Experimental and numerical investigations of stable crack growth of axial surface flaws in a pressure vessel

Stable crack growth of a surface flaw in a pressure vessel has been investigated experimentally and numerically. The results show that a purely J-based concept of ductile fracture is not able to predict the local crack extension of the surface flaw correctly. To explain the canoe shape of the grown crack, the local crack tip constraint has to be taken into account.     

Fracture mechanics analysis of a pressure vessel with a semi-elliptical surface crack using elastic-plastic FEM-calculations

Results of an elastic-plastic three dimensional finite element analysis for a semi-elliptical surface crack inside a pressure vessel is presented. The calculations were performed by the finite element program ADINA, incorporating von Mises yield condition and isotropic hardening. The calculations were performed up to that pressure level where general yield of the ligament takes place. The results of the finite element analysis are compared with figures obtained from analytical procedures of elastic as well as of elastic-plastic fracture mechanics.     

Analysis of stable crack growth across welded fusion line: Japanese round-robin

Bimaterial CT specimens are numerically analyzed in the elastic-plastic states. By changing the material constants and the distance between the crack tip and the phase boundary, the parametric analyses are conducted. J integral evaluated by the line integration is compared with that obtained by the empirical formula by Merkel-Corten. The effects of the inhomogeneities on the accuracy of the J integral evaluation are discussed. Next the stable crack growth analyses are conducted. Using the relation between a and load-load line displacement obtained experimentally, the generation phase analyses are carried out. J integral, T^* integral and CTOA are evaluated and the effects of the fusion line are discussed.     

Large stable crack growth in fracture mechanics specimens

According to the J concept, information is reported about the crack resistance behaviour up to 8 mm crack growth of side-grooved CT-25 as well as CCT-25 specimens made from German standard steel StE 460. Numerical simulations controlled by J_R curves make the calculation of J from the stresses and strains of specimen models during large crack growth feasible. These data allow a comparison to standards and rules describing the evaluation of J from experiments. Using stress, strain and displacement fields from a plane-strain finite-element analysis, the extended J concept is discussed concerning larger ductile crack growth. Additionally, the distribution of other fracture mechanics parameters such as the crack tip opening displacement (CTOD) and the crack tip opening angle (CTOA) are presented for larger crack growth.     

Ductile crack growth simulation from near crack tip dissipated energy

A method to calculate ductile tearing in both small scale fracture mechanics specimens and cracked components is presented. This method is based on an estimation of the dissipated energy calculated near the crack tip. Firstly, the method is presented. It is shown that a characteristic parameter G_fr can be obtained, relevant to the dissipated energy in the fracture process. The application of the method to the calculation of side grooved crack tip (CT) specimens of different sizes is examined. The value of G_fr is identified by comparing the calculated and experimental load line displacement versus crack extension curve for the smallest CT specimen. With this identified value, it is possible to calculate the global behaviour of the largest specimen. The method is then applied to the calculation of a pipe containing a through-wall thickness crack subjected to a bending moment. This pipe is made of the same material as the CT specimens. It is shown that it is possible to simulate the global behaviour of the structure including the prediction of up to 90-mm crack extension. Local terms such as the equivalent stress or the crack tip opening angle are found to be constant during the crack extension process. This supports the view that G_fr controls the fields in the vicinity near the crack tip.     

Ductile crack growth in pre-cracked CVN specimens: numerical studies

This study describes plane strain, finite element analyses to model ductile crack extension in pre-cracked Charpy specimens subjected to static and impact loading. The Gurson–Tvergaard (GT) dilatant plasticity model for voided materials describes the degradation of material stress capacity. Fixed-size, computational cell elements defined over a thin layer along the crack plane provide an explicit length scale for the continuum damage process. Outside of this layer, the material remains undamaged by void growth, consistent with metallurgical observations. The finite strain constitutive models include the effects of high strain rates on the material flow properties. Parametric studies focusing on numerically generated R-curves quantify the relative influence of impact velocity, material strain rate sensitivity, and properties of the computational cells (thickness and the initial cell porosity). In all cases, impact loading elevates significantly the R-curve by increasing the amount of background plasticity. The strong effects of impact loading on the driving force for cleavage fracture are illustrated through evolution of the Weibull stress. The analyses suggest a negligible, additional effect of tearing on the Weibull stress under impact loading. Validation of the computational cell approach to predict loading rate effects on R-curves is accomplished by comparison to static and impact experimental sets of R-curves for three different steels.     

2D crack growth simulation with an energetic approach

It is well known that the tearing resistance curve J–Δa is not a material property. A recent approach, based on an energetic critical parameter to model ductile tearing propagation, is used to model 3D effects. The approach considered in this work aims to estimate the dissipated energy in the fracture process during ductile tearing represented by an intrinsic parameter G_fr. A fracture criterion, which accounts for the crack extension length, is defined and lies on a critical energy release rate, noted G_c, which is compared to G_fr. Previously, this parameter was obtained from a numerical local energy release rate, which handicaps the application field of the approach: a fine mesh for the whole propagation area was needed and the criterion allowed only to model 1D propagation. A new manner to estimate G_c is then proposed in this article, based on the J plastic part variation, which allows to model 2D propagation by defining a local criterion. This new calculation method is validated on a CT specimen made in Tu52b ferritic steel, by comparing the results obtained from the two methods of G_c calculation. Then, the 2D crack growth case is studied, by modelling the propagation in a ring, loaded in compression. It is shown that a 3D effect, such as tunnel effect, could be successfully represented with this approach.     

Monitoring of inside surface crack growth by strain measurement of the outside surface: A feasibility study

Cracks detected by in-service inspections are not always removed when they are judged to be not hazardous according to fitness-for-service evaluations. In order to secure the integrity of the cracked components, it is important to confirm that the cracks do not grow notably beyond the growth prediction conducted for the judgement. However, due to the limitation of accuracy of size determination by the current inspection techniques such as ultrasonic testing, it is difficult to know how much the cracks have grown since their previous measurement. In this study, feasibility of a crack growth monitoring method (outside strain monitoring method) was evaluated by finite element analyses and experiments. When a pipe deforms elastically due to internal pressure, the strain at its outside surface increases. The magnitude of strain near the crack differs from that at an uncracked portion, and the difference depends on the crack size. Elastic finite element analyses were performed for cracked pipes under internal pressure for various crack sizes. It was shown that, by measuring the change in strain at the outside surface of the cracked pipe, the crack size and how much the crack grew can be identified. In the experiment, cracked pipes were subjected to static internal pressure and strains for eight cracks of different sizes were measured. It was revealed that the maximum error was 0.44 mm for the estimation of crack depth of 4 mm and 0.28 mm for the estimation of 1 mm crack growth in the depth direction.     

Elastic-plastic finite element analyses of stable crack growth and fracture instability in a girth welded pipe

Detailed elastic-plastic finite element fracture mechanics analyses were conducted on a 16 inch diameter Type 304 stainless steel pipe containing a circumferential through-wall crack located in a girth weld. Calculations were performed to analyze the welded pipe treated as (1) a monolithic pipe entirely composed of the base metal, and (2) a composite of base metal and weldment. In the latter, each constituent was assigned distinct mechanical and fracture properties. In both solutions applied J values were calculated for a fixed axial load combined with a monotonically increasing applied bending moment. The material J-resistance curves appropriate for the two problems were each used to initiate and grow the initial crack in a stable manner until fracture instability occurred under load control. It was found that the extent of stable crack growth and the applied loads at fracture instability are distinctly different in the two analyses. It is concluded that more precise fracture mechanics approaches than those now in current use are required for accurate assessments of weld cracking problems.     

Creep crack growth assessment by means of a crack tip/far field concept

A method has been developed to assess crack initiation and crack growth behaviour in the creep range. The proposed method is based on a two-criteria-diagram, which covers the crack tip/far field situation. The approach is similar to the application of the elastic stress concentration factor K, in the creep rupture range.     

强流脉冲电子束表层改性过程的三维温度场数值模拟

采用了柱坐标系下的轴对称(三维简化)温度场模型,对低能(1～6J·cm-2)、强流(10～40kA·cm-2)、短脉冲(1～6μs)电子束辐照靶材过程中的温度场演化进行了数值模拟.结果表明,靶材经强流脉冲电子束轰击后,亚表层(深度0.12～0.24μm,径向0～0.13cm范围内)首先完成固液相变,熔体迅速突破外表层,形成火山坑;随后熔化层迅速扩大到深度0.99μm,径向约2.01cm范围内;辐照过程中的升降温速率达108～109K·s-1.随后的试验结果显示,重熔层深度约为1～2μm,辐照边界出现明显的过渡区,表层晶粒得到细化,这与模拟结果吻合.     

Prediction of residual stress distributions due to surface machining and welding and crack growth simulation under residual stress distribution

In nuclear power plants, stress corrosion cracking (SCC) has been observed near the weld zone of the core shroud and primary loop recirculation (PLR) pipes made of low-carbon austenitic stainless steel Type 316L. The joining process of pipes usually includes surface machining and welding. Both processes induce residual stresses, and residual stresses are thus important factors in the occurrence and propagation of SCC. In this study, the finite element method (FEM) was used to estimate residual stress distributions generated by butt welding and surface machining. The thermoelastic-plastic analysis was performed for the welding simulation, and the thermo-mechanical coupled analysis based on the Johnson-Cook material model was performed for the surface machining simulation. In addition, a crack growth analysis based on the stress intensity factor (SIF) calculation was performed using the calculated residual stress distributions that are generated by welding and surface machining. The surface machining analysis showed that tensile residual stress due to surface machining only exists approximately 0.2 mm from the machined surface, and the surface residual stress increases with cutting speed. The crack growth analysis showed that the crack depth is affected by both surface machining and welding, and the crack length is more affected by surface machining than by welding.     

稳定层结条件下建筑物体对流场影响的数值模拟研究北大核心CSCD

采用RNG k-ε湍流模型模拟不同理查森数(Ri_(b))下立方体建筑物对流场结构的影响,并与相应的风洞实验结果进行了比较。CFD对归一化风速的数值模拟结果与风洞实验结果较好吻合;随着Ri_(b)的增大气流运动逐渐受浮力驱动,建筑物背风面的空腔区逐渐减小,特别是Ri_(b)≥0.82时,浮力对流场的恢复起主导作用。Ri_(b)=0.21附近,流场结构从湍流对流场结构起主导作用转化成与层流类似,建筑物顶部的高归一化湍流动能(k/u_(H)^(2))区域随着回流区的消失而消失。随着下风向距离的增加,不同Ri_(b)对流场结构与k/u_(H)^(2)的影响逐渐显现。     

Analysis of a bending test on a full-scale PWR hot leg elbow containing a surface crack

EDF, in co-operation with Framatome, has conducted a large research programme on the mechanical behaviour of thermally aged cast duplex stainless steel elbows, which are part of the main primary circuit of French PWRs. One important task of this programme consisted of testing a full-scale PWR hot leg elbow. The elbow contained a semi-elliptical circumferential notch machined on the outer surface of the intrados, as well as casting defects located on the flanks. To simulate the end-of-life condition of the component regarding material toughness, it had previously undergone a 2400-h ageing heat treatment at 400°C. The test preparation and execution, as well as the material characterization programme, were handled by MPA. The test was conducted under constant internal pressure and in-plane bending (opening mode) at 200°C. For safety reasons, it took place at an open air-site: the Meppen military test ground. At the maximum applied moment (6000 kN m), the notch did not initiate. This paper presents the results of the experiment and the results of the fracture mechanics analysis, based on finite element calculations.     

Determination of crack initiation and crack resistance using compact specimens, and comparison with results of numerical simulation of dynamically loaded wide plates

Static and dynamic crack resistance curves for the ferritic steel 20 MnMoNi 5 5 and the austenitic steel X6 CrNi 18 11 were determined for compact tension specimens, using a modified key curve method which contains a numerical calculation of the key curves. The method is described and verified under quasi-static loading. The J integral evaluation according to the ASTM standard (which at present is only applicable for ferritic steels under quasi-static loading) did not show in any case a considerable difference compared with the energy release rate approach. The numerical simulation of tests was carried out for wide plates made of austenitic material on the 12 MN high speed tensile testing machine at MPA Stuttgart.     

某型虚拟冲击器的设计及数值模拟

虚拟冲击器能够吸入空气中的气溶胶并收集特定粒径的颗粒。一般来说,常用的虚拟冲击器的切割粒径较大,工作流量也较大,对于某些限制流量的工况可能不适用。在本研究中,开发了一种新型多缝虚拟冲击器,且喷嘴附近注入清洁空气,能够减小气溶胶在冲击器内的损失。通过数值模拟的方法分析该虚拟冲击器的性能,结果表明,即使总流量为36 L/min,也能获得0.08 atm的低压降,利用具有清洁空气的狭缝喷嘴虚拟冲击器,可将切割粒径降到0.2~0.4 μm,并以1.8 L/min的流量收集起来。     

Experimental investigation on ductile stable crack growth emanating from wire-cut notch in AISI 4340 steel

An experimental investigation on the stable crack growth (SCG) behaviour in AISI 4340 using CT type specimen with a sharp slit (0.05 mm) under mode I and mixed modes (I and II) loading is presented. The slit was made in the specimen through wire cutting technique. Different combinations of loading angle and ratio of original crack length to specimen width (a₀/W) are examined. Data concerned with direction of initial crack extension, load–load line displacement (L–LLD) diagrams, initiation and maximum loads, range of stable crack growth, crack tip blunting, crack front geometry, fracture surfaces and their scanning electron micrographs are obtained. A noticeable blunting effect is observed prior to crack initiation. Although the crack initiates from a straight front, a considerable front tunnelling effect occurs as the crack extends. Under mixed mode, the crack extension takes place initially almost along a straight path, inclined with the main crack. The loading angle and initial crack length affect the initiation (P_i) and maximum (P_max) loads significantly, but the ratio between P_max and P_i remains almost constant. The direction of initial stable crack extension due to mixed mode loading is determined throughout an elastic finite element analysis. There is a good agreement between the experimental and predicted results.     

Creep-fatigue crack propagation behavior in a surface cracked plate

A series of experiments were performed in order to clarify the surface crack growth behavior under creep-fatigue condition. Type 304 stainless steel was tested at 550°C and 650°C. Specimens were plates with a surface notch. Loading patterns were axial fatigue, bending fatigue, axial creep-fatigue and bending creep-fatigue. As results were obtained: (1) the beach mark method was available to measure the changes of the crack front shape after the test; (2) the electrical potential method was available to measure the changes of the crack front shape in real time; (3) the crack front shape was affected by the loading mode; and (4) ΔJ and ΔJ_c calculated from the proposed simplified method could characterize the surface crack growth rate.     

Boundary element analysis on interaction of external surface crack and embedded crack in a pressurized cylinder

This paper analyzes the interaction of external semi-elliptical surface crack and embedded elliptical crack in a longitudinal plane of a pressurized cylinder. No numerical solution appears to be available in the literature so far. The analyzed ratios of the crack depth to crack length (b_S/a_S and b_E/a_E) are 0.25 and 1.0; the distance between both cracks (s₁/b_min) ranges from 0.5 to 2.0. In total 24 crack configurations are analyzed and the stress intensity factors along the crack front are presented. The numerical results show that the interaction makes the stress intensity factors along the crack fronts increased for both the surface crack and the embedded crack, compared with the single surface crack and single embedded crack. For the given crack sizes, the stress intensity factors for both the surface crack and embedded crack increase with the decrease of the distance between two cracks. The numerical analyses are carried out by the hybrid boundary element method.     

Optimization of a pebble bed configuration for quasi-direct numerical simulation

A high temperature reactor (HTR) is envisaged to be one of the renewed reactor designs to play a role in nuclear power generation including process heat applications. The HTR design concept exhibits excellent safety features due to the low power density and the large amount of graphite present in the core which gives a large thermal inertia in the event of an accident such as loss of coolant. However, the possible appearance of hot spots in the pebble bed cores of HTR may affect the integrity of the pebbles. This has drawn the attention of several scientists to understand this highly three-dimensional complex phenomenon. A good prediction of the flow and heat transport in such a pebble bed core is a challenge for CFD based on the available turbulence models and computational power. Such models need to be validated in order to gain trust in the simulation of these types of flow configurations. Direct numerical simulation (DNS), while imposing some restrictions in terms of flow parameters and numerical tools corresponding to the available computational resources, can serve as a reference for model development and validation. In the present article, a wide range of numerical simulations has been performed in order to optimize a pebble bed configuration for quasi-DNS which may serve as reference for validation.