Effects Of Crack Location Research Articles

Calculation and Discussion for Crack Driving Force of Dissimilar Metal Welded Joint of Nuclear Power Equipment Nozzle and Safe End

This study investigates the effects of the material mechanical properties heterogeneity and strength mismatch variation on crack driving forces for cracks in a dissimilar metal welded joint (DMW) of a reactor pressure vessel inlet nozzle to the safe end. Linear elastic and elastic-plastic analyses are carried out to calculate the stress intensity factor (SIF) and J-integral for cracks in the DMW. The effects of crack locations, crack depths, and strength mismatch factors on the SIF and J-integral are studied. The SIF results obtained by finite element analysis are compared with those obtained by the influence function method adopted in the nuclear power code. Results show that the effect of crack location on the SIF can be ignored. The SIFs calculated by the influence function method for cracks in the DMW are basically reasonable, although its conservatism is slightly insufficient. Moreover, with moving the crack location from the nozzle through buttering and weld metal to the safe end, the J-integral increases. The effect of the crack location and strength mismatch factors on the J-integral is essentially caused by variation of the plastic zone and the material properties of the crack front. The crack sizes affect the level of influence of the crack location and the strength mismatch factors on the J-integral. The J-integral increases with decrease of the strength mismatch factor.

A concerted experimental and numerical approach for frequency based non-destructive analysis of Bi-directional cracked laminated composite beams

ABSTRACT The effects of single and multiple transverse open cracks on the dynamic properties of woven fibre laminated composite beam (LCB) under free vibration by experimental and numerical approaches are explored in this research work. The experimental modal testing is performed n laminated glass/epoxy composite beams using vibration Fast Fourier Transformation (FFT) analyser system. The finite element simulation software ABAQUS is used as the platform for numerical modal analysis to arrive at the natural frequencies. Within the test domain of modal analysis, the simulated results are finely agreed with the empirical test results. The effects of crack location, relative crack depth, boundary conditions and fibre orientations on the modal frequency of the cracked LCB are explored under free vibration. The results of the study conclude that the maximum decrease in frequencies is observed for 0° ply oriented single and multi-cracked LCB. Furthermore, the results elicit that the presence of crack positioned nearer to the restrained end exhibits more reduction in vibration frequencies for any particular crack depth. Within the frequency domain, the present research approach can be employed as an effective tool for the detection and analysis of crack or crack-like defects in LCB structures in any applied field of engineering.

An experimental and FEA approach to investigate effect of cracks on a rotor bearing system

The field of rotordynamics primarily focuses on the analysis and characterization of lateral and torsional vibrations of rotor bearing system. In this study, the lateral vibrations of a single disc rotor bearing system are studied. The effect of crack location, crack depth, and number of cracks has been studied for structural health monitoring of shafts. For the finite element approach, Ansys version 19.0 is used, and a modal analysis was conducted in order to determine the participation factor and bending modal frequencies. Also, a Campbell diagram for critical speeds and whirl direction is plotted. A single-disc rotor bearing system is treated as a simply supported case. Experimental performance has been carried out on a self-designed testbed, and results are obtained using a DEWEsoft FFT Analyzer. A plot of the frequency spectrum is plotted for all shaft cases. After comparing FEA and Experimental results, a maximum variation of 5 percent was found. The investigational results are corelated; hence, the above methodology for rotordynamic analysis may be suggested.

Nonlinear dynamic analysis on centrifugal stiffening of rotating cracked tapered functionally graded beam for flap-wise vibrations

Vibration-based condition monitoring for remotely located rotating blades is one of the important aspects to avoid sudden breakdown of the machinery. Vibration analysis of damaged blades provides the information to identify the damage during operation. In this work, dynamic attributes of rotating cracked tapered cantilever functionally graded material (FGM) beams for various tapered configurations are investigated using energy method. The nonlinearity due to in plane stretching as a result of large deformations is taken in to consideration. Nonlinear governing equations for cracked rotating tapered FGM beams are generated by optimizing the energy functional. An iterative algorithm is developed to solve the derived nonlinear equations. The effects corresponding to location of crack and centrifugal stiffening on the various modes has been presented for different tapered configurations, material indices, crack depths and rotational speeds. Crack compensating speeds are studied and reported for different tapered ratios and crack parameters for the first time. The effect of crack location and crack depth on the first two nonlinear frequency ratios is also investigated for different tapered configurations and material indices. The influence of centrifugal stiffening on nonlinear responses of FGM beams is presented for various crack parameters and tapered configurations.

Parametric Analysis of the Nonlinear Dynamics of a Cracked Cantilever Beam

Abstract Structural damage occurs in a variety of civil, mechanical, and aerospace engineering systems, and it is critical to effectively identify such damage in order to prevent catastrophic failures. When cracks are present in a structure, the breathing phenomenon that occurs between crack surfaces typically triggers nonlinearity in the dynamic response. In this work, in order to thoroughly understand the nonlinear effect of cracks on structural dynamics, two modeling approaches are integrated to investigate the crack-induced nonlinear dynamics of cantilever beams. First, a modeling method referred to as the discrete element (DE) method is employed to construct a model of a cracked beam. The DE model is able to characterize the breathing phenomenon of cracks. Next, a simulation technique referred to as the hybrid symbolic-numeric computational (HSNC) method is used to analyze the nonlinear response of the cracked beam. The HSNC method provides an efficient way to evaluate both stationary and nonstationary dynamics of cracked systems since it combines efficient linear techniques with an optimization tool to capture the system’s nonlinear response. The proposed computational platform thus enables efficient multiparametric analysis of cracked structures. The effects of crack location, crack depth, and excitation frequency on the cantilever beam are parametrically investigated using the proposed method. Nonlinear features such as subharmonic resonance, nonstationary motion, multistability, and frequency shift are also discussed in this paper.

Effect of crack on dynamic characteristics of corn combine harvester frame

The frame is an integral part of the corn harvester and is the mounting carrier for all components, so a high strength frame structure is a basic requirement for a high level corn harvester. Corn harvesters often operate in harsh conditions on farmland and have a high intensity of concentrated operating hours. This often leads to fatigue cracks in the frame, which can affect the operational life of the harvester seriously and even result in accidents. Therefore the vibration characteristics of the frame structure of corn harvesters with cracks need to be investigated. Firstly, the typical experimental platform of the frame structure of the corn harvester with cracks is established, according to the structural characteristics and force situation of the frame of the corn harvester during operation. Then, the vibration characteristics of the frame with cracks in the longitudinal beam and the frame with cracks in the crossbeam were subject to different excitation frequencies and excitation amplitudes. Finally, the effects of crack location, excitation frequency and excitation amplitude on the vibration characteristics of the harvester frame structure were investigated by analyzing the time domain and frequency domain plots of the experimental results of the frame vibration characteristics under various conditions. The results of the study can provide reference for frame structure fault diagnosis and fault localization.

Effects of crack location and depths for an iron bar: A Finite Element approach

Structural Health Monitoring has become a significant issue in numerous engineering fields and industries. Early detection of damage such as cracks, as well as their depth and location, could be a major research topic. In this research, the natural frequency of a cylindrical solid shapes iron bar together with two half-circle surface crack has been investigated by Finite Element Method (FEM). Vibration Analysis has been used to predict response and different crack depths are the main parameters for analysis to access structural integrity performance of the domain. It is found that lowest frequency of intact bar was higher than the lowest frequency of the cracked bar, and frequencies decreased as the crack depth increased. Using this method very small sizes crack (minimum 0.05 mm) can be defined in any structural body.

Effect of crack location on buckling and dynamic stability in plate frame structures

It is well known that damages affect the dynamic characteristics of the structures in such a way that they may lead those structures to fail. Therefore, it is essential to construct a reliable mathematical model for estimating the effect of the damage in these structures. In this study, the effect of the straight, through-thickness crack and its location on the thin single-bay one-storey, two-bay-one-storey, and single-bay two-storey plate frames is investigated. For this purpose, a four-node quadrilateral plate bending and membrane elements are combined to perform finite element free vibration analysis of the healthy and cracked thin plate frame structures. The Classical Plate Theory is employed to satisfy the strain and stress conditions of these thin structures. A computer code is written using MATLAB to obtain the first three natural frequencies, critical buckling loads, and the first unstable regions of the healthy and cracked thin structures. To ensure the validity of the employed mathematical model, a convergence analysis is performed via ANSYS. The effect of crack location in plate frame structures is investigated by measuring the differences between the healthy and cracked structures’ first three buckling modes and the first unstable region. It is seen that the bending regions of the buckling modes are more affected by the crack than the other zones. Besides, crack occurrence within these regions has more impact on the first unstable regions. Accordingly, it has been revealed that the bending regions are the weakest locations of the frame structures. Therefore, potential cracks occurred within these regions may affect the structural integrity more than those of emerged in other regions.

Effects of the crack location on the dynamic response of multi-storey frame subjected to the passage of a high-speed train

The high-speed railways require more viaduct than a conventional railway. When the viaduct is subjected to high-amplitude vibrations for a long time, the fatigue-induced crack formation can occur . The presence of a crack changes the stiffness of the structure. Depending on the location of the crack, the reduction effect in stiffness varies. In this study, the presence of a single crack in a multi-storey frame structure, which is considered as a viaduct model, has been investigated. Effects of crack location on the dynamic response are investigated via 3D velocity-crack location-dynamic magnification factor (or maximum displacement) graphs. The train is modelled as a four-axle two-bogie multi-body system with 10 DOF and moving at a constant speed. The finite element method, based on Euler–Bernoulli beam theory, is used to simulate the vibrations of the coupled vehicle-structure system. Wilson-theta time integration scheme is used to solve the equation of motion. It has been determined that when the crack is located at the midpoint of the top beam, the highest effect on the dynamic response is observed.

Fracture studies on carbon steel straight pipes having off-centred circumferential through-wall crack under finite compliance

The level-3 Leak-Before-Break (LBB) assessment of nuclear piping system is based on simplified fracture mechanics calculations. A postulated through-wall circumferential crack is shown to be stable even under extreme loading conditions. An important aspect of this fracture assessment, which is generally not considered, is the reduction in load at the cracked section that occurs due to the local and global compliance of the piping system. In this study, the effect of piping system compliance, crack size and crack location on the load carrying capacity of SA-333 Gr. 6 carbon steel pipes was analysed. Experimental investigations were performed on 8״ NB Schedule 100 pipes (Outer diameter 219 mm and wall thickness of approx. 12.6 mm) under quasi-static four point bending loads. Out of the six fracture tests, one specimen had a through-wall circumferential crack at the centre (along the length of pipe) and the remaining five tests had off-centred cracks. While the initial crack size showed a weak influence on the load carrying capacity of a stiff piping system, the effect of crack location was, however, quite significant. Calculations based on twice-elastic slope (TES) method and limit analysis of uncracked piping system (in some cases) for evaluation of load carrying capacity of pipes under finite compliance may lead to large safety margins.

A study on effect of crack on free vibration of thick rectangular plate with initial geometric imperfection using differential quadrature method

In this study, vibration of initially imperfect cracked thick plate has been investigated using the differential quadrature method. The crack modeled as an open crack using a no-mass linear spring. The governing equations of vibration of a cracked plate are derived using the Mindlin theory and considering the effect of initial imperfection in Von-Karman equations. Differential equations are discretized using the differential quadrature method and are converted to a non-standard eigenvalue problem. Finally, natural frequencies and mode shapes of the cracked plate are obtained solving this eigenvalue problem. The accuracy of the proposed approach is verified using the results presented in other references. Various examples of the cracked plate problem have been solved utilizing the proposed method and effects of selected parameters such as crack depth, length and position have been checked. It is demonstrated that increasing the length and the depth of the crack decrease the plate stiffness and natural frequencies. Moreover, the effects of crack location on natural frequencies are more complicated, since they depend on the mode shapes, and when the crack is placed at a node-line, it will not influence the frequencies.

Research on geometric features of phase diagram and crack identification of cantilever beam with breathing crack

Geometric features of the phase diagram of a cantilever beam with a breathing crack are investigated. Influences of crack properties on the phase diagram geometry are studied and a method for crack identification based on phase diagram features is proposed. The pixel method is used to estimate different phase diagram areas. Multiple crack identification indexes are defined under the conditions of primary and super-harmonic resonance. The effects of crack location and depth on each index are analyzed. The contour lines for multiple identification indexes are used to estimate crack parameters. Numerical calculations indicate that the phase diagrams for super-harmonic resonance are more sensitive to crack parameters and that the proposed method is both feasible and effective.

Effect of Crack on Dynamic Characteristics of Simple Supported Beam

Simple supported beam is extensively applied in practical engineering structure. Crack is a common damage in simple supported beam and has greatly influences on the dynamic characteristics of the system. In this study, effect of crack on dynamic characteristics of simple supported beam is studied. The model of simple supported beam with crack damage is established by finite element (FE) method firstly. Then, effect of crack location and crack depth on dynamic characteristics of the simple supported beam is studied by comparison with the case when no crack occurs. Results of simulation studies conclude that crack with different location and depth will change natural frequencies differently and the effects of crack location on natural frequencies are related to the vibration model of the simple supported beam. This conclusion provides a good reference for simple supported beam structure performance optimization, damage detection and localization.

Effect of crack location on vibration analysis of partially cracked isotropic and FGM micro-plate with non-uniform thickness: An analytical approach

An analytical model is presented for nonlinear vibration analysis of variable thickness, thin isotropic and functionally graded rectangular micro-plate containing a partial crack located within the centre line of the plate. Linear and parabolic thickness variation is considered in one or both the in-plane directions of the plate. The thickness variation is such that the volume of the plate is equal to that of the uniform thickness plate. The continuous line crack is parallel to one of the edges of the plate. The equations of motion are derived using the equilibrium principle based on Classical Plate Theory while the size effect is incorporated using the modified couple stress theory. The partial crack is represented by bending moment and in-plane force according to the simplified line spring model. The effect of in-plane forces is considered by employing the Berger's formulation. The derived governing equation is converted into a cubic nonlinear Duffing equation by employing Galerkin's method. The effect of nonlinearity is established by deriving the frequency response equation for the cracked variable thickness plate using the method of multiple scales. The nonlinear frequency response curves show the phenomenon of bending hardening or softening. The influence of crack length, crack location, internal material length scale parameter, boundary conditions, gradient index, unidirectional and bidirectional taper constant on the fundamental frequency of square plate is demonstrated. Similar to uniform thickness plate, it is found that the presence of crack affects the vibration characteristics of variable thickness plate. When compared to uniform thickness plate, the effect of crack can be reduced by varying the thickness of the plate. Thus, it is concluded that in a given volume, it is better to employ variable thickness plate as far as the vibration characteristics are considered.

On crack detection in curved beams using change of natural frequency

In this study, an inverse method for the purpose of identifying the parameters of a single-edge crack in a curved beam is investigated. This method requires both numerical and experimental natural frequencies. The differential quadrature element method (DQEM) is introduced to get the numerical ones. For the purpose of implementing the DQEM the beam is divided into some elements and the governing equations, the continuity and the boundary conditions, are exerted on these elements to create an eigenvalue problem which is solved to obtain the required frequencies. A rotational spring whose stiffness is a function of crack depth is used to model the crack. An objective function with the variables of crack location and depth which is the weighted mean squared error between experimental and numerical frequencies is defined. The artificial bee colony algorithm (ABC) an optimization algorithm inspired by the natural foraging behavior of honeybees is used to minimize the aforementioned objective function and obtain crack parameters. To investigate the accuracy of this non-destructive, fast and easy method, an experimental modal analysis test is conducted on a cracked beam. The results indicate that the position and depth of the crack can be determined successfully using this method. This test is done five times with a different crack depth each time, to show the efficiency of the method for all cracks even small ones. A brief investigation is also done on the effect of crack location and depth on the natural frequencies.

Delamination of Multilayered Functionally Graded Beams with Material Nonlinearity

Delamination fracture in multilayered functionally graded, split cantilever beams is analyzed with account taken of the nonlinear behavior of the material. The fracture is studied analytically in terms of the strain energy release rate. The mechanical behavior of the material is described by a power-law stress–strain relation that is not symmetric for tension and compression. The beam can have an arbitrary number of vertical layers of different thickness. Each layer can have different material properties. Besides, the material in each layer is functionally graded along the layer thickness. Also, the delamination fracture can occur at any interface. The strain energy release rate is derived by analyzing the complementary strain energy of the beam. The solution obtained is applied to elucidating the effects of crack location, material gradient and material nonlinearity on the delamination fracture behavior of multilayered functionally graded beam configuration. It is found that the material nonlinearity leads to increase of the strain energy release rate, which implies that the material nonlinearity should be taken into account in the fracture mechanics based safety design of multilayered functionally graded structural members and components.

Effect of crack location on vibration analysis of cracked FGM plate under thermal environment

In the present work, the effect of crack location on the fundamental frequency of functionally graded thin rectangular plate is presented under the influence of thermal environment. The proposed new analytical model is developed using Kirchhoff’s classical plate theory and the crack terms are induced using the well known simplified line spring model (LSM). Thermal moments and in-plane compressive forces are considered to incorporate the effect of thermal environment. The solution for governing equation is obtained using Galerkin's method. The fundamental frequency of the FGM plate as affected by crack length, crack location, uniform rise in temperature and gradient index is presented for simply supported boundary condition. It is found that the results obtained for natural frequencies are significantly affected by rise in temperature, crack length and its location.

Delamination analysis of a layered elastic-plastic beam

PurposeThe purpose of this paper is to perform a theoretical analysis of delamination fracture behaviour of the Crack Lap Shear layered beam configuration taking into account the material non-linearity. A delamination crack located arbitrarily along the beam height was considered in this study.Design/methodology/approachThe beam mechanical behaviour was described by using the Ramberg-Osgood stress-strain relation. Fracture was analysed by applying the J-integral approach. Besides by using symmetric Ramberg-Osgood stress-strain curve, fracture was investigated also by Ramberg-Osgood stress-strain curve that is not symmetric with respect to tension and compression. The J-integral solutions were verified by performing elastic-plastic analyses of the strain energy release rate.FindingsThe effects of crack location and material properties on the non-linear fracture behaviour were evaluated. It was found that the material non-linearity leads to increase of the J-integral values. Therefore, the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members composed by layered materials. The analytical solutions derived are very useful for parametric investigations of delamination fracture with considering the material non-linearity. The results obtained can be applied for optimisation of the beam structure with respect to fracture performance.Originality/valueThe present study contributes for the understanding of delamination fracture in layered beams that exhibit non-linear material behaviour.

Investigation of the Effect of Material on Undamped Free Vibration of Cantilever Beams with Uniform Single Surface Crack

Crack detection in structures is a critical area of research where the developments have been made out since decades. Various techniques are available for early identification and quantification of cracks to predict and prevent the unexpected sudden failure of structure and ensure uninterrupted service. Use of vibration analysis for detecting crack is one of the widely used techniques which offer lots of advantages over other like it is easier and less costly method and can be used for inaccessible components. The present work attempts to use modal analysis through FEA to investigate the effect of crack on natural frequency of vibration in beams of different materials, for three different crack location. From the result, it has been inferred that among Structural Steel (SS), Aluminium alloy (Al) and Gray Cast Iron (CI), the natural frequency is highest for Al beam and lowest for CI beam. Introduction of crack reduces the natural frequency of vibration, however, the effect of crack location on frequency is not uniform for different modes. Also, the trend is similar in beams of all the materials.

Analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non-linearity

An analytical study of longitudinal fracture in two-dimensional functionally graded cantilever beam configurations is carried-out with taking into account the non-linear behavior of material. A longitudinal crack is located arbitrary along the beam cross-section height. The material is functionally graded along the width as well as along the height of beam. The external loading consists of a bending moment applied at the free end of lower crack arm. Fracture is studied in terms of the strain energy release rate by considering the beam complementary strain energy. The solution derived is verified by analyzing the longitudinal crack with the help of the J-integral. The distribution of J-integral value along the crack front is studied. The effects of crack location, material gradients and non-linear behavior of material on the fracture are elucidated. The analysis reveals that the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members and components made of two-dimensional functionally graded materials.