表面裂纹疲劳扩展的数值模拟

建立了一种无形状约束的模拟表面裂纹在线弹性断裂力学条件下疲劳扩展的数值方法,并研究了表面疲劳裂纹形状演化和裂纹尖端应力强度因子(SIF)的分布特征。该方法以三维有限单元技术和Paris疲劳裂纹扩展规律为基础,并在裂纹扩展增量计算中考虑了裂纹闭合影响。本文第一部分主要介绍模拟三维疲劳裂纹扩展的数值方法的理论背景和相关的技术细节。着重分析和讨论基于三维有限单元法计算裂纹SIF所涉及的几个主要问题:裂纹尖端单元网格密度对估算精度的影响;自由表面的影响及其修正方法;裂纹尖端非正交单元网格的影响及修正方法。     

单元类型和尺寸对裂尖疲劳塑性数值模拟的影响研究

本文采用Jiang-Sehitoglu循环塑性模型和多轴疲劳准则对紧凑拉伸式样裂尖的循环塑性变形、裂纹扩展速率和残余应力进行了有限元数值模拟,着重考察了单元的类型和最小单元尺寸对裂尖循环塑性和裂纹扩展速率的影响.紧凑拉伸试样的材料为1070钢,数值模拟采用了线性单元(四节点)和二次单元(八节点)两种单元,裂尖附近有限元单元的最小尺寸从0.007mm到0.24mm不等.文中将裂纹扩展速率的预测值与实验值进行了比较,通过对裂纹扩展速率的比较,确定在疲劳塑性分析时对单元类型和尺寸进行合理选取.     

表面裂纹疲劳扩展的数值模拟(Ⅱ)

根据Paris疲劳裂纹扩展规律,对拉伸和纯弯曲疲劳载荷下表面裂纹扩展进行了数值模拟。数值模型中,用三次样条函数曲线拟合裂纹尖端,在裂纹扩展增量计算中考虑了裂纹闭合影响。裂纹形状演化的模拟结果与Newman和Raju经验公式预测结果进行了比较,表明了所采用的数值模拟方法的实用性。研究发现,裂纹闭合对疲劳裂纹扩展过程中的裂纹形状演化以及裂纹尖端的应力强度因子(SIF)分布都有明显影响。同裂纹形状演化一样,疲劳裂纹扩展过程中裂纹尖端的SIF分布表现出明显的特征。最后,建议了一个简单函数来统一描述表面裂纹尖端的SIF分布。     

三维裂纹扩展轨迹的边界元数值模拟

提出了一种对三维裂纹扩展轨迹进行数值模拟的新方法。采用一种新的具有C^1连续性、高精度的单节点二次边界单元，使边界元(BEM)的分析效率和裂纹张开位移(COD)、应力强度因子(SIF)的精度大大提高。采用裂纹张开位移全场拟合法(GCDFP)求出裂纹面前缘的SIF，所得到的SIF达到与所用的COD资料同样的精度。使用Paris公式求出裂纹前缘各点的裂纹扩展增量，并用三次B样条函数对这些增量进行拟合，得到新的光滑裂纹前缘。根据以上思想方法，开发了具有较高的计算效率和精度的数值模拟软件。此软件可以自动跟踪裂纹扩展，得到裂纹扩展的轨迹。运用该软件对椭圆和矩形裂纹的扩展轨迹进行了数值模拟。其结果与理论上的预言完全一致，裂纹最后都趋于一个圆裂纹，具有实际指导意义。     

扭力轴三维裂纹扩展寿命仿真研究

对疲劳载荷谱作用下三维表面裂纹,采用双重边界元理论求解裂纹前沿的应力应变场,运用Forman理论、最小应变能密度法和Elber模型,计算裂纹前沿各点的扩展长度、扩展方向和应力强度因子等特征量.根据增量步下裂纹几何形状的改变,对裂纹面进行网格重划分和迭代计算,模拟三维裂纹的扩展,预测裂纹扩展寿命.扭力轴表面裂纹扩展的仿真结果表明该方法合理可行.     

动态断裂力学的无限相似边界元法

对弹性动力学的相似边界元法进行了进一步研究,推导了相应的计算公式,并在此基础上提出了动态断裂力学的无限相似边界元法.与传统的边界元法相比,相似边界元法由于只需在少数单元上进行数值积分,大大减少了计算量.对动态断裂力学问题,无限相似边界元法由于在裂纹尖端的边界上设置了逼近于裂纹尖端的无限个相似边界单元,可直接得到裂纹尖端具有奇异性的应力,而不需要设置奇异单元,从而突破了奇异单元对应力奇异性阶次的局限.另外,还讨论了无限相似边界元法得到的无限阶的线性代数方程组的求解方法.     

不均匀裂纹体疲劳裂纹扩展的实验研究和分析

本文提出了裂纹在硬区的软对硬不均匀裂纹体的力学分析模型.疲劳实验研究表明,这种不均匀性影响疲劳裂纹扩展速率.文中的疲劳载荷下不均匀裂纹体的边界元数值计算结果表明,随着疲劳裂纹的扩展,在相同扩展步下,裂纹距软硬区界面越近,裂纹张开位移的幅值△COD 越小,J 积分幅值△J 亦越小.不均匀性对疲劳裂纹扩展速率的影响,主要通过影响△J 来实现.裂纹与软硬区界面的距离越近,疲劳裂纹扩展速率越小.     

基于图像四叉树的改进型比例边界有限元法研究

为提高数值计算的精度, 断裂力学问题的数值模拟需要在裂纹扩展的局部区域采用较密的网格, 而远离裂纹扩展的区域可采用较疏的网格, 且对于裂纹扩展问题的数值模拟, 大多数数值方法又存在局部网格重剖分的问题. 论文提出了一种基于图像四叉树的改进型比例边界有限元法用于模拟裂纹扩展问题, 该方法可根据结构域几何外边界的图像全自动进行四叉树网格剖分, 无需任何人工干预, 网格剖分效率极高, 由于比例边界有限元法本身的优势, 四叉树网格的悬挂节点可以直接地视为新的节点, 无需任何特殊处理. 通过引入虚节点的思想, 将裂纹与四叉树单元边界交叉点作为虚节点, 虚节点的自由度作为附加自由度处理, 并采用水平集函数表征材料内部的裂纹面, 含不连续裂纹面的子域可通过节点水平集函数识别, 使得裂纹扩展时无需进行网格重剖分, 界面的几何特征通过比例边界有限元子域的附加自由度表征. 最后, 通过若干算例验证了该方法的性能, 建议的改进型比例边界有限元法在求解复合型应力强度因子和模拟材料内部裂纹扩展路径时均具有较高的精度.      

用可动节点有限元模型模拟裂纹扩展过程

本文针对裂纹扩展有限元模拟模型存在的问题,提出一种可动节点模型.使裂尖在单元尺度内任意移动,实现了扩展模拟连续性.加进松弛扩展,突出其所占比重,使模拟更加逼真.用弹塑性有限变形杂交元自编模拟裂纹扩展的通用FORTRAN 程序,对含中心裂纹铝板进行模拟,假定材料各向同性并遵守等向强化规律,采用米赛斯屈服准则和Drucker 塑性势流动理论做增量弹塑性静力分析,得到了与实验符合较好的结果.     

基于单元破裂的岩石裂纹扩展模拟方法

传统离散元方法在处理破裂问题时, 采用界面上的准则进行判断, 裂纹只能沿着单元边界扩展. 当物理问题存在宏观或微观裂隙时, 在界面上应用准则具有其合理性; 而裂纹沿着单元边界扩展, 使得裂纹路径受网格影响较大, 扩展方向受到限制. 针对上述情况, 可以基于单元破裂的方式, 构建连续- 非连续单元法, 并应用于岩石裂纹扩展问题的模拟. 该方法在连续计算时, 将单元离散为具有物理意义的弹簧系统, 在局部坐标系下由弹簧特征长度、面积求解单元变形和应力, 通过更新局部坐标系和弹簧特征量, 可进一步计算块体大位移、大转动, 连续问题计算结果与有限元一致, 同时提高了计算效率. 在此基础上, 引入最大拉应力与莫尔—库伦的复合准则, 判断单元破裂状态和破裂方向, 并采用局部块体切割的方式, 在单元内形成初始裂纹. 裂纹两侧相应增加新的计算节点, 同时引入内聚力模型描述裂纹两侧的法向、切向作用与张开度及滑移变形之间的关系. 按此方式, 裂纹尖端处的扩展路径可穿过单元内部和单元边界, 在扩展方向的选取上更为准确. 最后, 通过三点弯曲梁、单切口平板拉伸、双切口试样等典型数值试验, 模拟裂纹在拉伸、压剪等各种应力状态下的扩展问题, 并对岩石单轴压缩试验的破坏过程进行模拟, 分析裂纹形成与应力—应变曲线各阶段之间的对应关系. 结果表明: 连续—非连续单元法通过单元内部破裂的方式, 可以显示模拟裂纹萌生、扩展、贯通直至形成宏观裂缝的过程.      

INTERACTION OF THREE PARALLEL CRACKS IN RECTANGULAR PLATE UNDER CYCLIC LOADS

This paper presents a numerical approach for modeling the interaction between multiple cracks in a rectangular plate under cyclic loads. It involves the formulation of fatigue growth of multiple crack tips under ruixed-mode loading and an extension of a hybrid displacement discontinuity method （a boundary element method） to fatigue crack growth analyses. Because of an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single-region formulation. In the numerical simulation, remeshing of existing boundaries is not necessary for each increment of crack extension. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. As an example, the numerical approach is used to analyze the fatigue growth of three parallel cracks in a rectangular plate. The numerical results illustrate the validation of the numerical approach and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

A boundary element modeling of fatigue crack growth in a plane elastic plate

This paper presents an extension of a boundary element method to fatigue growth analysis of mixed-mode cracked plane elastic bodies. The method consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity element due to the author. In the boundary element implementation the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the modified maximum strain energy density criterion. In numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the boundary element method. Crack growth is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. Some numerical results of fatigue growth in a plane elastic plate with a center-inclined crack under uniaxial cyclic loading are given.     

Fatigue growth modeling of cracks emanating from a circular hole in infinite plate

This paper presents a numerical approach of fatigue growth analysis of cracks emanating from a hole in infinite elastic plate subjected to remote loads. It involves a generation of Bueckner’s principle and a hybrid displacement discontinuity method (a boundary element method) proposed recently by the senior author of the paper. Because of an intrinsic feature of the boundary element method, a general crack growth problem can be solved in a single region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is modeled conveniently by adding new boundary elements on the incremental crack extension to the previous crack boundaries. As an example, fatigue growth process of an inclined crack in an infinite plate under uniaxial cycle load is modeled to illustrate the effectiveness of the numerical approach. In addition, fatigue growth of cracks emanating from a circular hole in infinite elastic plate subjected to remote loads is investigated by using the numerical approach. Many numerical results are given     

FATIGUE GROWTH MODELING OF MIXED-MODE CRACK IN PLANE ELASTIC MEDIA

This paper presents an extension of a displacement discontinuity method with cracktip elements （a boundary element method） proposed by the author for fatigue crack growth analysis in plane elastic media under mixed-mode conditions. The boundary element method consists of the non-singular displacement discontinuity elements presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or right crack-tip element is placed locally at the corresponding left or right crack tip on top of the non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the maximum circumferential stress criterion. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the numerical approach. Crack growth is modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characteristics of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the fatigue growth process of cracks emanating from a circular hole in a plane elastic plate is simulated using the numerical simulation approach.     

An effective boundary element method for analysis of crack problems in a plane elastic plate

A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.     

SGBEM modeling of fatigue crack growth in particulate composites

The symmetric-Galerkin boundary element method (SGBEM) has previously been employed to model 2-D crack growth in particulate composites under quasi-static loading conditions. In this paper, an initial attempt is made in extending the simulation technique to analyze the interaction between a growing crack and clusters of perfectly bonded particles in a brittle matrix under cyclic loading conditions. To this end, linear elastic fracture mechanics and no hysteresis are assumed. Of particular interest is the role clusters of inclusions play on the fatigue life of particulate composites. The simulations employ a fatigue crack growth prediction tool based upon the SGBEM for multiregions, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating stress intensity factors, a Paris law for fatigue crack growth rates, and the maximum principal stress criterion for crack-growth direction. The numerical results suggest that this fatigue crack growth prediction tool is as robust as the quasi-static crack growth prediction tool previously developed. The simulations also show a complex interplay between a propagating crack and an inclusion cluster of different densities when it comes to predicting the fatigue life of particulate composites with various volume fractions.     

A novel singular finite element of mixed-mode crack problems with arbitrary crack tractions

A novel singular finite element is presented to study cracked plates with arbitrary traction acting on crack surfaces. Firstly, the analytical solution around crack tips is determined using the symplectic dual approach. Subsequently, the solution is used to develop a novel singular finite element, which depicts accurately the characteristic of singular stresses field near crack tips. And the novel element can be applied to solve cracked plates, and both Mode I and Mode II stress intensity factors can be determined directly and accurately. Lastly, two numerical examples are given to illustrate the present method.     

内部压力作用下矩形板中源于椭圆孔的分支裂纹应力强度因子的一种数值分析

应用一种边界元方法来研究内部压力作用下矩形板中源于椭圆孔的分支裂纹。该边界元方法由Crouch与Starfied建立的常位移不连续单元和笔者最近提出的裂尖位移不连续单元构成。在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界。本数值结果进一步证实这种数值方法对计算有限大板中复杂裂纹的应力强度因子的有效性,同时该数值结果可以揭示裂纹体几何对应力强度因子的影响。     

Stress intensity factors for asymmetric branched cracks in plane extension by using crack-tip displacement discontinuity elements

Stress intensity factors are important in the analysis of cracked materials. They are directly related to the fracture propagation and fatigue crack growth criteria. Based on the analytical solution (Crouch, S.L., 1976. Solution of plane elasticity problems by displacement discontinuity method, Int. J. Numer. Methods Eng. 10, pp. 301–343; Crouch, S.L., Starfield, A.M., 1983. Boundary Element Method in Solid Mechanics, with Application in Rock Mechanics and Geological Mechanics, London, Geore Allon and Unwin, Bonton, Sydney) to the problem of a constant discontinuity in displacement over a finite line segment in the x, y plane of an infinite elastic solid, recently, the crack-tip displacement discontinuity element which can be classified as the left and right crack-tip displacement discontinuity elements are developed by the author Yan, X., (in press. A special crack-tip displacement discontinuity element, Mechanics Research Communications) to model the crack-tip fields to more accurately compute the stress intensity factors of cracks in general plane elasticity. In the boundary element implementation the left or the right crack-tip displacement discontinuity element is placed locally at the corresponding left or right crack tip on top of the ordinary non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. To prove further the efficiency of the suggested approach and provide more results of the stress intensity factors, in this study, analysis of an asymmetric branched crack bifurcated from a main crack in plane extension is carried out.     

复杂载荷三维裂纹分析双重边界元法

提出可用于高温、高转速状态下的热动力机械三维含裂构件热弹性分析方法——双重边界元法.首先建立了考虑温度及离心载荷的双重边界积分方程组,并对边界积分方程组的选取及适用范围进行了讨论。然后提出角非快调元模型离散技术。接着提出超奇异积分方程分析去除奇异性方法及数值积分技术.数值算例表明计算结果与有关权函数解十分吻合,说明了用双重边界元法计算复杂载荷条件下三维应力强度因子的有效性.还讨论了有关热应力强度因子权函数解的适用范围.