Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 24

crack Related Abstracts

24 FE Analysis of the Notch Effect on the Behavior of Repaired Crack with Bonded Composite Patch in Aircraft Structures

Authors: Faycal Benyahia, Abdelmohsen Albedah, Bel Abbes Bachir Bouiadjra

Abstract:

In this paper, the finite element analysis is applied to study the performance of the bonded composite reinforcement or repair for reducing stress concentration at a semi-circular lateral notch and repairing cracks emanating from this kind of notch. The effects of the adhesive properties on the variation of the stress intensity factor at the crack tip were highlighted. The obtained results show that the stress concentration factor at the notch tip is reduced about 30% and the maximal reduction of the stress intensity factor is about 80%. The adhesive properties must be optimized in order to increase the performance of the patch repair or reinforcement.

Keywords: Composite, bonded repair, notch, crack, adhesive

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23 Three-Dimensional Numerical Analysis of the Harmfulness of Defects in Oil Pipes

Authors: B. Medjadji, L. Aminallah, B. Serier, M. Benlebna

Abstract:

In this study, the finite element method in 3-D is used to calculate the integral J in the semi-elliptical crack in a pipe subjected to internal pressure. The stress-strain curve of the pipe has been determined experimentally. The J-integral was calculated in two fronts crack (Ф = 0 and Ф = π/2). The effect of the configuration of the crack on the J integral is analysed. The results show that an external longitudinal crack in a pipe is the most dangerous. It also shows that the increase in the applied pressure causes a remarkable increase of the integral J. The effect of the depth of the crack becomes important when the ratio between the depth of the crack and the thickness of the pipe (a / t) tends to 1.

Keywords: Pipeline, crack, J integral, MEF

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22 Mechanical Characteristics on Fatigue Crack Propagation in Aluminum Plate

Authors: S. Lecheb, A. Nour, A. Chellil, H. Mechakra, H. Kebir, L. Addar

Abstract:

This paper present a mechanical characteristics on fatigue crack propagation in Aluminium Plate based on strain and stress distribution using the abaqus software. The changes in shear strain and stress distribution during the fatigue cycle with crack growth is identified. In progressive crack in the strain distribution and the stress is increase in the critical zone. Numerical Modal analysis of the model developed, prove that the Eigen frequencies of aluminium plate were decreased after cracking, and this reduce is nonlinear. These results can provide a reference for analysts and designers of aluminium alloys in aeronautical systems. Therefore, the modal analysis is an important factor for monitoring the aeronautic structures.

Keywords: Aluminum Alloys, Failure, Plate, crack

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21 Study of the Chronic Effects of CRACK on Some Biochemical Parameters Including Triglycerides, Cholesterol, HDL, LDL, VLDL, Amylase, Lipase, Albumin, Protein in Rat

Authors: Alireza Jafarzadeh, Bahram Amu-Oqhli Tabrizi, Hadi Khayat Nouri, Arash Khaki

Abstract:

30 head of adult Vistar rats were chosen to evaluate the chronic narcotic effects of crack on some biochemical parameters. The rats weighted approximately 200 to 250 g. They were divided into 5 groups of 6 and were housed in identical condition in terms of food and ambience. Rats were maintained at 12 hours light and 12 hours darkness. Rats were injected 7.8 mg/kg BW crack intraperitoneally. The groups one to four received daily medication for one to four weeks respectively. The control groups were injected identical dose of saline. The blood was taken from control and test groups then serum was separated from. Serum biochemical parameters of amylase, lipase, triglycerides, cholesterol, HDL, LDL, VLDL, protein and albumin were measured by diagnostic kits. Serum protein and albumin levels did not show statistically significant changes. Serum lipase and amylase showed significant changes both of which were increased. The serum levels of cholesterol, LDL and HDL demonstrated no significant changes. Triglycerides values showed a significant increase in serum. Serum VLDL in groups 3 and 4 exhibited significant changes compare to other groups.

Keywords: Protein, rat, cholesterol, crack, amylase, HDL, LDL, albumin, lipase, triglycerides, VLDL

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20 A Full-Scale Test of Coping-Girder Integrated Bridge

Authors: Heeyoung Lee, Woosung Bin, Kangseog Seo, Hyojeong Yun, Zuog An

Abstract:

Recently, a new continuous bridge system has been proposed to increase the space under the bridge and to improve aesthetic aspect of the urban area. The main feature of the proposed bridge is to connect steel I-girders and coping by means of prestressed high-strength steel bars and steel plate. The proposed bridge is able to lower the height of the bridge to ensure the workability and efficiency through a reduction of the cost of road construction. This study presents the experimental result of the full-scale connection between steel I-girders and coping under the negative bending moment. The composite behavior is thoroughly examined and discussed under the specific load levels such as service load, factored load and crack load. Structural response showed full composite action until the final load level because no relative displacement between coping and girder was observed. It was also found prestressing force into high-strength bars was able to control tensile stresses of deck slab. This indicated that cracks in deck slab can be controlled by above-mentioned prestressing force.

Keywords: Coping, crack, integrated bridge, full-scale test

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19 Finite Element Modeling of Influence of Roll Form of Vertical Scale Breaker on Decreased Formation of Surface Defects during Roughing Hot Rolling

Authors: A. Pesin, D. Pustovoytov, M. Sverdlik

Abstract:

During production of rolled steel strips the quality of the surface of finished strips influences steel consumption considerably. The most critical areas for crack formation during rolling are lateral sides of slabs. Deformation behaviors of the slab edge in roughing rolling process were analyzed by the finite element method with Deform-3D. In this study our focus is the analysis of the influence of edger’s form on the possibility to decrease surface cracking during roughing hot rolling.

Keywords: FEM, crack, roughing hot rolling, bulging

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18 Reliability Enhancement by Parameter Design in Ferrite Magnet Process

Authors: Won Jung, Wan Emri

Abstract:

Ferrite magnet is widely used in many automotive components such as motors and alternators. Magnets used inside the components must be in good quality to ensure the high level of performance. The purpose of this study is to design input parameters that optimize the ferrite magnet production process to ensure the quality and reliability of manufactured products. Design of Experiments (DOE) and Statistical Process Control (SPC) are used as mutual supplementations to optimize the process. DOE and SPC are quality tools being used in the industry to monitor and improve the manufacturing process condition. These tools are practically used to maintain the process on target and within the limits of natural variation. A mixed Taguchi method is utilized for optimization purpose as a part of DOE analysis. SPC with proportion data is applied to assess the output parameters to determine the optimal operating conditions. An example of case involving the monitoring and optimization of ferrite magnet process was presented to demonstrate the effectiveness of this approach. Through the utilization of these tools, reliable magnets can be produced by following the step by step procedures of proposed framework. One of the main contributions of this study was producing the crack free magnets by applying the proposed parameter design.

Keywords: Reliability, Process Optimization, Taguchi method, crack, ferrite magnet

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17 Study of the Toughening by Crack Bridging in Mullite Alumina Zirconia Ceramics

Authors: F. Gheldane, S. Bouras

Abstract:

Crack propagation behaviour of alumina mullite zirconia ceramic is investigated under monotonic and cyclic loading by means SENB bending method. This material show R-curve effects, i.e. an increase in crack growth resistance with increasing crack depth. The morphological study showed that the resistance of the crack propagation is mainly connected to the crack bridging. The value of bridging stress is in good agreement with the literature. Furthermore, cyclic-loading fatigue is caused by a decrease in the stress-shielding effect, due to degradation of bridging sites under cyclic loading.

Keywords: crack, alumina mullite zirconia, R-curve, bridging, toughening

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16 In situ Modelling of Lateral-Torsional Vibration of a Rotor-Stator with Multiple Parametric Excitations

Authors: B. X. Tchomeni, A. A. Alugongo, L. M. Masu

Abstract:

This paper presents a 4-DOF nonlinear model of a cracked of Laval rotor established based on Energy Principles. The model has been used to simulate coupled torsional-lateral response of the cracked rotor stator-system with multiple parametric excitations, namely, rotor-stator-rub, a breathing transverse crack, unbalanced mass, and an axial force. Nonlinearity due to a “breathing” crack is incorporated by considering a simple hinge model which is suitable for small breathing crack. The vibration response of a cracked rotor passing through its critical speed with rotor-stator interaction is analyzed, and an attempt for crack detection and monitoring explored. Effects of unbalanced eccentricity with phase and acceleration are investigated. By solving the motion equations, steady-state vibration response is obtained in presence of several rotor faults. The presence of a crack is observable in the power spectrum despite the excitation by the axial force and rotor-stator rub impact. Presented results are consistent with existing literature and could be adopted into rotor condition monitoring strategies

Keywords: crack, rotor, rubbing, axial force, non linear

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15 Calculating Stress Intensity Factor of Cracked Axis by Using a Meshless Method

Authors: S. Shahrooi, A. Talavari

Abstract:

Numeral study on the crack and discontinuity using element-free methods has been widely spread in recent years. In this study, for stress intensity factor calculation of the cracked axis under torsional loading has been used from a new element-free method as MLPG method. Region range is discretized by some dispersed nodal points. From method of moving least square (MLS) utilized to create the functions using these nodal points. Then, results of meshless method and finite element method (FEM) were compared. The results is shown which the element-free method was of good accuracy.

Keywords: crack, stress intensity factor, torsional loading, meshless method

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14 Fracture Mechanics Modeling of a Shear-Cracked RC Beams Shear-Strengthened with FRP Sheets

Authors: Shahriar Shahbazpanahi, Alaleh Kamgar

Abstract:

So far, the conventional experimental and theoretical analysis in fracture mechanics have been applied to study concrete flexural- cracked beams, which are strengthened using fiber reinforced polymer (FRP) composite sheets. However, there is still little knowledge about the shear capacity of a side face FRP- strengthened shear-cracked beam. A numerical analysis is herein presented to model the fracture mechanics of a four-point RC beam, with two inclined initial notch on the supports, which is strengthened with side face FRP sheets. In the present study, the shear crack is forced to conduct by using an initial notch in supports. The ABAQUS software is used to model crack propagation by conventional cohesive elements. It is observed that the FRP sheets play important roles in preventing the propagation of shear cracks.

Keywords: Strengthening, FRP, shear, crack

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13 Analysis of the Plastic Zone Under Mixed Mode Fracture in Bonded Composite Repair of Aircraft

Authors: W. Oudad, H. Fikirini, K. Boulenouar

Abstract:

Material fracture by opening (mode I) is not alone responsible for fracture propagation. Many industrial examples show the presence of mode II and mixed mode I + II. In the present work the three-dimensional and non-linear finite element method is used to estimate the performance of the bonded composite repair of metallic aircraft structures by analyzing the plastic zone size ahead of repaired cracks under mixed mode loading. The computations are made according to Von Mises and Tresca criteria. The extension of the plastic zone which takes place at the tip of a crack strictly depends on many variables, such as the yield stress of the material, the loading conditions, the crack size and the thickness of the cracked component, The obtained results show that the presence of the composite patch reduces considerably the size of the plastic zone ahead of the crack. The effects of the composite orientation layup (adhesive properties) and the patch thickness on the plastic zone size ahead of repaired cracks were analyzed.

Keywords: crack, J integral, elastic-plastic, patch, plastic zone

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12 Time-Frequency Modelling and Analysis of Faulty Rotor

Authors: B. X. Tchomeni, A. A. Alugongo, T. B. Tengen

Abstract:

In this paper, de Laval rotor system has been characterized by a hinge model and its transient response numerically treated for a dynamic solution. The effect of the ensuing non-linear disturbances namely rub and breathing crack is numerically simulated. Subsequently, three analysis methods: Orbit Analysis, Fast Fourier Transform (FFT) and Wavelet Transform (WT) are employed to extract features of the vibration signal of the faulty system. An analysis of the system response orbits clearly indicates the perturbations due to the rotor-to-stator contact. The sensitivities of WT to the variation in system speed have been investigated by Continuous Wavelet Transform (CWT). The analysis reveals that features of crack, rubs and unbalance in vibration response can be useful for condition monitoring. WT reveals its ability to detect non-linear signal, and obtained results provide a useful tool method for detecting machinery faults.

Keywords: Nonlinear, crack, Continuous wavelet, discrete wavelet, high acceleration, low acceleration, rotor-stator, rub

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11 Failure Analysis of Pipe System at a Hydroelectric Power Plant

Authors: Ali Göksenli, Barlas Eryürek

Abstract:

In this study, failure analysis of pipe system at a micro hydroelectric power plant is investigated. Failure occurred at the pipe system in the powerhouse during shut down operation of the water flow by a valve. This locking had caused a sudden shock wave, also called “Water-hammer effect”, resulting in noise and inside pressure increase. After visual investigation of the effect of the shock wave on the system, a circumference crack was observed at the pipe flange weld region. To establish the reason for crack formation, calculations of pressure and stress values at pipe, flange and welding seams were carried out and concluded that safety factor was high (2.2), indicating that no faulty design existed. By further analysis, pipe system and hydroelectric power plant was examined. After observations it is determined that the plant did not include a ventilation nozzle (air trap), that prevents the system of sudden pressure increase inside the pipes which is caused by water-hammer effect. Analyses were carried out to identify the influence of water-hammer effect on inside pressure increase and it was concluded that, according Jowkowsky’s equation, shut down time is effective on inside pressure increase. The valve closing time was uncertain but by a shut down time of even one minute, inside pressure would increase by 7.6 bar (working pressure was 34.6 bar). Detailed investigations were also carried out on the assembly of the pipe-flange system by considering technical drawings. It was concluded that the pipe-flange system was not installed according to the instructions. Two of five weld seams were not applied and one weld was carried out faulty. This incorrect and inadequate weld seams resulted in; insufficient connection of the pipe to the flange constituting a strong notch effect at weld seam regions, increase in stress values and the decrease of strength and safety factor

Keywords: Failure analysis, crack, shock wave, hydroelectric plant, welding seam

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10 Dynamic Modeling of Orthotropic Cracked Materials by X-FEM

Authors: S. Houcine Habib, B. Elkhalil Hachi, Mohamed Guesmi, Mohamed Haboussi

Abstract:

In this paper, dynamic fracture behaviors of cracked orthotropic structure are modeled using extended finite element method (X-FEM). In this approach, the finite element method model is first created and then enriched by special orthotropic crack tip enrichments and Heaviside functions in the framework of partition of unity. The mixed mode stress intensity factor (SIF) is computed using the interaction integral technique based on J-integral in order to predict cracking behavior of the structure. The developments of these procedures are programmed and introduced in a self-software platform code. To assess the accuracy of the developed code, results obtained by the proposed method are compared with those of literature.

Keywords: Composites, crack, X-FEM, stress intensity factor, dynamic orthotropic behavior

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9 Fracture and Dynamic Behavior of Leaf Spring Suspension

Authors: S. Lecheb, A. Chellil, H. Mechakra, H. Kebir, S. Attou

Abstract:

Although leaf springs are one of the oldest suspension components they are still frequently used, especially in commercial vehicles. Being able to capture the leaf spring characteristics is of significant importance for vehicle handling dynamics studies. The main function of leaf spring is not only to support vertical load but also to isolate road induced vibrations. It is subjected to millions of load cycles leading to fatigue failure. It needs to have excellent fatigue life. The objective of this work is its use of Abaqus software to locate the most stressed areas and predict the areas in which it occurs in fatigue and crack of leaf spring and calculate the stress and frequencies of this model.

Keywords: stress, crack, natural frequencies, leaf spring

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8 Interaction between the Main Crack and Dislocation in the Glass Material

Authors: A. Mezzidi, H. Hamli Benzahar

Abstract:

The present study evaluates the stress and stress intensity factor during the propagation of a crack at presence of a dislocation near of crack tip. The problem is formulated using a glass material having an equivalent elasticity modulus and a Poisson ratio. In this research work, the proposed material is a plate form with a main crack in one of these ends and a dislocation near this crack, subjected to tensile stresses according to the mode 1 opening. For each distance between the two cracks, we can determine these stresses. This study is treated by finite elements method by using the software (ABAQUS) rate. It is shown here in that obtained results agreed with those determined by other researchers

Keywords: Glass, finite element, crack, dislocation

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7 Racism in Drug Policies: A Report on United States Legislation

Authors: Frederick Monyepao

Abstract:

Crack cocaine first appeared on the scene in the form of cocaine freebasing in the late 1970s. Stockbrokers, investment bankers, rock stars, Hollywood elites, and a few pro athletes were regular users of the substance. As criminogenic factors associated with substance abuse began to surface, congress passed new legislation. The laws led to the increase of health coverage insurances and the expansion of hospitals. By the mid-1980s, crack use spread into America's inner cities among impoverished African Americans and Latinos. While substance abuse increased among minority communities, legislation pertaining to substance abuse evolved. The prison industry also expanded the number of cells available. A qualitative approach was taken, drawing from a range secondary sources for contextual analysis. This paper traces out the continued marginalisation and racist undertones towards minorities as perpetuated by certain drug policies. It was discovered that the new legislation on crack was instrumental in the largest incarcerations the United States ever faced. Drug offenders increased in prisons eightfold from 1986 to 2000. The paper concludes that American drug control policies are consistently irrational and ineffective when measured by levels of substance use and abuse. On the contrary, these policies have been successful as agents of social control in maintaining the stratification patterns of racial/ethnic minorities and women. To move beyond prohibition, radical law and policy reform may require a change in narratives on substance use.

Keywords: Racism, Substance abuse, Drug Policy, Minorities, crack

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6 Experimental Investigation on Performance of Beam Column Frames with Column Kickers

Authors: Raquib Ahsan, Saiada Fuadi Fancy, Fahim Ahmed, Shofiq Ahmed

Abstract:

The worldwide use of reinforced concrete construction stems from the wide availability of reinforcing steel as well as concrete ingredients. However, concrete construction requires a certain level of technology, expertise, and workmanship, particularly, in the field during construction. As a supporting technology for a concrete column or wall construction, kicker is cast as part of the slab or foundation to provide a convenient starting point for a wall or column ensuring integrity at this important junction. For that reason, a comprehensive study was carried out here to investigate the behavior of reinforced concrete frame with different kicker parameters. To achieve this objective, six half-scale specimens of portal reinforced concrete frame with kickers and one portal frame without kicker were constructed according to common practice in the industry and subjected to cyclic incremental horizontal loading with sustained gravity load. In this study, the experimental data, obtained in four deflections controlled cycle, were used to evaluate the behavior of kickers. Load-displacement characteristics were obtained; maximum loads and deflections were measured and assessed. Finally, the test results of frames constructed with three different types of kicker thickness were compared with the kickerless frame. Similar crack patterns were observed for all the specimens. From this investigation, specimens with kicker thickness 3″ were shown better results than specimens with kicker thickness 1.5″, which was specified by maximum load, stiffness, initiation of first crack and residual displacement. Despite of better performance, it could not be firmly concluded that 4.5″ kicker thickness is the most appropriate one. Because, during the test of that specimen, separation of dial gauge was needed. Finally, comparing with kickerless specimen, it was observed that performance of kickerless specimen was relatively better than kicker specimens.

Keywords: crack, cyclic, kicker, load-displacement

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5 On Crack Tip Stress Field in Pseudo-Elastic Shape Memory Alloys

Authors: Gulcan Ozerim, Gunay Anlas

Abstract:

In shape memory alloys, upon loading, stress increases around crack tip and a martensitic phase transformation occurs in early stages. In many studies the stress distribution in the vicinity of the crack tip is represented by using linear elastic fracture mechanics (LEFM) although the pseudo-elastic behavior results in a nonlinear stress-strain relation. In this study, the HRR singularity (Hutchinson, Rice and Rosengren), that uses Rice’s path independent J-integral, is tried to formulate the stress distribution around the crack tip. In HRR approach, the Ramberg-Osgood model for the stress-strain relation of power-law hardening materials is used to represent the elastic-plastic behavior. Although it is recoverable, the inelastic portion of the deformation in martensitic transformation (up to the end of transformation) resembles to that of plastic deformation. To determine the constants of the Ramberg-Osgood equation, the material’s response is simulated in ABAQUS using a UMAT based on ZM (Zaki-Moumni) thermo-mechanically coupled model, and the stress-strain curve of the material is plotted. An edge cracked shape memory alloy (Nitinol) plate is loaded quasi-statically under mode I and modeled using ABAQUS; the opening stress values ahead of the cracked tip are calculated. The stresses are also evaluated using the asymptotic equations of both LEFM and HRR. The results show that in the transformation zone around the crack tip, the stress values are much better represented when the HRR singularity is used although the J-integral does not show path independent behavior. For the nodes very close to the crack tip, the HRR singularity is not valid due to the non-proportional loading effect and high-stress values that go beyond the transformation finish stress.

Keywords: shape memory alloys, crack, stress distribution, HRR singularity

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4 Effect the Use of Steel Fibers (Dramix) on Reinforced Concrete Slab

Authors: Faisal Ananda, Junaidi Al-Husein, Oni Febriani, Juli Ardita, N. Indra, Syaari Al-Husein, A. Bukri

Abstract:

Currently, concrete technology continues to grow and continue to innovate one of them using fibers. Fiber concrete has advantages over non-fiber concrete, among others, strong against the effect of shrinkage, ability to reduce crack, fire resistance, etc. In this study, concrete mix design using the procedures listed on SNI 03-2834-2000. The sample used is a cylinder with a height of 30 cm and a width of 15cm in diameter, which is used for compression and tensile testing, while the slab is 400cm x 100cm x 15cm. The fiber used is steel fiber (dramix), with the addition of 2/3 of the thickness of the slabs. The charging is done using a two-point loading. From the result of the research, it is found that the loading of non-fiber slab (0%) of the initial crack is the maximum crack that has passed the maximum crack allowed with a crack width of 1.3 mm with a loading of 1160 kg. The initial crack with the largest load is found on the 1% fiber mixed slab, with the initial crack also being a maximum crack of 0.5mm which also has exceeded the required maximum crack. In the 4% slab the initial crack of 0.1 mm is a minimal initial crack with a load greater than the load of a non-fiber (0%) slab by load1200 kg. While the maximum load on the maximum crack according to the applicable maximum crack conditions, on the 5% fiber mixed slab with a crack width of 0.32mm by loading 1250 kg.

Keywords: Fiber, slab, crack, load, dramix

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3 Material Fracture Dynamic of Vertical Axis Wind Turbine Blade

Authors: Ahmed Chellil, Brahim Safi, Samir Lecheb, Hamza Mechakra, Houcine Kebir

Abstract:

In this paper we studied fracture and dynamic behavior of vertical axis wind turbine blade, the VAWT is a historical machine, it has many properties, structure, advantage, component to be able to produce the electricity. We modeled the blade design then imported to Abaqus software for analysis the modes shapes, frequencies, stress, strain, displacement and stress intensity factor SIF, after comparison we chose the idol material. Finally, the CTS test of glass epoxy reinforced polymer plates to obtain the material fracture toughness Kc.

Keywords: Material, Frequency, crack, blade, SIF

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2 Numerical Analysis of Crack's Effects in a Dissimilar Welded Joint

Authors: Daniel N. L. Alves, Marcelo C. Rodrigues, Jose G. de Almeida

Abstract:

The search for structural efficiency in mechanical systems has been strongly exerted with aim of economic optimization and structural safety. As soon, to understand the response of materials when submitted to adverse conditions is essential to design a safety project. This work investigates the presence of cracks in dissimilar welded joints (DWJ). Its fracture toughness responses depend upon the heterogeneity present in these joints. Thus, this work aim analyzing the behavior of the crack tip zone located in a buttery dissimilar welded joint (ASTM A-36, Inconel, and AISI 8630 M) used in the union of pipes present in the offshore oil production lines. The crack was placed 1 mm from fusion line (FL) Inconel-AISI 8630 M toward the AISI 8630 M. Finite Element Method (FEM) was used to analyze stress and strain fields generated during the loading imposed on the specimen. It was possible observing critical stress area by the numerical tool as well as a preferential plastic flow was also observed in the sample of dissimilar welded joint, which can be considered a harbinger of the crack growth path. The results obtained through numerical analysis showed a convergent behavior in relation to the plastic flow, qualitatively and quantitatively, in agreement with previous performed.

Keywords: Numerical Analysis, crack, dissimilar welded joint, strain field, the stress field

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1 Comparison of Two-Phase Critical Flow Models for Estimation of Leak Flow Rate through Cracks

Authors: Tadashi Watanabe, Jinya Katsuyama, Akihiro Mano

Abstract:

The estimation of leak flow rates through narrow cracks in structures is of importance for nuclear reactor safety, since the leak flow could be detected before occurrence of loss-of-coolant accidents. The two-phase critical leak flow rates are calculated using the system analysis code, and two representative non-homogeneous critical flow models, Henry-Fauske model and Ransom-Trapp model, are compared. The pressure decrease and vapor generation in the crack, and the leak flow rates are found to be larger for the Henry-Fauske model. It is shown that the leak flow rates are not affected by the structural temperature, but affected largely by the roughness of crack surface.

Keywords: roughness, crack, leak, critical flow

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