Search results for: stress crack resistance

Authors: F. Gheldane, S. Bouras

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

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Authors: F. Husem, M. E. Turan, Y. Sun, H. Ahlatci, I. Tozlu

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Residual stress and fatigue crack growth rates are important to determine mechanical behavior of rails. This study aims to make relationship between residual stress and fatigue crack growth values in rails. For this purpose, three R260 quality rails (0.6-0.8% C, 0.6-1.25 Mn) were chosen. Residual stress of samples was measured by cutting method that is related in railway standard. Then samples were machined for fatigue crack growth test and analyze was completed according to the ASTM E647 standard which gives information about parameters of rails for this test. Microstructure characterizations were examined by Light Optic Microscope (LOM). The results showed that residual stress change with fatigue crack growth rate. The sample has highest residual stress exhibits highest crack growth rate and pearlitic structure can be seen clearly for all samples by microstructure analyze.

Keywords: residual stress, fatigue crack growth, R260, SEM, ASTM E647

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Authors: Muhammad Naweed, Usman Tariq Murtaza, Waseem Siddique

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A pallet body approach is a finite element-based computational approach used for the modeling and assessment of a three-dimensional surface crack. The approach is capable of inserting the crack in an engineering structure and generating high-quality hexahedral mesh in the cracked region of the structure. The approach is capable of computing the stress intensity factors along a semi-elliptical surface crack numerically. The objective of this work is to present that the stress intensity factors produced by the approach can be used with confidence for capturing the parameters during the fatigue crack growth.

Keywords: pallet body approach, semi-elliptical surface crack, stress intensity factors, fatigue crack growth

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Authors: A. Mezzidi, H. Hamli Benzahar

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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: crack, dislocation, finite element, glass

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Authors: R. Z. Wang, B. C. Lin, C. H. Huang

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This study proposes a new method to simulate the crack propagation under mode-I loading using Vector Form Intrinsic Finite Element (VFIFE) method. A new idea which is expected to combine both VFIFE and J-integral is proposed to calculate the stress density factor as the crack critical in elastic crack. The procedure of implement the cohesive crack propagation in VFIFE based on the fictitious crack model is also proposed. In VFIFIE, the structure deformation is described by numbers of particles instead of elements. The strain energy density and the derivatives of the displacement vector of every particle is introduced to calculate the J-integral as the integral path is discrete by particles. The particle on the crack tip separated into two particles once the stress on the crack tip satisfied with the crack critical and then the crack tip propagates to the next particle. The internal force and the cohesive force is applied to the particles.

Keywords: VFIFE, crack propagation, fictitious crack model, crack critical

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Authors: S. Lecheb, A. Nour, A. Chellil, H. Mechakra, N. Hamad, H. Kebir

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The work involves develops attended by a numerical execution of the eXtend Finite Element Method premises a measurement by the fracture process cracked so many cracked plates an application will be processed for the calculation of the stress intensity factor SIF. In the first we give in statically part the distribution of stress, displacement field and strain of composite plate in two cases uncrack/edge crack, also in dynamical part the first six modes shape. Secondly, we calculate Stress Intensity Factor SIF for different orientation angle θ of central crack with length (2a=0.4mm) in plan strain condition, KI and KII are obtained for mode I and mode II respectively using X-FEM method. Finally from crack inclined involving mixed modes results, the comparison we chose dangerous inclination and the best crack angle when K is minimal.

Keywords: stress intensity factor (SIF), crack orientation, glass/epoxy, natural frequencies, X-FEM

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Authors: A. Tavangari, N. Salehzadeh

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In the crack growth analysis, the Stress Intensity Factor (SIF) is a fundamental prerequisite. In the present study, the mode I stress intensity factor (SIF) of three-dimensional penny-Shaped crack is obtained in an isotropic elastic cylindrical medium with arbitrary dimensions under arbitrary loading at the top of the cylinder, by the semi-analytical method based on the Rayleigh-Ritz method. This method that is based on minimizing the potential energy amount of the whole of the system, gives a very close results to the previous studies. Defining the displacements (elastic fields) by hypothetical functions in a defined coordinate system is the base of this research. So for creating the singularity conditions at the tip of the crack the appropriate terms should be found.

Keywords: penny-shaped crack, stress intensity factor, fracture mechanics, Ritz method

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Authors: Chong Wang, Alexandre Urbano Hoffmann

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Interaction between a crack and a trapezoidal aggregate in a single edge notched concrete beam is simulated using boundary element method with an automatic crack extension program. The stress intensity factors of the growing crack are obtained from the J-integral. Three crack extension paths: deflecting around the particulate, growing along the interface and penetrating into the particulate are achieved in terms of the mismatch state of mechanical characteristics of matrix and the particulate. The toughening is also given by the ratio of stress intensity factors. The results reveal that as stress shielding occurs, toughening is obtained when the crack is approaching to a stiff and strong aggregate weakly bonded to a relatively soft matrix. The present work intends to help for the design of aggregate reinforced concretes.

Keywords: aggregate concrete, boundary element method, two-phase composite, crack extension path, crack/particulate interaction

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

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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: J integral, pipeline, crack, MEF

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Authors: Farej Ahmed Emhmmed

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Fracture of duplex stainless steels (DSS) was investigated in air and in 3.5 wt % NaCl solution. Tow sets of fatigued specimens were heat treated at 475ºC for different times and pulled to failure either in air or after kept in 3.5% NaCl with polarization of -900 mV/ SCE. Fracture took place in general by ferrite cleavage and austenite ductile fracture in transgranular mode. Specimens measured stiffness (Ms) was affected by the aging time, with higher values measured for specimens aged for longer times. Microstructural features played a role in "blocking" the crack propagation process leading to lower the CTOD values specially for specimens aged for short times. Unbroken ligaments/ austenite were observed at the crack wake. These features may exerted a bridging stress, blocking effect, at the crack tip giving resistance to the crack propagation process i.e the crack mouth opening was reduced. Higher stress intensity factor Kıc values were observed with increased amounts of crack growth suggesting longer zone of unbroken ligaments in the crack wake. The bridging zone was typically several mm in length. Attempt to model the bridge stress was suggested to understand the role of ligaments/unbroken austenite in increasing the fracture toughness factor.

Keywords: stainless steels, fracture toughness, crack keying effect, ligaments

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Authors: Zhuang He, Andrei Kotousov

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All current experimental methods for determination of stress intensity factors are based on the assumption that the state of stress near the crack tip is plane stress. Therefore, these methods rely on strain and displacement measurements made outside the near crack tip region affected by the three-dimensional effects or by process zone. In this paper, we develop and validate an experimental procedure for the evaluation of stress intensity factors from the measurements of the out-of-plane displacements in the surface area controlled by 3D effects. The evaluation of stress intensity factors is possible when the process zone is sufficiently small, and the displacement field generated by the 3D effects is fully encapsulated by K-dominance region.

Keywords: digital image correlation, stress intensity factors, three-dimensional effects, transverse displacement

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

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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, plate, crack, failure

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Authors: Alae Lamtai, Said Elkoun, Hniya Kharmoudi, Mathieu Robert, Carl Diez

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This study applies Taguchi's design of experiment methodology and grey relational analysis (GRA) for multi objective optimization of an industrial recycling line. This last is composed mainly of a mono and twin-screw extruder and a filtration system. Experiments were performed according to L₁₆ standard orthogonal array based on five process parameters, namely: mono screw design, screw speed of the mono and twin-screw extruder, melt pump pressure, and filter mesh size. The objective of this optimization is to improve the durability of the Polyethylene (PE) blend by decreasing the loss of Stress Crack resistance (SCR) using Notched Crack Ligament Stress (NCLS) test and Unnotched Crack Ligament Stress (UCLS) in parallel with increasing the gain of Izod impact strength of the Polyethylene (PE) blend before and after recycling. Based on Grey Relational Analysis (GRA), the optimal setting of process parameters was identified, and the results indicated that the mono-screw design and screw speed of both mono and twin-screw extruder impact significantly the mechanical properties of recycled Polyethylene (PE) blend.

Keywords: Taguchi, recycling line, polyethylene, stress crack resistance, Izod impact strength, grey relational analysis

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Authors: Osama A. Terfas, Abdelhakim A. Hameda, Abdusalam A. Alktiwi

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An investigation on ductile crack growth of shallow semi-elliptical surface cracks with a/w=0.2, a/c=0.33 under bending was carried out, where a is the crack depth, w is the plate thickness and c is the crack length at surface. Finite element analysis and experiments were modelling and the crack growth model were verified with experimental data. The results showed that the initial crack shape was no longer maintained as the crack developed under ductile tearing. The maximum growth at the deepest point at early stages was stopped when the crack depth reached half thickness and growth occurred beneath surface. Excellent agreement in the crack shape patterns was observed between the experiments and the crack growth model.

Keywords: crack growth, ductile tearing, mean stress, surface cracks

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Authors: Ikram Slamani, Hicheme Ferdjani

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This study focuses on analyzing a Griffith crack situated at the center of an infinite strip. The problem is reformulated as a hyper-singular integral equation and solved numerically using second-order Chebyshev polynomials. The primary objective is to calculate the stress intensity factor in mode 1, denoted as K1. The obtained results reveal the influence of the strip width and crack length on the stress intensity factor, assuming stress-free edges. Additionally, a comparison is made with relevant literature to validate the findings.

Keywords: center crack, Chebyshev polynomial, hyper singular integral equation, Griffith, infinite strip, stress intensity factor

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

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In this work, repaired crack in 6061-T6 aluminum plate with composite patches presented, firstly we determine the displacement, strain, and stress, also the first six mode shape of the plate, secondly we took the same model adding central crack initiation, which is located in the center of the plate, its size vary from 20 mm to 60 mm and we compare the first results with second. Thirdly, we repair various cracks with the composite patch (carbon/epoxy) and for (2 layers, 4 layers). Finally, the comparison of stress, strain, displacement and six first natural frequencies between un-cracked specimen, crack propagation and composite patch repair.

Keywords: composite patch repair, crack growth, aluminum alloy plate, stress

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Authors: F. J. Ma, A. K. H. Kwan

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Crack caused by shrinkage movement of concrete is a serious problem especially when restraint is provided. It may cause severe serviceability and durability problems. The existing prediction methods for crack width of concrete due to shrinkage movement are mainly numerical methods under simplified circumstances, which do not agree with each other. To get a more unified prediction method applicable to more sophisticated circumstances, finite element crack width analysis for shrinkage effect should be developed. However, no existing finite element analysis can be carried out to predict the crack width of concrete due to shrinkage movement because of unsolved reasons of conventional finite element analysis. In this paper, crack width analysis implemented by finite element analysis is presented with pseudo-discrete crack model, which combines traditional smeared crack model and newly proposed crack queuing algorithm. The proposed pseudo-discrete crack model is capable of simulating separate and single crack without adopting discrete crack element. And the improved finite element analysis can successfully simulate the stress redistribution when concrete is cracked, which is crucial for predicting crack width, crack spacing and crack number.

Keywords: crack queuing algorithm, crack width analysis, finite element analysis, shrinkage effect

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Authors: M. Benachour, N. Benachour, M. Benguediab

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In this investigation, variation of cyclic loading effect on fatigue crack growth is studied. This study is performed on 2024 T351 and 7050-T74 aluminum alloys, used in aeronautical structures. The propagation model used in this study is NASGRO model. In constant amplitude loading (CA), the effect of stress ratio has been investigated. Fatigue life and fatigue crack growth rate were affected by this factor. Results showed an increasing in fatigue crack growth rates (FCGRs) with increasing stress ratio. Variable amplitude loading (VAL) can take many forms i.e with a single overload, overload band etc. The shape of these loads affects strongly the fracture life and FCGRs. The application of a single overload (ORL) decrease the FCGR and increase the delay crack length caused by the formation of a larger plastic zone compared to the plastic zone due without VAL. The fatigue behavior of the both material under single overload has been compared.

Keywords: fatigue crack growth, overload ratio, stress ratio, generalized willenborg model, retardation, al-alloys

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Authors: Gulcan Ozerim, Gunay Anlas

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

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Authors: Abdoulnabi Tavangari, Nasim Salehzadeh

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We presume a cylindrical medium that is under a uniform loading and there is a penny shaped crack located in the center of cylinder. In the crack growth analysis, the Stress Intensity Factor (SIF) is a fundamental prerequisite. In the present study, according to the RITZ method and by considering a cylindrical coordinate system as the main coordinate and a local polar coordinate, the mode-I SIF of threedimensional penny-shaped crack is obtained. In this method the unknown coefficients will be obtained with minimizing the potential energy that is including the strain energy and the external force work. By using the hook's law, stress fields will be obtained and then by using the Irvine equations, the amount of SIF will be obtained near the edge of the crack. This question has been solved for extreme medium in the Tada handbook and the result of the present research has been compared with that.

Keywords: three-dimensional cracks, penny-shaped crack, stress intensity factor, fracture mechanics, Ritz method

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

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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: crack, dramix, fiber, load, slab

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Authors: Jehnming Lin

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In the laser cleavage of glass, the laser is mostly adopted as a heat source to generate a thermal stress state on the substrates. The crack propagation of the soda-lime glass in the laser thermal cleavage with the straight-turning paths was investigated in this study experimentally and numerically. The crack propagation was visualized by a high speed camera with the off-line examination on the micro-crack propagation. The temperature and stress distributions induced by the laser heat source were calculated by ANSYS software based on the finite element method (FEM). With the cutting paths in various turning directions, the experimental and numerical results were in comparison and verified. The fracture modes due to the normal and shear stresses were verified at the turning point of the laser cleavage path. It shows a significant variation of the stress profiles along the straight-turning paths and causes a change on the fracture modes.

Keywords: laser cleavage, glass, fracture, stress analysis

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Authors: M. Benachour, N. Benachour, M. Benguediab

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In this investigation an empirical study was made on fatigue crack initiation on 7075 T6 and 7075 T71 al-alloys under constant amplitude loading. At initiation stage, local strain approach at the notch was applied. Single Edge Notch Tensile specimen with semi circular notch is used. Based on experimental results, effect of mean stress, is highlights on fatigue initiation life. Results show that fatigue life initiation is affected by notch geometry and mean stress.

Keywords: fatigue crack initiation, al-alloy, mean stress, heat treatment state

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Authors: Samaila Bawa Muazu

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Hydration process, crack potential and setting time of concrete grade C30, C40 and C50 were separately monitored using non-contact electrical resistivity apparatus, a novel plastic ring mould and penetration resistance method respectively. The results show highest resistivity of C30 at the beginning until reaching the acceleration point when C50 accelerated and overtaken the others, and this period corresponds to its final setting time range, from resistivity derivative curve, hydration process can be divided into dissolution, induction, acceleration and deceleration periods, restrained shrinkage crack and setting time tests demonstrated the earliest cracking and setting time of C50, therefore, this method conveniently and rapidly determines the concrete’s crack potential. The highest inflection time (ti), the final setting time (tf) were obtained and used with crack time in coming up with mathematical models for the prediction of concrete’s cracking age for the range being considered. Finally, ANSYS numerical simulations supports the experimental findings in terms of the earliest crack age of C50 and the crack location that, highest stress concentration is always beneath the artificially introduced expansion joint of C50.

Keywords: concrete hydration, electrical resistivity, restrained shrinkage crack, setting time, simulation

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Authors: Volkmar Nolting

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Fatigue crack growth prediction has become an important topic in both engineering and non-destructive evaluation. Crack propagation is influenced by the mechanical properties of the material and is conveniently modelled by the Paris-Erdogan equation. The critical crack size and the total number of load cycles are calculated. From a Larson-Miller plot the maximum operational temperature can for a given stress level be determined so that failure does not occur within a given time interval t. The study is used to determine a reasonable inspection cycle and thus enhances operational safety and reduces costs.

Keywords: fracturemechanics, crack growth prediction, lifetime of a component, structural health monitoring

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

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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: bonded repair, notch, crack, adhesive, composite

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Authors: Mohammad Ridzwan Bin Abd Rahim, Siegfried Schmauder, Yupiter HP Manurung, Peter Binkele, Meor Iqram B. Meor Ahmad, Kiarash Dogahe

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This paper deals with the short crack initiation of the material P91 under cyclic loading at two different temperatures, concluded with the estimation of the short crack initiation Wöhler (S/N) curve. An artificial but representative model microstructure was generated using Voronoi tessellation and the Finite Element Method, and the non-uniform stress distribution was calculated accordingly afterward. The number of cycles needed for crack initiation is estimated on the basis of the stress distribution in the model by applying the physically-based Tanaka-Mura model. Initial results show that the number of cycles to generate crack initiation is strongly correlated with temperature.

Keywords: short crack initiation, P91, Wöhler curve, Voronoi tessellation, Tanaka-Mura model

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Authors: Thomas Jin-Chee Liu

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In this paper, the thermo-electro-structural coupled-field in a cracked metal plate is studied using the finite element analysis. From the computational results, the compressive stresses reveal near the crack tip. This conclusion agrees with the past reference. Furthermore, the compressive condition can retard and stop the crack growth during the Joule heating process.

Keywords: compressive stress, crack tip, Joule heating, finite element

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Authors: Anurag Niranjan, Michael Fitzpatrick, Yin Jin Janin, Jazeel Chukkan, Niall Smyth

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Fillet welds are used in joining longitudinal stiffeners in ship structures. Welding residual stresses in fillet welds are generally distributed in a non-uniform manner, as shown in previous research the residual stress redistribution occurs under the cyclic loading that is experienced by such joints during service, and the combination of the initial residual stress, local constraints, and loading can alter the stress field in ways that are extremely difficult to predict. As the residual stress influences the crack propagation originating from the toe of the fillet welds, full understanding of the residual stress field and how it evolves is very important for structural integrity calculations. Knowledge of the residual stress redistribution in the presence of a flaw is therefore required for better fatigue life prediction. Moreover, defect assessment procedures such as BS7910 offer very limited guidance for flaw acceptance and the associated residual stress redistribution in the assessment of fillet welds. Therefore the objective of this work is to study a surface-breaking flaw at the weld toe region in a fillet weld under cyclic load, in conjunction with residual stress measurement at pre-defined crack depths. This work will provide details of residual stress redistribution under cyclic load in the presence of a crack. The outcome of this project will inform integrity assessment with respect to the treatment of residual stress in fillet welds. Knowledge of the residual stress evolution for this weld geometry will be greatly beneficial for flaw tolerance assessments (BS 7910, API 591).

Keywords: fillet weld, fatigue, residual stress, structure integrity

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Authors: Jeries J. Abou-Hanna, Bradley Storm

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This paper looks to reduce the complexity of determining stress intensity factors while maintaining high levels of accuracy by the use of a linearized layering approach. Many techniques for stress intensity factor determination exist, but they can be limited by conservative results, requiring too many user parameters, or by being too computationally intensive. Multiple notch geometries with various crack lengths were investigated in this study to better understand the effectiveness of the proposed method. By linearizing the average stresses in radial layers around the crack tip, stress intensity factors were found to have error ranging from -10.03% to 8.94% when compared to analytically exact solutions. This approach proved to be a robust and efficient method of accurately determining stress intensity factors.

Keywords: fracture mechanics, finite element method, stress intensity factor, stress linearization

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