Stress Intensity Factors of a circumferential surface crack at the outside of a thermally loaded pipe

Stress intensity factors were calculated for partly circumferential surface cracks at the outside of a pipe. The pipe is loaded by internal pressure and by thermal stresses. The weight functions method is used to calculate averaged weighted stress intensity factors at the deepest point and at the surface points of the crack. The evaluation of temperatures and stresses in the pipe and the application of the weight functions method are described. Numerical results are given for an application to steam generator tubes.     

Stress intensity factors for long axial surface cracks at the outer wall of a pipe loaded by stress gradients

By means of the finite element method crack opening displacements were calculated for long axial surface cracks at the outer wall of a pipe. The wall thickness to inner radius ratio of the pipe was 1 to 10. Following a procedure introduced be Mattheck et al. weight functions were evaluated by means of the finite element results. Using these weight functions it is possible to calculate stress intensity factors for arbitrary radially varying stress distributions. In this paper stress intensity factors were evaluated for a constant hoop stress loading as well as for stress distributions with a linear and a quadratic dependence on the radius.     

Stress Intensity Factors for slender surface cracks

A calculation procedure for plates with semi-elliptical surface cracks under tension and bending with aspect ratios of a/c ≤ 0.2 and arbitrary relative crack depths a/t is presented. For the computation an improved line spring model is used. K₁-values are calculated along the crack contour. For the deepest point of a surface crack the K₁-values are terminated by two well known threshold curves: The upper bound curve is identical with the solution for the edge crack (a/c = 0). The lower bound is described by the results after Newman and Raju for a/c = 0.2. The present K₁-values are in good agreement with both curves. For high a/t-ratios the maximum K₁-value is found between the deepest and the surface edge point (Q′ and Q″) of the crack. This result could explain among others that crack growth does not conserve the semi-elliptical shape sometimes.     

Stress intensity factors for circumferential semielliptical surface cracks in a pipe under thermal loading

Stress intensity factors are calculated at the deepest point and at the surface points of circumferential semielliptical surface cracks in a thermally shocked pipe. The method of calculation is based on weight functions following a proposal by Munz et al. Numerical values of the stress intensity factors are given for a wide range of crack depths and crack lengths considering a pipe with a wall thickness to inner radius ratio of $\text{1}\text{10}$.     

Calculation of Stress Intensity Factors for axial semi-elliptical surface cracks in a pipe with cladding loaded thermally

By means of the weight functions method stress intensity factors were calculated for axial semi-elliptical surface cracks in a pipe with cladding. The component is loaded by a thermoshock. Starting from a stress-free state the inner surface of the cladding is suddenly cooled down. The time-dependent temperature and hoop stress distributions of the uncracked component were calculated for the loading case considered. Numerical values of the stress intensity factors at the deepest point and at the surface points of the crack were evaluated at different time steps for a wide range of crack depths and crack lengths.     

Calculation of Stress Intensity Factors for semi-elliptical surface cracks in a turbine rotor

Stress intensity factors based on linear elastic behaviour were calculated for semi-elliptical surface cracks in the front face of a cylindrical disk. The small semi-axis of the cracks coincides with the axis of rotation of the disk. The disk represents a part of a turbine rotor and is used to simplify the calculations. The uncracked rotor is loaded by a radial varying hoop stress distribution, caused by rotation, thermal gradients and the influence of the turbine blades. Following a procedure proposed by Mattheck at al. [1] the stress points of the cracks were calculated by means of the weight functions method.     

Assessment of partly circumferential cracks in pipes

This paper presents a new method for predicting the stress intensity factors around a partly circumferential elliptical surface crack in a pipe. The solution is applicable to structures with both double and single curvature. The technique involves a conformal transform in conjunction with a semi-analytical approach that uses a finite element model to obtain the stress distribution in the undamaged structure. By using an indirect methodology, the model development is simplified and the analysis time is minimised. As such a coarse mesh can be used to obtain solutions for multiple crack geometries. Three examples are presented to verify this methodology. They include a partly circumferential elliptical crack under uniform tension, a pipe subject to a residual stress field, and a problem involving double curvature. For simple loading the solution compares with other published solutions to within 5% for an external crack, and to within 15% for an internal crack. For more complex loading conditions the majority of the solutions were within 5% of other published results at the deepest point, and most solutions at the surface agreed to within 15%. For the problem involving double curvature, the solutions agreed to within 4% for an internal crack, and 15% for an external crack.     

Stress intensity factors for a wide range of long-deep semi-elliptical surface cracks, partly through-wall cracks and fully through-wall cracks in tubular members

To calculate the rate of fatigue crack growth in tubular members, one approach is to make use of the fracture mechanics based Paris law. Stress intensity factors (SIF) of the cracked tubular members are prerequisite for such calculations. In this paper, stress intensity factors for circumferential deep semi-elliptical surface crack (a/t > 0.8), semi-elliptical partly through-wall crack and fully through-wall crack cracks in tubular members subjected to axial tension are presented. The work has produced a comprehensive set of equations for stress intensity factors as a function of a/T, c/πR and R/T for deep surface cracks. For the partly through-wall cracks and fully through-wall cracks, two sets of bounding stress intensity factor equations were produced based on which all stress intensity factors within the range of parameters can be obtained by interpolation.     

Stress intensity factors for surface cracks at countersunk holes

Fatigue crack growth from countersunk fastener holes loaded in remote tensile loading was studied using the transparent polymer PMMA. A single edge corner crack at the bottom of the plate and a single internal surface crack at the sharp intersection between the bore and the countersink were induced in the PMMA specimens by pre-cracking. The specimens were then fatigue tested under constant amplitude remote tensile loading and the ‘back-calculation’ method was used to determine stress intensity factors at several crack front locations. When variations in fatigue crack closure were taken into account, the experimental stress intensity factors agreed well with the computational results at selected crack fronts.     

Stress Intensity Factors at the Intersection of a Crack and Pore Channels with Various Cross-Sections

Changes of stress intensity factors (SIF) of a flat main crack with rectilinear front which cuts the system of regular parallel pore channels normally to their direction are determined. Channels had cross-sections in the form of a circle, an equilateral triangle, a triangle with the concave sides of constant curvature and a starlike crack. It is shown that SIF on the main and channel cracks may have comparable values.     

Limit pressures of 90° elbows with circumferential surface cracks

This paper provides approximate limit pressure solutions for circumferential cracked elbows, resulting from small strain finite element limit analyses using elastic-perfectly plastic materials. Circumferential through-wall and constant-depth surface cracks of which the circumferential lengths are limited to 50% of the circumference are considered. Two locations along the longitudinal direction are considered; one in the centre of the elbow, and the other in the junction between the elbow and the attached straight pipe. Along the circumference, either extrados or intrados cracks are considered. It is found that limit pressures of circumferential cracked elbows are not affected by the presence of the circumferential surface crack, unless it is sufficiently deep and long. Moreover, normalized limit pressures with respect to un-cracked limit pressures decrease almost linearly with increasing the relative crack depth and length. Based on finite element results, approximate closed-form solutions for limit pressures are proposed.     

Leak-before-break analysis of a pipe containing circumferential defects

Assessment of aged offshore structures based on current and historical data is a critical issue for the life extension of offshore structures. The leak-before-break (LBB) concept was first developed and applied in the nuclear power industry to ensure the safety of the pressurized components in nuclear power plants. This concept can also be applied as a robust and cost effective tool for structural integrity management of offshore structures that are either partly submerged (jackets, semi-submersible, ships), or contain fluids (pipes, pressure vessels). The core idea of LBB consists of guaranteeing that enough time is available between the moment a crack breaks through the hull or wall, causing a detectable leakage, and the moment when the crack becomes unstable, causing a structural failure. This paper presents a case study of applying the LBB concept for a tether string that is part of the mooring system of an offshore structure. The tether string is a steel pipe containing circumferential defects. The critical through-thickness crack size was calculated with ductile tearing being taken into account. It has been found that the choice of failure criterion has a significant impact on the determination of the critical through-thickness crack size, which might have influence on the verification of leak-before-break. The effect of residual stress on leak-before-break has also been studied.     

Ductile fracture simulation of 304 stainless steel pipes with two circumferential surface cracks

In this paper, ductile fracture behaviours of 304 stainless steel pipes with two circumferential surface cracks under pure bending are simulated using finite element damage analyses. Simulations are based on the stress‐modified fracture strain model with the concept that the critical accumulated damage for progressive cracking is assumed to be dependent on an element size. The proposed method can predict not only maximum loads but also complex ductile fracture patterns observed in experiments.     

Experimental investigation of the outer wave field at the open end of a pipe

The results of investigating the external wave field radiated from the open end of a tube on the linear and nonlinear resonance intervals are presented. The presence of a velocity amplitude maximum in the wall zone near the open end is detected. The limits of vortex motion of the gas within the tube are determined. The flow core in the wave field is investigated.Translated from Inzhenerno-fizicheskie Zhurnal, Vol. 61, No. 5, pp. 714–716, November, 1991.     

Stress intensity factors for circumferential through‐wall cracks in thin‐walled cylindrical shells subjected to tension and torsion

In order to assess the structural integrity of tubular members or pipes containing circumferential through‐wall cracks, their stress intensity factor solutions are required. While stress intensity factors for tension and bending are available, few solutions exist for the case of torsion, even though these components may also be subjected to torque. In this paper, the finite element method is used to compute the stress intensity factors for this geometry under tension and torsion. Shell elements are employed to compute the results for thin shells by the means of the displacement extrapolation technique. The computed results indicate that the available analytical solution for torsional loading, which is based on shallow shell theory, is nonconservative for long cracks in thin shells. Shallow shell theory is in general not applicable to long cracks, and the present work is therefore able to provide solutions for a wider range of crack lengths than what is currently available.     

墙体表面的网状裂纹最大宽度测量

建筑物墙体裂纹是重要的安全隐患,检测混凝土墙体表面的裂纹及测量其最大宽度,已引起众多关注.现介绍基于图像处理的智能检测方法,即根据裂纹像素点分布特征,利用连通域面积大小来提取裂纹,并删除伪裂纹等杂质,再对含有分支或网状裂纹进行局部处理,根据裂纹特征像素点的位置关系获取聚类近似初始值,之后利用K-means聚类算法不断迭代计算裂纹特征像素点到其对应直线的最短距离,并以此将图像中的像素点归为不同方向的裂纹类.最后,利用分类好的裂纹像素点分别进行边缘检测与最大宽度测量并比较,来获取含有交叉裂纹的最大宽度值.本文获得的水平裂纹最大宽度的相对误差为2.968%,斜垂裂纹最大宽度的相对误差为5.188%.     

贯穿裂纹管局部柔度系数的理论与试验研究

根据线性断裂力学理论和应变能释放原理,推导了考虑裂纹张开状态的圆周贯穿裂纹管的附加局部柔度方程,利用自适应的Simpson数值积分方法计算裂纹引起的局部柔度系数,并根据得到的局部柔度系数,建立了以扭转弹簧模拟裂纹行为的裂纹管模型。进行了裂纹管的动力模型试验,通过裂纹管模型固有频率的试验值与理论值对比分析验证局部柔度系数的正确性。研究结果表明:裂纹管固有频率的试验值与使用"弹簧铰"裂纹管模型求得的理论值基本吻合,验证了贯穿裂纹管局部柔度系数的合理性。