梯度复合材料应力强度因子计算的梯度扩展单元法

推导了一种适用于梯度复合材料断裂特性分析的梯度扩展单元, 采用细观力学方法描述材料变化的物理属性, 通过线性插值位移场给出了4节点梯度扩展元随空间位置变化的刚度矩阵, 并建立了结构的连续梯度有限元模型。通过将梯度单元的计算结果与均匀单元以及已有文献结果进行对比, 证明了梯度扩展有限元(XFEM)的优越性, 并进一步讨论了材料参数对裂纹尖端应力强度因子(SIF)的影响规律。研究结果表明: 随着网格密度的增加, 梯度单元的计算结果能够迅速收敛于准确解, 均匀单元的计算误差不会随着网格细化而消失, 且随着裂纹长度和属性梯度的增大而增大; 属性梯度和涂层基体厚度比的增大导致涂覆型梯度材料的SIF增大; 裂纹长度的增加和连接层基体厚度比的减小均导致连接型梯度材料的SIF增大。     

采用无单元法计算含边沿裂纹功能梯度材料板的应力强度因子

本文采用无单元法分析了功能梯度材料的断裂力学问题。无单元法采用基于滑动最小二乘近似的位移插值形式,节点布置变得非常自由。这种插值形式不仅很好地反映了材料变形,而且使得无单元法在分析功能梯度材料时可以方便地采用各个积分点处的材料特性。数值计算结果表明无单元法在分析功能梯度材料力学行为方面具有较高的效率和精度。     

余能积分提取法计算应力强度因子

本文利用最小余能原理导出了一种计算应力强度因子的积分提取法，本方法的特点是只要已知位移场就可切口尖端附近的任意围线区域内进行应力强度因子的积分提取，对不同的问题及对任意张切口和任意多材料问题具通用性，文中给出基于有限元线法（ＦｉｎｉｔｅＥｌｅｍｅｎｔＭｅｔｈｏｄｏｆＬｎｅ，简称ＦＥＭＯＬ）求解的单材料和双材料反平面切口问题及平面切口问题初步实施方案，给出了数值算例表明，本法原理简单，行之有效，为计     

基于有限单元法对动态应力强度因子进行数值计算的研究*

运用ANSYS 商用有限元软件,采用非奇异单元和Newmark 积分算法,通过最小二乘法拟合,准确的获得了多个模型动态应力强度因子的解。所使用的方法适用范围广,这对于运用线弹性断裂动力学解决工程中的实际问题是有益的和必要的。     

梯度复合材料裂纹扩展路径和起裂载荷的有限元分析

为了模拟功能梯度材料(FGM)在工程应用中可能会出现的断裂问题并计算相应的开裂载荷,通过编写用户自定义UEL子程序将梯度扩展单元嵌入到ABAQUS软件中模拟功能梯度材料的物理场,并编写交互能量积分后处理子程序计算裂纹尖端的混合模式应力强度因子(SIF),采用最大周向应力准则编写子程序计算裂纹的偏转角,并模拟了裂纹扩展路径,计算了裂纹的起裂载荷。讨论了材料梯度参数对裂纹扩展路径以及起裂载荷的影响规律。通过与均匀材料的对比,验证了功能梯度材料断裂性能的优越性。研究表明:外载平行于梯度方向时,垂直梯度方向的初始裂纹朝着等效弹性模量小的方向扩展,且偏转角在梯度指数线性时出现峰值,并随着组分弹性模量比的增加而变大;当外载和初始裂纹均平行于梯度方向时,材料等效弹性模量和断裂韧性的增加或者梯度指数的减小都导致起裂载荷变大。     

单位分解增强自然单元法计算应力强度因子

自然单元法是一种新兴的无网格数值计算方法,但应用于裂纹问题计算时,其近似函数并不能准确反映裂纹尖端附近应力场的奇异性,需要在缝尖附近增大结点布置密度以获得一定的计算精度。在单位分解框架下将缝尖渐近位移场函数嵌入到自然单元法近似函数中,应用伽辽金过程获得平衡方程的离散线性方程,用相互作用能量积分方法计算了混合模式裂纹的应力强度因子。算例分析表明:单位分解增强自然单元法可以方便地处理裂纹问题,在不增加结点布置密度的情况下可有效提高应力强度因子的计算精度。     

新的估算表面裂纹应力强度因子经验公式

该文给出了新的估算拉伸和纯弯曲载荷下表面裂纹应力强度因子的经验公式。根据疲劳裂纹扩展的数值模拟结果确定强度因子分布函数;利用按已知应力强度因子分布函数求裂纹形状及相应应力强度因子的方法计算给定尺寸的表面裂纹的应力强度因子;通过对数值结果的曲线回归得到估算表面裂纹应力强度因子经验公式。利用该公式对有限厚度和宽度平板内表面裂纹的应力强度因子进行了估算,并与已知的半椭圆形表面裂纹的应力强度因子解进行了比较。该文结果为估算表面裂纹应力强度因子提供了一种新的途径。     

求解双材料界面裂纹应力强度因子的扩展有限元法

基于双材料界面裂纹尖端的基本解,构造扩展有限元法(eXtended Finite Element Methods, XFEM)裂尖单元结点的改进函数。有限元网格剖分不遵从材料界面,考虑3种类型的结点改进函数：弱不连续改进函数、Heaviside改进函数和裂尖改进函数,建立XFEM的位移模式,给出计算双材料界面裂纹应力强度因子(Stress Intensity Factors, SIFs)的相互作用积分方法。数值结果表明：XFEM无需遵从材料界面剖分网格,该文的方法能够准确评价双材料界面裂纹尖端的SIFs。     

表面裂纹应力强度因子计算及扩展跟踪的权函数法

 介绍了一种显式的权函数法,并将这种方法用于圆柱形容器接管外拐角表面裂纹的应力强度因子计算和扩展跟踪上.结果表明,权函数法可以用于分析各种载荷下不同形状的裂纹.就一般的工程问题而言,权函数法不失为一种与有限元法互补的方便有效的分析方法.     

梯度复合材料热传导分析的梯度单元法

给出了一种适用于梯度复合材料热传导分析的梯度单元, 采用细观力学方法描述材料变化的热物理属性, 通过线性插值和高阶插值温度场分别给出了4节点和8节点梯度单元随空间位置变化的热传导刚度矩阵。推导了在温度梯度载荷和热流密度载荷作用下, 矩形梯度板的稳态温度场和热通量场精确解。基于该精确解对比了连续梯度模型和传统的离散梯度模型的热传导有限元计算结果, 验证了梯度单元的有效性, 并讨论了相关参数对梯度单元的影响。结果表明, 梯度单元和均匀单元得到的温度场基本一致; 当热载荷垂直于材料梯度方向时, 梯度单元能够给出更加精确的局部热通量场; 当热载荷平行于材料梯度方向时, 4节点梯度单元性能恶化, 8节点梯度单元和均匀单元的计算结果与精确解吻合很好。     

二维压电材料动强度因子的扩展有限元计算

采用扩展有限元求解二维弹性压电材料动断裂问题。扩展有限元的网格独立于裂纹,因此网格生成可大大地简化,且裂纹扩展时不需重构网格。采用相互作用积分技术计算动强度因子。比较了标准的力裂尖加强函数和力-电裂尖加强函数对动强度因子的影响,结果表明标准的力裂尖加强函数能有效地分析压电材料动断裂问题。分析了极化方向对动强度因子的影响。数值分析表明采用扩展有限元获得的动强度因子与其他数值方法解吻合得很好。     

Stress intensity factors computation for bending plates with extended finite element method

The modelization of bending plates with through‐the‐thickness cracks is investigated. We consider the Kirchhoff–Love plate model, which is valid for very thin plates. Reduced Hsieh–Clough–Tocher triangles and reduced Fraejis de Veubeke–Sanders quadrilaterals are used for the numerical discretization. We apply the eXtended Finite Element Method strategy: enrichment of the finite element space with the asymptotic bending singularities and with the discontinuity across the crack. The main point, addressed in this paper, is the numerical computation of stress intensity factors. For this, two strategies, direct estimate and J‐integral, are described and tested. Some practical rules, dealing with the choice of some numerical parameters, are underlined. Copyright © 2012 John Wiley & Sons, Ltd.     

Stress intensity factor evaluations for a curved crack in orthotropic particulate composites using an interaction integral method

This paper develops a domain-independent interaction integral (DII-integral) for extracting mixed-mode stress intensity factors (SIFs) for orthotropic materials with complex interfaces. The DII-integral does not require material property gradients, and moreover its validity is not affected by material interfaces. Combined with the extended finite element method (XFEM), the DII-integral is employed to investigate a straight crack in an orthotropic functionally graded plate and a curved crack in orthotropic particulate composites.     

XFEM analysis of the effects of voids,inclusions and other cracks on the dynamic stress intensity factor of a major crack

This paper is devoted to the extraction of the dynamic stress intensity factor (DSIF) for structures containing multiple discontinuities (cracks, voids and inclusions) by developing the extended finite element method (XFEM). In this method, four types of enrichment functions are used in the framework of the partition of unity to model interface discontinuity within the classical finite element method. In this procedure, elements that include a crack segment, the boundary of a void or the boundary of an inclusion are not required to conform to discontinuous edges. The DSIF is evaluated by the interaction integral. After the effectiveness of the implemented XFEM program is verified, the effects of voids, inclusions and other cracks on the DSIF of a stationary major crack are investigated by using XFEM. The results show that the dynamic effects have an influence on the path independence of the interaction integral, and these voids, inclusions and other cracks have a significant effect on the DSIF of the major crack.     

Fracture mechanics analysis using the wavelet Galerkin method and extended finite element method

This paper presents fracture mechanics analysis using the wavelet Galerkin method and extended finite element method. The wavelet Galerkin method is a new methodology to solve partial differential equations where scaling/wavelet functions are used as basis functions. In solid/structural analyses, the analysis domain is divided into equally spaced structured cells and scaling functions are periodically placed throughout the domain. To improve accuracy, wavelet functions are superposed on the scaling functions within a region having a high stress concentration, such as near a hole or notch. Thus, the method can be considered a refinement technique in fixed‐grid approaches. However, because the basis functions are assumed to be continuous in applications of the wavelet Galerkin method, there are difficulties in treating displacement discontinuities across the crack surface. In the present research, we introduce enrichment functions in the wavelet Galerkin formulation to take into account the discontinuous displacements and high stress concentration around the crack tip by applying the concept of the extended finite element method. This paper presents the mathematical formulation and numerical implementation of the proposed technique. As numerical examples, stress intensity factor evaluations and crack propagation analyses for two‐dimensional cracks are presented. Copyright © 2012 John Wiley & Sons, Ltd.     

基于应力强度因子评估WCP形状对WCP/Fe复合材料热疲劳裂纹扩展行为的影响

应力强度因子在断裂力学中广泛应用于预测由远程载荷或残余应力引起的裂缝尖端附近应力状态。本文基于平面应力条件下应力强度因子建立WC_P形状与其尖端应力之间的规律,利用有限元分析软件对含不同形状WC_P的WC_P/Fe复合材料的热应力进行模拟仿真,研究WC_P形状对WC_P/Fe复合材料热疲劳裂纹扩展行为的影响。研究结果表明,WC_P的形状显著影响应力强度因子,进一步影响WC_P/Fe复合材料的热疲劳裂纹扩展行为。含球状和不规则状WC_P的WC_P/Fe复合材料的极限抗压强度分别约为460 MPa和370 MPa。含不规则状WC_P的WC_P/Fe复合材料因应力集中而容易产生脆性开裂现象。通过热震实验进行验证,发现实验结果与模拟仿真结果相近,说明有限元法的准确性,同时为WC_P/Fe复合材料的热疲劳裂纹扩展行为研究提供科学依据和理论基础。      

Stress intensity factor error index for finite element analysis with singular elements

An error index for the stress intensity factor (SIF) obtained from the finite element analysis results using singular elements is proposed. The index was developed by considering the facts that the analytical function shape of the crack tip displacement is known and that the SIF can be evaluated from the displacements only. The advantage of the error index is that it has the dimension of the SIF and converges to zero when the actual error of the SIF by displacement correlation technique converges to zero. Numerical examples for some typical crack problems, including a mixed mode crack, whose analytical solutions are known, indicated the validity of the index. The degree of actual SIF error seems to be approximated by the value of the proposed index.     

Computational modeling of strong and weak discontinuities using the extended finite element method

In this article, the extended finite element method is employed to solve problems, including weak and strong discontinuities. To this end, a level set framework is used to represent the discontinuities location, and the Heaviside and Branch function are included in the standard finite element method. The case of two arbitrary curved cracks is solved numerically and stress intensity factor (SIF) values at the crack tips are calculated based on the evaluation of the crack tip opening displacement. Afterwards, J-integral methodology is adopted to evaluate the SIFs for isotropic and anisotropic bi-material interface crack problems. Numerical results are verified with those presented in the literature.