Structural modelling and testing of failed high energy pipe runs: 2D and 3D pipe whip

The sudden rupture of a high energy piping system is a safety-related issue and has been the subject of extensive study and discussed in several industrial reports (e.g. [2], [3], [4]). The dynamic plastic response of the deforming pipe segment under the blow-down force of the escaping liquid is termed pipe whip. Because of the potential damage that such an event could cause, various geometric and kinematic features of this phenomenon have been modelled from the point of view of dynamic structural plasticity. After a comprehensive summary of the behaviour of in-plane deformation of pipe runs [9], [10] that deform in 2D in a plane, the more complicated case of 3D out-of-plane deformation is discussed. Both experimental studies and modelling using analytical and FE methods have been carried out and they show that, for a good estimate of the “hazard zone” when unconstrained pipe whip motion could occur, a large displacement analysis is essential. The classical, rigid plastic, small deflection analysis (e.g. see [2], [8]), is valid for estimating the initial failure mechanisms, however it is insufficient for describing the details and consequences of large deflection behaviour.     

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part I: analytical models

Leak-before-break (LBB) analyses for circumferentially cracked pipes are currently being conducted in the nuclear industry to justify elimination of pipe whip restraints and jet impingement shields which are present because of the expected dynamic effects from pipe rupture. The application of the LBB methodology requires calculation of leak rates. The leak rates depend on the crack-opening area of the through-wall crack in the pipe. In addition to LBB analyses which assume a hypothetical flaw size, there is also interest in the integrity of actual leaking cracks corresponding to current leakage detection requirements in NRC Regulatory Guide 1.45, or for assessing temporary repair of Class 2 and 3 pipes that have leaks, as are being evaluated in ASME Section XI. The objectives of this study were to review, evaluate, and refine current predictive models for performing crack-opening-area analyses of circumferentially cracked pipes. A three-phase effort was undertaken to accomplish this goal. It is described here in a series of three papers generated from this study. In this first paper (Part I — Analytical models), a comprehensive review is performed to determine the current state-of-the-art in predicting crack-opening displacements for circumferentially cracked pipes under pure bending, pure tension, and combined bending and tension loads. Henceforth, new and improved analytical models and some preliminary results are presented for cases where current methods are inadequate or there are no available methods. Also, based on this review, a number of appropriate predictive models are identified for a systematic evaluation of their accuracy. The results of their evaluations will be presented and examined in the forthcoming companion papers (Part II — Model validations [1] and Part III — Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) [2].     

核电站高中能管道断管影响探讨

在设计核电站时,须对安全壳内外的高能与中能管道进行发生假想性断管事件及其后续效应的设计分析。这些管道一旦发生破裂,泄漏的高能量流体将对管道施加很大的横向力,使管道产生高速运动,即管道甩动。这种高速运动的管道可能会对周围结构造成严重破坏,因而引起世界上各主要发展核电国家的重视,并开展了大量的研究工作。详细叙述常规岛侧高中能管道断管位置的判定准则、假想破口的类型、断管的后续影响及其防护等。还进一步介绍有关管道断裂甩动问题的各种计算方法,如力矩平衡法、能量平衡法、有限元法等。     

Application of plastic analysis to the pipe whip problem

The problem of design against pipe whip is briefly reviewed and some methods of calculation applicable to the problem are considered. Emphasis is given to two methods of analysis.The first makes use of the ‘FRUSTA’ programme; this method only considers the moment deflections so that it can only be regarded as a simplified approach leading to approximate results.As an alternative, a fully 3-D plastic element method is considered (the PAPS element), the basic hypotheses being briefly reviewed. Comparisons between the two approaches are provided. Finally, a model including restraint aspects is discussed which allows the consideration of V bars, plastic elements, dampers and friction type restraints.Typical examples are given and discussed.     

A practical application of an evaluation model for the restraint effect of pressure-induced bending on a plastic crack opening

This paper presents an evaluation model for the restraint effect of pressure-induced bending (PIB) on the opening of a circumferential through-wall crack (TWC) and a result of its application to the calculation of crack-opening displacement (COD) of postulated cracks for a practical leak-before-break (LBB) analysis. Three-dimensional finite element analyses with different crack lengths, restraint conditions, pipe geometries, magnitudes of internal pressure, and material tensile properties were used to investigate the influence of each parameter on the PIB restraint for the plastic COD. From these investigations, we proposed an evaluation model based on elastic–perfectly plastic behavior. Comparison with finite element analysis results demonstrated that the proposed model reliably estimated the PIB restraint effect on the plastic crack opening of a circumferential TWC and properly reflected the effect of each parameter within the range over which the analytical expression was derived. The model was then used to calculate restrained CODs of postulated cracks for a practical LBB analysis. When plastic crack behavior was considered, the PIB restraint effect was considerable for some LBB analysis cases of the primary piping systems in a typical nuclear power plant. This effect was estimated to be negligible by existing linear elastic-based models.     

Analysis of externally loaded bolted joints: Analytical,computational and experimental study

The behaviour of a simple single-bolted-joint under tensile separating loads is analysed using conventional analytical methods, a finite element approach and experimental techniques. The variation in bolt force with external load predicted by the finite element analysis conforms well to the experimental results. It is demonstrated that certain detailed features such as thread interaction do not need to be modelled to ensure useful results. Behaviour during the pre-loading phase of use agrees with previous long-standing studies. However, the pre-loading analysis does not carry over to the stage when external loading is applied, as is normally assumed and it is shown that the current, conventional analytical methods substantially over-predict the proportion of the external load carried by the bolt. The basic reason for this is shown to be related to the non-linear variation in contact conditions between the clamped members during the external loading stage.     

Moment resistance of steel pipes subjected to combined loads

The first part of this paper provides a review of recent investigations on steel pipes subjected to combined loads. Attention is given to studies involving both numerical and experimental components aimed at quantifying the modified moment resistance of pipes subjected to internal pressure and axial force. The comparison of experimental and finite element results indicate that the nonlinear shell finite element analysis is a reliable tool for predicting moment capacities of pipes. The second part of the paper reports two additional full-scale tests recently conducted at the University of Ottawa aimed at expanding the existing experimental database to pipes subjected to more complex load combinations involving twisting moment and shear (in addition to axial force, internal pressure, and bending). The finite element analysis for both tests is shown to provide excellent predictions of pipe moment capacity. The third part of the paper is a systematic parametric study based on the FEA model verified in previous and present investigations, aimed to assess the ability of pipe sections to attain their modified elastic and/or plastic moment resistance as predicted by analytically derived interaction equations. The parameters investigated are the applied torsion, internal pressure, axial force, and the diameter-to-thickness ratio of the pipe.     

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part II: model validations

This is the second paper in a series of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. This paper (Part II—Model Validations) focuses on the evaluation of current analytical models, discussed in the first paper (Part I—Analytical Models) as well as finite element models for conducting crack-opening-area analyses of pipes with circumferential through-wall cracks. The evaluation was performed by direct comparisons of the predicted results with the test data from full-scale pipe fracture experiments. The results from 25 full-scale pipe fracture experiments, conducted in the Degraded Piping Program, the International Piping Integrity Research Group Program and the Short Cracks in Piping and Piping Welds Program, were used to verify the analytical models. The main objective was the evaluation of engineering analysis procedures (estimation methods) as well as the ability of the finite element method to predict crack-opening displacements and shapes in pipes with circumferential through-wall cracks. Statistics were developed to quantify the accuracy of the current predictive models. A wide variety of pipe fracture tests involving cracks in base metals, weld metals and bimetallic weld metals were analyzed. Pipes containing both simple through-wall cracks and complex cracks were evaluated.     

Non-linear dynamic analysis of piping system using the pseudo force method

Simple piping systems are composed of linear elastic elements and can be analysed using conventional linear methods. The introduction of constraint springs, separated from the pipe with clearance gaps, to such systems to cope with the pipe whip or other extreme excitation conditions introduces non-linearities to the system, such non-linearities being associated with the gaps. Since these spring-damper constraints are usually limited in number, discretely located and produce only weak non-linearities, the analysis of linear systems including these non-linearities can be carried out by using modified linear methods. In particular, the application of pseudo force methods, wherein the non-linearities are treated as displacement-dependent forcing functions acting on the linear system, was investigated.The non-linearities induced by the constraints are taken into account as generalised pseudo forces on the right-hand side of the governing dynamic equilibrium equations. Then an existing linear elastic finite element piping code, EPIPE, was modified to permit application of the procedure. This option was inserted such that the analysis could be performed using either the direct integration method or via a modal superposition method, the Newmark-Beta integration procedure being employed in both methods. The modified code was proof tested against several problems taken from the literature or developed with the non-linear dynamics code, OSCIL. The problems included a simple pipe loop, a cantilever beam and a lumped mass system subjected to pulsed and periodic forcing functions. The problems were selected to gauge the overall accuracy of the method and to ensure that it properly predicted the jump phenomena associated with non-linear systems.Implementation of the method was found to be straightforward with the simplest iteration procedure for the pseudo force vector sufficing. The results predicted with the method agreed in all important aspects with existing solutions as well as those generated with other methods. As with linear analyses, the modal superposition solution mode was found to be the most efficient; however, exhibiting slightly greater inaccuracies.     

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part III: off-center cracks,restraint of bending,thickness transition and weld residual stresses

This is the third of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. The first two papers1, 2[Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part I—Analytical models. International Journal of Pressure Vessels and Piping, (this issue). Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part II—Model validations. International Journal of Pressure Vessels and Piping, (this issue).] dealt with crack-opening-area analysis of pipes assuming simple loading, pipe and crack geometries, and boundary conditions. This paper (Part III—Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) examines several practical aspects of crack-opening-area analysis involving off-center cracks, restraint of pressure-induced bending, girth-weld nozzle cracks at thickness transition, and weld-induced residual stresses. Currently, there are no engineering methods or guidelines available to analyze pipes under these conditions. Both linear-elastic and elastic–plastic finite element analyses were conducted to determine quantitatively their effects on various crack-opening characteristics. From the results of these analyses, recommendations are made on how an off-center crack can be analyzed based on fracture-mechanics equations for a centered crack. It was found when the restraint of bending effects become important and how they should be taken into account. Cracks located in the thickness transition with thickness gradients on both sides of a nozzle girth weld were analyzed. Finally, simplified finite element simulations were performed to determine if the residual stresses should be considered and when they become important for crack-opening evaluations.     

Image based modelling of stress–strain behaviour in carbon/carbon composites

Abstract

Numerical modelling is based on two fundamentals: first, developing a finite element (FE) mesh that represents faithfully the sample structure; and second, using reliable input data. In this paper, a methodology for creating image based FE meshes from X-ray microtomography (XMT) data sets of two 2D woven carbon–carbon composites (graphitised and ungraphitised) that are candidate materials for nuclear applications is described. Input data for the mechanical properties of the constituent phases are determined by nanoindentation. Compressive tests are also performed to generate experimental stress–strain curves to validate the predictions. The results showed good correlation between the experimental and numerically modelled stress–strain curves, therefore giving confidence in the approach. The stress distributions within the structure were also modelled. These showed the effect of pore shape on stress shielding. These predictions were also compared with simple analytical models for the structure. The image based models showed better agreement.     

Effects of attached straight pipes on finite element limit analysis for pipe bends

The effect of the length of an attached straight pipe on the plastic limit load of a 90° pipe bend under combined pressure and bending is quantified, based on finite element (FE) limit analyses using elastic–perfectly plastic materials with the small geometry change option. Systematic FE limit analyses of pipe bends with various lengths of the attached pipe are performed. It is shown that the effect of the length of the attached straight pipe on plastic limit loads can be significant, and the limit loads tend to decrease with decrease of the length of the attached straight pipe. In the limiting case of no attachment, the limit loads are found to be close to existing analytical solutions.     

Experimental calibration of stress intensity factor for piping with circumferential through-wall crack

A survey of the literature shows that the existing stress intensity factor solutions for circumferential through-walled cracks in piping may be classified into three categories. One category is based on Sanders' analytical results for long pipe cracks, with various corrections in the short crack range and different curve-fitting formulae to give convenient closed form expressions. The second category consists of various independent finite element solutions. Each of these solutions is for a discrete pipe geometry and crack length and so is not practical to be used in fracture mechanics analysis. Lastly there is Kanninen & Zahoor's solution, derived independently of Sanders' results. Comparison showed that the results from the first two categories roughly agreed but were vastly different from Kanninen & Zahoor's results. Experimental calibration using the strain gauge method and the fatigue crack growth rate back-tracking method has been carried out. The experimental results agreed with the family of solutions derived from Sanders' work. Details about this experimental calibration are presented.     

鼓泡式烟气脱硫原理性试验台气体流动冷模试验

描述了鼓泡式烟气脱硫原理性试验台气体流动冷模试验及结果。试验发现,对管外喷射,三种试验管型中底端封口的喷射管鼓泡层高度和压力降的变化都非常稳定;对管内喷射,随喷射速度和喷射管插入深度的变化,喷射器压力降波动很大,很不稳定。因而建议工程应用时采用管外喷射。采用PIV仪器对底端封口喷射管管外喷射的速度场进行测定,试验发现,在气液充分混合区域内,气泡的运动轨迹非常复杂,形成大量的涡团,气液剧烈扰动;在速度超过16m／s,涡团主要存在管壁附近,中间气体形成腾涌,对气液接触非常不利。     

Hydrogen jet fires in a passively ventilated enclosure

This paper describes a combined experimental, analytical and numerical modelling investigation into hydrogen jet fires in a passively ventilated enclosure. The work was funded by the EU Fuel Cells and Hydrogen Joint Undertaking project Hyindoor. It is relevant to situations where hydrogen is stored or used indoors. In such situations passive ventilation can be used to prevent the formation of a flammable atmosphere following a release of hydrogen. Whilst a significant amount of work has been reported on unignited releases in passively ventilated enclosures and on outdoor hydrogen jet fires, very little is known about the behaviour of hydrogen jet fires in passively ventilated enclosures. This paper considers the effects of passive ventilation openings on the behaviour of hydrogen jet fires. A series of hydrogen jet fire experiments were carried out using a 31 m³ passively ventilated enclosure. The test programme included subsonic and chocked flow releases with varying hydrogen release rates and vent configurations. In most of the tests the hydrogen release rate was sufficiently low and the vent area sufficiently large to lead to a well-ventilated jet fire. In a limited number of tests the vent area was reduced, allowing under-ventilated conditions to be investigated. The behaviour of a jet fire in a passively ventilated enclosure depends on the hydrogen release rate, the vent area and the thermal properties of the enclosure. An analytical model was used to quantify the relative importance of the hydrogen release rate and vent area, whilst the influence of the thermal properties of the enclosure were investigated using a CFD model. Overall, the results indicate that passive ventilation openings that are sufficiently large to safely ventilate an unignited release will tend to be large enough to prevent a jet fire from becoming under-ventilated.     

Failure pressure of straight pipe with wall thinning under internal pressure

The failure pressure of pipe with wall thinning was investigated by using three-dimensional elastic–plastic finite element analyses (FEA). With careful modeling of the pipe and flaw geometry in addition to a proper stress–strain relation of the material, FEA could estimate the precise burst pressure obtained by the tests. FEA was conducted by assuming three kinds of materials: line pipe steel, carbon steel, and stainless steel. The failure pressure obtained using line pipe steel was the lowest under the same flaw size condition, when the failure pressure was normalized by the value of unflawed pipe defined using the flow stress. On the other hand, when the failure pressure was normalized by the results of FEA obtained for unflawed pipe under various flaw and pipe configurations, the failure pressures of carbon steel and line pipe steel were almost the same and lower than that of stainless steel. This suggests that the existing assessment criteria developed for line pipe steel can be applied to make a conservative assessment of carbon steel and stainless steel.     

Theoretical analysis of local indentation on pressured pipes

A quasi-static analysis is presented in this paper for in-service pressurised pipelines subjected to an external impact. Based on the assumed simple rigid, perfectly plastic deformation model, a simple relationship is obtained between the external denting force F and the maximum dent depth δ₀. Results from the theoretical analysis are in reasonable agreement with results from finite element analyses. These show that the pressure p=p_in−p_out has a large influence on the pipe resistance to the indentation, where p_in and p_out are the internal and external pressure, respectively. For the same dent depth, a higher external denting force is required for pipes with higher pressure, p. The difference of the required force between a lowly pressurised pipe and a highly pressurised pipe increases with increasing denting depth.     

某低速柴油机活塞冷却油管装配抗脱松力分析

某型船用低速柴油机活塞冷却油管在运行中发生脱落。为了研究不同装配尺寸对冷却油管装配抗脱松力的影响规律,采用有限元方法研究冷却油管与连接法兰过盈接触面接触压力分布情况,并通过与理论计算值的对比分析验证了有限元结果的合理性。然后通过理论计算得到装配尺寸对冷却油管抗脱松力的影响规律,从而指导活塞冷却油管与法兰面装配过盈量的合理设置。     

Determination of the elastic-plastic fracture mechanics Z-factor for alloy 182 weld metal flaws

One of the ways that the ASME Section XI code incorporates elastic-plastic fracture mechanics (EPFM) in the Section XI Appendix C flaw evaluation procedures for circumferential cracks is through a parameter called Z-factor. This parameter allows the simpler limit-load (or Net-Section-Collapse) solutions to be used with a multiplier from EPFM analyses. This paper shows how 3-D finite element (FE) analyses were employed to investigate the sensitivity of the crack-driving force as a function of crack location (i.e., crack in the center of weld, or closer to the stainless or low alloy steel sides) in an Alloy 182 dissimilar metal weld (DMW), and how an appropriate (or equivalent) stress-strain curve was determined for use in the J-estimation schemes. The J-estimation schemes are then used to cover a wider range of variables, i.e., pipe diameters, cracks lengths, and also incorporate crack growth by ductile tearing. The Z-factor equations as a function of pipe diameter were calculated using the LBB.ENG2 J-estimation scheme along with the most conservative equivalent stress-strain curve from the FE analyses. The proposed Z-factor approach was then validated against an Alloy 182 DMW full-scale pipe test that had a circumferential through-wall crack in the fusion line. The predicted EPFM maximum load showed excellent agreement with the experimental result. Furthermore, it was shown that the proposed Z-factor equation is not sensitive to the location of the crack.     

Local and global collapse pressure of longitudinally flawed pipes and cylindrical vessels

Limit loads can be calculated with the finite element method (FEM) for any component, defect geometry, and loading. FEM suggests that published long crack limit formulae for axial defects under-estimate the burst pressure for internal surface defects in thick pipes while limit loads are not conservative for deep cracks and for pressure loaded crack-faces. Very deep cracks have a residual strength, which is modelled by a global collapse load. These observations are combined to derive new analytical local and global collapse loads. The global collapse loads are close to FEM limit analyses for all crack dimensions.