Stable growth of a central crack

The elastic fracture behavior of a plate subjected to uniform stress surrounding two equal cracks inclined at an angle is investigated. The orientation of the crack plane with applied stress can be varied. Among the cases are: (1) two cracks inclined symmetrically with respect to the vertical and horizontal applied stress, and (2) one crack is horizontal while the other is inclined to the vertical applied stress. The strain energy density criterion is used for determining the combined crack and load arrangement that correspond to the lowest critical load at global instability. The direction of crack initiation is also determined. Quantitative results pertaining to the fracture characteristics are given in graphical forms.     

节理充填物厚度对运动裂纹扩展的影响

为研究冲击载荷作用下节理充填物厚度对裂纹扩展行为的影响，以石膏为有机玻璃预制裂纹充填物，利用新型数字激光动态焦散线实验系统，对3种不同节理充填物厚度的有机玻璃进行三点弯冲击实验。实验结果表明，相同冲击载荷作用下，竖向预制裂纹均竖直向上扩展，是典型的Ⅰ型裂纹，充填物越厚，竖向裂纹越容易起裂。竖直裂纹扩展至水平预制裂纹后，充填物厚度为1、3、5 mm的试件的水平预制裂纹汇聚能量的时间分别为433、2 200、2 580 μs，起裂时的应力强度因子分别为635.2、742.4、906.8 kN/m3/2，表明充填物越厚，水平裂纹越难起裂。水平预制裂纹扩展过程中共发生2次曲裂，是典型的Ⅰ-Ⅱ复合型裂纹，节理充填物越厚，其扩展轨迹越弯曲；当裂纹扩展至距离试件上边界3 mm时，扩展方向偏离第1次裂纹曲裂切线而朝向试件上边界扩展，试件最终断裂，测量发现充填物厚度为1、3、5 mm的试件的断裂点与冲击载荷作用点的距离分别为16.5、11.0、6.0 mm。     

Three-dimensional mixed-mode stress intensity factors for cracks in functionally graded materials using enriched finite elements

Three-dimensional enriched finite elements are used to compute mixed-mode stress intensity factors (SIFs) for three-dimensional cracks in elastic functionally graded materials (FGMs) that are subject to general mixed-mode loading and constraint conditions. The method, which advantageously does not require special mesh configuration/modifications and post-processing of finite element results, is an enhancement of previous developments applied so far on isotropic homogeneous and isotropic interface cracks. The spatial variation of FGM material properties is taken into account at the level of element integration points. To validate the developed method, two- and three-dimensional mixed-mode fracture problems are selected from the literature for comparison. Two-dimensional cases include: inclined central crack in a large FGM medium under uniform tensile strain and stress loadings, a slanted crack in a finite-size FGM plate under exponentially varying tensile stress loading and an edge crack in a finite-size plate under shear traction load. The three-dimensional example models a deflected surface crack in a finite-size FGM plate under uniform tensile stress loading. Comparisons between current results and those from analytical and other numerical methods yield good agreement. Thus, it is concluded that the developed three-dimensional enriched finite elements are capable of accurately computing mixed-mode fracture parameters for cracks in FGMs.     

Spread of plasticity from stacked stress concentrations

A large elastic solid containing an infinite sequence of slitlike relaxed cracks with a constant distance of vertical separation is considered. The solid is deforming under plane strain shear conditions (mode II). The plastic relaxation around each of the cracks is represented by a suitable distribution of edge dislocations coplanar with the crack itself, the distribution being determined from a singular integral equation. This equation is solved numerically using an expansion of the non-singular part of the kernel in a series of Chebyshev polynomials. Solutions are obtained for the extent of spread of plasticity from each crack and for the associated dislocation distribution as a function of the crack spacing and the applied load. The results are applied to a brief discussion of the fracture process at stress concentrations using the crack opening displacement criterion.     

Mixed mode fatigue crack growth in test coupons made from 2024-T3 aluminum

In this paper, two different fracture criteria are applied to determine the crack trajectory or angle of crack propagation in test specimens containing inclined cracks emanating from open holes. Also, different crack growth rate models are assumed for each criterion. The maximum principal stress criterion is used with a crack growth-rate equation based on an effective stress intensity factor. The strain energy density criterion is used with a crack growth-rate equation corresponding to an effective strain energy density factor. The crack growth-rate models for each criterion were constructed using unpublished fatigue crack growth data for 2024-T3 aluminum.     

爆炸荷载作用下模型介质裂纹扩展试验与分析

为研究爆炸载荷作用下裂隙介质裂纹扩展规律,以含人工裂隙的有机玻璃薄板为介质,分别以炮孔中心到人工裂隙垂直距离L和人工裂隙长度D为变量,采用单发雷管爆炸加载试验模型进行试验。试验结果表明,爆炸荷载作用将使裂隙介质形成径向裂纹、翼裂纹、层裂裂纹和似层裂裂纹;人工裂隙能够阻隔径向裂纹的扩展,径向裂纹的扩展对距离L比长度D更敏感;翼裂纹是爆炸绕射波或绕射波与压缩应力波共同作用产生的,翼裂纹的长度随距离L增加而降低;入射压缩应力波与反射拉伸应力波叠加形成的净拉伸应力拉裂介质形成层裂效应、引起径向裂纹弯曲形成似层裂效应,层裂裂纹和似层裂裂纹几乎平行于人工裂隙。研究结果可为裂隙岩体爆破设计、冲击矿压防治和结构工程防护等提供理论依据。     

基于相场法的周期性多孔结构断裂行为研究

周期性多孔结构具有质量轻、比密度低、比强度高、隔音等优良特点, 同时也能很好地满足结构-功能一体化的需求, 在许多领域具有广泛的应用前景. 目前, 对周期性多孔结构在复杂载荷下的力学响应和断裂行为的研究较少. 采用细观力学和相场方法相结合, 基于二维代表性体积单元RVE模型, 施加能实现比例加载的周期性边界条件, 研究周期性多孔结构在复杂多轴比例加载状态下的裂纹萌生位置、断裂模式、承载极限及其变化规律. 本文的数值模拟结果表明: 首先, 周期性多孔结构在竖直方向拉伸载荷作用下, 裂纹均从孔边萌生并沿水平方向同步扩展; 其次, 在双轴载荷作用下, 随着水平载荷的增加, 结构在竖直方向的极限拉伸载荷逐渐增大; 当双轴拉伸载荷等值时, 结构的抗拉强度达到最大, 此时断裂模式呈现为十字正交型开裂; 最后, 面内剪切应力的引入会导致结构的拉伸强度极限降低, 孔边裂纹的萌生位置和扩展路径发生偏移, 裂纹模式从单S型转变为双弧线型, 裂纹向水平位置上相邻的孔洞扩展. 随着水平载荷的增加, 裂纹模式最终转变为斜裂纹, 从孔边对角线位置萌生并沿着45°方向扩展.      

层状磁电复合材料界面共线裂纹平面问题分析

本文研究了面内电磁势载荷作用下双层压电压磁复合材料中共线界面裂纹问题．考虑了压电材料的导磁性质和压磁材料的介电性质,引入了界面电位移和磁感强度的连续性条件．利用Fourier 变换得到一组第二类Cauchy 型奇异积分方程．进一步导出了相应问题的应力强度因子、电位移强度因子和磁感强度强度因子的表达式,给出了应力强度因子的数值结果．结果表明电磁载荷会导致界面裂纹尖端I、II 混合型应力奇异性,同时还伴随着电位移和磁感强度的奇异性．比较了双裂纹左右端的应力强度因子,发现在面内极化方向上施加面内磁势载荷时共线裂纹内侧尖端区域的两个法向应力场发生互相干涉增强．     

Spread of plasticity from a stack of cracks under mode I conditions

The paper studies the extent of plastic relaxation around the tips of an infinite sequence of slitlike cracks contained in a large elastic solid. The cracks have a constant distance of vertical separation, and the solid is deforming under tensile loading (mode I). The plastic region around each of the crack tips coplanar with the crack itself is represented by a suitable distribution of edge dislocations, which is determined from equilibrium considerations. The latter lead to a singular integral equation which is solved numerically. The solution procedure is uniformly valid for any crack spacing. Furthermore, an alternate perturbation technique is used for widely spaced cracks. Solutions are obtained as a function of the crack spacing and the applied tensile load, and the results discussed from the point of fracture initiation at stresss concentrations.     

Biaxial Load Effect on Crack Initiation for Orthotropic Materials

This paper is concerned with the study of the elastostatic fracture response of an orthotropic plate with an inclined crack and subjected at infinity to a biaxial uniform load. To this end an unconventional approach to the derivation of the complex variable expressions of the elastic fields is proposed. The above formulation has been used to solve the boundary value problem as superposition of Mode-I and Mode-II crack problems and it is shown that the near tip asymptotic expressions of stress and displacement fields are affected by non-singular terms originated by load biaxiality. The maximum circumferential tensile stress criterion is applied in order to investigate the effects of non-singular terms on the angle of crack extension.     

Morphology of horizontal cracks in swelling soils

Horizontally formed cracks in the network of cracked swelling soils tend to influence water and solute transport. An approach is suggested for estimating the mean width and volume of horizontal cracks. It is assumed that the nearly horizontal cracks appear as a result of inhomogeneous soil subsidence caused by rapid drying and shrinkage of thin layers at the walls of vertical cracks. Compared with the moist soil matrix, at the same soil depth, horizontal cracks originate as ruptures in stretched layers of the drying walls of vertical cracks. A characteristic of the average inhomogeneity of soil subsidence, i.e., the mean potential relative subsidence (MPRS) depending on the soil depth is defined. It is calculated on the basis of linear shrinkage in the clay soil matrix and at the walls of vertical cracks of different depths, and on two geometrical parameters of crack networks. They are namely the maximum crack depth and the thickness of the upper intensive-cracking layer. The absolute value and sign of the derivative of the MPRS function with respect to soil depth determine the specific volume of horizontal cracks (horizontal-cracks porosity), and their mean width as functions of depth. Model predictions are obtained using published data on variation of linear shrinkage with depth in 19 soil profiles. For lack of data specific to horizontal-crack characteristics model, predictions were compared with data on vertical cracks and subsidence at the soil surface. Satisfactory agreement was obtained for all soil depths up to the maximum crack depth.     

Interaction between collinear periodic cracks in an infinite piezoelectric body

The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping technique, the general periodic solutions for collinear cracks are obtained. The stress intensity factors and the size of saturation strips are derived analytically, and their dependencies on the ratio of the periodicity on the half-length of the crack are analyzed in detail. Numerical results show the following two facts. (1) When h/l>4.0, the stress intensity factors become almost identical to those of a single crack in an infinite piezoelectric body. This indicates that the interaction between cracks can be ignored in establishing the criterion for the crack initiation in this case. (2) The speed of the saturation strip size of periodic cracks approaching that of a single crack depends on the electric load applied at infinity. In general, a large electric load at infinity is associated with a slow approaching speed.     

Transient thermal fracture of cracked plates

The effects of a transient thermal load on a cracked plate are studied experimentally using photothermoelasticity. The three crack configurations of an edge crack, an interior vertical crack and an interior crack inclined at 45 deg are analyzed. In each case, the initially heated plates are subjected to cooling along the edge, while the faces of the plate are either completely insulated, or noninsulated, or in a third case, they are covered with heated transparent Plexiglas plates. It is shown that among the three cracks, the largest transient maximum stress-intensity factor occurs for the edge crack. The inclined crack is subjected to a mixed-mode loading. Among the three cooling conditions, the most severe is the insulated faces case while the noninsulated is the least severe. The relative effect of the cooling conditions on the stress-intensity factors for the three crack types is different enough that the results with one cooling condition would not represent those of another one. A comparison of the experimental transient stress-intensity factors for the vertical crack cases to the finite-element results shows good agreement.     

Nonlocal theory solution of two collinear cracks in the functionally graded materials

In this paper, the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti-plane shear loading is investigated by means of nonlocal theory. The traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present near the crack tips. The nonlocal elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials. The magnitude of the finite stress field depends on the crack length, the distance between two cracks, the parameter describing the functionally graded materials and the lattice parameter of the materials.     

Fracture mechanics of a tension-shear macrocrack in rocks

Fracture in rocks is influenced by anisotropy and existence of faults. Fracture initiation and propagation is often under the combined presence of sliding and opening of preexisting cracks. Linear-elastic fracture-mechanics (LEFM) has been used as a model for describing the propagation of a main crack in materials such as rocks, concrete, ceramics, etc. However, the presence of the fracture process zone which includes interlocking of grains and ligament connections results in deviations from perfectly brittle behavior. These effects are more pronounced in mixed-mode fracture, which involves crack initiation under the combined presence of tension-shear or compression-shear stresses.Specimens of Indiana limestone with a preexisting inclined notch were studied to observe the fracture process under a mixed-mode state of stress. Experimental monitoring involved using the electronic speckle-pattern interferometry (ESPI) technique to monitor strains and crack-propagation paths with high sensitivity. A scanning electron microscope (SEM) was used to examine the specimen for the presence of microcracks. Experimental results were subsequently evaluated using a mixed-mode fracture theory and finite-element computations.It was possible to visually observe the pre-peak and post-peak development of the fracture process zone. Developments in the crack-tip strain concentration were observed at and beyong the peak load. While the experiments conducted involved tension-shear cracks, the possibility of extending the concepts to compression-shear cracks was also explored. The possibilities and limitations of using the fracture-mechanics approach to understanding fracture in rocks were subsequently discussed.Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13.     

Antiplane mechanical and inplane electric time-dependent load applied to two coplanar cracks in piezoelectric ceramic material

This work is concerned with the dynamic response of two coplanar cracks in a piezoelectric ceramic under antiplane mechanical and inplane electric time-dependent load. The cracks are assumed to act either as an insulator or as a conductor. Laplace and Fourier transforms are used to reduce the mixed boundary value problems to Cauchy-type singular integral equations in Laplace transform domain. A numerical Laplace inversion algorithm is used to determine the dynamic stress and electric displacement factors that depend on time and geometry. A normalized equivalent parameter describing the ratio of the equivalent magnitude of electric load to that of mechanical load is introduced in the numerical computation of the dynamic stress intensity factor (DSIF) which has a similar trend as that for the pure elastic material. The results show that the dynamic electric field will impede or enhance crack propagation in a piezoelectric ceramic material at different stages of the dynamic electromechanical load. Moreover, the electromechanical response is greatly affected by the ratio of the crack length to the ligament between the cracks. The stress and electric displacement intensity factor can be combined by the energy density factor or function to address the fracture of piezoelectric materials under the combined influence of electromechanical loading.     

孔边裂纹对SH波的散射及其动应力强度因子

采用Ｇｒｅｅｎ函数法研究任意有限长度的孔边裂纹对ＳＨ波的散射和裂纹尖端场动应力强度因子的求解．取含有半圆形缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解作为Ｇｒｅｅｎ函数,采用裂纹“切割”方法并根据连接条件建立起问题的定解积分方程,得到动应力强度因子的封闭解答．最后给出了孔边裂纹动应力强度因子的算例和结果,并讨论了圆孔的存在对动应力强度因子的影响     

Slope stability analysis using fracture mechanics approach

The analysis of slope failure is complicated due to its mechanism as well as the geological history of the slope. In classical slope stability analysis, the slope failure is assessed using the basic continuum mechanics or the limit equilibrium approach. This analysis, however, must be slightly modified when tension cracks exist at the upper edge of the slope. From post-mortem analyses of slope failures in the past, it was found that tension cracks had some considerable importance affecting the failure mechanism of the slope.Some attempts had also been directed in the past towards simple vertical cut slopes with tension cracks. Terzaghi [40]. Using an elasto-plastic model and a few analytical assumptions, Terzaghi [40] obtained an expression for a critical height of a vertical cut slope. However, since the stress distribution is changing during crack propagation, the failure mechanism cannot in principle conjecture from a static (undisturbed) stress field alone. In this report, a unified numerical approach combining Finite Element Method (FEM), fracture mechanics and remeshing technique is used to model the failure analysis of vertical cut slopes with tension cracks. Using this approach, the crack can be extended incrementally under a certain energy based failure criterion (Strain Energy Density criterion - SED) while taking into account the existing stress singularity field in the vicinity of the crack-tip.The use of fracture mechanics in soils, however, poses some difficulties in obtaining its relevant parameters due to the granular structure of soil. Because of its granular structure, the shear strength of soil depends on cohesion and the applied confining pressure making the determination of fracture parameters in soil difficult. These relevant parameters are not yet available in literature and hence, certain assumptions and interpolations had to be made in obtaining these parameters. Future research direction in this area is badly needed. Using a certain set of soil properties and crack geometry, a series of curves relating parameters S (Strain Energy Density Factor) and a non-dimensional variable N ( = H/C - slope height vs. crack distance from edge ratio) for vertical cut slopes can be constructed through numerous parametric studies. These curves can serve as a quick guide to obtain the critical height for a given vertical cut slope geometry with tension cracks.     

脆性固体中内聚断裂点阵列的扩张行为及间隔影响

建立一个一维模型, 分析脆性材料中多个等间距虚拟断裂点在均匀应变率拉伸作用下的扩张断裂过程. 采用线弹性波动方程组描述材料内部动力学关系, 采用线性内聚力断裂模型(linear cohesive fracture model)描述虚拟断裂点的扩张行为, 根据初始均匀拉伸条件和虚拟裂纹等间距假设给出定解条件, 形成一个初边值问题. 采用Laplace变换方法求解控制方程组, 得到虚拟断裂点扩张过程中内聚应力随时间变化曲线, 以及发生完全断裂的临界时间和单位裂纹体(碎片)的临界膨胀位移. 在此基础上分析应变率和裂纹间距对碎裂发生时间及单元裂纹体临界膨胀位移的影响. 在假设脆性材料在自然碎裂过程中单元裂纹体临界膨胀位移最小的基础上,进一步研究应变率对碎片尺度的影响.      

基于修正权函数的多裂纹无网格模拟

本文采用了一种基于不连续场修正权函数的无网格方法来处理二维平面多裂纹问题。相较于传统的无网格断裂不连续场和奇异场模拟方法,修正权函数法算法简便易实现。采用修正权函数处理多裂纹时,只需要对每一段裂纹周围节点的权函数进行修正,就能同时模拟多裂纹不连续位移场和多裂尖奇异场。本文采用基于不连续场修正权函数的无单元Galerkin方法（EFGM）,对Y型裂纹板、十字型裂纹板和孔边双裂纹板进行了分析。数值结果表明,在不引入扩展基函数情况下,通过修正权函数法能够得到精度较高的应力强度因子解,能较好地拟合多裂纹的裂尖奇异场。