裂纹面分布加载裂尖SIFs分析的广义参数Williams单元北大核心CSCD

带裂缝服役是工程结构的常态,由于流体侵入到裂缝内部,裂纹面直接受荷,使得裂缝进一步扩展,甚者影响结构的安全性.广义参数Williams单元(简记W单元)在分析断裂问题中,利用Williams级数建立裂尖奇异区的位移场,通过求解广义刚度方程可直接获得应力强度因子(stress intensity factors,SIFs),具有高精高效性;但W单元需满足奇异区内裂纹面自由的边界条件,故在分析裂纹面加载的问题中受限.该文基于SIFs互等,在等效奇异区范围中,将裂纹面的荷载等效为奇异区外围边界裂纹面上的集中力,避免奇异区内裂纹面受荷,故采用W单元即可简便计算.算例分析表明:等效奇异区尺寸取裂纹长度的1/20,等效荷载系数P建议取2.0,W单元计算精度均满足1%的误差限,证明该文在奇异区裂纹面受荷等效处理方法上具有合理性、通用性,克服了W单元在分析裂纹面加载问题的局限性.     

Efficient crack growth analyzes by combining fast methods for BEM

The combination of fast methods for the boundary element method (BEM) for efficient crack growth analyzes is presented. Due to the nonlinearity of fatigue crack growth an incremental procedure has to be applied. Within each increment a stress analysis is needed. Based on the asymptotic stress field the stress intensity factors (SIFs) are calculated by an extrapolation method. Then, a new crack front is determined by a reliable 3D crack growth criterion. Finally, the numerical model has to be updated for the next increment. The time dominant factor in each increment is the computation of the stress field. Due to the stress concentration problem the BEM is utilized. To speed-up the calculation several independent fast methods are exploited. An algebraic technique is the adaptive cross approximation (ACA) method which is acting on the system matrix itself. The application of the substructure technique leads to a blockwise band matrix and therefore to reduced memory requirements. Further savings in memory and computation time are reached by modelling cracks with the dual discontinuity method (DDM) and using the ACA method in each substructure. The efficiency of the combined methods is shown by a complex industrial example. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

圆形孔口裂纹的反平面剪切问题的解析解

利用复变函数方法,通过构造保角映射,研究了带裂纹的圆形孔口的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子.在极限情形下,求得Griffith裂纹在裂纹尖端处应力强度因子,这与已有的结果完全一致.最后数值算例给出了半经和裂纹长度对应力强度因子的影响.     

A boundary element analysis for stress intensity factors of multiple circular arc cracks in a plane elasticity plate

In this paper, a numerical approach for analyzing interacting multiple cracks in infinite linear elastic media is presented. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks, the original problem is divided into a homogeneous problem (the one without cracks) subjected to remote loads and a multiple crack problem in an unloaded body with applied tractions on the crack surfaces. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements proposed recently by the author. Test examples are given to illustrate that the numerical approach is very accurate for analyzing interacting multiple cracks in an infinite linear elastic media under remote uniform stresses. In addition, the displacement discontinuity method with crack-tip elements is used to analyze a multiple crack problem in a finite plate. It is found that the boundary element method is also very accurate for investigating interacting multiple cracks in a finite plate. Specially, a generalization of Bueckner’s principle and the displacement discontinuity method with crack-tip elements are used to analyze multiple circular arc crack problems in infinite plate in tension (including: Two Collinear Circular Arc Cracks, Three Collinear Circular Arc Cracks, Two Parallel Circular Arc Cracks, Three Parallel Circular Arc Cracks and Two Circular Arc Cracks) in a plane elasticity plate. Many results are given.     

一维六方准晶中带双裂纹的椭圆孔口问题的解析解

利用复变函数方法,通过构造保角映射,研究了一维六方准晶中带双裂纹的椭圆孔口的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子,在极限情形下,不仅可以还原为已有的结果,而且求得一维六方准晶中带双裂纹的圆形孔口问题、十字裂纹问题在裂纹尖端的应力强度因子．     

一维正方准晶垂直于准周期方向具有不对称共线裂纹的圆形孔口问题

利用复变函数方法,通过构造广义保角映射,研究了一维正方准晶垂直于准周期方向具有不对称共线裂纹的圆形孔口问题,给出了各应力分量在象平面的复表示,并得到该裂纹尖端的应力强度因子.在极限情形下,给出一维正方准晶中具有对称共线裂纹的圆形孔口,带单裂纹的圆形孔口和Griffith裂纹在裂纹尖端的应力强度因子.     

一维六方准晶中带三条不对称裂纹的圆形孔口问题的解析解

利用复变函数方法,通过构造保角映射,研究了一维六方准晶中带不对称三裂纹的圆形孔口的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子,在极限情形下,不仅可以还原为已有的结果,而且求得一维六方准晶中L裂纹问题在裂纹尖端的应力强度因子.     

Interaction of multiple cracks in a rectangular plate

This paper is concerned with interaction of multiple cracks in a finite plate by using the hybrid displacement discontinuity method (a boundary element method). Detail solutions of the stress intensity factors (SIFs) of the multiple-crack problems in a rectangular plate are given, which can reveal the effect of geometric parameters of the cracked body on the SIFs. The numerical results reported here illustrate that the boundary element method is simple, yet accurate for calculating the SIFs of multiple crack problems in a finite plate.     

Stress intensity factors for the Brazilian disc with a short central crack: Opening versus closing cracks

Closed form expressions are obtained for the stress intensity factors (SIFs) in case of a Brazilian disc with a short central crack, the length of which does not exceed one fifth of the disc radius. The disc is loaded by uniform radial pressure along two finite symmetric arcs of its periphery. The solution is achieved using the method of complex potentials introduced by Kolosov and Muskhelishvili. The advantage of the expressions obtained is that they are valid both for cracks under opening mode as well as for closing cracks. For the first case (opening cracks) the results of the present study are compared with existing approximate solutions and it is concluded that the agreement is excellent as long as the length of the crack remains relatively small compared to the radius of the disc. Regarding the case of a closing mode crack the procedure proposed here (based on a recent alternative approach of the cracked Brazilian disc) leads to a physically acceptable deformed crack shape instead to an unnatural crack with overlapped lips. At the same moment the dependence of the SIFs on the properties of the material is eliminated.     

一维正方准晶沿准周期方向穿透的抛物线裂纹问题

利用广义复变函数方法研究了一维正方准晶材料中周期平面的抛物线裂纹问题,通过建立广义保角映射,将物理平面的抛物线裂纹外映射到数学平面里的单位圆内.得出了声子场和相位子场的应力分量在像平面下的复表示,并且得到了抛物线裂纹尖端的应力强度因子.并在特殊情况下,所得结果与Griffith裂纹的结果一致.     

Simulation of 2D linear crack growth under constant load using GFVM and two-point displacement extrapolation method

A new approach to model two-dimensional linear crack propagation, based on the Galerkin Finite Volume Method (GFVM), is proposed. The displacement field is calculated using the GFVM method by solving two-dimensional equilibrium equations on an unstructured triangular mesh. An essential feature of this method is that it does not require matrix operations; hence, it obviously reduces computation time. The Two-Point Displacement Extrapolation (TPDE) technique is employed to calculate Stress Intensity Factors (SIFs). The accuracy of the structural solver that has been developed is evaluated using five test cases. In the first example, a Timoshenko cantilever beam, carrying an end point load, is analyzed. In the second and third examples, stress intensity factors are computed for edge and inner crack development in plates under transient loading. The GFVM results are then compared with their counterparts that resulted from the Explicit Finite Element Method (E-FEM). The comparison indicates that the FVM has an accuracy close to E-FEM, whereas the FVM drastically reduces the computational time. A case study is conducted to simulate the gradual propagation of crack. The results computed by the numerical simulation presented are in excellent agreement with the corresponding results from the analytical solution as well as experimental measurements.     

一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题

依据一维六方准晶压电材料反平面问题的基本方程,利用复变函数方法,通过引入适当的保角映射,研究了一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题,并利用Cauchy积分理论,得到电不可通和电可通边界条件下的应力场和位移场的复表示以及裂纹尖端场强度因子的解析表达式.     

幂函数型曲线裂纹平面问题的一般解

通过构造一个新的、精确的和通用的保角映射,利用Muskhelishvili复势法研究了任意自然数次幂的幂函数型曲线裂纹的平面弹性问题,给出了远处受单向拉伸载荷下裂纹尖端Ⅰ型和Ⅱ型应力强度因子的一般解．当幂次取不同的自然数时,可以退化为若干已有的结果．通过数值算例,讨论了幂函数型曲线裂纹的系数、幂次及在x轴上的投影长度对Ⅰ型和Ⅱ型应力强度因子的影响规律．     

点群6一维六方准晶椭圆孔口与半无限裂纹反平面弹性问题的解析解

导出了点群6-维六方准晶反平面弹性问题的控制方程.利用复变方法,给出了点群6-维六方准晶在周期平面内的反平面弹性问题的应力分量以及边界条件的复变表示,通过引入适当的保角变换,研究了点群6-维六方准晶中带有椭圆孔口与半无限裂纹的反平面弹性问题,得到了椭圆孔口问题应力场的解析解,给出了半无限裂纹问题在裂纹尖端处的应力强度因子的解析解.在极限情形下,椭圆孔口转化为Griffith裂纹,并得到该裂纹在裂尖处的应力强度因子的解析解.当点群6-维六方准晶体的对称性增加时,其椭圆孔口与半无限裂纹的反平面弹性问题的解退化为点群6mm-维六方准晶带有椭圆孔口与半无限裂纹的反平面弹性问题的解。     

一维正交准晶中具有四条裂纹的椭圆孔口问题的解析解

运用广义复变函数方法,通过构造适当的广义保角映射,研究了一维正交准晶中具有四条裂纹的椭圆孔口的平面弹性问题.通过引入应力函数,把平面弹性问题的基本方程简化为一个四阶偏微分方程,从而给出了各个应力分量在像平面的复表示,求得了裂纹尖端的应力强度因子的解析解.当描述缺陷的各参数发生变化时,该文的结果不仅可以还原已有文献中的结论,还可给出多种常见缺陷构型的应力强度因子,为工程力学分析提供了理论依据.     

A novel size independent symplectic analytical singular element for inclined crack terminating at bimaterial interface

Cracks often exist in composite structures, especially at the interface of two different materials. These cracks can significantly affect the load bearing capacity of the structure and lead to premature failure of the structure. In this paper, a novel element for modeling the singular stress state around the inclined interface crack which terminates at the interface is developed. This new singular element is derived based on the explicit form of the high order eigen solution which is, for the first time, determined by using a symplectic approach. The developed singular element is then applied in finite element analysis and the stress intensity factors (SIFs) for a number of crack configurations are derived. It has been concluded that composites with complex geometric configurations of inclined interface cracks can be accurately simulated by the developed method, according to comparison of the results against benchmarks. It has been found that the stiffness matrix of the proposed singular element is independent of the element size and the SIFs of the crack can be solved directly without any post-processing.     

平面弹性裂纹分析的一种有效边界元方法

提出了一种简单而有效的平面弹性裂纹应力强度因子的边界元计算方法．该方法由Crouch与Starfield建立的常位移不连续单元和闫相桥最近提出的裂尖位移不连续单元构成A·D2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．算例(如单向拉伸无限大板中心裂纹、单向拉伸无限大板中圆孔与裂纹的作用)说明平面弹性裂纹应力强度因子的边界元计算方法是非常有效的．此外,还对双轴载荷作用下有限大板中方孔分支裂纹进行了分析．这一数值结果说明平面弹性裂纹应力强度因子的边界元计算方法对有限体中复杂裂纹的有效性,可以揭示双轴载荷及裂纹体几何对应力强度因子的影响．     

Influence of inclusion on the stress intensity factors under thermomechanical loads in a PM superalloy

The interaction between a round inclusion and a crack under thermomechanical loading is analyzed based on a modified body force method. The traction-free condition on the crack line is mended by adding the resultant force induced by thermal stress to the force equilibrium equations, so that the coupling of mechanical and thermal loads could be taken into account. The series of integral equations can be discretized to a set of linear equations. Stress intensity factors (SIFs) are obtained through solving the linear equations. The calculated results in this paper are compared to those in open references to validate the method and code. The method is applied to a case of FGH95 PM superalloy containing Al₂O₃ inclusions under mechanical and thermal loads. The results show that the thermal load has little effect on SIF, while the mechanical load is the dominant factor.