Significance of the elastic peak stress evaluated by FE analyses at the point of singularity of sharp V-notched components

The paper presents an expression useful to estimate the notch stress intensity factor (NSIF) from finite element analyses carried out by using a mesh pattern with a constant element size. The evaluation of the NSIF from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. The usefulness of the presented expression is that (i) only the elastic peak stress numerically evaluated at the V‐notch tip is needed and no longer the whole stress–distance set of data; (ii) the adopted meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. The proposed expression needs the evaluation of a virtual V‐notch tip radius, i.e. the radius which would produce the same elastic peak stress than that calculated by FEM at the sharp V‐notch tip by means of a given mesh pattern. Once such a radius has been theoretically determined for a given geometry, the expression can be applied in a wide range of notch depths and opening angles.     

3D J‐integral evaluation using the computation of line and surface integrals

In the analysis of fracture mechanics of structures using three‐dimensional (3D) J‐integral, an integral evaluation of line and surface is required. However, because surface integral evaluation requires the calculation of the second derivative of displacement field and commercial finite element codes cannot calculate it, then this portion of the integral is neglected in some research. In this paper, a method for computing 3D J‐integral is presented using finite element analysis. In the analysis, the second derivative evaluation of displacement field is employed. The method is implemented in calculating the J‐integral of some 3D cracks and results are compared to well‐known reference values. The results show that the method is reliable and is suitable for applications in engineering. The portion of 3D J‐integral, namely the surface integral value is investigated and it is shown that neglecting this portion can introduce considerable error in the final results.     

Computation of stress intensity factors for a 2-D body from displacements at an arbitrary location

An approach to stress intensity factor computation is presented which allows accurate estimation using a simple finite element program and a coarse mesh of elements. The stress intensity factor is obtained from what we term the Crack-Displacement (C-D) Factor. This involves the rate of change of displacements with crack length at the same location remote from the crack due to two loading conditions. One loading condition is merely that applied to the cracked body. The other loading condition is a virtual line force applied at the location at which the displacement rates are computed. The accuracy of the procedure is demonstrated for uniform tensile stresses applied to a center-cracked panel and an edge-cracked strip.     

Stress and Failure Analysis of Brittle Matrix Composites. Part II: Failure Analysis

A linear elastic fracture mechanics analysis of a cylindrical element of matrix with a single fiber and two matrix annular cracks perpendicular to the fiber direction under longitudinal tensile load was undertaken. The order of singularity and the angular dependence of the stress field in the neighborhood of the crack periphery were determined by using the stress function approach proposed by Zak and Williams. The stress intensity factor was evaluated by combining the results of the local stress solution with a finite element analysis. The case of fiber debonding originating from the periphery of the annular cracks was also studied. For that problem both opening-mode and sliding-mode stress intensity factors and the strain energy release rate were determined. These results help to understand the various failure mechanisms including matrix cracking, debonding along interfaces and kinking of interface cracks into fibers in brittle matrix composites. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fracture analysis for ceramic ball in backflow valve

Ceramic balls have been used as components of devices, such as those found in high‐pressure pumps for automobiles and industrial machines. In the backflow valve, for example, a ceramic ball is in contact with a conical surface. Fractures of ceramic balls are extremely rare. It is important to investigate the cause of these rare fractures to guarantee higher reliability in the backflow valve. In this paper, the fracture mechanism and strength are discussed for an equivalent normal stress σ_eq beneath the contact region and the maximum principal stress σ_p near the contact boundary using stress intensity from fracture mechanics. The fracture surface of the ceramic ball was formed perpendicular to load direction. We assumed that fracture origins (defect/crack) existed on lines through three high stresses that analysed by finite element method. Actual fracture of a ceramic ball was found to be caused by the equivalent normal stress beneath contact region and not to be caused by the Hertz principal stress. Stress intensity factor (SIF) was clarified to depend on pressure, taper angle, CrN‐coating thickness and the friction factor of the inside of the valve hole. A pre‐existing defect size involved in failure was estimated by the SIF using three‐dimensional elliptic defects and equivalent normal stress. Therefore, the actual fracture of a ceramic ball, which rarely occurs, could be evaluated by considering three‐dimensional elliptic defects and the Weibull distribution of defects.     

三维杆系结构的几何非线性有限元分析

为了更准确地描述杆系结构的几何非线性性能,建立了一种基于三维梁单元有限元分析的计算方法。引入了考虑两方向曲率和扭转角变化的坐标转换矩阵来描述任意增量下的单元平移和转动;采用了包括轴向变形和扭转的非线性项的刚度矩阵来考虑高阶非线性项的影响。应用广义位移控制法进行增量迭代,编制了相应的三维梁单元非线性计算程序NL_Beam3D。通过对几个例子进行的分析,验证了该方法可较好地考虑结构几何非线性。     

Internal–external circumferential crack behaviour in the cement layer of total hip replacement

This study aimed to investigate crack behaviour at the internal and external surfaces of the cement layer in total hip replacement. A three‐dimensional model of the femur with the cemented prosthesis was developed and analysed. Cracks were placed on the internal, external and both internal and external surfaces of the cement layer. Stress intensity factors were measured during gait. Results revealed that the stress intensity factors modes I and III were the most dominant in the crack propagation in the cement layer. The domain of mode I was the medial and lateral sides of the cement layer. Meanwhile, the domain of mode III was the anterior and posterior sides of the cement layer. The stress intensity factor and distance from the distal end indicated an inverse relationship. The internal and external cracks had no significant interaction. Moreover, stress intensity factors at the external surface of the cement layer were higher than those on the internal surface.     

矩形钢管K型节点复合型应力强度因子计算方法研究

相比圆形钢管桁架,矩形钢管桁架在施工方面具有一定的技术经济优势,并已广泛应用于桥梁工程中,鉴于断裂力学法评估该类结构疲劳性能的需要,该文探讨矩形钢管K型节点在支管拉压平衡荷载作用下的应力强度因子计算方法。提出带表面裂纹矩形钢管K型节点有限元建模方法,并与试验进行验证;通过参数分析,研究节点和裂纹几何参数对节点几何修正系数Y的影响;多元回归分析拟合得到矩形钢管K型节点应力强度因子计算公式及其修正后的设计计算公式,并通过算例分析给出基于断裂力学的钢管节点剩余疲劳寿命评估方法。结果表明：有限元结果与试验结果比值均值为1.012,变异系数为0.034,两者最大差值仅为5.5%,表明有限元计算结果可靠;节点几何参数2γ、τ与Y呈正相关,θ与Y呈负相关,其原因主要在于节点相贯线处刚度和受拉荷载变化,改变了裂纹尖端应力场,从而影响了裂纹扩展速率,裂纹几何参数c/a与Y呈正相关,但影响不明显,a/t₀与Y呈负相关;提出的应力强度因子计算公式与有限元计算结果吻合良好,且修正后用于设计的计算公式具有95%的可靠度;圆形钢管节点应力强度因子高于矩形钢管节点,平均提高24.9%,说明在相同荷载工况下,圆形钢管节点裂纹扩展速率更快,算例分析也进一步验证该结论,圆形钢管节点剩余疲劳寿命为2.1×10⁵次,低于矩形钢管节点的剩余疲劳寿命2.3×10⁵次。     

Stress intensity factors and weight functions for deep semi-elliptical surface cracks in finite-thickness plates

ABSTRACT Three-dimensional finite element analyses have been conducted to calculate the stress intensity factors for deep semi-elliptical cracks in flat plates. The stress intensity factors are presented for the deepest and surface points on semi-elliptic cracks with a/t -values of 0.9 and 0.95 and aspect ratios ( a/c ) from 0.05 to 2. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were combined with corresponding results for surface cracks with a/t = 0.6 and 0.8 to derive weight functions over the range 0.05 ≤  a/c  ≤ 2.0 and 0.6 ≤  a/t  ≤ 0.95. The weight functions were then verified against finite element data for parabolic or cubic stress distributions. Excellent agreements are achieved for both the deepest and surface points. The present results complement stress intensity factors and weight functions for surface cracks in finite thickness plate developed previously.     

空间桁架大位移问题的有限元分析

本文在T.L.坐标下,利用能量原理,同时导出了空间杆元精确的割线刚度矩阵和切线刚度矩阵显式。文中采用几种方法实现了空间桁架大位移分析的几何非线性有限元解法。算例表明,本文导出的两个刚度矩阵可极为有效的分析各类空间桁架的几何非线性问题,且使程序具有极好的调试性。     

工程结构有限元分析的应力奇异问题及抑制方法

针对工程结构有限元分析产生的应力奇异现象进行了研究,并提出了应力奇异抑制方法。将应力奇异分为结构几何突变应力奇异、约束刚度突变应力奇异、材料性能突变应力奇异问题。利用ANSYS Workbench仿真平台,分别建立了3种典型应力奇异模型,并进行了数值模拟分析。研究结果表明：有限元分析过程中存在应力奇异现象的本质是约束刚度突变问题所造成,通过修正模型及约束等效措施能够抑制应力奇异现象。     

一种新的集成非线性杆件单元刚度矩阵的方法

对于非线性杆件单元,本文提出一种新的简便有效的集成单元刚度矩阵的算法。该方法直接从结构力学中的位移法的概念出发,通过解析积分或数值积分求解积分算子,由积分算子线性组合,能快速求解考虑弯、剪、扭、轴压等各种非线形刚度的杆件单元的刚度矩阵。该方法具有广泛的普适性,能适用于所有多项式、插值多项式、解析式、离散点描述的变刚度、变截面直杆的单元刚度矩阵集成计算。文中通过求解线性直杆单元刚度矩阵验证了该方法的正确性。