海洋平台K型管节点的疲劳裂纹扩展分析Ⅱ:数值分析

对于已含初始裂纹平台管节点的寿命预测很大程度上依靠应力强度因子的精确值,而复杂载荷条件下的节点应力强度因子的计算尚无参数方程直接确定.本文提出了一种含表面裂纹的K节点的有限元网格产生方法,即把整个K节点划分为几个子区域,每个子区域的网格具有不同类型的单元和不同的密度.这种方法在控制网格密度,尤其是控制沿着裂纹边缘单元的边长比方面有其独特的优越性,当所有子区域的网格自动产生后,容易得到整个结构的有限元模型.同时用J积分和位移外推插值法分别计算了一个K型节点沿着裂纹前缘的应力强度因子值,发现:试验得到的应力强度因子值和提出的模型计算结果非常吻合,证明了所提有限元模型的准确性.     

辛奇异元方法与含裂纹结构加固问题分析

本文借助于辛体系本征解展开原理和辛共轭正交关系,提出一种辛奇异元模型.并结合有限元软件形成一种新的数值方法和对含裂纹结构分析思路.其最大优势在于:直接给出裂纹的应力强度因子;不受单元网格密度的局限;不受路径的影响.利用该奇异元对含裂纹结构加固问题进行分析,发现了一些特殊的规律.为含裂纹结构加固技术提供依据.     

海洋平台TT型管节点的极限强度分析

利用非线性有限元方法分析了轴向力作用下多平面TT节点的极限强度。在数值分析中,采用三维20结点固体单元模拟管道结构和焊缝形状,将结构有限元网格划分为不同区域,每个区域的网格独立产生,通过合并形成整个结构的有限元网格。通过控制位移增量法得到了加载过程中载荷和位移之间的关系曲线。使用ABAQUS软件分析了TT节点在支管端部承受轴向载荷的变形及与外部载荷之间的关系,得到了不同参数影响下的TT节点极限强度。     

滚动接触下的轨道表面三维裂纹研究方法

针对已有的求解三维裂纹的应力强度因子方法工作量大、难以实现复杂的三维模型建立的问题,提出了一种求解广义移动荷载下三维裂纹尖端应力强度因子的普遍方法。采用包络式三维实体建模方法,有效避免了三维裂纹有限元模型网格划分时因受限于拓扑误差容忍而出现网格划分失败的现象;通过MATLAB三维插值施加节点荷载,解决了不规则三维裂纹有限元模型施加复杂空间荷载的难题。计算结果表明:荷载中心距离裂纹中心约4mm时裂纹尖端应力强度因子达到最大值7.41×107Pa·m1/2;轮轨接触疲劳以张开型为主。此外,给出了最大应力强度因子条件下裂纹尖端塑性区的分布及裂纹扩展情况,可为轮轨滚动接触疲劳的研究及设计提供一定的参考。     

扩展有限元裂尖场精度研究

论述了扩展有限元方法和基本原理,研究了单元类型(四边形单元和三角形单元、线性单元和二次单元)、网格密度、J积分区域半径等因素对裂尖局部应力场(应力强度因子)计算精度的影响。研究发现,上述因素对裂尖应力强度因子计算的收敛速度与稳定性影响不大,证实了XFEM可以用较少的节点获得较高的裂尖场精度,并提出了通过固定裂尖附加区半径可以进一步改善XFEM的收敛速度。     

状态向量的扩展有限元方法研究

利用哈密顿正则方程的半解析法计算单元位移场和应力场,可以得到精度比较高的解.但此半解析法在计算应力尖峰区域时,该区域要细化网格.当裂纹扩展时,又要重新生成刚度矩阵进行求解,导致求解效率降低.利用扩展有限元处理裂纹的不连续性,当裂纹扩展时可以避免网格的重构.为充分利用状态向量方程和扩展有限元的优势,该文将两者结合起来分析材料的断裂问题:计算应力强度因子和模拟裂纹扩展.最后通过算例分析,验证了该文提出方案的可行性.     

拉伸螺杆半椭圆表面裂纹应力强度因子

将拉伸螺杆简化为理论应力集中系数Kt不同的带“V”形缺口圆杆,采用裂纹尖端为20节点奇异单元的三维有限元模型,对螺杆半椭圆表面裂纹的应力强度因子进行了计算.给出了具有普遍性意义的螺杆表面裂纹应力强度因子公式.为验证本文计算结果的有效性,还将本文M22×1.5螺杆的应力强度因子计算结果与试验结果进行了对比.     

焊接残余应力对含缺陷管道 TK?值的影响研究

为给含缺陷焊接管道脆性断裂的进一步研究提供基础,本文采用本征应变与局部应力相结合的方法模拟了两种典型的焊接残余应力,并计算了含内表面环向裂纹的管道分别在这两种残余应力作用下的应力强度因子K和裂尖约束应力T .计算结果表明:管道厚度方向的应力分布决定了裂纹根部的K ?值,沿着管道厚度呈拉应力分布的残余应力对应较大的K值与较小的T 值, T而沿着管道厚度总体呈弯曲分布的残余应力对应较小的K值与较大的T 值;在残余应力分布和管道厚度都相同的条件下,管道内径对K ?值的影响随着裂纹深度的增大而加强.T     

基于p型有限元法和围线积分法计算复合型应力强度因子

传统有限元法由于采用低阶插值计算应力强度因子时,需要划分的网格数较多,收敛速度较慢,得到的应力强度因子精度不足。p型有限元法在网格确定时通过增加插值多项式的阶数来提高计算精度,具有网格划分少、收敛速度快、精度高、自适应能力强等特点。本文采用基于p型有限元法的有限元计算软件StressCheck计算得到应力场和位移场,并由围线积分法导出混合型应力强度因子(SIFs)。通过几个经典算例,分析了围线的选择对计算精度的影响,计算了不同裂纹长度、不同裂纹角度和裂纹在应力集中区域不同位置时的应力强度因子。并将数值结果、理论解与文献中其他数值计算方法所得的部分结果进行了对比分析,结果表明自由度数不大于7000时,导出的应力强度因子相对误差最大不超过1.2%,数值解表现出较高的精度及数值稳定性。     

三维编织复合材料渐进损伤的非线性模型及强度分析

建立了考虑周期性位移边界条件的细观体胞模型,对三维编织复合材料的渐进损伤过程进行数值模拟。采用Eshelby-Mori—Tanaka方法计算含损伤裂纹的材料的剐度矩阵,并将有限元网格尺寸和单元裂纹尺寸引入损伤演化方程,有效地降低了模拟结果对有限元网格的依赖程度。通过计算得到了材料应力应变的非线性关系和失效时的极限强度,并分析了材料的破坏机理。结果表明,大编织角材料的破坏模式主要是基体失效与纤维横向拉剪破坏,模拟计算结果与文献中的实验值吻合较好。     

海洋平台K型管节点的疲劳裂纹扩展分析Ⅰ:试验测试

对承受疲劳载荷的海洋平台K型管节点首先进行了静力测试,确定了沿着焊缝的热应力区的应力分布及热应力区最大应力点的位置,从而判断裂纹产生的位置;然后通过专用测试设备提供循环疲劳载荷,用ACPD(Alternating Current Potential Drop,即交流电流势能落差法)技术检测裂纹的产生和增长过程,得到裂纹最深点,用S-N曲线估算其疲劳寿命。对已有裂纹的K型管节点,用应力强度因子估计其剩余寿命。同时用测试的结果验证了S-N的准确性和可靠性。     

K型管节点的应力集中系数研究

采用有限元法分析了K型管节点在承受轴力作用下的应力集中系数. 用三维固体单元模 拟结构,模拟中对不同区域分别划分网格,每个区域的网格独立产生后,再形成整个结构的 有限元网格. 使用ABAQUS软件分析了200组在轴向循环载荷作用下的节点数值模型,获得 了K节点在轴向循环载荷作用下沿焊缝的应力集中系数(SCF),并对主管和支管的SCF进行 研究,得出了节点几何参数对主管和支管的SCF及极值位置的影响规律.     

直接计算应力强度因子的扩展有限元法

系统地给出了直接计算应力强度因子的扩展有限元法。该方法以常规有限元法为基础,利用单位分解法思想,通过在近似位移表达式中增加能够反映裂纹面的不连续函数及反映裂尖局部特性的裂尖渐进位移场函数,间接体现裂纹面的存在,从而无需使裂纹面与有限元网格一致,无需在裂尖布置高密度网格,也不需要后处理就可以直接计算出应力强度因子,并且大大简化了前后处理工作。最后通过两个简单算例验证了该方法的精度,分析了影响计算结果的因素,并与采用J积分计算的应力强度因子作了对比,得出了两种方法计算精度相当的结论。     

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。     

A domain-independent integral for computation of stress intensity factors along three-dimensional crack fronts and edges by BEM

The present work deals with an evaluation of stress intensity factors (SIFs) along straight crack fronts and edges in three-dimensional isotropic elastic solids. A new numerical approach is developed for extraction, from a solution obtained by the boundary element method (BEM), of those SIFs, which are relevant for a failure assessment of mechanical components. In particular, the generalized SIFs associated to eigensolutions characterized by unbounded stresses at a neighbourhood of the crack front or a reentrant edge and also that associated to T-stress at the crack front can be extracted. The method introduced is based on a conservation integral, called H-integral, which leads to a new domain-independent integral represented by a scalar product of the SIF times some element shape function defined along the crack front or edge. For sufficiently small element lengths these weighted averages of SIFs give reasonable pointwise estimation of the SIFs. A proof of the domain integral independency, based on the bi-orthogonality of the classical two-dimensional eigensolutions associated to a corner problem, is presented. Numerical solutions of two three-dimensional problems, a crack problem and a reentrant edge problem, are presented, the accuracy and convergence of the new approach for SIF extraction being analysed.     

Selection of finite-element mesh parameters in modeling the growth of hydraulic fracturing cracks

The effect of the mesh geometry on the accuracy of solutions obtained by the finite-element method for problems of linear fracture mechanics is investigated. The guidelines have been formulated for constructing an optimum mesh for several routine problems involving elements with linear and quadratic approximation of displacements. The accuracy of finite-element solutions is estimated based on the degree of the difference between the calculated stress-intensity factor (SIF) and its value obtained analytically. In problems of hydrofracturing of oil-bearing formation, the pump-in pressure of injected water produces a distributed load on crack flanks as opposed to standard fracture mechanics problems that have analytical solutions, where a load is applied to the external boundaries of the computational region and the cracks themselves are kept free from stresses. Some model pressure profiles, as well as pressure profiles taken from real hydrodynamic computations, have been considered. Computer models of cracks with allowance for the pre-stressed state, fracture toughness, and elastic properties of materials are developed in the MSC.Marc 2012 finite-element analysis software. The Irwin force criterion is used as a criterion of brittle fracture and the SIFs are computed using the Cherepanov–Rice invariant J-integral. The process of crack propagation in a linearly elastic isotropic body is described in terms of the elastic energy release rate G and modeled using the VCCT (Virtual Crack Closure Technique) approach. It has been found that the solution accuracy is sensitive to the mesh configuration. Several parameters that are decisive in constructing effective finite-element meshes, namely, the minimum element size, the distance between mesh nodes in the vicinity of a crack tip, and the ratio of the height of an element to its length, have been established. It has been shown that a mesh that consists of only small elements does not improve the accuracy of the solution.     

CTS试样I/II混合型断裂特性数值计算研究

采用CTS试样研究I/II混合型断裂特性计算裂纹前缘应力强度因子时可采用解析公式,一旦裂纹发生扩展,解析公式便不再适用。文中采用有限元法研究紧凑拉伸剪切（CTS）试样在I/II平面混合型加载下的裂纹扩展行为。采用ANSYS建立CTS试样I/II混合型测试系统有限元模型,为模拟真实受力状态,在CTS试样-销-扇型夹具以及扇型夹具-销-U型夹具之间分别建立接触对进行接触力学分析。通过与解析公式结果进行对比验证了该数值方法的可靠性。采用最大环向应力准则（MTS）,模拟了CTS试样不同加载角度下的裂纹扩展路径,获得了裂纹扩展路径中应力强度因子随裂纹长度的变化曲线,解释了裂纹扩展路径不与外载荷方向垂直的原因。结合文中计算结果,在CTS试样I/II混合型裂纹扩展速率实验测得裂纹长度与寿命的关系曲线a-N的基础上,便可得到材料I/II型混合型裂纹扩展速率曲线。     

MESHLESS METHOD FOR 2D MIXED-MODE CRACK PROPAGATION BASED ON VORONOI CELL

A meshless method integrated with linear elastic fracture mechanics (LEFM) is presented for 2D mixed-mode crack propagation analysis. The domain is divided automatically into sub-domains based on Voronoi cells, which are used for quadrature for the potential energy. The continuous crack propagation is simulated with an incremental crack-extension method which assumes a piecewise linear discretization of the unknown crack path. For each increment of the crack extension, the meshless method is applied to carry out a stress analysis of the cracked structure. The J-integral, which can be decomposed into mode I and mode II for mixed-mode crack, is used for the evaluation of the stress intensity factors (SIFs). The crack-propagation direction, predicted on an incremental basis, is computed by a criterion defined in terms of the SIFs. The flowchart of the proposed procedure is presented and two numerical problems are analyzed with this method. The meshless results agree well with the experimental ones, which validates the accuracy and efficiency of the method.     

Application of hypersingular integral equation method to three-dimensional crack in electromagnetothermoelastic multiphase composites

A three-dimensional crack problem in electromagnetothermoelastic multiphase composites (EMTE-MCs) under extended loads is investigated in this paper. Using Green’s functions, the extended general displacement solutions are obtained by the boundary element method. This crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations, in which the unknown functions are the extended displacement discontinuities. Then, the behavior of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main-part analysis method of hypersingular integral equations. Analytical solutions for the extended singular stresses, the extended stress intensity factors (SIFs) and the extended energy release rate near the crack front in EMTE-MCs are provided. Also, a numerical method of the hypersingular integral equations for a rectangular crack subjected to extended loads is put forward with the extended displacement discontinuities approximated by the product of basic density functions and polynomials. In addition, distributions of extended SIFs varying with the shape of the crack are presented. The results show that the present method accurately yields smooth variations of extended SIFs along the crack front.     

Experimental and numerical analysis of fretting crack formation based on 3D X-FEM frictional contact fatigue crack model

Nowadays, numerical simulation of 3D fatigue crack growth is easily handled using the eXtended Finite Element Method coupled with level set techniques. The finite element mesh does not need to conform to the crack geometry. Most difficulties associated to complex mesh generation around the crack and the re-meshing steps during the possible propagation are hence avoided. A 3D two-scale frictional contact fatigue crack model developed within the X-FEM framework is presented in this article. It allows the use of a refined discretization of the crack interface independent from the underlying finite element mesh and adapted to the frictional contact crack scale. A stabilized three-field weak formulation is also proposed to avoid possible oscillations in the local solution linked to the LBB condition when tangential slip is occurring. Two basic three-dimensional numerical examples are presented. They aim at illustrating the capacities and the high level of accuracy of the proposed X-FEM model. Stress intensity factors are computed along the crack front. Finally an experimental 3D ball/plate fretting fatigue test with running conditions inducing crack nucleation and propagation is modeled. 3D crack shapes defined from actual experimental ones and fretting loading cycle are considered. This latter numerical simulation demonstrates the model ability to deal with challenging actual complex problems and the possibility to achieve tribological fatigue prediction at a design stage based on the fatigue crack modeling.