A Numerical Investigation of an Abnormal Phenomenon of Stress Intensity Factor(SIF)in a Cracked T-Butt Joint Accounting for Welding Effect

Industry design standards such as BS 7910 deployed some empirical formulas for the prediction of stress intensity factor(SIF) based on simulation results from traditional finite element method(FEM).However,such FEM simulation occasionally failed to convince people due to the large discrepancies compared with engineering practice.As a consequence,inaccuracy predictions via such formulas in engineering standards inevitably occur,which will compromise the safety of structures.In our previous research work,an abnormal phenomenon of SIF in a cracked T-butt joint accounting for welding effect has been observed.Compared with BS 7910,the calculation results of SIF at the surface points of welded specimens cannot be well predicted,with a large discrepancy appearing.In order to explore such problem with an abnormal increase at the surface points of cracked welded specimens,a numerical investigation in terms of SIF among BS 7910,XFEM,and FEM is performed in this paper.Numerical models on both a simple cracked plate without welding effect and a cracked T-butt joint with welding effect are developed through ABAQUS.Parametric studies in terms of the effects of varied crack depth to thickness ratio(a/T) and the effects of crack depth to crack half-length ratio(a/c) are carried out.Empirical solutions from BS 7910 are used for comparison.It is found that the XFEM can provide predictions of SIF at both the crack deepest point and crack surface point of a simple cracked plate as accurate as FEM.For a T-butt joint with a transverse stiffener,a large discrepancy in terms of the weld magnification factors(Mk) occurs at the crack surface point compared with empirical predictions.An exceptional increase of von Mises stress gradient in regions close to the weld-toe is found through the simulation of FEM,whereas a constant stress gradient is obtained through XFEM.The comparison results indicate an inappropriate prediction of SIF by the utilization of the empirical formulas in BS 7910.A more reasonable prediction of the SIF at the surface point of a crack is obtained by the XFEM.Therefore,further updating of the empirical solutions in BS7910 for SIF accounting for welding effect is recommended.

Enhancing Stress Intensity Factor Reduction in Cracks Originating from a Circular Hole in a Rectangular Plate under Uniaxial Stress through Piezoelectric Actuation

Circular holes are commonly employed in engineering designs;however, they often serve as locations where cracks initiate and propagate. This paper explores a novel approach to structural repair by utilizing piezoelectric actuators. The primary focus of this study is to investigate the influence of an adhesively bonded piezoelectric actuator patch placed above a circular hole on the stress intensity factor (SIF) in an aluminium plate. The plate is subjected to uniaxial tensile stress, while the piezoelectric actuator is excited with varying voltage levels. The analysis is conducted using the finite element method (FEM), a powerful numerical technique for simulating complex structures. The study assesses the stress distribution and employs the SIF as an adequate criterion for evaluating the impact of different patch configurations. The results indicate a strong correlation between the applied voltage and the SIF. Whether the SIF increases or decreases depends on the polarization of the piezoelectric actuator. Particularly noteworthy is the finding that rectangular patches in a horizontal orientation significantly reduce the SIF compared to other patch geometries. Moreover, double-sided patches exhibit a pronounced decrease in the SIF compared to single-sided patches. In summary, this research underscores the potential of piezoelectric actuators in mitigating stress intensity in structures with circular hole with crack initiation. It offers valuable insights into the influence of applied voltage, patch geometry, and patch placement on the SIF, thereby contributing to developing effective strategies for enhancing structural integrity.

An analytical solution for the stress field and stress intensity factor in an infinite plane containing an elliptical hole with two unequal aligned cracks

The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.

Evaluation of mixed-mode stress intensity factors by extended finite element method

Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationallv efficient.

Comprehensive investigation of stress intensity factors in rotating disks containing three-dimensional semi-elliptical cracks

Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working con- ditions is an essential issue. In this paper, a comprehensive study of stress intensity factors （SIFs） in rotating disks containing three-dimensional （3D） semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical prop- erties, rotational velocity, and orientation of cracks on SIFs in rotating disks under cen- trifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as mechanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature.

Closed form solution of stress intensity factors for cracks emanating from surface semi-spherical cavity in finite body with energy release rate method

In this paper, a new semi-analytical and semi-engineering method of the closed form solution of stress intensity factors （SIFs） of cracks emanating from a surface semi-spherical cavity in a finite body is derived using the energy release rate theory. A mode of crack opening displacements of a normal slice is established, and the normal slice relevant functions are introduced. The proposed method is both effective and accurate for the problem of three-dimensional cracks emanating from a surface cavity. A series of useful results of SIFs are obtained.

Digital Image Correlation Using Specific Shape Function for Stress Intensity Factor Measurement

The stress intensity factor (SIF) is a critical parameter associated with the fracture behaviour of materials. In this paper, we select the displacement function around a crack tip as the shape function of the digital image correlation (DIC), which makes it possible to directly calculate the SIF by the correlation scheme. Moreover, we use a non-rectangular subset, which can reduce the influence of plastic deformation and crack width on the DIC measurement accuracy. We measured the SIF of a mode I crack in a super-hard aluminium alloy specimen to verify the performance of the proposed method. Our experimental results show that a DIC with a specific shape function can be used to accurately and efficiently calculate the SIF. Furthermore, we also present a practical application of our proposed method for determining the SIF, crack propagation angle and crack tip displacement. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.

Stress and Fracture Strength Analysis for Three-Way Pipes

Three-way pipes, T and Y pipes, are very important connecting components in pipeline systems, their strength are related to the safety of pipelines. In the case that crack is not detected in the three-way pipe, ANSYS finite element program version 5.6 is applied to study the stress distribution of the three-way pipe and to obtain the optimum fillet radius in the crotch region of the two pipes. The reasonable intersection angle of the two pipes is also obtained. In the case that a surface crack is detected in the three-way pipe, the maximum stress intensity factor (SIF) near the front of the surface crack is studied.

Theoretical and numerical studies of crack initiation and propagation in rock masses under freezing pressure and far-field stress

Water-bearing rocks exposed to freezing temperature can be subjected to freezeethaw cycles leading tocrack initiation and propagation, which are the main causes of frost damage to rocks. Based on theGriffith theory of brittle fracture mechanics, the crack initiation criterion, propagation direction, andcrack length under freezing pressure and far-field stress are analyzed. Furthermore, a calculation methodis proposed for the stress intensity factor （SIF） of the crack tip under non-uniformly distributed freezingpressure. The formulae for the crack/fracture propagation direction and length of the wing crack underfreezing pressure are obtained, and the mechanism for coalescence of adjacent cracks is investigated.In addition, the necessary conditions for different coalescence modes of cracks are studied. Using thetopology theory, a new algorithm for frost crack propagation is proposed, which has the capability todefine the crack growth path and identify and update the cracked elements. A model that incorporatesmultiple cracks is built by ANSYS and then imported into FLAC3D. The SIFs are then calculated using aFISH procedure, and the growth path of the freezing cracks after several calculation steps is demonstratedusing the new algorithm. The proposed method can be applied to rocks containing fillings such asdetritus and slurry. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

圆杆和螺纹及板表面裂纹的扩展形态与SIF实验解分析

在对圆杆、圆杆表面多环形槽和螺纹根部表面裂纹应力强度因子(SIF)进行了实验研究的基础上,分析了3种SIF实验解相互间的差异和共性,在3种试件中,表面裂纹SIF值无论在裂纹最深点还是表面点,均以螺纹联接时最高,圆杆表面多环形槽次之,圆杆的值为最低,同时,还讨论了在以上3种情况下其表面裂纹前缘的扩展形态,并相现有的平面板在拉伸、弯曲疲劳载荷作用下,其表面裂纹的扩展前缘进行了比较,指出:它们虽然都是椭圆曲线的一部分,有相同的裂纹形状比a/C随裂纹深度比a/R增大而减小的变化规律,但圆杆与拉抻板的断口形态接近,而圆杆表面多环形槽和螺纹根部的断口形态则处于板的拉伸与弯曲之间。

缺口悬臂梁振动疲劳裂纹扩展行为研究

航空飞行器在服役过程中会经受大量复杂的随机振动载荷,其结构易发生振动疲劳进而导致损伤甚至失效,造成严重损失。以铝合金悬臂梁结构件为对象,开展振动疲劳试验与理论分析,研究随机振动载荷下含裂纹梁的应力强度因子求解方法,提出一种基于Hudson理论的时域法,结合经典的Paris公式估算振动疲劳裂纹扩展寿命。结果表明:本文提出的基于Hudson理论的时域法的寿命预测结果优于试验对比估算结果,验证了该方法能够有效描述随机振动裂纹扩展行为。

V形斜缺口薄板结构应力场评估方法研究

文中对含有复杂V形倾斜角的薄板结构应力场进行了理论分析和数值研究.通过建立奇异强度因子as与缺口应力强度因子N-SIF的关系,获得无量纲的N-SIF,在此基础上建立一系列不同几何尺寸、张开角与倾斜角下的有限板宽的斜裂纹切口薄板模型,对切口的应力场进行简化与拟合.通过控制变量法得到奇异强度因子与无量纲N-SIF的关系曲线,拟合得到简易的V形倾斜角的薄板结构应力场和N-SIF评估公式.将拟合出的N-SIF简化计算公式和有限元计算结果与传统文献计算结果进行对比与误差分析.结果表明:拟合出的应力场公式精度较高,可实现复杂倾斜角下V形切口应力场的快速评估.

基于比例边界有限元法计算应力强度因子的不确定量化分析

应力强度因子是预测荷载作用下结构中裂纹产生和扩展的重要参数。半解析的比例边界有限元法结合了有限元和边界元法的优势,在裂纹尖端或存在奇异应力的区域不需要局部网格细化,可以直接提取应力强度因子。在比例边界有限元法计算应力强度因子的框架下,引入随机参数进行蒙特卡罗模拟(Monte Carlo simulation, MCS),并提出一种新颖的基于MCS的不确定量化分析。与直接的MCS不同,采用奇异值分解构造低阶的子空间,降低系统的自由度,并使用径向基函数对子空间进行近似,通过子空间的线性组合获得新的结构响应,实现基于MCS的快速不确定量化分析。考虑不同荷载状况下,结构形状参数和材料属性参数对应力强度因子的影响,使用改进的MCS计算应力强度因子的统计特征,量化不确定参数对结构的影响。最后通过若干算例验证了该算法的准确性和有效性。

T型接头焊趾表面裂纹应力强度因子的简化计算方法

T型接头是船舶与海洋结构物的典型结构形式之一,其焊趾处常常是疲劳热点区域。T型接头焊趾表面裂纹的应力强度因子是船舶与海洋结构的、基于断裂力学安全评定和疲劳寿命预测的基础。本文对T型接头表面裂纹应力强度因子的计算方法,尤其是Bow ness等人提出的T型接头焊趾表面裂纹应力强度因子的计算公式进行了分析,在此基础上导出了形式简单,物理意义明确的T型接头焊趾表面裂纹应力强度因子的简化计算公式,并和相关的应力强度因子的计算结果进行了比较,证明了本文简化方法的可行性。

不锈钢在扭转／拉伸复合载荷下近门槛值的疲劳裂纹扩展行为

研究了带环状预裂纹的奥氏体不锈钢圆棒试样在循环扭转／拉伸复合载荷下,门槛值附近的疲劳裂纹扩展行为,分析了复合加载时不同载荷比对裂纹扩展的影响,对裂纹扩展的初始阶段进行了详细研究,用应力强度因子表征了裂纹扩展开始的门槛值,提出了椭圆方程表达的疲劳裂纹扩展开始的门槛值模型,该方程可在裂纹尖端位移准则的基础上导出,疲劳裂纹扩展停止的门槛值条件也可用椭圆方程表达。

初始压应力场对爆生裂纹行为演化效应的实验研究

采用自主设计的动静组合加载系统,实现了在模型试件中产生静态应力场和爆炸动应力场,并对动静组合应力场中爆生裂纹的扩展行为演化特征进行焦散线实验研究,探讨初始应力场对爆生裂纹扩展规律的影响效应。通过对四周施加均布载荷和不施加载荷的两组试件进行实验,对比分析两组试件中爆生裂纹的扩展长度、速度和裂纹尖端动态应力强度因子随时间的变化规律,发现在垂直于裂纹扩展方向的压应力降低了裂纹尖端的应力集中程度,阻碍了裂纹的扩展,而平行于裂纹扩展方向的压应力对裂纹的扩展基本没有影响。

双向受载裂纹板的碳纤维复合材料补片的胶接修补分析

建立了碳纤维复合材料补片胶接修补双向受载裂纹板的3D有限元模型,分析了补片的单面胶接修补效果,探讨了补片材料、铺层顺序、补片长度及载荷比等对裂纹应力强度因子的影响规律。结果表明:复合材料补片的存在使裂纹板垂直裂纹方向载荷和平行裂纹板方向载荷发生耦合作用,从而影响补片修补效果。平行裂纹方向的压应力可降低裂纹尖端的应力集中因子,而拉应力可提高裂纹尖端的应力集中因子。

围压对巴西裂纹圆盘应力强度因子影响分析

为了研究围压对巴西裂纹圆盘应力强度因子的影响,使用权函数方法得到了围压作用下巴西裂纹圆盘的应力强度因子,进而得到径向集中荷载与围压共同作用下的应力强度因子的计算公式。在此基础上,从理论上分析了围压对巴西裂纹圆盘应力强度因子的影响,分析结果表明:围压对II型应力强度因子无影响,纯围压作用下裂纹趋于闭合;围压和集中力共同作用下,I型应力强度因子随着围压的增大而减小。对比分析了数值分析与理论结果,分析表明,理论与数值结果吻合良好,从而表明了理论分析的正确性。此外,还研究了围压对纯II型裂纹加载条件的影响,结果表明,纯II型裂纹的临界加载角随着围压增大而减小,直至为0。因此,当围压较大时,加载角为0°左右所发生的断裂不一定全是纯I型断裂。

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。

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。