Numerical analysis of quasi-static crack branching in brittle solids by a modified displacement discontinuity method

Mechanism of quasi-static crack branching in brittle solids has been analyzed by a modified displacement discontinuity method. It has been assumed that the pre-existing cracks in brittle solids may propagate at the crack tips due to the initiation and propagation of the kink (or wing) cracks. The originated wing cracks will act as new cracks and can be further propagated from their tips according to the linear elastic fracture mechanics (LEFM) theory. The kink displacement discontinuity formulations (considering the linear and quadratic interpolation functions) are specially developed to calculate the displacement discontinuities for the left and right sides of a kink point so that the first and second mode kink stress intensity factors can be estimated. The crack tips are also treated by boundary displacement collocation technique considering the singularity variation of the displacements and stresses near the crack tip. The propagating direction of the secondary cracks can be predicted by using the maximum tangential stress criterion. An iterative algorithm is used to predict the crack propagating path assuming an incremental increase of the crack length in the predicted direction (straight and curved cracks have been treated). The same approach has been used for estimating the crack propagating direction and path of the original and wing cracks considering the special crack tip elements. Some example problems are numerically solved assuming quasi-static conditions. These results are compared with the corresponding experimental and numerical results given in the literature. This comparison validates the accuracy and applicability of the proposed method.     

Quasistatic thermal crack extension in the interfaces of bounded self-stressed multiphase compounds

The quasistatic growth of straight interface cracks in thermally loaded brittle multiphase solids consisting of two circular segments of brittle materials with different thermoelastic properties which are glued together at the interface with a special glass seal has been investigated. The resulting mixed boundary-value problems of the stationary plane thermoelasticity have been solved by applying the finite element method. Moreover, fracture mechanical data like crack surface displacements and strain energy release rates governing the propagation behavior of a quasistatic extending thermal interface crack have been calculated. The data obtained have been compared with the results of special cooling experiments in multiphase composite structures in which curved thermal cracks in one of the circular segments occur.     

Domain switching effect on fracture of piezoelectric solids

Rational design of smart sensors and actuators that consist of piezoelectric solids requires a thorough understanding of the constitutive behavior of this material under mechanical and electrical loading. Domain switching is the cause of significant nonlinearity in the constitutive behavior of piezoelectric solids, which may be enhanced in the presence of cracks. In this paper, the response of piezoelectric solids is formulated by coupling thermal, electrical, and mechanical effects. The corresponding finite element equations are derived and applied in the solution of the piezoelectric center crack problems. The effects of domain switching are evaluated on the near tip stress intensity factors.     

用边界元方法分析复合材料中的裂纹问题

利用层状材料的广义Klevin基本解，建立了计算三维层状材料中的裂纹边界元方法。采用边界元方法中的多区域方法和能反映均匀介质中裂纹尖端应力场和位移场特征的面力奇异单元。裂纹的应力强度因子由裂纹面上的位移经插值计算得到。算例分析表明，本文建议的方法可以获得较高的计算精度。     

梯度材料中矩形裂纹的对偶边界元方法分析

采用对偶边界元方法分析了梯度材料中的矩形裂纹. 该方法基于层状材料基本解,以非裂纹边界的位移和面力以及裂纹面的间断位移作为未知量. 位移边界积分方程的源点配置在非裂纹边界上,面力边界积分方程的源点配置在裂纹面上. 发展了边界积分方程中不同类型奇异积分的数值方法. 借助层状材料基本解,采用分层方法逼近梯度材料夹层沿厚度方向力学参数的变化. 与均匀介质中矩形裂纹的数值解对比,建议方法可以获得高精度的计算结果. 最后,分析了梯度材料中均匀张应力作用下矩形裂纹的应力强度因子,讨论了梯度材料非均匀参数、夹层厚度和裂纹与夹层之间相对位置对应力强度因子的影响.      

脆性固体碎裂过程中的最快卸载特性

脆性固体在高应变率拉伸过程中常破碎为多块碎片.论文通过一个一维理论模型,研究动态脆性碎裂过程中固体内部载荷卸载规律,以及碎片尺度的计算方法.假设一维固体中裂纹等间距分布、同时起裂,研究均匀应变率拉伸作用下裂纹阵列的扩张过程.采用线弹性波动方程组描述未断裂固体的动力学关系,采用粘滞断裂模型(cohesive fracture model)描述裂纹的扩张行为,形成完整的初边值问题.采用沿特征线的有限差分计算格式求解控制方程组,得到固体在碎裂过程不同时刻下单位裂纹体内部的应力分布曲线,以及单位裂纹体平均应力随时间的变化规律,确定单位裂纹体达到完全断裂所需要的时间.在给定应变率下,分析不同裂纹间距下的碎裂卸载时间,以及使单位裂纹体以最快速度完全卸载所对应的最佳裂纹间距,并以此间距估算脆性固体在自然动态碎裂过程中的平均碎片尺度.进一步研究了具有不同粘滞性断裂特性的脆性固体的碎片尺度计算数值的差异.     

The dynamic behaviour of slender structures with cross-sectional cracks

A dynamic model for beams with cross-sectional cracks is discussed. It is shown that a crack can be represented by a consistent, static flexibility matrix. Two different methods for the determination of the flexibility matrix are discussed. If the static stress intensity factors are known, the flexibility matrix can be determined from an integration of these stress intensity factors. Alternatively, static finite element calculations can be used for the determination of the flexibility matrix. Both methods are demonstrated in the present paper. The mathematical model was applied to an edge-cracked cantilevered beam and the eigenfrequencies were determined for different crack lengths and crack positions. These results were compared to experimentally obtained eigenfrequencies. In the experiments, the cracks were modelled by sawing cuts. The theoretical results were, for all crack lengths, in excellent agreement with the experimental data. The dynamic stress intensity factor for a longitudinally vibrating, centrally cracked bar was determined as well. The results compared very well with dynamic finite element calculations. The crack closure effect was experimentally investigated for an edge-cracked beam with a fatigue crack. It was found that the eigenfrequencies decreased, as functions of crack length, at a much slower rate than in the case of an open crack.     

软铁磁材料平面裂纹问题的耦合场

由磁弹性问题的线性化理论导出磁场下平面软铁磁体问题的控制方程和复势解。利用复势解和奇异积分方程方法,对面内磁场和远场载荷作用下的含裂纹无限大软铁磁平面问题进行了求解,得到耦合场的解。并对不同磁力模型的结果和磁场与机械载荷共同作用下的裂尖应力强度因子进行了讨论。     

带凸缘弯曲梁应力集中区内表面裂纹应力强度因子的研究

用三维光弹性冻结应力实验技术与修正的多点超定法相结合研究了带凸缘弯曲梁应力集中区内表面裂纹的应力强度因子。分析了不同过渡圆弧的应力集中对两种表面裂纹(半圆形表面裂纹与前缘直线表面裂纹)的影响。用实验方法得到了应力强度因子放大系数的数值.结果表明,应力集中对浅裂纹的影响是更大的,是不可忽视的,但放大系数随表面裂纹的几何形状变化很小。这些对管节点的断裂力学评估提供了有价值的实验依据.     

Fatigue crack growth through residual stress fields—theoretical and experimental studies on thick-walled cylinders

Experiments are described which determined the effects of various residual stress distributions on the growth rate of fatigue cracks. For each stress distribution, the contribution (K_RS) to the net stress intensity at the crack tip is determined, and a comparison is then made with the behaviour predicted using a fracture mechanics approach based on a weight function analysis and a simple crack closure model. The example studied is a thickwalled pressure vessel containing a longitudinal crack which grows radially from the inner surface; fatigue cracks were grown under laboratory conditions in ring test specimens. sectioned from vessels which had been cold-expanded by different amounts to increase their pressure limits, and so contained various complex residual stress distributions. The experiments provide direct evidence that the effects of residual stress (and by extension, thermal stress) on the crack tip stress intensity may be modelled conveniently using weight function techniques, and can be incorporated satisfactorily in fatigue crack growth analyses.     

高温蒸汽作用下花岗岩热破裂的试验研究

利用自主研制的对流加热原位开采模拟实验台和真三轴压力机,研究了不均匀地应力状态下注蒸汽花岗岩热破裂的破裂规律.在本次试验条件下,花岗岩发生脆性破裂温度为483℃,蒸汽压力为10.6 MPa;高温高压蒸汽作用下,花岗岩除了在沿着垂直于最小主应力方向产生主裂缝,还会由于热破裂,在其他方向产生一定数量随机分布的次生裂缝;不同方向裂缝的形成,对于形成相互连通的空问裂隙网络有实际意义,从而有助于提高地热开采效率.     

The simulation of dynamic crack propagation using the cohesive segments method

The cohesive segments method is a finite element framework that allows for the simulation of the nucleation, growth and coalescence of multiple cracks in solids. In this framework, cracks are introduced as jumps in the displacement field by employing the partition of unity property of finite element shape functions. The magnitude of these jumps are governed by cohesive constitutive relations. In this paper, the cohesive segments method is extended for the simulation of fast crack propagation in brittle solids. The performance of the method is demonstrated in several examples involving crack growth in linear elastic solids under plane stress conditions: tensile loading of a block; shear loading of a block and crack growth along and near a bi-material interface.     

竖向裂缝对功能梯度板的热响应影响

采用条单元法分析了竖向裂缝对功能梯度板的热响应影响。功能梯度板的材料属性沿板厚方向连续线性变化,温度变化热源作用于带竖向裂缝的功能梯度板上。通过研究得出了裂缝距离热源不同位置、不同长度裂缝及不同频率温度变化热源等状态时,功能梯度板上表面的热响应情况。采用条单元法研究带竖向裂缝的功能梯度板的热响应问题,为带裂缝的功能梯度板的热研究提供了一定的指导。     

Thermal shock analyses for a strip containing an infinite row of periodically distributed cracks normal to its edge

The transient thermal stress problem of a semi-infinite plate containing an infinite row of periodically distributed cracks normal to its edge is investigated in this paper. The elastic medium is assumed to be cooled suddenly on the crack-containing edge. By the superposition principle, the formulation leads to a mixed boundary value problem, with the negating tractions arisen from the thermal stresses for a crack-free semi-infinite plate. The resulting singular integral equation is solved numerically. The effects on the stress intensity factors due to the presence of periodically distributed cracks in a semi-infinite plate are illustrated. For both the edge crack and the embedded crack arrays, the stress intensity factors increase, due to the reduction of the shielding effect, as the stacking cracks are more separated. For the case of embedded crack array, one has the further conclusion that the stress intensity factors decline as the crack array shifts from the plate edge.     

A nonlocal theory for brittle fracture

In this paper, a nonlocal theory of fracture for brittle materials has been systematically developed, which is composed of the nonlocal elastic stress fields of Griffith cracks of mode-I, II and III, the asymptotic forms of the stress fields at the neighborhood of the crack tips, and the maximum tensile stress criterion for brittle fracture. As an application of the theory, the fracture criteria of cracks of mode-I, II, III and mixed mode I–II, I–III are given in detail and compared with some experimental data and the theoretical results of minimum strain energy density factor.     

THERMAL FRACTURE OF FUNCTIONALLY GRADED PLATE WITH PARALLEL SURFACE CRACKS

This work examines the fracture behavior of a functionally graded material （FGM） plate containing parallel surface cracks with alternating lengths subjected to a thermal shock. The thermal stress intensity factors （TSIFs） at the tips of long and short cracks are calculated using a singular integral equation technique. The critical thermal shock △Tc that causes crack initiation is calculated using a stress intensity factor criterion. Numerical examples of TSIFs and △Tc for an Al2O3/Si3N4 FGM plate are presented to illustrate the effects of thermal property gradation, crack spacing and crack length ratio on the TSIFs and △Tc. It is found that for a given crack length ratio, the TSIFs at the tips of both long and short cracks can be reduced significantly and △Tc can be enhanced by introducing appropriate material gradation. The TSIFs also decrease dramatically with a decrease in crack spacing. The TSIF at the tips of short cracks may be higher than that for the long cracks under certain crack geometry conditions. Hence, the short cracks instead of long cracks may first start to grow under the thermal shock loading.     

不同倾角预制裂纹缺陷与运动裂纹的相互作用

为了研究运动裂纹与不同倾角预制裂纹缺陷之间的作用机制,采用数字激光动态焦散线方法对含不同倾角预制裂纹缺陷的三点弯曲梁进行冲击实验。研究结果表明,在冲击载荷作用下,预制裂纹缺陷尖端均产生了次生裂纹;当运动主裂纹与预制裂纹缺陷贯通时,次生裂纹不会立即起裂,而是经过0~10 μs的能量积蓄后,次生裂纹才起裂;运动主裂纹应力强度因子峰值与次裂纹起裂时的应力强度因子值均随预制裂纹倾角的增大而增大。     

Experimental dynamic analysis of cracked free-free beams

The use of modal-analysis techniques as nondestructive methods for the detection of cracks in beams is a current field of interest for various researchers. However, an extensive search of the published literature shows that there is very little information on experimental results, thus making it almost impossible for theoretical researchers to use published experimental data to validate their models.The authors, who are currently working in the field of crack detection through modal analysis, performed an extensive experimental dynamic analysis of free-free beams with the objective of validating theoretical techniques, under development, for the prediction of the location and depth of cracks in straight beams. This paper describes the first part of the authors' work. The experimental techniques used are described and results obtained for various locations and depths of cracks in a straight free-free beam are presented.     

脆性断裂的非局部力学理论

本文提出一种脆性材料断裂的非局部力学理论,内容包括:Ⅰ、Ⅱ、Ⅲ型Griffith裂纹的非局部弹性应力场,裂纹尖端邻域非局部弹性应力场的渐近形式,脆性开裂的最大拉应力准则。文中给出了这种理论应用于三种基本型裂纹和Ⅰ-Ⅱ、Ⅰ-Ⅲ复合型裂纹临界开裂条件的计算结果,并把它们与一些试验资料和最小应变能密度因子理论进行了对比。     

带有半埋藏空间裂纹的Cr12构件电磁热止裂分析

对带有半埋藏环形裂纹的Cr12标准拉伸试件进行了电磁热止裂研究.通过ZL-2型放电装置实现了半埋藏空间裂纹的止裂实验,采用微机控制电子万能试验机完成了止裂前后试件拉伸性能测试,同时计算了电磁热止裂前后应力强度因子的变化;建立了超强脉冲电流放电瞬间,环形裂纹尖端附近电流绕流、温度场和热应力场的数值分析模型,通过热-电耦合和热-机械耦合两个过程得到了脉冲放电瞬间拉伸试件中的电流矢量场、温度场和热应力场.研究表明:脉冲电流放电瞬间,围绕裂纹尖端金属熔化,钝化了裂尖,并围绕裂尖形成了热压应力场,得到了超细化的金属组织,止裂后抗拉强度得到了提高,达到了止裂的目的.