A finite element model for crack arrestor design in gas pipelines

Steel rings are frequently used as crack arrestor devices in steel gas transmission pipelines to prevent the possibility of long running axial cracks. These arrestors have the effect of reducing the pipe opening as the crack propagates. This decreases the available crack driving force and, as a result, crack arrest can take place. This essentially is a second line of defence against catastrophic failure in the event that crack initiation cannot always be prevented. This paper describes a novel analysis methodology that has been developed to investigate the suitability of these crack arrestors. This is based on a fluid/structure/fracture interaction package, PFRAC. Here, a curved beam element has been implemented into PFRAC to simulate the behaviour of the arrestor. The contact conditions between the pipe wall and the arrestor, along with the various computational procedures, are described here. Several numerical results for a cracked pipe with arrestors are presented along with comparisons with pipes that do not have arrestors.     

断裂动力学有限元程序的开发及在天然气管道裂纹扩展问题上的应用

许多工程问题是由于流（气）体压力导致了结构开裂,裂纹迅速扩展或者止裂,这被认为是断裂动力学最前沿的研究领域。本文描述了应用于分析流体／结构／断裂耦合作用问题的计算程序ＰＦＲＡＣ（ＰｉｐｅｌｉｎｅＦＲａｃｔｕｒｅＡｎａｌｙｓｉｓＣｏｄｅ）,和它在天然气管道裂纹迅速扩展问题上的应用。基于断裂动力学的模式,提出了裂纹扩展和止裂的判据。对于裂纹驱动力的计算,给出了节点力释放技术和能量平衡方法的具体应用。根据实际管道开裂试验的数据,提出了便于非耦合作用计算的裂纹后面气体压力衰减模式。针对钢制和塑料制天然气工程管道,给出了部分计算和试验的结果。     

Crack retardation equations for the propagation of branched fatigue cracks

The stress intensity factors (SIF) associated with branched fatigue cracks can be considerably smaller than that of a straight crack with the same projected length, causing crack growth retardation or even arrest. This crack branching mechanism can quantitatively explain retardation effects even when plasticity induced crack closure cannot be applied, e.g. in high R-ratio or in some plane strain controlled fatigue crack growth problems. Analytical solutions have been obtained for the SIF of branched cracks, however, numerical methods such as Finite Elements (FE) or Boundary Elements (BE) are the only means to predict the subsequent curved propagation behavior. In this work, a FE program is developed to calculate the path and associated SIF of branched cracks, validated through experiments on 4340 steel ESE(T) specimens. From these results, semi-empirical crack retardation equations are proposed to model the retardation factor along the crack path. The model also considers the possible interaction between crack branching and other retardation mechanisms.     

能量平衡结合有限元数值计算分析天然气管道裂纹稳定扩展问题

本文提出了在天然气管道裂纹稳定扩展问题中，应用能量平衡方法结合有限元数值计算结果来分析计算裂纹驱动力。能量数值计算采用了可模拟动裂纹在管道上扩展的有限元程序ＰＦＲＡＣ，它包括了对未开裂管道和裂纹扩展管道的能量计算。通过分析外力作功和内部能量在裂纹扩展时的变化率，应用能量平衡方法计算了裂纹驱动力，并与在ＰＦＲＡＣ程序中应用节点力释放方法计算的裂纹驱动力的结果进行了比较     

Automated dynamic fracture procedure for modelling mixed-mode crack propagation using explicit time integration brick finite elements

Several fracture codes have been developed in recent years to perform analyses of dynamic crack propagation in arbitrary directions. However, general-purpose, commercial finite-element software which have capabilities to do fracture analyses are still limited in their use to stationary cracks and crack propagation along trajectories known a priori . In this paper, we present an automated fracture procedure implemented in the large-scale, nonlinear, explicit, finite-element code DYNA3D which can be used to simulate dynamic crack propagation in arbitrary directions. The model can be used to perform both generation- and application-phase simulations of self-similar as well as non-self-similar dynamic crack propagation in linear elastic structures without user intervention. It is developed based on dynamic fracture mechanics concepts and implemented for three-dimensional solid elements. Energy approach is used in the model to check for crack initiation/propagation. Dynamic energy release rate and stress intensity factors are determined from far-field finite-element field solutions using finite-domain integrals. Fracture toughness is input as a function of crack-tip velocity, and when the criterion for crack growth is satisfied, an element deletion-and-replacement re-meshing procedure is used along with a gradual nodal release technique to update the crack geometry and model the crack propagation. Direction of crack propagation is determined using the maximum circumferential stress criterion. Numerical simulations of experiments involving non-self-similar crack propagation are performed, and results are presented as verification examples.     

Ductile failure analysis and crack behavior of X65 buried pipes using extended finite element method

This paper aims to study the ductile fracture mechanism of API X65 buried pipes including crack initiation and propagation using the extended finite element method (XFEM). First, the crack evolution histories of X65 specimens with initial crack-like flaws during tensile and three-point bending tests are illustrated, and the numerical results are compared with experimental data. In addition, effects of different crack configurations, damage initiation and evolution criteria are investigated. Second, the burst processes of straight pipes with initial gouge flaws are presented, and the FE results are compared with assessment in related standards and experiments. Finally, the crack onset and growth of buried pipes due to deflection arising from landslide movements are predicted, and the numerical results are compared with previous study. Particularly, the internal pressure, wall thickness, and soil properties on crack behavior and limit load-bearing ability are investigated. This paper provides a fundamental support for the integrity assessment and safety evaluation of buried pipes.     

Rapid crack propagation and arrest in the dcb specimen—an improved numerical analysis

A two-dimensional linear elastodynamic analysis of crack initiation, fast crack propagation and crack arrest in the DCB specimen is presented. The analysis is performed using the previously developed SMF2D code in its generation mode. The experimentally measured crack tip motion, as well as the specimen's geometry and its material characteristics, serve as input to the simulation. The dynamic stress intensity factor, the dynamic energy release rate and the various distributions of energies are subsequently evaluated. The numerical results are found to be in very good agreement with analytical and experimental findings.     

Finite element simulation of fast fracture in steel DCB specimen

Results of a numerical simulation, based on an energy consistent moving singularity dynamic finite element procedure, of fast crack propagation and arrest in a high strength steel DCB specimen are presented. The influence of material properties of high strength steel on dynamic crack propagation and arrest is investigated. The influence of the loss of constact of specimen with the loading wedge is also critically examined. The present numerical results are compared with available experimental data. It is found that the present results agree well with available experimental data, and the crack arrest toughness values obtained in the present analysis correlate well with the ratio of the maximum kinetic energy of the specimen to the input energy.     

Using the X-FEM method to model the dynamic propagation and arrest of cleavage cracks in ferritic steel

Although initiation criteria have been the subject of many publications, the phenomena associated with the propagation and arrest of brittle cracks have not. To be able to predict the dynamic behaviour of cleavage cracks, we made a series of experiments and associated numerical studies. Tests of crack propagation and arrest were carried out on specimens of two different geometries (Compact Tension and compression ring) made of the 16MND5 ferritic steel of which French nuclear reactor vessels are constructed. The elastic-viscoplastic behaviour of this material was characterised and its nature was taken into account in the numerical simulations. The eXtended Finite Element Method (X-FEM) was developed in CAST3M finite element analysis software to enable fine, effective modelling of crack propagation. Propagation models based on principal stress were studied and it was found that critical cleavage stress depended on loading rate. The use of criteria calibrated for Compact Tension specimens gave excellent results in predictive calculations for similar specimens, and also for compression rings in both mode I and mixed-mode. The speed and path of crack predicted with the numerical simulations were in close agreement with the experimental results.     

Crack arrest and stress dependence of laser-induced surface damage in fused-silica and borosilicate glass

Results of experiments on stress-inhibited laser-driven crack growth and stress-delayed laser-damage initiation thresholds in fused silica, borosilicate glass (BK-7), and cleaved bulk silica are presented. A numerical model is developed to explain the crack arrest in fused silica. Good agreement is obtained between the model and a finite-element code. The crack arrest is demonstrated to be the result of the breaking of a hoop-stress symmetry that is responsible for crack propagation in fused silica.     

Dynamic crack propagation in rubber-modified composite models

The dynamic crack propagation behaviour of several rubber-modified composite models has been studied. In all cases the method of high speed photography along with the method of dynamic caustics was used. Results of crack propagation mode observation, fracture toughness and crack propagation velocity measurements are presented here. Especially in the case of two complex inclusions it was found that the crack propagation mode is highly rate dependent. At low test rates the crack growth tends to follow an almost straight crack path while an increase in strain rate in general results in the formation of a kink in the interparticle area. In the same area a crack propagation delay, and in some cases arrest, was observed while both the crack propagation velocity v and dynamic stress intensity factor K _i ^d showed an intense variation. For the sake of comparison, specimens with one and/or two press-fitting inclusions as well as with two holes were fractured under dynamic loads. In all cases both qualitative and quantitative results were obtained.     

Effect of material plasticity on fatigue crack propagation under complex stress state

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. However, this fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, a modification has been made to G _max criterion to implement the consideration of the plastic strain energy. This criterion is extended to study the fatigue crack growth characteristics of mixed mode cracks in steel pipes. To predict crack propagation due to fatigue loads, a new elasto-plastic energy model is presented. This new model includes the effects of material properties like strain hardening exponent n, yield strength σ_y and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

管道的断裂与落锤撕裂试验

介绍了避免油、气集输管道低应力断裂扩展的上裂原理与速度判据。管道裂纹的扩展速度主要取决于管道钢的转变温度ＦＡＴＴ。ＦＡＴＴ可由落锤撕裂试验测定。论述了落锤撕裂试验的特点、方法和标准，以及该试验在管道钢材、压力容器钢和船体结构钢薄板上的应用情况。     

Improvements of explicit crack surface representation and update within the generalized finite element method with application to three‐dimensional crack coalescence

This paper presents improvements to three‐dimensional crack propagation simulation capabilities of the generalized finite element method. In particular, it presents new update algorithms suitable for explicit crack surface representations and simulations in which the initial crack surfaces grow significantly in size (one order of magnitude or more). These simulations pose problems in regard to robust crack surface/front representation throughout the propagation analysis. The proposed techniques are appropriate for propagation of highly non‐convex crack fronts and simulations involving significantly different crack front speeds. Furthermore, the algorithms are able to handle computational difficulties arising from the coalescence of non‐planar crack surfaces and their interactions with domain boundaries. An approach based on moving least squares approximations is developed to handle highly non‐convex crack fronts after crack surface coalescence. Several numerical examples are provided, which illustrate the robustness and capabilities of the proposed approaches and some of its potential engineering applications. Copyright © 2013 John Wiley & Sons, Ltd.     

3D adaptive finite element modeling of non-planar curved crack growth using the weighted superconvergent patch recovery method

In this paper, an adaptive finite element analysis is presented for 3D modeling of non-planar curved crack growth. The fracture mechanical evaluation is performed based on a general technique for non-planar curved cracks. The Schollmann’s crack kinking criterion is used for the process of crack propagation in 3D problems. The Zienkiewicz-Zhu error estimator is employed in conjunction with a weighted SPR technique at each patch to improve the accuracy of error estimation. Applying the proposed technique to 3D non-planar curved crack growth problems shows significant improvements particularly at the boundaries and near crack tip regions. Several numerical examples are presented to illustrate the robustness of the proposed technique.     

Crack propagation toward a desired path by controlling the force direction

Controlling the crack propagation along a desired path has important applications in fabrication. We propose a method for extending a crack along a desired trajectory by controlling the direction of an applied external point force. Examples of crack propagation along arc and sinusoidal paths are illustrated, and verified through numerical simulations based on the extended finite element method (XFEM).     

Numerical analysis of debond propagation in the single fibre fragmentation test

A numerical analysis, using the Boundary Element Method, of the stress state within the specimen in the single fibre fragmentation test is presented first. Thermal residual stresses and fibre–matrix interfacial friction along the debonding crack faces have been considered in the study. Special attention has been paid to the axial stresses along the fibre and the interfacial tractions and relative displacements in the neighbourhood closest to the debonding crack tips. In order to analyse the debond propagation, the associated Energy Release Rate has been evaluated from the near-tip elastic solution. Numerical results show that both the effects of thermal residual stresses and of fibre–matrix interfacial friction are opposed to the debond propagation. Additionally, the effect of the debond propagation on the load transfer through the interface has been studied, showing that fibre–matrix interfacial friction has a weak influence on the distance needed to re-establish the nominal axial load within the fragment.     

Dynamic crack propagation and arrest in orthotropic DCB fiber composite specimens

An orthotropic double cantilever beam (DCB) model is used to study dynamic crack propagation and arrest in 90° unidirectional Hercules AS/3501-6 graphite fiber epoxy composites. The dynamic fracture toughness of the composite is determined from tests performed on the long-strip specimen and DCB crack arrest experiments are conducted. By using the dynamic fracture toughness in a finite-difference solution of the DCB governing partial differential equations, a numerical solution of the crack propagation and arrest events is computed. Excellent agreement between the experimental and numerical crack arrest results are obtained.     

Fully automated mixed mode crack propagation analyses based on tetrahedral finite element and VCCM (virtual crack closure-integral method)

The authors have been developing a crack propagation analysis system that can deal with arbitrary shaped cracks in three-dimensional solids. The system is consisting of mesh generation software, a large-scale finite element analysis program and a fracture mechanics module. To evaluate the stress intensity factors, virtual crack closure-integral method (VCCM) for the quadratic tetrahedral finite element is adopted and is included in the fracture mechanics module. The rate and direction of crack propagation are predicted by using appropriate formulae based on the stress intensity factors. In this paper, the crack propagation system is briefly described and some numerical results are presented.