Macro-meso fracture evolution mechanism of hollow cylindrical granite with different hole diameters under conventional triaxial compression

In order to study and analyze the stability of engineering rock mass under non-uniform triaxial stress and obtain the evolution mechanism of the whole process of fracture,a series of conventional triaxial compression tests and three-dimensional numerical simulation tests were carried out on hollow granite specimens with different diameters.The bearing capacity of hollow cylindrical specimen is analyzed based on elasticity.The results show that:1)Under low confining pressure,the tensile strain near the hole of the hollow cylindrical specimen is obvious,and the specimen deformation near the hole is significant.At the initial stage of loading,the compressive stress and compressive strain of the specimen are widely distributed.With the progress of loading,the number of microelements subjected to tensile strain gradually increases,and even spreads throughout the specimen;2)Under conventional triaxial compression,the cracking position of hollow cylinder specimens is concentrated in the upper and lower parts,and the final fracture mode is generally compressive shear failure.The final fracture mode of complete specimen is generally tensile fracture.Under high confining pressure,the tensile cracks of the sample are concentrated in the upper and lower parts and are not connected,while the cracks of the upper and lower parts of the intact sample will expand and connect to form a fracture surface;3)In addition,the tensile crack widths of intact and hollow cylindrical specimens under low confining pressure are larger than those under high confining pressure.

Numerical Computation of Stress Intensity Factors for Bolt-hole Corner Crack in Mechanical Joints

The three-dimensional finite element method is used to solve the problem of the quarter-elliptical comer crack of the bolt-hole in mechanical joints being subjected to remote tension. The square-root stress singularity around the corner crack front is simulated using the collapsed 20-node quarter point singular elements. The contact interaction between the bolt and the hole boundary is considered in the finite element analysis. The stress intensity factors （SIFs） along the crack front are evaluated by using the displacement correlation technique. The effects of the amount of clearance between the hole and the bolt on the SIFs are investigated. The numerical results indicate that the SIF for mode I decrease with the decreases in clearance, and in the cases of clearance being present, the corner crack is in a mix-mode, even if mode I loading is dominant.

Crack stop holes in steel bridge decks:Drilling method and effects

Force analysis using a compact tension model, as recommended by ASTM, was carried out on a crack stop hole. The stress before, and after, drilling the hole was compared in terms of stress concentration and stress gradient. The optimum drilling location and diameter were studied through analysis of different locations and diameters. By analyzing the effects of flank holes and an additional hole, drilling advice was proposed and fatigue testing of the cracks in a steel bridge deck with a crack stop hole was conducted. The results show that the stress at the crack tip with a crack stop hole decreased, and the major principal stress around the hole was distributed accordingly. The optimum position of the crack stop hole centre was where the centre of the crack stop hole was situated behind the crack and the hole edge coincided with the crack tip. Therefore, hole diameters larger than 8 mm, or those weakening the section by 10%, were suggested as the best diameters. In terms of multi-hole crack stopping, a flank hole was not recommended. The optimum horizontal position of flank holes was at a distance of 1/4 of a single hole diameter from, and in front of, the single hole. Besides, the experiment showed that crack stop hole could only prevent cracks from growing and had no influence on crack growth rate.

Analytical Solutions of Cracks Emanating from an Elliptic Hole in an Infinite Plate under Tension

It is a common phenomenon that the cracks originating from a hole can cause structural damage in engineering.However,the fracture mechanics studies of hole edge crack problems are not sufficient.The problem of an elliptical hole with two collinear edge cracks of unequal length in an infinite plate under uniform tension at infinity is investigated.Based on the complex variable method,the analytical solutions of stress functions and stress intensity factors are provided.The stress distribution along the axes and the edge of the elliptical hole is given graphically.The numerical results show that there is obvious stress concentration near the hole and cracks,and the stresses tend to applied loads at distances far from the defect,which conform to Saint-Venant’s principle.Hence,the stress functions are proved to be right.Under special conditions,the present configuration becomes the Griffith crack,two symmetrical cracks emanating from an elliptical hole,two cracks of unequal length emanating from a circular hole,a crack at the edge of a circular hole,or a crack emanating from an elliptical hole.Compared with available results,stress intensity factors for these special shapes of ellipses and cracks show good coincidence.The stress intensity factor for two cracks of unequal length at the edge of an elliptical hole increases with the crack length and the major-to-minor axis ratio of the elliptical hole.The stress distribution in an infinite plate containing an elliptic hole with unsymmetrical cracks is given for the first time.

Exact Solutions for Piezoelectric Materials with an Elliptic Hole or a Crack under Uniform Internal Pressure

The existing investigations on piezoelectric materials containing an elliptic hole or a crack mainly focus on remote uniform tensile loads.In order to have a better understanding for the fracture behavior of piezoelectric materials under different loading conditions,theoretical and numerical solutions are presented for an elliptic hole or a crack in transversely isotropic piezoelectric materials subjected to uniform internal pressure and remote electro-mechanical loads.On the basis of the complex variable approach,analytical solutions of the elastic and electric fields inside and outside the defect are derived by satisfying permeable electric boundary condition at the surface of the elliptical hole.As an example of PZT-4 ceramics,numerical results of electro-elastic fields inside and outside the crack under various electric boundary conditions and electro-mechanical loads are given,and graphs of the electro-elastic fields in the vicinity of the crack tip are presented.The non-singular term is compared to the asymptotic one in the figures.It is shown that the dielectric constant of the air in the crack has no effect on the electric displacement component perpendicular to the crack,and the stresses in the piezoelectric material depend on the material properties and the mechanical loads on the crack surface and at infinity,but not on the electric loads at infinity.The figures obtained are strikingly similar to the available results.Unlike the existing work,the existence of electric fields inside an elliptic hole or a crack is considered,and the piezoelectric solid is subjected to complicated electro-mechanical loads.

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.

Anti-plane Analysis of a Circular Hole withThree Unequal Cracks in One-dimensionalHexagonal Piezoelectric Quasicrystals

This paper employes variable function method and the technique of conformal mappingto discuss the anti-plane problem of a circular hole with three unequal cracksin a one-dimensional （1D） hexagonal piezoelectric quasicrystal. Based on the piezoelectricityfundamental equations of quasicrystal materials and the symmetry of1D hexagonal quasicrystal and its linear piezoelectricity effect, 1D hexagonal quasicrystalcontrol equations of anti-plane problem are derived. Applying Cauchyintegral formula, the analytical expressions for the crack tip filed intensity factorsare presented with the assumption that the crack are electrical impermeable andelectrical permeable. With the variation of the hole-size and the crack length, someof the new model of crack are obtained. In the absence of the electric load, theresults match with the classical ones. The numerical results indicate the effects ofgeometric parameters on the field intensity factors. It is verified that the horizontalcrack length and the circle radius can easily promote crack growth. Researchon such issues will provide reliable theoretical value for the engineering materialspreparation and application.

An analytical solution for the stress field and stress intensity factor in an infinite plane containing an elliptical hole with two unequal aligned cracks

The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.

Effect of holes on in-plane shear(Mode Ⅱ) crack sub-critical propagation of rock

Shear-box(i.e.compression-shear) test and newly designed electrically conductive adhesive method were used to measure shear crack sub-critical propagation time and rate of sandstone specimen.Different cubic specimens with and without holes were tested to study the effect of holes on the shear crack sub-critical propagation.Numerical and experimental results show that three independent variables of hole,the interval distance S,the distance between the center of hole and the crack tip L,and hole radius R,have different contribution to the ratio of stress intensity factor of the specimen with holes to that of the specimen without hole,KⅡ/KⅡ0.Increasing S and decreasing L and R will result in the decrease of KⅡ/KⅡ0 and help crack arrest.The weight relation of the independent variables for KⅡ/KⅡ0 is S>L>R.The specimen DH3 with the largest value of S and the smallest values of L and R has the longest sub-critical crack propagation time and the smallest sub-critical crack propagation rate.Adding two suitable holes symmetrically to the original crack plane in rock specimen is considered to be a potential method for crack arrest of rock.

THE FUNDAMENTAL SOLUTIONS FOR THE PLANE PROBLEM IN PIEZOELECTRIC MEDIA WITH AN ELLIPTIC HOLE OR A CRACK

Based on the complex potential method, the Greed’s functions of the plane problem in transversely isotropic piezoelectric media with an elliptic hole are obtained in terms of exact electric boundary conditions at the rim of the hole. When foe elliptic hole degenerates into a crack, the fundamental solutions for the field intensity factors arc given. The general solutions for concentrated and distributed loads applied on the surface of the hole or crack are produced through the superposition of fundamental solutions With the aid of these solutions , some erroneous results provided previously in other works are pointed out More important is that these solutions can be used as the fundamental solutions of boundary element method to solve more practical problems in piezoelectric media.

Analytic solutions to problem of elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals

By means of the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals is investigated. The solution of the stress intensity factor （SIF） for mode III problem has been found. Under the condition of limitation, both the known results and the SIF solution at the crack tip of a circular hole with two straight cracks and cross crack in one-dimensional hexagonal quasicrystals can be obtained.

Screw dislocations interacting with two asymmetrical interfacial cracks emanating from an elliptical hole

The interaction between screw dislocations and two asymmetrical interfacial cracks emanating from an elliptic hole under loads at infinity is studied. The closed-form solution is derived for complex potentials. The stress intensity factor and the critical applied stress for the dislocation emission are also calculated. In the limiting cases, well-known results can be obtained from the present solutions. Moreover, new exact solutions for a screw dislocation interacting with some complicated cracks are derived. The results show that the shielding effect increases with the increase in the length of the other cracks and the minor semi axis, but decreases with the increase of dislocation azimuth. The repulsion acting on the dislocation from the other phase and the other crack extend in the horizontal direction, which makes the dislocation emission at the crack tip take place more easily, but the minor semi axis of the elliptical hole extending in the vertical direction makes it more difficult.

SCATTERING OF SH-WAVE BY CRACKS ORIGINATING AT AN ELLIPTIC HOLE AND DYNAMIC STRESS INTENSITY FACTOR

The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.

STRESS INTENSITY FACTORS OF A PLATE WITH TWO CRACKS EMANATING FROM AN ARBITRARY HOLE

In this paper, Muskhelishvili complex function theory and boundary collocation method are used to calculate the stress intensity factors (SIF) of a plate with two cracks emanating from an arbitrary hole. The calculated examples include a circular, elliptical, rectangular, or rhombic hole in a plate. The principle and procedure by the method is not only rather simple, but also has good accuracy. The SIF values calculated compare very favorably with the existing solutions. A t the same time,the method can be used far different finite plate with two cracks emanating from a hole with more complex geometrical and loading conditions. It is an effective unified approach for this kind of fracture problems.

Experimental Study and Numerical Simulation Using Extended Finite Element Method (XFEM) Combined with Cohesive Zone Model (CZM), of Crack Growth Induced by Non-Explosive Expansive Material on Two Neighboring Circular Holes of A Gneiss Rock

The Non-explosive expansion material (NEEM) is a method more environmentally friendly than the harmful conventional rock fracturing techniques. However, it is slower and very costly. Thus, any means of economizing their use is very desirable. This paper investigates the crack growth between two neighboring holes of a gneiss rock internally pressurized by NEEM mixed with water with the aim to evaluate the influence of holes spacing (center-to-center distance), on the initiation and growth of cracks. Field experimental results reveal that crack starts earlier and grows faster with increasing ambient temperature. But when the ambient temperature is above 28°C, the NEEM is “blown out” of the holes. At these ambient temperatures, the surrounding rocks are hot and cannot dissipate efficiently the heat generated by the hydration reaction. The best filling time was found to be in the evening when the daily hot temperature has drooped. The time to first crack increases as hole diameter decreases. The 3D numerical modeling and simulation of crack growth between two neighboring holes internally pressurized by NEEM using ABAQUS (XFEM/CZM) software shows a good agreement with the theoretical and experimental results.

THE SOLUTION OF A CRACK EMANATING FROM AN ARBITRARY HOLE BY BOUNDARY COLLOCATION METHOD

In this paper a group of stress functions has been proposed for the calculation of a crack emanating from a hole with different shape (including circular, elliptical, rectangular, or rhombic hole) by boundary collocation method. The calculation results show that they coincide very well with the existing solutions by other methods for a circular or elliptical hole with a crack in an infinite plate. At the smae time, a series of results for different holes in a finite plate has also been obtained in this paper. The proposed functions and calculation procedure can be used for a plate of a crack emanating from an arbitrary hole.

Weight Function Method for Stress Intensity Factor of Internal Surface Semi-elliptical Crack in Elliptical Holes

The hatches for inspecting are usually designed with elliptical holes in airplane structures, so computation of the stress intensity factor of three dimensional crack at elliptical holes is pivotal for damage tolerance analysis of these structures. In this paper, weight function is derived for a two dimensional through cracks at elliptical holes by applying a compounding method. Stress intensity factor formulas for an internal surface semi-elliptical crack in elliptical holes are obtained wing the three dimensional weight function method. Stress intensity factors for an internal surface semi-elliptical crack in elliptical holes under remote tension are computed. At the same time, research on how radius of curvature for elliptical holes affect stress intensity factors was conducted. Stress intensity factors decrease when radius of curvature increases. Some results and conclusions which are of practical value are given.

炮孔间距对偏心不耦合装药贯通裂纹扩展的影响

为研究光面爆破中偏心不耦合装药炮孔间距对贯通裂纹扩展的影响,利用同心不耦合装药的孔壁压力计算公式并结合应力波叠加原理,推导偏心不耦合装药的炮孔间距计算方法。基于求得的炮孔间距范围,计算3种岩石介质在不同炮孔间距条件下贯通裂纹的扩展位置,并选择砂岩材料进行数值模拟。结果表明:偏心不耦合装药爆破中,贯通裂纹主要集中于偏心侧;抗拉强度大的岩石,贯通裂纹偏离炮孔连心线的程度也较大。砂岩的炮孔间距为60 cm时,贯通裂纹扩展方向与炮孔连心线重合,连心线下方出现裂纹比较集中的贯通区域;炮孔间距的增大导致贯通裂纹远离炮孔连心线,从而造成欠挖。偏心不耦合装药爆破后,偏心侧岩石的损伤明显大于非偏心侧。

含开孔与含裂缝的复合材料层压板拉伸剩余强度评估

为研究含开孔和裂缝的碳纤维增强树脂基复合材料(CFRP)层压板在拉伸载荷作用下的剩余强度,针对四种典型铺层、两类损伤形式、四种损伤尺寸的约200件试验件进行了试验研究。结果表明:对于具有相同铺层、相同宽度的复合材料层压板,开孔直径与裂缝长度相等时,两类层压板有相同的剩余强度;加载过程中,裂缝根部较早出现裂缝、分层,应力重新分配,降低了裂缝根部的应力集中。基于损伤区纤维断裂判据、经典层压板理论及复变函数理论的强度计算方法能较准确地计算出含开孔的复合材料层压板剩余强度;计算含裂缝复合材料层压板剩余强度时可将裂缝损伤等效为开孔损伤,计算结果与试验结果吻合较好。

宽孔距爆破模型试验及近场动力学计算研究

针对宽孔距爆破破岩技术中炮孔密集系数合理取值的问题,在总结国内外宽孔距爆破破岩机理的基础上,开展了炮孔密集系数为1.7、2.5、3.5、4.5的有机玻璃板室内爆破试验,并基于常规态型近场动力学原理,开发了爆破计算模块,对宽孔距爆破破岩中裂纹扩展过程、介质位移响应规律进行了研究。结果表明:临空面一侧的径向裂纹受到临空面反射拉伸应力波的作用,表现出向临空面拐角分叉的特征,并逐渐向临空面扩展,最后形成主裂纹组成漏斗形状。在最小抵抗线固定不变条件下,随着炮孔密集系数的增加,应力降低区逐渐增大,同排炮孔间的径向贯通裂隙消失,过大的炮孔密集系数也进一步造成前后排孔间贯通裂纹消失,最后导致单孔爆破的情况发生。位移计算结果进一步证实了上述规律,并且当炮孔密集系数较小时,前排炮孔留下的岩埂刚好被后排炮孔爆破破碎,随着炮孔密集系数的增大,后排孔爆破对前排炮孔所留下的岩埂破碎作用效果逐渐降低。建议实际工程中根据岩体力学性质、地质条件以及爆破目的适当调整密集系数来降低炸药单耗与大块率。