to continuum mechanics. We introduce a classical criterion of mixed mode crack propagation based on the value of the stress intensity factors, obtained by the analysis of two adjacent contacts near a crack tip. Hence, the toughness becomes a direct parameter of the model, without any calibration procedure. We verify the consistency of the formulation as well as its convergence by comparison with theoretical solutions of tensile cracks, a pre‐cracked beam, and an inclined crack under biaxial stress. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
13.
A new criterion to predict crack propagation trajectory in anisotropic rocks with incorporating the concept of T-stress in formulating stress field near the crack tip was developed. The developed criterion along with enrichment functions and interaction integral in the extended finite element method (XFEM) framework made a sophisticated tool in modeling fracturing process in anisotropic media. Numerical results indicated that stress intensity factors considerably depend on orientation of anisotropy axes and ratio of the elastic modulus. The proposed formulation for anisotropic media provides a more accurate prediction of crack propagation trajectory compared with conventional methods, especially in mixed mode conditions. 相似文献
14.
为研究不同孔洞-裂隙（简称"孔-隙"）赋存条件下的裂纹扩展规律,利用RFPA软件,对不同裂纹倾角及不同非均质系数下的岩体破坏进行数值模拟分析,获得其裂纹扩展过程、声发射规律、应力-应变曲线,同时与原试验结果进行对比验证。结果表明:完整试样裂纹沿着剪切方向产生,含孔-隙试样裂纹沿裂隙尖端及孔口侧边产生;翼裂纹贯穿试件的同时,在预制裂纹尖端或孔口侧边产生水平方向的次生裂纹,并产生分叉,非均质系数影响次生裂纹走向;压载前期试样以拉破坏为主,压载后期以拉-剪组合破坏为主,次生裂纹的产生与剪切破坏有关;声发射累计能量与声发射累计数前期缓慢增大,后期迅速增大,预制裂纹倾角越小,非均质系数越大,声发射累计能量越大;不同裂纹倾角及不同非均质系数试件的应力-应变曲线均经历3个阶段:弹性变形阶段、非线性变形阶段及残余变形阶段,孔-隙的存在降低了试样的峰值强度,影响试件的脆性度。研究结果为进一步认识孔-隙相互作用规律提供了参考。 相似文献
15.
An energy approach is proposed as a complement to the stress approach commonly considered for investigating soil desiccation cracking. The elastic strain energies before and after crack initiation are estimated by both numerical and analytical solutions. The energy released by cracking is then compared with the fracture energy to discuss crack initiation conditions. This leads to combined energy and stress conditions for crack initiation following Leguillon's theory. An approximate analytical solution is derived from a variational formulation of the porous elastic body equations. A cohesive zone model and finite element code are used to simulate crack propagation in an unsaturated porous body. This analysis shows that the energy criterion is reached before the stress criterion, and this can explain unstable crack propagation at the beginning. The approximate analytical solution allows predicting correctly the crack depth and opening in its initiation stage. 相似文献
16.
在传统键基近场动力学模型的基础上,提出可以反映岩石类材料应力-应变变化特点的改进型模型,弥补了传统近场动力学模型在模拟岩石类材料时无法反映岩石内应力随应变先增加再减小最后破坏这一特性的不足。运用改进型模型,对含有单裂纹试件在不同预制裂纹角度及拉伸荷载条件下的裂纹扩展过程进行了数值模拟,分析了开裂角度在不同预制裂纹角度及拉伸荷载条件下的变化。结果表明：预制角度及拉伸荷载对开裂角度都有影响,在试件周围拉荷载接近的情况下会获得较小的开裂角,并且在拉荷载一定的条件下开裂角会有先增加后减少的规律。同时模拟了含裂纹岩石在单轴压缩条件下的裂纹扩展情况,将数值模拟的结果与室内试验的结果对比,验证了所提出新模型的有效性。所提出的新模型可以较好地模拟岩石类材料在拉荷载条件下的力学特性,在岩石数值模拟方面有着较为广泛的应用前景。 相似文献
17.
G. S. Wang 《国际地质力学数值与分析法杂志》2005,29(15):1457-1483
In this paper, the interaction of double‐periodical cracks is accurately solved based on the isolating analysis procedure, superposition principle, pseudo‐traction method, Chebyshev polynomial expansion and crack‐surface collocation technique. The jump displacement crossing crack faces, the average additional strain and therefore the effective compliance of the double‐periodically cracked plate are directly determined. The numerical results for axial‐symmetrically distributed double‐periodical cracks, general double‐periodical cracks with one collinear direction as well as two sets of double‐periodical cracks with same size and square distribution are given in this paper. And the partial typical numerical results are compared with the previous works. The analysis shows that the anisotropy induced by the general double‐periodical cracks is generally not orthogonal anisotropy. Only when the double‐periodical cracks are axial‐symmetrically distributed, is the anisotropy orthogonal. In this special cases, the effective engineering constants (consist of effective elastic modulus, the effective Poisson's ratio, the effective shear modulus) of cracked plate versus crack spacing, in the plane stress and plane strain conditions, respectively, are analysed. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
18.
裂隙性介质因其复杂的结构和可观的藏储量一直是资源勘查领域的重点研究对象。基于Hudson裂隙理论对裂隙介质中不同裂隙参数（数密度、角度、纵横比）下变化井径的井场响应进行数值模拟,得到如下结果：在裂隙数密度较小的情况下,纵波、横波以及斯通利波幅度对井径变化响应较敏感;在裂隙角度较大的情况下,斯通利波幅度对井径变化响应较敏感;在裂隙角度较小的情况下,横波幅度对井径变化响应较敏感;在裂隙纵横比较小的情况下,纵波、横波以及斯通利波幅度对井径变化响应较敏感;在频率-波数二维谱中,随着井径的增大,波动激发强度峰值所在的频率带以及波动的首次激发频率都向低频区域移动。由此认为：弹性波在裂隙性介质中传播时在受井径变化的影响下产生规律性响应,应用Hudson裂隙理论模拟裂隙介质的井场响应可以系统地分析裂隙参数和井径变化对声波传播规律的影响,进而指导实地裂隙储层声波测井勘探工作。 相似文献
19.
Cheng Zhao Yimeng Zhou Qingzhao Zhang Chunfeng Zhao Hiroshi Matsuda 《国际地质力学数值与分析法杂志》2020,44(3):353-370
To deeply understand the cracking mechanical behavior of brittle rock materials, numerical simulations of a rock specimen containing a single preexisting crack were carried out by the expanded distinct element method (EDEM). Based on the analysis of crack tips and a comparison between stress- and strain-based methods, the strain strength criterion was adopted in the numerical models to simulate the crack initiation and propagation processes under uniaxial and biaxial compression. The simulation results indicated that the crack inclination angle and confining pressure had a great influence on the tensile and shear properties, peak strength, and failure behaviors, which also showed a good agreement with the experimental results. If the specimen was under uniaxial compression, it was found that the initiation stress and peak strength first decreased and then increased with an increasing inclination angle α. Regardless of the size of α, tensile cracks initiated prior to shear cracks. If α was small (such as α ≤ 30°), the tensile cracks dominated the specimen failure, the wing cracks propagated towards the direction of uniaxial compression, and the propagation of shear cracks was inhibited by the high concentration of tensile stress. In contrast, if α was large (such as α ≥ 45°), mixed cracks dominated the specimen failure, and the external loading favored the further propagation of shear cracks. Analyzing the numerical results of the specimen with a 45° inclination angle under biaxial compression, it was revealed that lateral confinement had a significant influence on the initiation sequence and the mechanical properties of new cracks. 相似文献
20.
The phase field model represents sharp cracks by diffusive mushy-zone and can simulate crack propagation automatically. Propagation and coalescence of quasi-static cracks in Brazilian disks are investigated by a phase field model. The phase field modeling is implemented in Comsol Multiphysics and initially verified by a benchmark of three-point bending test. The Brazilian disk specimens containing no initial crack, a single and two pre-existing cracks subjected to compression are then tested by the phase field model. Crack propagation patterns along with the load–displacement curves are fully discussed. Meanwhile, the effects of length scale parameter and critical energy release rate on crack propagation are evaluated. In addition, the effect of crack inclination angle on the pre-cracked Brazilian disk specimens is also investigated. The numerical results obtained by the phase field model are in good agreement with previous experimental and numerical results.
相似文献