含垂直界面有限裂纹层状介质的断裂分析

研究层状介质含垂直于界面有限裂纹的断裂力学问题。利用积分变换方法，引入位错密度函数，导出了反映裂纹尖端奇异性的奇异积分方程组，并求得对应于裂纹出现在层内、扩展到界面以及穿越界面形成反射裂纹等三种情况的奇异性系数。最后运用Chebyshev、Jacobi等正交多项式化奇异积分方程组为代数方程组，进而求得裂纹尖端的应力强度因子。

有限宽中心裂纹板在裂纹面受一对偏心反平面集中力的弹塑性分析

有限宽裂纹板的弹塑性分析是弹塑性断裂力学中最困难的问题之一。本文对有限宽裂纹板在裂纹面任意点受一对反平面集中力的情形采用裂纹线场分析方法，将各场量在裂纹线附近展开，利用平衡方程和屈服准则进行弹塑性分析，这种分析不需要作小范围屈服的假定。通过裂纹线上的弹塑性应力场在弹塑性边界上进行匹配得出荷载与裂纹线上塑性区长度之间的关系，进而分析得出荷载的不同位置和板宽所对应的临界荷载。

有限宽板中心裂纹断裂过程区的长度和位移公式

对岩石、混凝土和陶瓷等准脆性材料进行断裂分析 ,有必要研究裂纹前端的断裂过程区所起的作用以及各种因素对它的影响。本文提出分析有限宽中心裂纹板剪切断裂过程区的方法 ,此方法基于D -B模型的叠加原理 ,考虑了压剪断裂的摩擦阻力 ,并将有限板宽影响简化为载荷的修正 ,以非常简便的方法推导出计算断裂过程区长度和位移的公式 ,这些公式补充了现有文献只有“无限大”板的解的不足。利用这些公式 ,分析各种参数对断裂过程区长度和位移的影响变得非常方便。

多参量断裂力学广义杂交/混合裂纹有限元法

通过研究广为人知的断裂力学单变量八节点位移裂纹QPE元和Akin族奇异单元法 ,本文运用经典局部裂纹解析解 ,与非协调假设应力杂交 混合元列式方法相结合 ,提出用于分层各向异性材料的多变量半解析假设应力奇异广义杂交 /混合裂纹有限元法 ,能克服现有位移裂纹元法的域应力分布精度低和高次单元所需计算容量大的局限性 ,互为补充 ,更有利于结构裂纹扩展分析和应用研究。文中设计了一个半解析奇异裂纹平面单元 ,各向同性材料板算例验证了退化二次八节点协调位移裂纹元及六节点非协调奇异应力裂纹元 ,说明采用稀疏及加密单元网格 ,两类裂纹单元分别从上下逼近收敛于实验和理论参考解 ,可得到吻合程度较好的 1/r奇异应变和应力分量以及应力强度因子值 。

有限平板共线裂纹断裂过程的数值模拟和实验研究

采用有限元数值模拟和光弹实验方法分析了各向同性材料共线多裂纹应力场及其强度参量.建立了有限弹性平板内三条共线裂纹计算模型,应用ABAQUS软件的VCCT方法分析计算各向同性材料共线裂纹的裂纹尖端的应力场、应变场分布规律及应力强度因子.并通过光弹实验实测了6061铝板共线裂纹试件的裂纹尖端的应力强度因子.研究结果表明,实验和数值模拟所得的应力云图相似,应力强度因子值基本一致,验证了提出的应力强度因子计算模型的有效性.

基于XFEM的裂纹扩展分析

采用ABAQUS/Standard对生产线中的一个易损件进行了三维有限元分析.根据结构受力状态,将该结构简化成一个平面应力的裂纹扩展模型,并采用目前最新的有限元裂纹扩展技术(XFEM)计算结构的裂纹扩展情况.计算结果表明,有限元计算与实际结构裂纹扩展情况一致.同时,根据计算结果提出了结构改进的设计建议.

点群6一维六方准晶狭长体中有限长Griffith裂纹的反平面问题

利用复变函数法,通过构造新的保角变换,研究了裂纹面受剪切作用下点群6一维六方准晶狭长体中有限长Griffith裂纹的断裂行为,得到了裂纹尖端处应力强度因子的解析解.当狭长体高度趋于无穷时,该解析解退化为无限大点群6一维六方准晶中有限长Griffith裂纹问题的解.

一维六方准晶中平行螺型位错与有限长裂纹的相互作用

论文采用解析函数理论,利用Muskhelishvili著名的复变函数方法,给出了无限大一维六方准晶中多条平行螺型位错与有限长直裂纹相互作用的解析解,并得到了裂纹尖端的场强度因子和作用在位错上的像力.数值算例讨论了镜像力、场强度因子随位错位置的变化,及位错的位置与分布对广义应力场的影响.

An adaptive finite element procedure for crack propagation analysis

This paper presents the adaptive mesh finite element estimation method for analyzing 2D linear elastic fracture problems. The mesh is generated by the advancing front method and the norm stress error is taken as a posteriori error estimator for the h-type adaptive refinement. The stress intensity factors are estimated by a displacement extrapolation technique. The near crack tip displacements used are obtained from specific nodes of natural six-noded quarter-point elements which are generated around the crack tip defined by the user. The crack growth and its direction are determined by the calculated stress intensity factors. The maximum circumference theory is used for the latter. In evaluating the accuracy of the estimated stress intensity factors, four cases are tested consisting of compact tension specimen, three-point bending specimen, central cracked plate and double edge notched plate. These were carried out and compared to the results from other studies. The crack trajectories of these specimen tests are also illustrated.

Wing crack model subjected to high hydraulic pressure and far field stresses and its numerical simulation

By considering the effect of hydraulic pressure filled in wing crack and the connected part of main crack on the stress intensity factor at wing crack tip, a new wing crack model exerted by hydraulic pressure and far field stresses was proposed. By introducing the equivalent crack length lcq of wing crack, two terms make up the stress intensity factor K1 at wing crack tip： one is the component K（1） for a single isolated straight wing crack of length 2l subjected to hydraulic pressure in wing crack and far field stresses, and the other is the component K1^（2） due to the effective shear stress induced by the presence of the equivalent main crack. The FEM model of wing crack propagation subjected to hydraulic pressure and far field stresses was also established according to different side pressure coefficients and hydraulic pressures in crack. The result shows that a good agreement is found between theoretical model of wing crack proposed and finite element method （FEM）. In theory, an unstable crack propagation is shown if there is high hydraulic pressure and lateral tension. The wing crack model proposed can provide references for studying on hydraulic fracturing in rock masses.

Finite element modeling for analysis of cracked cylindrical pipes

The characteristic properties of shell element with similar shapes are used to generate a so-called super element for the analysis of the crack problems for cylindrical pressure vessels. The formulation is processed by matrix condensation without the involvement of special treatment. This method can deal with various singularity problems and it also presents excellent results to crack problems for cylindrical shell. Especially,the knowledge of the kind of singular order is not necessary in super element generation; it is very economical in terms of computer memory and programming. This method also exhibits versatility to solve the problem of kinked crack at cylindrical shell.

Dynamic Crack Propagation Analysis Using Scaled Boundary Finite Element Method

The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.

Fracture properties of epoxy asphalt mixture based on extended finite element method

Crack is found to be a major distress that affects the performance of the epoxy asphalt pavement.An extended finite element method was proposed for investigating the fracture properties of the epoxy asphalt mixture.Firstly,the single-edge notched beam test was used to analyze the temperature effect and calculate the material parameters.Then,the mechanical responses were studied using numerical analysis.It is concluded that 5℃ can be selected as the critical temperature that affects the fracture properties,and numerical simulations indicate that crack propagation is found to significantly affect the stress state of the epoxy asphalt mixture.The maximum principal stress at the crack surface exhibits different trends at various temperatures.Numerical solution of stress intensity factor can well meet the theoretical solution,especially when the temperature is lower than 5℃.

Tunnel failure in hard rock with multiple weak planes due to excavation unloading of in-situ stress

Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a deep circular tunnel in a rock mass with multiple weakness planes using a 2D combined finite element method/discrete element method(FEM/DEM).Conventional triaxial compression tests were performed on typical hard rock(marble)specimens under a range of confinement stress conditions to validate the rationale and accuracy of the proposed numerical approach.Parametric analysis was subsequently conducted to investigate the influence of inclination angle,and length on the crack propagation behavior,failure mode,energy evolution,and displacement distribution of the surrounding rock.The results show that the inclination angle strongly affects tunnel stability,and the failure intensity and damage range increase with increasing inclination angle and then decrease.The dynamic disasters are more likely with increasing weak plane length.Shearing and sliding along multiple weak planes are also consistently accompanied by kinetic energy fluctuations and surges after unloading,which implies a potentially violent dynamic response around a deeply-buried tunnel.Interactions between slabbing and shearing near the excavation boundaries are also discussed.The results presented here provide important insight into deep tunnel failure in hard rock influenced by both unloading disturbance and tectonic activation.

Towards fully automatic modelling of the fracture process in quasi-brittle and ductile materials:a unified crack growth criterion

Fully automatic finite element(FE) modelling of the fracture process in quasi-brittle materials such as concrete and rocks and ductile materials such as metals and alloys,is of great significance in assessing structural integrity and presents tre-mendous challenges to the engineering community. One challenge lies in the adoption of an objective and effective crack propagation criterion. This paper proposes a crack propagation criterion based on the principle of energy conservation and the cohesive zone model(CZM) . The virtual crack extension technique is used to calculate the differential terms in the criterion. A fully-automatic discrete crack modelling methodology,integrating the developed criterion,the CZM to model the crack,a simple remeshing procedure to accommodate crack propagation,the J2 flow theory implemented within the incremental plasticity framework to model the ductile materials,and a local arc-length solver to the nonlinear equation system,is developed and im-plemented in an in-house program. Three examples,i.e.,a plain concrete beam with a single shear crack,a reinforced concrete(RC) beam with multiple cracks and a compact-tension steel specimen,are simulated. Good agreement between numerical predictions and experimental data is found,which demonstrates the applicability of the criterion to both quasi-brittle and ductile materials.

Evaluation of mixed-mode stress intensity factors by extended finite element method

Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationallv efficient.

An Analysis on the Transmission Shaft Fracture of Screw Drill

The transmission shaft of the underground screw drill fractured when milling-shoe and grinding bridge plug was applied to the coiled tubes in a horizontal well of Sichuan province, but the position of this transmission shaft fracture did not occur at the minor-diameter retracting position and reducing position that were easy to fracture. An analysis of the transverse planes of the fracture found that the cause of the transmission shaft fracture surface was that the defects of the initial surface were propagating to cracks and gave rise to the fracture under torque load. To specifically know well the strength of the transmission shaft under damaging fracture, a statics analysis was conducted on the transmission shaft through ANSYS finite element simulation software, and the finite element models under no cracks, different-depth circumferential cracks, and similar situation of the transverse planes of fracture were established respectively. An analysis of the crack-free finite element model found that the fracture of the transmission shaft was really not caused by the self-structure of the transmission shaft; an analysis of circumferential crack finite element model found that strong stress concentration would appear in the tip of cracks, and the value of the stress would increase along with the increase of the circumferential crack depth, the stress of the entire crack top tended to fluctuate like waves, and also the strength of the transmission shaft was greatly impacted by the presence of cracks; an analysis of the similar crack finite element model found that stress concentration would appear in the tip of cracks, and the initial cracks always started to propagate from the tip of the external surface of the transmission shaft and would propagate inward until the propagating areas of two cracks overlapped, and finally reached the position of transient interruption, and then the transmission shaft fractured completely and the fracture strength was onlv 1/5 of that under no cracks.

Longitudinal crack on slab surface at straightening stage during continuous casting using finite element method

Deformation behavior of slab at the straightening stage during continuous casting was simulated by the explicit dynamic finite element method,and the stress distribution along the width direction of the slab and its change regularity at slab center during continuous casting were obtained.The influence of distribution and change of stress on the propagation of longitudinal cracks on slab surface was discussed.The results show that the tensional stress appears on slab surface at the inner arc side and the compressive stress appears on slab surface at the outer arc side at stages 6-8 in straightening zone during continuous casting.Longitudinal cracks generally appear on slab top surface and do not appear on slab bottom surface,which are also observed in industry.

Investigation of the Process Parameters on the Blanking of AISI 304 Stainless Steel by Using Finite Element Method

Blanking is a major process and has a wide range of usage in manufacturing industry. The general concept of blanking seems a simple one but governing parameters are many and have a complex relationship which directly affect the quality of the produced parts （blanks） and also the energy efficiency of the process. The main problem is the lack of prediction capabilities of the effect of these parameters that lead to time, money and labor consuming trial and error procedures in experimental studies. Usage of FEM based programs to simulate blanking to obtain numerical results and observe the shearing mechanism is a cheap and a detailed way for industrial applications. In this study five different clearances （1%, 3%, 5%, 10% and 20%） and three different thicknesses （t = 2 mm, t = 3 mm and t = 4 mm） were used for simulation and experimental studies of the blanking process. Simulations were executed by using the FEM program, Deform 2-D. Investigations were made on the parameters related to crack progression like crack initiation and crack propagation angles, indentation angle, rollover angle and depth and also the related blanking energy values. The results of the present paper are in agreement with the results of experimental studies.

Effect of crack face contact on dynamic stress intensity factors for a hole-edge crack

In order to determine the dynamic stress intensity factors(DSIFs)for a single edge crack at the center hole of a finite plate under a compressive step loading parallel to the crack,the finite element method was employed to solve the cracked plate problem.The square-root stress singularity around the crack tip was simulated by quarter point singular elements collapsed by 8-node two-dimensional isoparametric elements.The DSIFs with and without considering crack face contact situations were evaluated by using the displacement correlation technique,and the influence of contact interaction between crack surfaces on DSIFs was investigated.The numerical results show that if the contact interaction between crack surfaces is ignored,the negative mode I DSIFs may be obtained and a physically impossible interpenetration or overlap of the crack surfaces will occur.Thus the crack face contact has a significant influence on the mode I DSIFs.