Search results for: crack tip plastic zones

Authors: Morteza Raki, Abolghasem Zabihollah, Omid Askari

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Cantilever beam is a simplified sample of a lot of mechanical components used in a wide range of applications, including many industries such as gas turbine blade. Due to the nature of the operating conditions, beams are subject to variety of damages especially crack propagates. Crack propagation may lead to catastrophic failure during operation. Therefore, online detection of crack presence and its propagation is very important and may reduce possible significant cost of the whole system failure. This paper aims to investigate the effect of cracks presence and crack propagation on one end fixed beam`s vibration. A finite element model will be developed for the blade in which the modal response of the structure with and without crack will be studied. 

Keywords: blade, crack propagation, health monitoring, modal analysis

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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: 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: Wentao He, Jingxi Liu, De Xie

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It is necessary to manage the fatigue crack growth (FCG) once those cracks are detected during in-service inspections. In this paper, a simulation program (FCG-System) is developed utilizing the commercial software ABAQUS with its object-oriented programming interface to simulate the fatigue crack path and to compute the corresponding fatigue life. In order to apply FCG-System in large-scale marine structures, the substructure modeling technique is integrated in the system under the consideration of structural details and load shedding during crack growth. Based on the nodal forces and nodal displacements obtained from finite element analysis, a formula for shell elements to compute stress intensity factors is proposed in the view of virtual crack closure technique. The cracks initiating from the intersection of flange and the end of the web-stiffener are investigated for fatigue crack paths and growth lives under water pressure loading and axial force loading, separately. It is found that the FCG-System developed by authors could be an efficient tool to perform fatigue crack growth analysis on marine structures.

Keywords: crack path, fatigue crack, fatigue live, FCG-system, virtual crack closure technique

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Authors: Somnath Bhattacharya, Kamal Sharma, Vaibhav Sonkar

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Composite materials emerged in the middle of the 20th century as a promising class of engineering materials providing new prospects for modern technology. Recently, a new class of composite materials known as functionally graded materials (FGMs) has drawn considerable attention of the scientific community. In general, FGMs are defined as composite materials in which the composition or microstructure or both are locally varied so that a certain variation of the local material properties is achieved. This gradual change in composition and microstructure of material is suitable to get gradient of properties and performances. FGMs are synthesized in such a way that they possess continuous spatial variations in volume fractions of their constituents to yield a predetermined composition. These variations lead to the formation of a non-homogeneous macrostructure with continuously varying mechanical and / or thermal properties in one or more than one direction. Lightweight functionally graded composites with high strength to weight and stiffness to weight ratios have been used successfully in aircraft industry and other engineering applications like in electronics industry and in thermal barrier coatings. In the present work, elastic-plastic crack growth problems (using Ramberg-Osgood Model) in an FGM plate under cyclic load has been explored by extended finite element method. Both edge and centre crack problems have been solved by taking additionally holes, inclusions and minor cracks under plane stress conditions. Both soft and hard inclusions have been implemented in the problems. The validity of linear elastic fracture mechanics theory is limited to the brittle materials. A rectangular plate of functionally graded material of length 100 mm and height 200 mm with 100% copper-nickel alloy on left side and 100% ceramic (alumina) on right side is considered in the problem. Exponential gradation in property is imparted in x-direction. A uniform traction of 100 MPa is applied to the top edge of the rectangular domain along y direction. In some problems, domain contains major crack along with minor cracks or / and holes or / and inclusions. Major crack is located the centre of the left edge or the centre of the domain. The discontinuities, such as minor cracks, holes, and inclusions are added either singly or in combination with each other. On the basis of this study, it is found that effect of minor crack in the domain’s failure crack length is minimum whereas soft inclusions have moderate effect and the effect of holes have maximum effect. It is observed that the crack growth is more before the failure in each case when hard inclusions are present in place of soft inclusions.

Keywords: elastic-plastic, fatigue crack, functionally graded materials, extended finite element method (XFEM)

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Authors: J. Y. Lee, H. S. Lim, S. H. Yoon

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This paper presents an analysis of the diagonal crack widths of RC members with various types of materials by simulating a compatibility-aided truss model. The analytical results indicated that the diagonal crack width was influenced by not only the shear reinforcement ratio but also the yield strength of shear reinforcement and the compressive strength of concrete. The yield strength of shear reinforcement and the compressive strength of concrete decreased the diagonal shear crack width of RC members for the same shear force because of the change of shear failure modes. However, regarding the maximum shear crack width at shear failure, the shear crack width of the beam with high strength materials was greater than that of the beam with normal strength materials.

Keywords: diagonal crack width, high strength stirrups, high strength concrete, RC members, shear behavior

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Authors: Dmitrii Starikov, Evgeny Rybakov, Denis Zhuravlev

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Plastic for 3D printing is very necessary material part for printers. But plastic production is technological process, which implies application of different control algorithms. Possible algorithms of providing set diameter of plastic fiber are proposed and described in the article. Results of research were proved by existing unit of filament production.

Keywords: ABS-plastic, automation, control system, extruder, filament, PID-algorithm

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Authors: Norie A. Akeel, Z. Sajuri, A. K. Ariffin

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This paper discusses the effect of different loading analysis on crack initiation life of wheel/rail in the contact region. A simulated three dimensional (3D) elasto plastic model of a wheel/rail contact is modeled using the fine mesh technique in the contact region by using Finite Element Method FEM code ANSYS 11.0 software. Different loads of approximately from 70 to 140 KN was applied on the wheel tread through the running surface on the railhead surface to simulate stress distribution (Von Mises) and a life prediction of the crack initiation under rolling contact motion. Stress analysis is achieved and the fatigue life to the rail head surface is calculated numerically by using a multi-axial fatigue life of crack initiation model. All results obtained from the previous researches are compared with this research.

Keywords: FEM, rolling contact, rail track, stress distribution, fatigue life

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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: Elkedrouci Lotfi, Diao Bo, Pang Sen, Li Yi

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Deterioration of reinforced concrete structures is a serious concern in the construction engineering, largely due to chloride induced corrosion of reinforcement. Chloride penetration is markedly influenced by one or several major factors at the same time such as cuing in combination with different crack widths which have spectacular effect on reinforced concrete structures. This research presents the results of an experimental investigation involving reinforced concrete beams with three different crack widths ranging from 0 to 0.2mm, curing temperatures of 20°C or 40°C and water-to-cement of 0.5. Chloride content profiles were determined under non-steady state diffusion at 20°C. Based on the obtained results, higher chloride content was obtained under condition of high curing temperature in combination with large crack more than 0.1mm and there are no significant differences between narrow crack width (less than 0.1 mm) and beams without crack (0mm).

Keywords: crack width, high curing temperature, rapid chloride migration, reinforced concrete beam

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Authors: Sukrit Ghorai

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Proof of controlling crack width is a basic condition for securing suitable performance in serviceability limit state. The cracking in concrete can occur at any time from the casting of time to the years after the concrete has been set in place. Most codes struggle with offering procedure for crack width calculation. There is lack in availability of design charts for designers to compute crack width with ease. The focus of the study is to utilize design charts and parametric equations in calculating crack width with minimum error. The paper contains a simplified procedure to calculate crack width for reinforced concrete (RC) sections subjected to bending with axial tensile force following the guidelines of Euro code [DS EN-1992-1-1 & DS EN-1992-1-2]. Numerical examples demonstrate the application of the suggested procedure. Comparison with parallel analytical tools support the validity of result and show the percentage deviation of crack width in both the procedures. The technique is simple, user-friendly and ready to evolve for a greater spectrum of section sizes and materials.

Keywords: concrete structures, crack width calculation, serviceability limit state, structural design, bridge engineering

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Authors: Seon Soon Choi

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The essential purpose is to present the good fatigue crack propagation model describing a stochastic fatigue crack growth behavior in a rolled magnesium alloy, AZ31, under various load ratio conditions. Fatigue crack propagation experiments were carried out in laboratory air under four conditions of load ratio, R, using AZ31 to investigate the crack growth behavior. The stochastic fatigue crack growth behavior was analyzed using an interpolation of random variable, Z, introduced to an empirical fatigue crack propagation model. The empirical fatigue models used in this study are Paris-Erdogan model, Walker model, Forman model, and modified Forman model. It was found that the random variable is useful in describing the stochastic fatigue crack growth behaviors under various load ratio conditions. The good probabilistic model describing a stochastic fatigue crack growth behavior under various load ratio conditions was also proposed.

Keywords: magnesium alloys, fatigue crack propagation model, load ratio, interpolation of random variable

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Authors: G. A. Rombach, A. Faron

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Crack formation and growth in reinforced concrete members are, in many cases, the cause of the collapse of technical structures. Such serious failures impair structural behavior and can also damage property and persons. An intensive investigation of the crack propagation is indispensable. Numerical methods are being developed to analyze crack growth in an element and to detect fracture failure at an early stage. For reinforced concrete components, however, further research and action are required in the analysis of shear cracks. This paper presents numerical simulations and continuum mechanical modeling of bending shear crack propagation in a three-dimensional reinforced concrete beam without transverse reinforcement. The analysis will provide a further understanding of crack growth and redistribution of inner forces in concrete members. As a numerical method to map discrete cracks, the extended finite element method (XFEM) is applied. The crack propagation is compared with the smeared crack approach using concrete damage plasticity. For validation, the crack patterns of real experiments are compared with the results of the different finite element models. The evaluation is based on single span beams under bending. With the analysis, it is possible to predict the fracture behavior of concrete members.

Keywords: concrete damage plasticity, crack propagation, extended finite element method, fracture mechanics

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Authors: Arjita Biswas, Sandeep Potnis

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Plastic roads (bituminous roads using waste plastic in the wearing course ) have now become familiar in the Road Construction Sector in India. With the Indian Road Congress Code (IRC SP: 98 -2013), many agencies are coming forward to implement Plastic Roads in India. This paper discuss and compare about the various properties of bituminous mix with 8% waste plastic and normal bituminous mix. This paper also signifies the performance of both the types of roads after 4 months of age under loading conditions. Experiments were carried out to evaluate its performance. The result shows improved performance of plastic roads.

Keywords: bituminous roads, experiments, performance, plastic roads

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Authors: Li Hui, Riyadh Hindi

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Concrete structures frequently suffer from crack formation, a critical issue that can significantly reduce their lifespan by allowing damaging agents to enter. Traditional methods of crack detection depend on manual visual inspections, which heavily relies on the experience and expertise of inspectors using tools. In this study, a more efficient, computer vision-based approach is introduced by using the lightweight MobileNetV2 neural network. A dataset of 40,000 images was used to develop a specialized crack evaluation algorithm. The analysis indicates that MobileNetV2 matches the accuracy of traditional CNN methods but is more efficient due to its smaller size, making it well-suited for mobile device applications. The effectiveness and reliability of this new method were validated through experimental testing, highlighting its potential as an automated solution for crack detection in concrete structures.

Keywords: Concrete crack, computer vision, deep learning, MobileNetV2 neural network

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Authors: Abdelouaheb Rouabhi

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In order to study the plastic resource of structures, the elastic-plastic single degree of freedom model described by Prandtl diagram is widely used. The generalization of this model to tow degree of freedom beyond the scope of a simple rigid-plastic system allows investigating the plastic resource of structures under complex disproportionate by individual components of deformation (earthquake). This macro-model greatly increases the accuracy of the calculations carried out. At the same time, the implementation of the proposed macro-model calculations easier than the detailed dynamic elastic-plastic calculations existing software systems such as ANSYS.

Keywords: elastic-plastic, single degree of freedom model, rigid-plastic system, plastic resource, complex plastic deformation, macro-model

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Authors: A. Kouadri-Henni, L. Barrallier

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The objective of the study was to characterize the properties of a magnesium alloy welded by friction stir welding (FSW). The results led to a better understanding of the relationship between this process, the microstructure and anisotropic properties of alloy materials. Welding principally leads to a large reduction in grain size in welded zones due to the phenomenon of dynamic recrystallization. The most remarkable observation was that crystallographic textures changed from a base metal with one texture in two zones: the thermo-mechanically affected and stir welded zones. The latter zone has the peculiarity of possessing a marked texture with two components on the basal plane and the pyramidal plane. These characteristics disappeared in the TMAZ, which had only one component following the basal plane. These modifications have been explained by the nature of the plastic deformation in these zones, which occurs at a moderate temperature in the TMAZ and high temperature in the SWZ. In the same time, we compared this evolution with the nature and the level of the residual stresses obtained by X-ray diffraction.

Keywords: texture christallography, residual stresses, FSW process

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Authors: Rana Atta Ur Rahman, Daniel Juhre

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Initiation of crack during fatigue of casting alloys are noticed mainly on the basis of experimental results. Crack initiation and strength of fatigue of AA320 are summarized here. Load sequence effect is applied to notify initiation phase life. Crack initiation at notch root and fatigue life is calculated under single & two-step mechanical loading (ML) with and without combined thermal cycling (CTC). An Experimental setup is proposed to create the working temperature as per alloy applications. S-N curves are plotted, and a comparison is made between crack initiation leading to failure under different ML with & without thermal loading (TL).

Keywords: fatigue, initiation, SN curve, alloy

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Authors: Sifatullah Bahij, Safiullah Omary, Francoise Feugeas, Amanullah Faqiri

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Plastic packages have been broadly used for a long time. Such widespread usage of plastic has resulted in an increased amount of plastic wastes and many environmental impacts. Plastic wastes are one of the most significant types of waste materials because of their non-degradation and low biodegradability. It is why many researchers tried to find a safe and environmentally friendly solution for plastic wastes. In this goal, in the civil engineering industry, many types of plastic wastes have been incorporated, as a partial substitution of aggregates or as additive materials (fibers) in concrete mixtures because of their lengthier lifetime and lower weight. This work aims to study the mechanical properties (compressive, split tensile and flexural strengths) of concrete with a water-cement ratio (w/c) of 0.45 and with the incorporation of non-woven PET plastic sheets. Five configurations -without PET (reference), 1-layer sheet, 2-side, 3-side, and full sample wrapping- were applied. The 7, 14 and 28-days samples’ compressive strengths, flexural strength and split tensile strength were measured. The outcomes of the study show that the compressive strength was improved for the wrapped samples, particularly for the cylindrical specimens. Also, split tensile and flexural behaviors of the wrapped samples improved significantly compared to the reference ones. Moreover, reference samples were damaged into many parts after mechanical testing, while wrapped specimens were taken by the applied configurations and were not divided into many small fragments. Therefore, non-woven fabrics appeared to improve some properties of the concrete.

Keywords: solid waste plastic, non-woven polyethylene terephthalate sheets, mechanical behaviors, crack pattern

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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: Francis Gbogbo, Angelica Ama Essandoh, Wendy Teresa Baffoe, Henry Groos, Charles Mario Boateng, Emmanuel Robert Blankson

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Baseline data on plastic landing by fishers and monitoring of this is important in evaluating the success of plastic waste management efforts. This study investigated plastic and fish landed by beach seine fishers in Ghana, together with the rate of plastic deposition on an adjoining beach. Plastic constituted 31.6% of the total catch, and 41.7% of the fish landed by weight. There were significant differences between the average weight of fish (139.58±53.6kg) and plastic (65.73±14.6kg) landed per fishing session and the catch per unit effort of fish (183.4±76.7 kg/day) and plastic (88.4±35.2 kg/day). The mean weight of plastic landed per fishing session was higher than the mean weight of each of the 26 species of fisheries. The rate of plastic deposition on the beach was 8.1±2.5 plastic items per m2 per tidal cycle or 0.35±0.11kg plastic per m2 per tidal cycle, with food packs and tableware dominating the deposited plastic. The results suggested that ongoing water sachets and plastic bottle recycling in Ghana are yielding results and calls for targeted efforts in plastic food packs and tableware management.

Keywords: fishig, landing, plastic waste, intertidal area, fishing effort

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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: Morgan Johansson, Joosef Leppanen, Mathias Flansbjer, Fabio Lozano, Josef Makdesi

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Concrete is commonly used for protective structures and how impact loading affects different types of concrete structures is an important issue. Often the knowledge gained from static loading is also used in the design of impulse loaded structures. A large plastic deformation capacity is essential to obtain a large energy absorption in an impulse loaded structure. However, the structural response of an impact loaded concrete beam may be very different compared to a statically loaded beam. Consequently, the plastic deformation capacity and failure modes of the concrete structure can be different when subjected to dynamic loads; and hence it is not sure that the observations obtained from static loading are also valid for dynamic loading. The aim of this paper is to investigate the residual plastic deformation capacity in reinforced concrete beams subjected to drop weight impact tests. A test-series consisting of 18 simply supported beams (0.1 x 0.1 x 1.18 m, ρs = 0.7%) with a span length of 1.0 m and subjected to a point load in the beam mid-point, was carried out. 2x6 beams were first subjected to drop weight impact tests, and thereafter statically tested until failure. The drop in weight had a mass of 10 kg and was dropped from 2.5 m or 5.0 m. During the impact tests, a high-speed camera was used with 5 000 fps and for the static tests, a camera was used with 0.5 fps. Digital image correlation (DIC) analyses were conducted and from these the velocities of the beam and the drop weight, as well as the deformations and crack propagation of the beam, were effectively measured. Additionally, for the static tests, the applied load and midspan deformation were measured. The load-deformation relations for the beams subjected to an impact load were compared with 6 reference beams that were subjected to static loading only. The crack pattern obtained were compared using DIC, and it was concluded that the resulting crack formation depended much on the test method used. For the static tests, only bending cracks occurred. For the impact loaded beams, though, distinctive diagonal shear cracks also formed below the zone of impact and less wide shear cracks were observed in the region half-way to the support. Furthermore, due to wave propagation effects, bending cracks developed in the upper part of the beam during initial loading. The results showed that the plastic deformation capacity increased for beams subjected to drop weight impact tests from a high drop height of 5.0 m. For beams subjected to an impact from a low drop height of 2.5 m, though, the plastic deformation capacity was in the same order of magnitude as for the statically loaded reference beams. The beams tested were designed to fail due to bending when subjected to a static load. However, for the impact tested beams, one beam exhibited a shear failure at a significantly reduced load level when it was tested statically; indicating that there might be a risk of reduced residual load capacity for impact loaded structures.

Keywords: digital image correlation (DIC), drop weight impact, experiments, plastic deformation capacity, reinforced concrete

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Authors: Zellagui Redouane, Bellaouar Ahmed, Lachi Mohammed

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The railway axles are the essential parts in the bogie of train, and its failure creates a big problem in the railway transport; during the work of this parts we noticed a premature deterioration. The aim has been presented a predictive model allowing the identification of the probable causes that are the cause of these premature deterioration. The results are employed for predicting fatigue crack growth in the railway axle, Also we want to present the variation value of stress intensity factor in different positions of elliptical crack tip. The modeling of axle in performed by the SOLID WORKS software and imported into ANSYS.

Keywords: crack growth, static load, railway axle, lifetime

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Authors: Tao Qu, Chandra Prakash, Vikas Tomar

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The interfaces between organic and inorganic phases in natural materials have been shown to be a key factor contributing to their high performance. This work analyzes crack propagation in a 2-ply laminate subjected to uniaxial tensile mode-I crack propagation loading that has laminate properties derived based on biological material constituents (marine exoskeleton- chitin and calcite). Interfaces in such laminates are explicitly modeled based on earlier molecular simulations performed by authors. Extended finite element method and cohesive zone modeling based simulations coupled with theoretical analysis are used to analyze crack propagation. Analyses explicitly quantify the effect that interface mechanical property variation has on the delamination as well as the transverse crack propagation in examined 2-ply laminates.

Keywords: chitin, composites, interfaces, fracture

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Authors: Marcel Meinhardt, Manfred Keuser, Thomas Braml

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Cracking of reinforced concrete is a complex phenomenon induced by direct loads or restraints affecting reinforced concrete structures as soon as the tensile strength of the concrete is exceeded. Hence it is important to predict where cracks will be located and how they will propagate. The bond theory and the crack formulas in the actual design codes, for example, DIN EN 1992-1-1, are all based on the assumption that the reinforcement bars are embedded in homogeneous concrete without taking into account the influence of transverse reinforcement and the real stress situation. However, it can often be observed that real structures such as walls, slabs or beams show a crack spacing that is orientated to the transverse reinforcement bars or to the stirrups. In most Finite Element Analysis studies, the smeared crack approach is used for crack prediction. The disadvantage of this model is that the typical strain localization of a crack on element level can’t be seen. The crack propagation in concrete is a discontinuous process characterized by different factors such as the initial random distribution of defects or the scatter of material properties. Such behavior presupposes the elaboration of adequate models and methods of simulation because traditional mechanical approaches deal mainly with average material parameters. This paper concerned with the modelling of the initiation and the propagation of cracks in reinforced concrete structures considering the influence of transverse reinforcement and the real stress distribution in reinforced concrete (R/C) beams/plates in bending action. Therefore, a parameter study was carried out to investigate: (I) the influence of the transversal reinforcement to the stress distribution in concrete in bending mode and (II) the crack initiation in dependence of the diameter and distance of the transversal reinforcement to each other. The numerical investigations on the crack initiation and propagation were carried out with a 2D reinforced concrete structure subjected to quasi static loading and given boundary conditions. To model the uncertainty in the tensile strength of concrete in the Finite Element Analysis correlated normally and lognormally distributed random filed with different correlation lengths were generated. The paper also presents and discuss different methods to generate random fields, e.g. the Covariance Matrix Decomposition Method. For all computations, a plastic constitutive law with softening was used to model the crack initiation and the damage of the concrete in tension. It was found that the distributions of crack spacing and crack widths are highly dependent of the used random field. These distributions are validated to experimental studies on R/C panels which were carried out at the Laboratory for Structural Engineering at the University of the German Armed Forces in Munich. Also, a recommendation for parameters of the random field for realistic modelling the uncertainty of the tensile strength is given. The aim of this research was to show a method in which the localization of strains and cracks as well as the influence of transverse reinforcement on the crack initiation and propagation in Finite Element Analysis can be seen.

Keywords: crack initiation, crack modelling, crack propagation, cracks, numerical simulation, random fields, reinforced concrete, stochastic

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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: 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: 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: Nidhal Jamia, Sami El-Borgi

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In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: functionally graded piezoelectric material (FGPM), mixed-mode crack, non-local theory, Schmidt method

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