On stress concentrations for isotropic/orthotropic plates and cylinders with a circular hole

Scale factors (SFs) are widely used in engineering applications to describe the stress concentration factor (SCF) of a finite width isotropic plate with a circular hole and under uniaxial loading. In this paper, these SFs were also found to be valid in an isotropic plate with biaxial loading and an isotropic cylinder with uniaxial loading or internal pressure, if a suitable hole to structure dimension ratio was chosen. The study was further expanded to consider orthotropic plates and cylinders with a center hole and under uniaxial loading. The applicable range of the SFs was given based on the orthotropic material parameters. The influence of the structural dimension on the SCF was also studied. An empirical calculation method for the stress concentrations for isotropic/orthotropic plates and cylinders with a circular hole was proposed and the results agreed well with the FEM simulations. This research work may provide structure engineers a simple and efficient way to estimate the hole effect on plate structures or pressure vessels made of isotropic or orthotropic materials.     

Three‐dimensional stress concentrations at circular pin holes in clearance‐fit lugs

The influences of thickness and bonding clearance on stress concentration factors (SCFs) at circular holes in pin‐loaded straight lugs are systematically investigated using the finite element method. The three‐dimensional effect on stress concentration at pin hole is strong when the thickness B of lug is higher than the radius R of pin hole. The maximum tensional SCF K_max normalized by its corresponding plane stress solution K_p–σ increases with increasing B/R when B/R is higher than 2 for all of r/R (the radius of pin to that of lug), and also increases with decreasing r/R for a given B/R. It is also found that the plane stress SCF K_p–σ nearly remains a constant when r/R < 0.98, but is strongly sensitive to r/R and increases by 30% with r/R changing from 0.98 to 1. On the other hand, the friction coefficient, Young's modulus and the load level have also influences on stress concentrations, which should not be neglected in design of structures. An empirical formula of the maximum SCF is obtained for convenience of engineering applications.     

单向拉伸条件下补片参数对复合材料胶接修复结构的影响

建立含中心半穿透圆孔的损伤金属板修补结构的三维有限元模型,以应力集中系数(Stress Concentration Factor,SCF)和挠度w作为复合材料胶接修复效果的指标,分析单向拉伸条件下,正方形补片的长度、厚度和铺层方式对修复效果的影响。结果表明:补片长度取孔直径的3.5倍、厚度取孔深度的0.6~0.8倍、铺层方式取0°/90°铺层时,复合材料单面修复含损伤裂纹板的效果较好。根据分析结果制备了实验件,进行了单向静拉伸实验,修补实验件的破坏强度比未修补实验件提高了10.1%。     

含椭圆型孔洞有限大电致伸缩材料板的二维问题

基于电致伸缩材料的基本方程, 该文采用Faber级数方法研究了含有椭圆型孔洞的有限大电致伸缩材料板在受到电载荷作用下的二维问题。采用各向同性体平面理论中的复势方法, 以Faber级数、保角映射及最小二乘边界配置技术为工具, 提出了含有单个椭圆孔的有限大电致伸缩材料板在电载荷作用下的级数解, 详细讨论了板的尺寸、孔洞的尺寸、孔洞的分布以及洞内的电场对于孔边应力的影响规律。最后通过几组数值算例, 讨论了各种参数的变化对孔周应力集中的影响, 并就特殊情况与文献中的一些结果进行了比较, 结果表明最小二乘边界配置法具有精度高、收敛速度快等优点。     

THE EFFECT OF MISALIGNMENT ON THE FATIGUE STRENGTH OF WELDED CRUCIFORM JOINTS

Abstract— The effect of axial misalignment on the fatigue strength of load-carrying transverse cruciform welded joints was investigated using experimental and fracture mechanics methods. Where failure occurred by cracking from the weld toe, misalignment significantly reduced the fatigue strength. The reduction could be predicted using a nominal stress concentration factor (SCF). Misalignment had less effect where failure was due to cracking through the weld metal; an expression was deduced for the SCF in this case. For fracture mechanics assessments, an expression for an effective stress intensity factor using the SCF and stress intensity factors for aligned welds was shown to agree with the finite element (FE) results. Predictions of the effect of misalignment using the FE results agreed with experimental data. Misaligned transverse load-carrying cruciform joints should be assessed for fatigue failure from the toe using the same SCF as for a butt weld with the same misalignment. For failure through the throat, an alternative expression for the SCF is recommended. Fracture mechanics assessments of misaligned joints should be carried out using an effective stress intensity factor derived from the SCF and stress intensity factors for aligned joints. These recommendations are now incorporated in British Standard PD 6493:1991.     

开口层板孔口缝合补强的有限元研究

为了研究复合材料开口缝合补强结构的不同缝合参数(针距、行距、边距、缝合线模量等)对孔边应力、应变分布的影响, 提出了一种缝合线计算模型。通过有限元模拟计算, 并结合实验结果, 分析讨论了孔边及邻近区域应力、应变的分布规律, 给出了孔口缝合参数合理的设计方法及相关结论。研究表明, 不同缝合参数对于孔边附近应力及应变集中有明显的影响。     

不同孔口形状对含孔复合材料板孔边应力状态影响的研究

对复合材料结构而言,孔口边界条件的建立和处理比金属材料要复杂得多。针对含不同孔形的复合材料板,根据非均质各向异性弹性理论和复变函数理论,通过保角映射方法建立精确的边界条件,解决了某些复杂孔形的边值问题。得到了含圆、矩形和六边形孔复合材料板孔边应力的解析解。并针对不同孔形在受外荷载作用的情况下的应力状态,以及它们对孔边应力集中系数的影响进行了探讨。     

Revisit of two classical elasticity problems by using the Trefftz method

In this paper, the two classical elasticity cases, Lamé problem and stress concentration factor (SCF), are revisited by using the Trefftz method instead of the inverse or semi-inverse approach in the previous study. First, the Timoshenko and Goodier's approach is reviewed. Based on the superposition principle and the concept of taking free body, the problem of stress concentration factor as well as Lamé problem can be solved without any difficulty in a direct way using the Trefftz method.     

Fictitious notch rounding concept applied to V-notches with end holes under mode 3 loading

The present technical note is aimed to provide a closed form expression for the microstructural support factor and for the fictitious notch radius in plates weakened by V-notches with root end-holes. Taking advantage of some recent closed form expressions for the stress distributions due to V-notches with end holes the fictitious notch rounding approach is applied here to mode 3 loading. The factor s for the V-notch with end holes is found to be strongly influenced by the opening angle and the new values are compared with the previous solution available in the literature and dealing with blunt V-notches. To validate the new expressions a comparison is carried out between the theoretical stress concentration factor (SCF) obtained from a rounded V-notch with a fictitiously enlarged end hole (of radius ρ_f) and the effective stress concentration factor obtained by integrating the relevant stress over the microstructural characteristic length (MCL), ρ^*, in a pointed V-notch. A sound agreement is found from the comparison. The range of validity of the present equations are limited to linear elasticity or in those cases where the plastic zone is very small with respect to the MCL of the material.     

Design procedure for reducing the stress concentration around circular holes in laminated composites

The stress concentration around a hole in a laminated composite may be decreased by increasing the thickness (bonding of two-dimensional panels) in this area. The problem may be described as an infinite orthotropic membrane with a finite circular orthotropic inclusion (ring) and a circular hole in the middle of the ring under arbitrary in-plane loading. A method for calculation of the stress concentration at the edge of the hole is presented. The method is based on the analytical solution for the case of an infinite inclusion. The finite dimensions of the inclusion are taken into account by means of a correction coefficient which is established empirically by processing a large amount of finite element results.     

Time-domain fatigue assessment of ship side-shell structures

Loads acting on ship side-shell structures are complex and vary randomly over time. The current study proposes a direct calculation procedure for the fatigue assessment of ship side-shell structures. The calculation procedure is characterised by nonlinear time-domain hydrodynamic simulations followed by finite element (FE) analyses. Sensitivity and feasibility analyses of the proposed time-domain procedure were carried out, and the calculated fatigue damages were compared with full-scale measurements made on a container vessel. Fatigue life analyses were carried out by both the spectral method and the time-domain approach. In addition, two approaches for local stress analysis are presented and discussed: an engineering-based definition of the stress concentration factor (SCF) and a proposed local stress factor (LSF) that utilises stress ranges extracted from the stress history. The results from the fatigue analysis using the LSF indicated a shorter fatigue life than the results obtained using the SCF. This difference is observed because the LSF accounts for the effects of wave-induced loads under ship operation conditions in a more realistic manner.     

Visco-elastoplastic stress concentration in a strip with a circular hole

The visco-elastoplastic stress concentration in a strip with a circular hole has been investigated for various rates of increase of stress by means of the photo-rheological method, using specimens of celluloid at 65C. The stress concentration factors at the stress raiser are considerably influenced by the stress rate. Such an effect cannot be analysed by ordinary photoplasticity in which the time effect is not taken into account.     

Numerical experiments on the determination of stress concentration factors

A brief discussion of relevant applications of the finite element method is presented, and two cases of relatively high stress concentration are considered. For a slot with semi–circular ends in a plate subjected to uniaxial stress, the stress concentration factors obtained numerically, by use of the finite element method, are compared with corresponding experimental results. The case of a corrugated hole in a plate under 1:1 biaxial stress is also examined, and stress concentration factors determined using the finite element approach are compared with exact values obtained by application of Muskhelishvili's method.     

K节点应力集中系数的试验和数值研究方法

工程中常用的评价海洋平台中管节点疲劳寿命的方法是使用S-N曲线。当管节点承受疲劳载荷作用的时候,可以通过数值或者试验方法得到沿着焊缝处的热点应力幅的大小。然后通过S-N曲线,可以预测此节点在破坏前可以承受疲劳载荷的循环次数。应力幅的大小可以由应力集中系数这个参数来确定。对K型节点在承受基本载荷作用下的应力集中系数进行了数值和试验分析,得到了各种基本载荷作用下K节点沿着焊缝处应力分布情况和极值应力点的位置。     

Investigation into stress transfer characteristics in alumina-fibre/epoxy model composites through the use of fluorescence spectroscopy

In composite materials, fibre/fibre interaction phenomena due to fibre failure are crucial in determining the composite fracture behaviour. Indeed, the redistribution of stress from a failed fibre to its intact neighbours, and stress concentration induced in the neighbouring fibres, determine the extent to which a break in one fibre will cause more breaks in others. In this paper, we have used fluorescence spectroscopy to study the stress transfer and redistribution induced by fibre fracture in two-dimensional Nextel-610 fibres/epoxy-resin micro-composites. The stress along the fibres was mapped at different load levels, and specimens with different inter-fibre distance were used to study the fibre content effect. The interfacial shear stress distribution along broken and intact fibres was derived by means of a balance of shear-to-axial forces argument. The experimental stress concentration factors (SCF) were smaller than values predicted from our model based on the cell assembly approach. As expected the 2D configuration allows access to the upper bound of the SCF in real composites. For the several specimens tested, a region of matrix yielding was observed behind the fibre fracture and no-debonding at the interface was detected. The measured SCF values agree well with those reported in recent study for carbon-fibre/epoxy model composites.     

Prediction of stress concentration factor of corrosion pits on buried pipes by least squares support vector machine

Concentrated working stress of a corrosion pit is known to be an important factor inducing the deterioration and consequently the breakage of a buried pipe. In this paper, we investigate the stress concentration factors (SCFs) of isolated elliptical corrosion pits using 3-D finite element analyses. The elliptical pits are fully characterized by their 3-D geometries, i.e., major and minor diameters and pit depth via a series of parametric studies of finite element pipe models. This is to quantify the effect of geometric variations of the pits on SCF. Realizing the fact that the 3-D finite element analysis is computationally intensive, efficient statistically predictive models have been developed based on least squares support vector machine (LS-SVM) realized in a ubiquitous spreadsheet platform. This approach shows very close predictions of SCF to the numerical findings for elliptical corrosion patterns on buried pipes. Particularly, two typical kernel functions have been adopted to cross validate the excellent performance of the LS-SVM method in SCF prediction of corroded pipes.     

A practical stress analysis for predicting fatigue limit of metal with axisymmetric complex surface

In order to predict the fatigue limit of a specimen with an axisymmetric complex surface, a practical method to estimate a stress concentration factor (SCF) of its surface was proposed. The roughness is coarse-grained by removing high frequency components and approximated with a parallel row of a local notch and innumerable average notches. Then, the notches are each approximated with the elliptical holes in the infinite plate, and the SCF is calculated approximately by superposing the elastic solutions of the holes. Moreover, FEM analyses were carried out on the various notch models which consist of the local notch and innumerable average notches to examine the application limit of the present method. Then, the validity of the application limit was examined by using the real roughness and the infinite parallel row of the various notches, and it was shown that the present method was available for the real roughness.     

螺栓夹持填充孔复合材料层压板层间应力分析

为了研究含螺栓复合材料层压板连接接头的层间应力分布规律,提出了采用填充孔形式和虚拟界面层方法求解层间应力,并建立了三维有限元模型对受面内压缩载荷的螺栓夹持填充孔层压板进行分析。结果表明:层压板层间应力集中不仅发生在孔边,还会在螺栓头边缘附近出现,且夹持力越大螺栓头边缘附近的层间应力集中越严重;合理的螺栓夹持力能改善孔边应力状态,提高孔边抵抗分层的能力,但无法改善螺栓头边缘附近的层间剪切应力集中状态。因此,在进行含螺栓夹持的层压板机械连接结构孔边层间强度设计时,也要考虑螺栓头边缘的层间剪切应力集中问题,以提高复合材料结构的安全性。     

Weld toe stress concentrations in multi-planar stiffened tubular KK joints

This paper reports a parametric stress analysis of various configurations of rack plate stiffened multi-planar welded KK joints using the finite element method. The KK joint finds application in the leg structure of offshore oil and gas jack-up platforms. The rack plate works as a stiffener which reduces the stress concentration at the brace/chord intersection. This could be an immense contribution to the increase in fatigue life of the joint, but other hot spot sites are introduced into the joint. The rack is also used for raising and lowering of the jack-up hull which gives the jack-up platform its jacking capability. Over 120 models using a combination of shell and solid elements have been built and analysed with ABAQUS. Non-dimensional joint geometric parameters (β, γ and Ω) are employed in the study, with the new parameter Ω being defined as the ratio of rack thickness to chord diameter. Stress concentration factors (SCFs) are calculated under applied axial and OPB (out-of-plane bending) loading. Three critical SCF locations are identified for each load case, with each location becoming the most critical based on the combination of the non-dimensional parameters selected for the joint. This is important as careful design can shift the critical SCF from an area inaccessible to NDT to one that can be easily inspected. The SCF values extracted from the models are used to derive six parametric equations through multiple regression analysis performed using MINITAB. The equations describe the SCF at the different locations as a function of the non-dimensional ratios. The equations not only allow the rapid optimisation of multi-planar joints but also can be used to quickly identify the location of maximum stress concentration and hence the likely position of fatigue cracks. This in itself is an invaluable tool for planning NDT procedures and schedules.     

Finite element method for orthotropic micropolar elasticity

The total potential energy for a body composed of an anisotropic micropolar linear elastic material is developed and used to formulate a displacement type finite element method of analysis. As an example of this formulation triangular plane stress (and plane couple stress) elements are used to analyze several problems. The program is verified by computing the stress concentration around a hole in an isotropic micropolar material for which an exact analytical solution exists. Several anisotropic material cases are presented which demonstrate the dependence of the stress concentration factor on the micropolar material parameters.