基于概率断裂力学的管道疲劳寿命分析

采用奇异单元模拟裂纹尖端应力场的奇异性,计算裂纹尖端的应力强度因子和张开应力.以概率论为基础,结合确定性疲劳断裂力学估算方法,考虑参数的不确定性和随机性,应用蒙特卡洛模拟法分析管道的疲劳寿命.结果表明：通过J积分计算得到的裂纹尖端张开应力与计算得到的管道工作应力基本相等.采用蒙特卡洛模拟法进行的一定可靠度和置信度下的疲劳寿命预测能反映评定参数的不确定性,较传统的断裂力学计算结果更安全.     

基于Cosserat理论的平面等参元

为解释材料在微尺度下的尺度效应,基于Cosserat理论,从势能泛函驻值条件出发提出构造8节点Serendipity平面等参元,并建立平面有限元法．每个节点拥有3个独立节点自由度,分别为2个方向的线位移和1个逆时针方向的角位移．用该方法分析含中心小孔的无限平板在单轴拉伸情况下的应力集中问题．数值计算结果与Cosserat理论的解析解非常符合,表明应力集中因数k受泊松比μ,常数c及a／l值的影响很大;由于偶应力的存在,小孔周围的应力分布明显小于经典弹性力学理论的预测．通过对材料常数c的调节可以将该方法推广应用于基于Mindlin偶应力理论的数值分析中．     

基于Abaqus柔度标定法的Q235材料断裂韧性仿真

为简便、准确地获得Q235材料的应力强度因子值和J积分值,用Abaqus对Q235材料进行有限元仿真,得到三点弯曲试样及其裂纹尖端区域的应力分布情况;针对裂纹尖端的奇异性,引入折叠单元进行裂纹尖端单元的奇异性建模.不同尺寸试件应力强度因子仿真值与试验值基本一致,表明该方法可以准确预测材料断裂参数.     

应力诱发压电薄膜晶内微裂纹演化的数值模拟

压电薄膜的制备和使用过程中不可避免地引入微裂纹等微观缺陷.在不同的内在物理机制和外界驱动力作用下,微裂纹会出现多种多样的形貌演化行为,甚至失稳并发生分裂,影响相关微元器件的各种性能.本文基于表面扩散和蒸发-凝结的经典理论,对应力诱发表面扩散下PZT薄膜晶内微裂纹的演化进行数值模拟.结果表明,在应力作用下,存在临界应力载荷,当应力载荷小于或等于该临界值时,微裂纹演化为稳定的形态;当应力载荷大于该临界值时,微裂纹发生失稳并分裂为多个裂腔,且应力载荷或微裂纹初始形态比的增大均会促进微裂纹的失稳分裂.     

微型Mindlin板非线性动力学模型的建立

随着MEMS技术工艺的发展,微型结构在工程领域的应用越来越广泛.对于微型结构,经典连续介质力学理论的本构关系中不包含任何特征长度尺度,不能反映结构在微米尺度下的尺寸效应.本文基于Von Karman大变形理论和一阶剪切变形理论,把考虑尺寸效应的应变梯度理论推广至微型Mindlin板的非线性问题.分别计算微结构的应变能,包括宏观变形应变能和微观变形应变能两部分,结合微型Mindlin板结构的动能及外力功,代入Hamilton原理,得到了微型Mindlin板在大变形情况下的非线性动力学方程及边界条件.     

滚动接触疲劳载荷对铁轨表面接触疲劳裂纹应力强度系数的影响

为研究轮轨滚动接触疲劳(Rolling Contact Fatigue,RCF)载荷对铁轨表面裂纹应力强度系数的影响,以UIC60铁轨轮廓尺寸为依据建立轮轨接触的三维有限元模型,通过改变RCF载荷大小、轮轨表面摩擦因数和接触中心位置等轮轨接触的输入参数,计算铁轨表面接触裂纹尖端的应力强度系数,分析RCF载荷对铁轨表面接触疲劳裂纹的影响.结果表明RCF载荷作为控制铁轨表面接触裂纹的重要因素,其变化直接导致裂纹尖端应力强度系数的变化,从而改变裂纹的扩展状况.为减缓铁轨表面裂纹的扩展,可以针对载荷采取均匀分布载重量、使用润滑剂降低轮轨摩擦因数等相应措施.     

滚动接触疲劳载荷对铁轨表面接触疲劳裂纹应力强度因子的影响

为研究轮轨滚动接触疲劳（Rolling Contact Fatigue,RCF）载荷对铁轨表面裂纹应力强度因子的影响,以UIC60铁轨轮廓尺寸为依据建立轮轨接触的三维有限元模型,通过改变RCF载荷大小、轮轨表面摩擦因数和接触中心位置等轮轨接触的输入参数,计算铁轨表面接触裂纹尖端的应力强度因子,分析RCF载荷对铁轨表面接触疲劳裂纹的影响. 结果表明RCF载荷作为控制铁轨表面接触裂纹的重要因素,其变化直接导致裂纹尖端应力强度因子的变化,从而改变裂纹的扩展状况;为减缓铁轨表面裂纹的扩展,可以针对载荷采取均匀分布载重量、使用润滑剂降低轮轨摩擦因数等相应措施.     

基于能量统一格式的多尺度有限元法

为分析简单晶体多尺度有限元计算的能量构成,利用能量最小原理得到在统一理论框架下多尺度有限元计算的统一格式,表明有限元计算可以在微观原子尺度下和在宏观连续介质尺度下进行多尺度有限元计算.基于简单晶体变形的特点说明过渡单元设计应遵守的原则,并指出理想过渡单元应该是类似于晶体结构的单元,对于较复杂的晶体,则应该利用空间群方法充分研究具有230种空间群的过渡单元的性质.引用EIDEL等的纳米压痕计算结果作为算例,表明在计算中无虚拟插值点,多级晶胞单元具有与原单胞相同的点群操作且位移场插值受晶体中原子间键长的约束.     

孔边角疲劳裂纹的扩展仿真及分析

给出了一种利用有限元技术模拟周期性张力载荷作用下孔边角裂纹扩展过程的方法。首先利用一系列点定义裂纹前沿，据此形成包含奇异单元的二维有限元网格，再扩展为三维网格．然后利用有限元法进行应力应变分析，最后使用Paris定律计算局部扩展增量．以此来更新裂纹的形状和尺寸。该方法还能够自动地重复执行扩展仿真。文中还对三个不同半径的四分之一椭圆形边角裂纹扩展过程进行了仿真和分析比较，以此来取得裂纹在扩展过程中的形状变化特征和不同方向上扩展的特征。     

圆柱形部件表面疲劳裂纹扩展仿真及分析

给出了一种利用有限元技术模拟周期性张力载荷作用下圆柱形部件内裂纹扩展过程的方法。首先利用一系列点定义裂纹前沿，据此形成包含奇异单元的二维有限元网格，再扩展为三维网格，然后利用有限元法进行应力应变分析，最后使用Paris定律计算局部扩展增量，以此来更新裂纹的形状和尺寸。该方法还能够自动地重复执行扩展仿真。文中还对具有不同半径比的椭圆形和具有不规则形状的初始裂纹的扩展过程进行了仿真和分析比较，以此来取得裂纹在扩展过程中的形状变化特征。     

基于二次插值重构有限元法的动态裂纹扩展模拟

基于二次插值重构有限元法（Twice interpolation Finite Element Method, TFEM）分析动态断裂力学问题并进行数值实验,考察TFEM在裂纹动态扩展模拟中的准确性和可靠性.由于TFEM保证节点处梯度场的连续性,因此裂尖附近的应力场可以得到较好的逼近.把该算法成功移植到自主开发的三维裂纹扩展仿真软件（ZonCrack）中.利用ZonCrack进行的裂纹扩展,分析结果表明：TFEM得到裂尖应力强度因子（Stress Intensity Factor, SIF)与解析解基本一致;裂纹扩展的模拟结果与实验值吻合良好.     

基于扩展有限元法的黏聚性裂缝模型的混凝土梁断裂过程模拟

为研究混凝土梁的断裂过程,提出用基于二维扩展有限元法（eXtended Finite ElementMethod,XFEM）的黏聚性裂缝模型模拟混凝土简支梁在集中载荷作用下的断裂过程.推导考虑近裂尖奇异性的基于XFEM的黏聚性裂缝模型,得出裂缝开度随裂缝长度的变化曲线;对上述模型与相关文献用有限元结合节点释放技术对相同时间的裂缝扩展的计算结果进行比较,二者结果吻合良好,并与实际裂缝扩展过程相符.计算结果证实基于XFEM的黏聚性裂缝模型能有效进行混凝土梁的断裂过程模拟.     

A variable power singular element for analysis of fracture mechanics problems

A variable power displacement formulated singular element is developed. The stress and displacement fields within the element are expressed in terms of singular and regular components. The singular components of these fields are shown to provide a more accurate representation of the singularity than the total field solutions. The problem of a crack terminating at a bi-material interface is solved for two extreme ratios of singular element radius to crack length. The solution shows that accurate results can be achieved for either case.     

Dual reciprocity boundary element method in Laplace domain applied to anisotropic dynamic crack problems

In this paper the dual reciprocity boundary element method in the Laplace domain for anisotropic dynamic fracture mechanic problems is presented. Crack problems are analyzed using the subregion technique. The dynamic stress intensity factors are computed using traction singular quarter-point elements positioned at the tip of the crack. Numerical inversion from the Laplace domain to the time domain is achieved by the Durbin method. Numerical examples of dynamic stress intensity factor evaluation are considered for symmetric and non-symmetric problems. The influence of the number of Laplace parameters and internal points in the solution is investigated.     

A singular ES-FEM for plastic fracture mechanics

The stress and strain fields around the crack tip for power hardening material, which are singular as r approaches zero, are crucial to fracture and fatigue of structures. To simulate effectively the strain and stress around the crack tip, we develop a seven-node singular element which has a displacement field containing the HRR term and the second order term. The novel singular element is formulated based on the edge-based smoothed finite element method (ES-FEM). With one layer of these singular elements around the crack tip, the ES-FEM works very well for simulating plasticity around the crack tip based on the small strain formulation. Two examples are presented with detailed comparison with other methods. It is found that the results of the presented singular ES-FEM are closer to reference solution, which demonstrates the applicability and the effectiveness of our method for the plastic field around the crack tip.     

Collapsed isoparametric element as a singular element for a crack normal to the bi-material interface

It is shown that the variable power singularity of the strain field at the crack tip can be obtained by the simple technique of collapsing quadrilateral isoparametric elements into triangular elements around the crack tip and adequately shifting the side-nodes adjacent to this crack tip. The collapsed isoparametric elements have the desired singularity at crack tip along any ray. The strain expressions for a single element have been derived and in addition to the desired power singularity, additional singularities are revealed. Numerical examples have shown that triangular elements formed by collapsing one side lead to excellent results.     

Three dimensional singular element

The finite element method has become a powerful tool for computation of stress intensity factors in fracture mechanics. The simulation of singular behavior in the stress field is accomplished using “quarter points,” following the methods of Barsoum[1] and Henshell-Shaw[2]. The analysis has also been extended to cubic elements [3] and transition elements [4]. However, these concepts cannot be easily extended to three dimensional cases without additional conditions. Progress has been hampered firstly due to a variety of possible shapes the element may possess near the singular edge of the crack, and secondly due to the complexity of algebraic expressions that have to be manipulated.

In the present investigation we extensively used MACSYMA[5], a large symbolic manipulation program at MIT, thereby alleviating some of these difficulties. A simple condition between mid-side nodes has been derived which simulates the proper singular behavior along the crack.

In the investigation we first study a simple collapsed brick element. This is then generalized to a curved crack front. A few results are derived which can be used to compute the stress intensity factors. The concept of the transitional element has also been outlined. The stability of singular element has been discussed. Some of these ideas have been applied to a specific problem with unusual crack geometry. The analysis was carried out using ADINA on VAX machine. ADINA was implemented on VAX by W. E. Lorensen.