用裂纹张开位移全场拟合法求应力强度因子-边裂纹问题

从一组给定的的裂纹张开位移（COD）资料求应力强度因子（SIF）的好方法应具有以下特征：（1）这个方法应最大限度地利用已知的COD信息；（2）数值计算只包含位移量；（3）后处理简单；（4）所得到的SIF的误差可由COD资料本身的误差来估计。该文将求内裂纹SIF的COD全场拟合法扩充应用到边裂纹问题，该方法具有上述优点。对几种典型的边裂纹用边界元法得到的COD资料，用这种方法得到了可靠性高、一致性好的SIF，其计算精度与所用的COD资料的平均精度具有相同的量级。     

三维热权函数法和多虚拟裂纹扩展技术

热权函数法直接利用温度场与热权函数的乘积的积分来求应力强度因子(SIF)的过渡过程，它可以免除对每一时刻进行热弹性力学有限元或边界元应力分析，计算效率大大提高。本文给出了三维热权函数法的基本方程，并提出了求解三维热权函数法基本方程的多虚拟裂纹扩展法(MVCE法)。在MVCE法中，可以引入无穷多个虚拟裂纹扩展模式；虚拟裂纹扩展模式与应力强度因子的插值直接相联系，所得到的方程组的系数矩阵是一个三对角矩阵，具有良好的计算性能。它对于裂纹前缘SIF分布急剧变化的情况，有良好的数值模拟能力。实例计算表明，MVCE法具有权高的计算效率，并具有很高的计算精度。     

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。     

巴西圆盘试样中心斜裂纹疲劳扩展轨迹的边界元模拟

提出了一个平面弹性体多裂纹疲劳扩展模型. 它主要涉及到复合型加载情况下多裂纹尖端疲劳扩展的数学模型及杂交位移不连续法(一种边界元法). 在数值模拟中, 对每一裂纹扩展增量分析时,在其先前的边界上增添裂纹扩展增量, 且只对新增添的裂纹扩展增量划分单元, 同时, 按照这种边界元法的实施方法对一些单元特征进行调整, 就可以方便地模拟裂纹扩展. 用这种数值方法模拟了巴西圆盘试样中心斜裂纹疲劳扩展轨迹,数值结果说明了预报模型的有效性, 揭示了裂纹体几何对疲劳扩展的影响.      

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。     

多裂纹扩展分析的边界元方法

采用边界元数值模拟和即时等效材料常数计算相结合的办法，只需模拟一个裂纹的扩展情况便可预测裂纹体的整体响应。针对准脆性材料的特点，采用粘性裂纹模型模拟裂纹开裂行为；采用二次裂纹扩展量作为增量控制变量，避免了软化及失稳分析中用力或位移作控制变量时遇到的困难。针对二交裂纹扩展路径未知情况，给出了预测和修正裂纹开裂界面的迭代技术，分析计算了含多个规则分布裂纹石膏板受压时的响应，并与实验结果进行了比较。结果表明该文方法的可行性与有效性。     

求解三维裂纹前缘SIF分布时间历程的通用权函数法和有限变分法

将三维热权函数法扩展为适用于表面力、体积力和温度载荷的通用权函数法(UWF).推导出以变分型积分方程表达的UWF法基本方程,从变分的角度,将求解三维热权函数法基本方程的多虚拟裂纹扩展法(MVCE)改造为可以适用于一般的变分型积分方程的一类新型数值方法--有限变分法(FVM).在FVM中可以引入无穷多种线性无关的局部变分模式,可以根据计算要求在求解域中插入任意多个计算节点,单一型裂纹问题FVM所得到的最终方程组的系数矩阵总是一个对称的窄带矩阵,而且对角元总是大数,具有良好的数值计算性能.FVM对于SIF沿裂纹前缘急剧变化的复杂情况具有较好的数值模拟能力和较高的计算精度,利用自身一致性,可以求得三维裂纹前缘SIF的高精度解.     

圆盘状裂纹前缘塑性区尺寸及张开位移估计

将Ｄｕｇｄａｌｅ模型推广到三维裂纹问题计算了圆盘状裂纹前缘塑性区尺寸,并结合断裂力学中的Ｂａｒｅｎｂｌａｔｔ－Ｄｕｇｄａｌｅ裂纹模型和三维Ｊ－积分原理计算了圆盘状裂纹前缘张开位移,得到了Ｊ－积分与裂纹张开位移的关系,最后用非线性有限元方法对圆盘状裂纹的前缘塑性区尺寸作了数值分析,确定了公式中的未知常数,并对其正确性作了数值验证,本文的工作推广了Ｄｕｇｄａｌｅ模型的应用范围。     

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.     

三维疲劳多裂纹扩展数值模拟的计算方法及程序设计

研究了含多条初始裂纹的紧固孔件的裂纹扩展模拟及裂纹扩展寿命。紧固孔形式为直通孔和沉头(有锪窝)孔,裂纹形式为孔边角裂纹,将裂纹前缘形状简化为二次曲线形式。采用更新网格法追踪裂纹扩展,并人为干预裂纹前缘形状,解决了裂纹前缘端点跨越模型角点时的网格畸变问题;在裂纹扩展法则中使用了AFGROW裂纹闭合模型,并引入多裂纹协调扩展算法,避免了逐一应力循环计算,缩短了计算时间;试件失效判据使用净截面屈服和裂纹前缘塑性区连通准则,试件满足任一判据即判定为失效;最后在ANSYS软件的基础上进行二次开发,设计了适应多种模型的全寿命自动分析程序,并使用VB语言编写了用户界面,分别对单孔和一排五孔两种平板试件从锪窝孔边起裂的角裂纹扩展进行了数值模拟,并与试验结果进行了对比。结果表明:使用AFGROW裂纹闭合模型对寿命的预测精度明显高于Paris模型,其寿命预测误差在5%以内;对位于模型表面的裂纹尺寸的模拟与试验结果吻合较好,并很好地模拟了五孔模型在发生裂纹连通之后加速扩展的情况。     

Two dimensional numerical simulation of crack kinking from an interface under dynamic loading by time domain boundary element method

The hybrid time-domain boundary element method, together with the multi-region technique, is applied to simulate the dynamic process of propagation and/or kinking of an interface crack in a two-dimensional bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations are employed with respect to each region. However, when the crack kinks into the matrix material, the non-hypersingular traction boundary integral equations are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack-tip controlled by the fracture criterion. Kinking of the interface crack is controlled by a criterion developed from the quasi-static one. Once the crack kinks into the matrix, its propagation is modeled by adding new elements of constant length to the moving crack-tip controlled by a criterion extended from the quasi-static maximum circumferential stress. The numerical results of the crack growth trajectory for different material combinations are computed and compared with the corresponding experimental results. Good agreement between numerical and experimental results implies that the present boundary element numerical method can provide an excellent simulation for the dynamic propagation and deflection of an interface crack.     

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.     

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.     

表面裂纹问题瞬态响应的边界元分析

本文将拉氏变换-边界元法用于表面裂纹问题的瞬态响应分析。文中讨论了拉氏反演参数的选择和动态应力强度因子的计算方法。作为程序的考核和离散方案的选择,分别地计算了水平柱体一端固定、另一端受p(t)=poH(t)载荷时的位移响应和具有贯穿裂纹的厚板在两种离散方案时的动态应力强度因子响应。最后,还计算了若干载荷工况的半圆表面裂纹板应力强度因子的瞬态响应,获得了有效的数值结果。     

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.     

Evaluation of stress intensity factors for bi-material interface cracks using displacement jump methods

The aim of the present work is to investigate the numerical modeling of interfacial cracks that may appear at the interface between two isotropic elastic materials. The extended finite element method is employed to analyze brittle and bi-material interfacial fatigue crack growth by computing the mixed mode stress intensity factors (SIF). Three different approaches are introduced to compute the SIFs. In the first one, mixed mode SIF is deduced from the computation of the contour integral as per the classical J-integral method, whereas a displacement method is used to evaluate the SIF by using either one or two displacement jumps located along the crack path in the second and third approaches. The displacement jump method is rather classical for mono-materials, but has to our knowledge not been used up to now for a bi-material. Hence, use of displacement jump for characterizing bi-material cracks constitutes the main contribution of the present study. Several benchmark tests including parametric studies are performed to show the effectiveness of these computational methodologies for SIF considering static and fatigue problems of bi-material structures. It is found that results based on the displacement jump methods are in a very good agreement with those of exact solutions, such as for the J-integral method, but with a larger domain of applicability and a better numerical efficiency (less time consuming and less spurious boundary effect).     

移动接触下求解二维闭合裂纹的双重迭代边界元法

使用子域边界元法对受移动接触弹性体作用下的二维闭合裂纹问题进行了数值计算。由于两弹性体的接触界面和裂纹表面的接触范围的大小和接触状态事先是未知的 ,对此 ,在两个接触表面同时采用迭代的方法进行了求解。在裂纹的每个裂尖上都采用了四分之一的奇异单元以保证裂尖位移场和应力场奇异性的满足。用我们编制的二维裂纹问题程序对一些中心裂纹问题进行了计算 ,计算结果与经典断裂力学的理论值比较吻合。在无摩擦的条件下 ,对一些具有不同角度且受移动接触弹性体作用下的闭合裂纹问题进行了数值计算 ,得到了一些耦合作用下的应力强度因子的计算结果     

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     

一种基于直接计算高阶奇异积分的断裂力学双边界积分方程分析法

相对于有限元法,边界单元法在求解断裂问题上有着独特的优势,现有的边界单元法中主要有子区域法和双边界积分方程法.采用一种改进的双边界积分方程法求解二维、三维断裂问题的应力强度因子,对非裂纹边界采用传统的位移边界积分方程,只需对裂纹面中的一面采用面力边界积分方程,并以裂纹间断位移为未知量直接用于计算应力强度因子.采用一种高阶奇异积分的直接法计算面力边界积分方程中的超强奇异积分;对于裂纹尖端单元,提供了三种不同形式的间断位移插值函数,采用两点公式计算应力强度因子.给出了多个具体的算例,与现存的精确解或参考解对比,可得到高精度的计算结果.